Astronomy

Astronomy is a two-person, data-heavy Division C event. For 2027 the theme is stellar evolution in normal and starburst galaxies: how stars are born, live and die, and how that life cycle plays out across whole galaxies, from quiet spirals like Andromeda to galaxies forming stars so fast they cannot keep it up for long. Teams answer questions and complete activities built on Hertzsprung–Russell (H-R) diagrams, spectra, light curves, proper motions, magnitudes, distance equations, images and data across the electromagnetic spectrum, and "multi-messenger" signals such as gravitational waves and neutrinos. The event rewards moving between a picture, a table and a physical argument, and then doing the arithmetic correctly. Teams that do well can say what a plot means, why an object looks the way it does, and what number follows from the formula, in that order.

Event format

The 2027 rules give no level-specific restrictions, so the scope below applies at invitationals, regionals, state and nationals alike. The rules do not mention any online imaging tool or supervisor-provided computer, so plan to work entirely from what you bring.

What the rules cover

The 2027 rules manual lists the data types first, then three content items. The table paraphrases each and says what to study.

Stars: balance, mass and the life cycle

Why a star is stable

A star stays stable for millions to billions of years because of hydrostatic equilibrium: at every layer, the outward push from hot gas and radiation balances the inward pull of gravity from the material above. If fusion slows, pressure drops, gravity compresses the core, the core heats, and fusion speeds up again. The fuel burns at whatever rate keeps the balance. Orbiting planets play no role, and a star is not stable merely because it is dense or massive.

The interstellar medium and nebulae

Stars are made from the interstellar medium (ISM), the gas and dust between the stars. By mass it is about 99% gas (roughly 70% hydrogen and 28% helium, like the stars themselves) and 1% dust (tiny grains of silicates, carbon and ices). The gas comes in phases at very different temperatures, and each phase shows up in a different band:

Cold H₂ emits almost nothing that can be observed directly, so astronomers map molecular clouds with CO, which is about ten thousand times rarer but radiates easily. Giant molecular clouds hold roughly 10⁴ to 10⁶ solar masses across tens of parsecs and are the main star factories in a galaxy.

A nebula is any interstellar cloud you can see. Tests ask you to sort them:

Emission and reflection nebulae and dark clouds mark star formation; planetary nebulae and supernova remnants mark stellar death.

An H II region is the ionized bubble around hot young stars. Only photons above 13.6 eV (shorter than 91.2 nm) ionize hydrogen, and only O and early B stars make many of them. Inside the bubble, ionization balances recombination; the equilibrium radius is the Strömgren radius, larger for hotter stars and for thinner gas. Because the O stars that power most H II regions live only a few million years (early B stars about 10 million), an H II region is proof of star formation within roughly the last 10 million years. That is why H-alpha imaging is the standard star-formation map of a galaxy.

From cloud to star

Why clouds collapse. A clump collapses when its gravity beats its internal gas pressure. The Jeans criterion puts this as a minimum mass: a clump heavier than the Jeans mass collapses.

Triggers. Something usually compresses a cloud past the Jeans limit: a supernova shock, the expanding H II region of a nearby massive star, a spiral-arm density wave, a collision between clouds, or, on the largest scale, a galaxy interaction. That last one is the bridge to starbursts.

Fragmentation. As a cloud collapses its density rises, so its Jeans mass falls and it breaks into many smaller collapsing cores. That is why stars form in clusters and associations rather than one at a time. Fragmentation stops when the cores become opaque and trap their heat.

Disks, jets and Herbig-Haro objects. A collapsing core spins faster as it shrinks (conservation of angular momentum), so infalling gas settles into a flat accretion disk around the protostar. Friction (viscosity) in the disk moves mass inward and angular momentum outward. Magnetic fields fling some gas out along the rotation axis as two opposite bipolar jets. Where a jet slams into surrounding gas at hundreds of km/s, the shock heats the gas to roughly 10,000 K and it glows in emission lines (H-alpha, [S II], [O I]). These glowing knots are Herbig-Haro (HH) objects. They are not stars; they are shock fronts, typically a fraction of a parsec from the young star, and they fade or change shape within decades to thousands of years. Finding HH objects means a protostar is actively accreting, often hidden inside a dark cloud or Bok globule.

Jet structure: the head of the jet, where it rams undisturbed gas, forms a curved bow shock (the terminal working surface); variations in the jet's speed make faster gas catch slower gas inside the jet, producing a chain of internal working surfaces that appear as evenly spaced knots. Comparing images taken years apart gives the knots' proper motions, typically 100–500 km/s.

What powers a protostar. A protostar has no fusion yet. It shines because it contracts: by the virial theorem, half of the gravitational energy released is radiated and half heats the interior ($2K + U = 0$ for a bound, stable system, where $K$ is the total thermal kinetic energy of the gas and $U$ is its gravitational potential energy, which is negative). So a contracting star gets hotter inside as it loses energy, until the core reaches about 10⁷ K and hydrogen fusion starts. Protostars are wrapped in dust, so they are seen mainly in the infrared and submillimeter. Astronomers sort young stellar objects into Classes 0, I, II and III as the envelope clears: Class 0 is deeply embedded, Class II is a classical T Tauri star with a disk, Class III has lost most of its disk.

Pre-main-sequence stars, T Tauri stars and brown dwarfs

Once the envelope clears, the young star becomes visible but is still contracting toward the main sequence. On the H-R diagram it follows two kinds of path:

• The Hayashi track: a nearly vertical path downward. The young star is fully convective, its surface temperature stays almost constant (around 3,500–4,500 K for low-mass stars), and its luminosity falls as its radius shrinks. A young star is therefore more luminous than it will be on the main sequence, because it is much larger.
• The Henyey track: once a radiative core develops, the star moves almost horizontally to the left at nearly constant luminosity, heating up as it contracts, until fusion starts and it settles on the zero-age main sequence (ZAMS).

Stars below about 0.5 $M_\odot$ reach the main sequence on the Hayashi track with little or no Henyey phase (below about 0.35 $M_\odot$ they stay fully convective even on the main sequence). Massive stars have barely any Hayashi phase and are still buried in their birth cloud when fusion starts. Contraction is fast for massive stars and slow for small ones: roughly 10⁵ years for a 15 $M_\odot$ star, a few tens of millions of years for the Sun, and over a hundred million years for a 0.5 $M_\odot$ star. The Sun's contraction timescale, the Kelvin–Helmholtz time $t_{KH} \approx GM^2/(RL)$, is about 30 million years.

T Tauri variability has three main causes: variable accretion (irregular, often large changes), rotating starspots (periodic changes over a few days) and magnetic flares (brief outbursts, especially in X-rays), with dust in the disk sometimes blocking the star. T Tauri stars are also magnetically very active: their strong fields (kilogauss) make large starspots that modulate their brightness as they rotate, hot chromospheres and coronas (emission lines, X-ray flares), and magnetospheres that channel disk gas onto the star in accretion columns. Their light combines the photosphere, accretion hot spots, the disk's infrared and chromospheric emission. In a young cluster the pre-main-sequence stars often sit at a spread of positions above the main sequence; read at face value, that age spread means star formation lasted several million years or came in more than one episode (though errors in luminosity and accretion history also smear it).

Disks evolve too: a gas-rich protoplanetary (accretion) disk lasts only a few million years; what remains around older stars is a thin debris disk of dust continually ground out of colliding rocky and icy bodies, seen as an infrared excess but with little gas and no accretion.

Lithium as a clock. Lithium is destroyed at only about 2.5 million K, so convection gradually carries it down and burns it. Strong lithium lines mean a star is young. The same fact gives the lithium test for brown dwarfs: a cool, faint object that still shows lithium when it is hundreds of millions of years old cannot be a star, because stars (and the heaviest brown dwarfs, above about 65 Jupiter masses) burn their lithium.

Brown dwarfs are objects below about 0.075–0.08 $M_\odot$ (about 75–80 Jupiter masses). They never get hot enough to sustain hydrogen fusion, so they are supported by electron degeneracy pressure and simply cool forever. Above about 13 Jupiter masses they briefly fuse deuterium, which is the usual dividing line between a brown dwarf and a planet. Their spectra define classes beyond M:

At the other end, stars much above about 150 $M_\odot$ are rare because their own radiation pressure approaches the Eddington limit and blows off their outer layers. Nature makes far more small stars than big ones: about three-quarters of main-sequence stars are M dwarfs, and O stars are a tiny fraction of a percent. The distribution of stellar masses at birth is the initial mass function.

A striking result is that the IMF looks nearly the same almost everywhere it can be measured in the Milky Way and nearby galaxies (roughly $dN/dM \propto M^{-2.35}$ above about 1 $M_\odot$, the Salpeter slope, flattening below about 0.5 $M_\odot$). Possible variations in extreme environments, such as massive ellipticals or starburst cores, are still debated.

Molecular clouds and the H II regions they spawn are often called stellar nurseries. The theory above is backed by direct observation: infrared and submillimeter telescopes (Spitzer, JWST, ALMA) see protostars still embedded in their envelopes, ALMA images their disks (some with gaps), and Hubble and JWST film jets and Herbig-Haro objects moving.

Mass decides everything

Stars form when cold clouds of molecular gas collapse, heat up and ignite hydrogen fusion near $10^7$ K. The long stable phase that follows is the main sequence. Fusion turns four protons into one helium nucleus: through the proton–proton chain in Sun-like and smaller stars, and through the CNO cycle in hotter, more massive stars (crossover near 1.3 solar masses).

Luminosity climbs steeply with mass. A useful approximation is $L \propto M^{3.5}$, and because lifetime scales as fuel over burn rate, $t \propto M/L \propto M^{-2.5}$. Massive stars are brilliant and short-lived; M dwarfs are faint and outlive everything. This one fact explains most of what a galaxy's light tells you: strong H-alpha emission means O stars formed within roughly the last 10 million years, and strong ultraviolet light means massive O and B stars formed within roughly the last 100 million years, because those stars cannot survive longer. (After a burst ends, A stars keep the light fairly blue for up to about a billion years; see post-starburst galaxies.)

Inside a main-sequence star

Fusion. In the proton–proton (pp) chain, the main branch runs:

1. $p + p \rightarrow {}^2\text{H} + e^+ + \nu_e$ (the slow step: a proton must turn into a neutron via the weak force)
2. ${}^2\text{H} + p \rightarrow {}^3\text{He} + \gamma$
3. ${}^3\text{He} + {}^3\text{He} \rightarrow {}^4\text{He} + 2p$

Net: four protons become one helium-4 nucleus, two positrons, two neutrinos and gamma rays, releasing 26.7 MeV, about 0.7% of the original mass ($E = mc^2$). The CNO cycle reaches the same net result using carbon, nitrogen and oxygen as catalysts: they are recycled, not consumed, though the cycle converts much of the carbon into nitrogen-14 (its slowest step is proton capture on nitrogen-14). The CNO rate climbs far more steeply with temperature (roughly $T^{17}$ against roughly $T^{4}$ for the pp chain), so it dominates in stars hotter in the core than about 17 million K, which means stars above about 1.3 $M_\odot$. The Sun's core is about 15.7 million K and runs mostly on the pp chain. The neutrinos escape straight out of the core; detecting them (and solving the "solar neutrino problem" through neutrino flavor oscillation) confirmed that the Sun is fusion-powered.

Why fusion works at "only" 15 million K. Two protons repel each other electrically (the Coulomb barrier); classically, the core would need roughly a thousand times hotter for them to touch. Fusion happens anyway because of quantum tunneling: a proton has a small chance of passing through the barrier. The fastest protons in the Maxwell–Boltzmann distribution are rare, while slow ones rarely tunnel, so most reactions happen in a narrow energy window, the Gamow peak, well above the average thermal energy. This is why fusion rates are so sensitive to temperature, and steeper still for the CNO cycle, where the barrier of carbon and nitrogen nuclei (charge 6–7) is higher.

Fusion happens only in the hot, dense core (and, in evolved stars, in burning shells around it), never in the photosphere, which is thousands of times too cool and thin; the one exception in this guide is the surface of an accreting white dwarf, where compressed hydrogen reaches fusion conditions in a nova.

Moving the energy out. Energy travels by radiation where the gas is fairly transparent and by convection where it is opaque or the energy flux is very concentrated:

A photon made in the Sun's core is absorbed and re-emitted so many times that the energy takes on the order of 10⁴–10⁵ years to random-walk out; the light that finally escapes comes from the photosphere, about 5,772 K. Above it lie the chromosphere and corona. The Sun's layers from the inside: core, radiative zone, convective zone, photosphere, chromosphere, corona.

Why stellar gas is opaque. In ionized gas, photons are blocked by electron (Thomson) scattering off free electrons (works at every wavelength), free–free absorption (a free electron absorbs a photon while passing an ion), bound–free absorption (photoionization), and bound–bound line absorption. In the cooler outer layers of the Sun the main source of visible opacity is the H⁻ ion (a hydrogen atom with an extra electron). Opacity is what traps energy and sets whether a layer is radiative or convective; the kappa mechanism in pulsating stars works because opacity in a partial-ionization (He II) zone rises when the layer is compressed, trapping heat.

The pp chain has side branches: in ppII, helium-3 joins helium-4 to make beryllium-7, which captures an electron to become lithium-7, which captures a proton and splits into two helium-4 nuclei; ppIII goes through boron-8 and gives the high-energy solar neutrinos. That proton capture on lithium-7 is the same reaction that destroys lithium in young stars.

Timescales. Three clocks set how stars behave:

The nuclear time is longest, which is why stars spend about 90% of their lives on the main sequence and why about 90% of the stars you see are main-sequence stars.

Mass–luminosity and lifetimes. For main-sequence stars only, $L \propto M^{a}$ with $a$ about 3.5–4 for Sun-like masses (flatter, about 2.3, for low-mass M dwarfs; nearly 1 for the most massive stars, which are held near the Eddington limit). Giants and white dwarfs do not follow it. With $t \propto M/L$:

A main-sequence star is not frozen in place. As helium builds up in the core, the core contracts slightly and heats, and the star slowly brightens: the young Sun was only about 70% as luminous as it is today. The main sequence is therefore a band, not a thin line.

Endpoints

Mass boundaries vary between textbooks and depend on composition and mass loss, so learn the pattern, not the exact numbers.

Iron is the dead end. Fusing iron absorbs energy instead of releasing it, so the iron core makes no heat of its own; silicon shell burning keeps adding iron to it until it reaches about 1.4 $M_\odot$, and then it collapses in under a second (details below). The rebound and the flood of neutrinos drive a core-collapse supernova (Type II if hydrogen lines show, Ib or Ic if the star had lost its envelope). Core-collapse supernovae only happen where massive stars were born recently, so a starburst galaxy produces them at a high rate, while an elliptical galaxy with no young stars essentially never does.

A white dwarf has a counterintuitive property that tests love: its radius shrinks as its mass grows. More mass means stronger gravity, which squeezes the degenerate electrons harder. At the Chandrasekhar limit, degeneracy pressure cannot win at all.

After the main sequence: Sun-like stars

When core hydrogen runs out, fusion stops at the center and the helium core, no longer supported, contracts and heats. Hydrogen keeps burning in a shell around it, faster than before because the shell sits on a hotter, denser core. The extra energy puffs the envelope up: the star swells and its surface cools. It crosses the subgiant branch and climbs the red giant branch (RGB) to a few thousand solar luminosities and more than 100 solar radii (about 2,300 $L_\odot$ and 170 $R_\odot$ at the Sun's RGB tip). A red giant is cool but luminous because its surface area is enormous ($L \propto R^2T^4$). Its convective envelope deepens and dredges fusion products to the surface (the first dredge-up).

The helium flash. The core keeps contracting until it reaches about 100 million K, hot enough for the triple-alpha process: three helium-4 nuclei make carbon-12 (through short-lived beryllium-8), and some carbon captures another helium nucleus to make oxygen-16. In stars below about 2 $M_\odot$ the core is electron-degenerate by then. Degeneracy pressure does not depend on temperature, so when helium ignites, the core heats without expanding, which speeds fusion further: a runaway called the helium flash. For a few seconds the core generates enormous power, but it is all absorbed in lifting the degeneracy; nothing is seen from outside. Stars above about 2 $M_\odot$ ignite helium gently, with no flash.

Core helium burning. The star settles down, shrinks and fuses helium in its core and hydrogen in a shell. Metal-poor stars sit on the horizontal branch (where it crosses the instability strip, they pulsate as RR Lyrae stars); metal-rich ones bunch up in the red clump. This phase lasts about 100 million years for the Sun, roughly 1% of its main-sequence life (about 10 billion years).

The asymptotic giant branch (AGB). When core helium runs out, the star has an inert, degenerate carbon–oxygen core inside a helium-burning shell and a hydrogen-burning shell. It climbs the AGB, brighter and larger than before. The helium shell ignites in periodic thermal pulses (every ~10⁴–10⁵ years). Pulses drive dredge-ups that carry carbon and s-process elements (made by slow neutron capture: strontium, barium, technetium and others) to the surface. Technetium has no stable isotope, so seeing it in a star's spectrum proves the star made it recently. When carbon outnumbers oxygen in the atmosphere, the star becomes a carbon star (C type: strong C₂ "Swan bands" and CN, no TiO); with C/O near 1 it is an S-type star (ZrO bands). AGB stars pulsate as Mira variables with periods of about 100–1,000 days and huge visual amplitudes (the radius swings by tens of percent and the surface temperature by a few hundred kelvin; the bolometric luminosity changes by only about a magnitude, but cool-phase molecules such as TiO absorb so much visible light that the V magnitude swings by more than 2.5), and they shed mass in slow, dusty winds (up to 10⁻⁴ $M_\odot$ per year in the final "superwind"). This dust and gas enriches the ISM with carbon and nitrogen.

Planetary nebula and white dwarf. Once the envelope is gone, the exposed core moves left across the H-R diagram at nearly constant luminosity, heating past about 30,000 K. Its ultraviolet light ionizes the gas it shed, which glows as a planetary nebula for roughly ten to a few tens of thousands of years while expanding at about 20–30 km/s. Typical emission: green [O III] at 500.7 nm, red H-alpha and [N II]. The name is historical: through small telescopes they looked like planet disks. Many are bipolar rather than round, shaped by companions, magnetic fields or disks. The central star stops fusing and cools as a white dwarf.

Not every star takes this whole path. Red dwarfs below about 0.5 $M_\odot$ never become hot enough to fuse helium; after tens of billions of years (near 0.5 $M_\odot$) to trillions of years (near 0.1 $M_\odot$) they will fade into helium white dwarfs (none has had time to form yet from a single star). Stars of about 0.5–2 $M_\odot$ have a helium flash; about 2–8 $M_\odot$ ignite helium quietly; both end as carbon–oxygen white dwarfs. Stars of roughly 8–10 $M_\odot$ can fuse carbon and end as oxygen–neon white dwarfs or in a weak electron-capture supernova.

After the main sequence: massive stars

Stars above about 8 $M_\odot$ never become degenerate in the core until the very end, so each fuel ignites smoothly when the core contracts enough. The star moves almost horizontally across the top of the H-R diagram between blue and red supergiant (sometimes back and forth in "blue loops"; Cepheids are intermediate-mass and massive stars, about 4–20 $M_\odot$, crossing the instability strip during these loops). Each stage burns the ashes of the last at a higher temperature and runs much faster, partly because heavier fuels release less energy per kilogram and partly because, from carbon burning on, the core loses most of its energy as neutrinos.

The result is an onion-shell structure: an iron core surrounded by shells burning silicon, oxygen, neon, carbon, helium and hydrogen, from the inside out. Iron-peak nuclei have the highest binding energy per nucleon, so nothing further can be gained by fusion.

Mass loss shapes the ending. Massive stars blow strong winds. The most massive can strip themselves (or be stripped by a binary companion through Roche-lobe overflow) down to their helium or carbon cores:

• Wolf–Rayet stars are hot (tens of thousands to over 100,000 K), stripped massive stars with very strong winds and broad emission lines of helium plus nitrogen (WN), carbon (WC) or oxygen (WO). They are among the most luminous stars, roughly 10⁵–10⁶ $L_\odot$, losing about 10⁻⁵ $M_\odot$ per year. The subtypes are a sequence of stripping: WN stars show nitrogen-rich, CNO-processed material from former hydrogen burning; further mass loss exposes helium-burning products in WC (carbon) and then WO (oxygen) stars. They come from stars that started above about 20–25 $M_\odot$ (lower in binaries) and are the likely progenitors of Type Ib and Ic supernovae. A galaxy whose spectrum shows the broad He II 468.6 nm "Wolf–Rayet bump" had a starburst only a few million years ago. Some central stars of planetary nebulae show Wolf–Rayet-like spectra and are labeled [WC]; they are low-mass stars, not true Wolf–Rayet stars.
• Luminous blue variables (LBVs) are very massive, unstable stars near the Eddington limit. They sit quiet for years, then swell and change temperature (and so their spectral type) or throw off whole solar masses in giant eruptions, which makes them hard to classify. Hypergiants (luminosity class 0 or Ia⁺) are the most luminous stars, losing mass heavily for the same reason.

Core collapse. When the iron core reaches about 1.4 $M_\odot$ and temperatures near 10¹⁰ K, two processes steal the pressure that holds it up: photodisintegration (energetic gamma rays break iron nuclei into helium nuclei and neutrons, absorbing energy) and electron capture ($p + e^- \rightarrow n + \nu_e$, also called neutronization), which removes the degenerate electrons. The core falls inward at up to about a quarter of the speed of light in under a second, until it reaches nuclear density, stiffens and rebounds. The outgoing shock stalls; it is revived mainly by heating from the flood of neutrinos. A neutron star (or black hole) is left behind.

Rarer endings. Very massive, metal-poor stars (helium cores of roughly 65–130 $M_\odot$) reach temperatures where gamma rays turn into electron–positron pairs. The lost radiation pressure triggers collapse and explosive oxygen burning that destroys the star completely: a pair-instability supernova, with no remnant. Massive stars whose cores collapse to rapidly spinning black holes can launch jets that make a long gamma-ray burst (a "collapsar", often with a broad-lined Type Ic supernova). At least some short gamma-ray bursts come from neutron-star mergers, as GW170817 proved.

Where the elements come from. Big Bang: hydrogen, helium, a little lithium. Fusion in stars: up to iron. s-process (slow neutron capture in AGB stars): about half the elements heavier than iron, such as barium and lead. r-process (rapid neutron capture in neutron-star mergers and possibly rare supernovae): the rest, including gold, platinum and uranium. Type Ia supernovae make most of the iron; core-collapse supernovae make most of the oxygen. Each generation of stars returns enriched gas to the ISM, which is why later generations are more metal-rich.

Hot stars drive fast winds by radiation pressure on spectral lines; cool giants lose mass in slow, dense, dusty winds because their gravity at the surface is weak.

White dwarfs and novae

A white dwarf is the exposed core of a low- or intermediate-mass star: typically about 0.6 $M_\odot$ packed into a sphere about the size of Earth (roughly 0.01 $R_\odot$), with an average density around 10⁹ kg/m³ (about a tonne per cubic centimeter). It is supported by electron degeneracy pressure: the Pauli exclusion principle forbids electrons from sharing a quantum state, so squeezing them into a small volume forces them into high-momentum states that push back. This pressure depends on density, not temperature, which is why a white dwarf cannot regulate itself like a normal star, and why any fusion that does start in degenerate matter runs away (helium flash, novae, Type Ia supernovae).

A white dwarf has no fuel, so it simply cools: it starts above 100,000 K, glows blue-white, and fades and reddens over billions of years. The coolest white dwarfs in a population give that population's age. A fully cooled black dwarf would take far longer than the current age of the universe, so none exist yet. White dwarf spectra are classed DA (hydrogen lines, the majority), DB (neutral helium), DO (ionized helium), DC (no lines), DQ (carbon) and DZ (metals).

Novae and their relatives. In a close binary where a white dwarf pulls gas from a companion overflowing its Roche lobe, the system is a cataclysmic variable. Hydrogen piles up on the white dwarf's surface, compressed and heated by its gravity and degenerate, until it ignites in a thermonuclear runaway (through the CNO cycle). The system brightens by roughly 8–15 magnitudes and blows off about 10⁻⁵–10⁻⁴ $M_\odot$: a classical nova. The white dwarf survives, so the process can repeat; recurrent novae do so within decades. A dwarf nova is smaller (2–6 magnitudes) and is caused not by fusion but by an instability in the accretion disk that suddenly dumps gas onto the white dwarf.

In AM Canum Venaticorum (AM CVn) systems a white dwarf accretes helium-rich gas from a second degenerate or semi-degenerate (helium) star in an orbit of only about 5–65 minutes. They are ultracompact, helium-accreting cataclysmic variables with no hydrogen in their spectra, and strong sources for future space-based gravitational-wave detectors such as LISA.

Classification, spectra and blackbody radiation

Spectral classes and luminosity classes

Spectral class tracks surface temperature. The order is O, B, A, F, G, K, M from hottest to coolest.

Each class is split into subclasses 0 (hottest) to 9: A0 is hotter than A9, and the Sun is G2. Cooler than M come the brown-dwarf classes L, T and Y (see brown dwarfs). Side branches exist for unusual compositions: W for Wolf–Rayet stars, C for carbon stars and S for stars with zirconium oxide bands. "Early" and "late" types mean hot and cool (O, B, A are early; K, M are late); the words are historical and say nothing about age.

The sequence was built at Harvard around 1900. Williamina Fleming, Antonia Maury and Annie Jump Cannon classified hundreds of thousands of spectra, and Cannon reordered the original alphabetical classes into the temperature sequence O B A F G K M. In 1925 Cecilia Payne(-Gaposchkin) showed that the differences come from temperature and that stars are made overwhelmingly of hydrogen and helium.

The luminosity class (a Roman numeral) separates stars of the same temperature by size. Giants have lower surface gravity and lower atmospheric density, so collisions broaden their lines less and their lines are narrower. That is how a spectrum alone gives both temperature and size, which is the basis of spectroscopic parallax. The full Morgan–Keenan (MK) system, also called the Yerkes system after the observatory where it was devised (1943):

An older notation (the Mount Wilson system) put a lowercase prefix in front of the spectral type instead: d dwarf, sg subgiant, g giant, c supergiant (so cM2 ≈ M2 I), plus sd subdwarf and wd white dwarf (modern white-dwarf types use D).

The luminosity gap between classes is largest for cool stars: an M giant is about ten thousand times as luminous as an M dwarf of the same temperature, while O supergiants and O dwarfs differ much less. Peculiarity codes follow the class: e emission lines; f N III and He II emission in O stars (a step toward Wolf–Rayet stars); p peculiar spectrum; m enhanced metal lines; n or nn broad, nebulous lines from fast rotation; s sharp lines; sh shell star; k interstellar lines present; var variable spectral type; and : marks an uncertain value. So "B2 IVe" is a hot subgiant with emission lines.

Why line strengths peak where they do

Line strength depends mainly on temperature, not abundance. Stars are roughly three-quarters hydrogen by mass almost everywhere, yet Balmer lines are weak in both O and M stars. In cool stars, few hydrogen atoms have electrons in the second level (where Balmer absorption starts); in very hot stars, most hydrogen is ionized. The lines peak in A stars near 10,000 K. Emission lines come from hot, thin gas, such as the ionized hydrogen regions around young massive stars. Strong H-alpha emission (656.3 nm, red) is the standard sign of current star formation in a galaxy.

Metallicity also changes a star's colors: crowded metal lines absorb blue and ultraviolet light (line blanketing), and extra opacity makes metal-rich stars of a given mass slightly larger and cooler, so they look redder; metal-poor stars of the same mass are bluer and lie slightly below the normal main sequence (subdwarfs).

Chemical composition shows up as metallicity: the fraction of elements heavier than helium. Each generation of stars enriches the gas with metals from supernovae and stellar winds, so metallicity is a clock for a population. Old halo and globular-cluster stars are metal-poor; young disk stars are metal-rich. The very first stars formed from almost pure hydrogen and helium left by the Big Bang.

How spectra form: Kirchhoff's laws and atomic lines

Kirchhoff's three laws say what kind of spectrum a source produces:

1. A hot, dense object (a solid, liquid or dense gas, like a star's interior) gives a continuous spectrum.
2. A hot, thin gas gives an emission-line spectrum: bright lines at wavelengths set by its atoms.
3. A cooler, thin gas in front of a hotter continuous source gives an absorption-line spectrum: dark lines at those same wavelengths.

A star's photosphere produces a continuous spectrum and its cooler outer atmosphere carves absorption lines into it. Nebulae (H II regions, planetary nebulae, Herbig-Haro objects, the gas in starbursts) are thin and hot, so they show emission lines.

Where lines come from. Electrons in an atom can only have certain energies. An electron jumping down emits a photon with exactly the energy difference; one absorbing a photon of exactly that energy jumps up. For hydrogen, the levels are $E_n = -13.6\ \text{eV}/n^2$, which gives the Rydberg formula.

Other lines worth knowing: Ca II H and K (396.8 and 393.4 nm, strongest in G and K stars); the sodium D doublet (589.0 and 589.6 nm); the G band of CH near 430 nm; TiO bands in M stars; He I (587.6 nm) in B stars and He II (468.6 nm) in O and Wolf–Rayet stars. Helium was discovered in 1868 as an unexplained yellow line in the Sun's spectrum before it was found on Earth.

Spectrographs split light by wavelength with a prism (refraction; bends blue more than red) or, more often, a diffraction grating (many fine lines; interference sends each wavelength to a different angle). Spectral resolution $\Delta\lambda$ is the smallest wavelength difference the instrument can separate; the resolving power $R = \lambda/\Delta\lambda$ sets the smallest velocity they can measure: $\Delta v \approx c/R$, so $R = 30{,}000$ resolves about 10 km/s.

Special lines in nebulae and galaxies.

• Forbidden lines, written in brackets, such as [O III] 495.9/500.7 nm, [N II] 654.8/658.4 nm and [S II] 671.6/673.1 nm, come from transitions so slow that collisions knock the electron out of the level first in any dense gas. Seeing them means very low density: nebulae, not stellar atmospheres.
• The 21 cm line (1420 MHz) comes from the electron's spin flipping relative to the proton's in neutral hydrogen. Any one atom does this only about once in ten million years, but there is so much hydrogen that the line maps cold gas throughout galaxies, even behind dust, and gives rotation curves.

What line shapes tell you.

A spectrum therefore gives temperature (which lines), composition and metallicity (line strengths at a known temperature), surface gravity and luminosity class (line widths), radial velocity (shifts), rotation (broadening), magnetic fields (splitting) and winds (P Cygni profiles).

Blackbody radiation

Stars radiate close to a blackbody: an idealized object that absorbs all radiation falling on it at every wavelength (so it reflects nothing) and, because it is a perfect absorber, is also the most efficient possible emitter at its temperature. Its spectrum depends only on temperature and is described by Planck's law; Wien's and the Stefan–Boltzmann laws follow from it. Everything above absolute zero radiates; at everyday temperatures the peak is in the infrared, which is why people, rooms and lava glow in thermal-infrared cameras, and why lava hot enough to glow red is still emitting mostly infrared.

Luminosity is power: the total energy a star emits per second, in watts (or erg/s, or solar luminosities, $L_\odot = 3.828\times10^{26}$ W). It does not depend on distance. Flux (apparent brightness) is the power received per square meter, which does. In cgs units, which many papers and tests use, luminosity is in erg/s (1 W = 10⁷ erg/s) and flux in erg s⁻¹ cm⁻² (1 W/m² = 10³ erg s⁻¹ cm⁻²). Radiometry vocabulary: power leaving a surface per unit area is radiant exitance (emittance; $\sigma T^4$ for a blackbody), power arriving per unit area is irradiance (the flux we measure), power per unit area per unit solid angle is radiance (intensity), and "spectral" versions are per unit wavelength or frequency (Planck's $B_\lambda$ is a spectral radiance). A light-year is a distance, the distance light travels in one year, about $9.46\times10^{15}$ m or 63,000 AU.

Adding up (integrating) Planck's law over all wavelengths and all directions gives the energy leaving each square meter of surface, $\sigma T^4$; multiplying by the surface area $4\pi R^2$ gives the Stefan–Boltzmann luminosity. Differentiating it to find the peak gives Wien's law.

Luminosity is intrinsic; flux is what arrives: $F = L/(4\pi d^2)$. Many questions give two of $L$, $F$, $d$ and ask for the third.

Peak wavelengths to remember: the Sun about 500 nm (blue-green, though the Sun looks white because it emits strongly across the whole visible band); a 300 K object about 10 μm (thermal infrared); 3,000 K about 1 μm (near infrared, so red giants peak just outside the visible); 30,000 K about 100 nm (ultraviolet). Color tracks temperature: in order of rising temperature a blackbody glows dull red, orange, yellow-white, white, then blue-white; no star looks green, because a blackbody peaking in green still emits plenty of red and blue light. The curve of blackbody colors on a color chart is the Planckian locus.

Color index. Astronomers measure color with filters. The standard Johnson–Cousins UBVRI set: U (ultraviolet, ~365 nm), B (blue, ~445 nm), V ("visual", green-yellow, ~551 nm), R (red, ~658 nm), I (near infrared, ~806 nm); in the infrared, J, H and K (~1.2, 1.6, 2.2 μm). The B−V color index is $m_B - m_V$. Because magnitudes run backwards, a hot star that is brighter in B has a smaller (even negative) B−V.

Doppler shifts

The H-R diagram

The H-R diagram plots luminosity (or absolute magnitude) upward against temperature (or color, or spectral class) decreasing to the right. The main sequence runs from hot, bright stars at upper left to cool, faint stars at lower right; giants and supergiants sit above and to the right; white dwarfs sit below and to the left. Because $L \propto R^2 T^4$, lines of constant radius run diagonally, which is how you read a star's size off the diagram.

Reading tricks: lines of constant radius run diagonally from upper left to lower right ($L \propto R^2T^4$); at fixed temperature, luminosity ratio = radius ratio squared. The axes may be labeled luminosity or absolute magnitude (up), and temperature, B−V color or spectral class (decreasing to the right). Both are logarithmic in practice.

For a whole population, the diagram is a clock. All stars in a cluster formed together, so the most massive leave the main sequence first. The point where the cluster's main sequence bends off toward the giants, the turnoff, marks the mass whose lifetime equals the cluster's age. A globular cluster's turnoff sits just below the Sun's mass (about 0.8 $M_\odot$), giving ages above 10 billion years. A cluster with blue O and B stars still on its main sequence is only a few million years old. Galaxies are mixtures of many such populations, which is why their integrated colors encode their star-formation histories.

Other cluster features tests ask about: blue stragglers (stars above the turnoff that should already have evolved; they are mergers or mass-transfer products in binaries), the horizontal branch and red giant branch of globular clusters, and the gap between the main-sequence turnoff and the giants (the subgiant region is crossed quickly, so few stars are caught there). Overestimating a cluster's distance makes its stars seem more luminous, hence more massive and shorter-lived at the turnoff, so the age comes out too young.

Variable stars as standard candles

Two kinds of pulsating star, Cepheids and RR Lyrae stars, are central to this topic because they measure distance. They pulsate inside the instability strip on the H-R diagram through the kappa (κ) mechanism: a layer where helium is being ionized a second time (He II → He III) becomes more opaque when compressed (κ is the symbol for opacity). It traps heat, the pressure builds and pushes the layer outward; as it expands the gas becomes more transparent, the heat escapes, and the layer falls back. The star acts like a heat engine with a valve.

Semiregular variables (SR) are red giants and AGB stars, often just below or beside the Miras, with smaller amplitudes and periods (tens to hundreds of days) that are only partly regular.

The Cepheid period–luminosity relation (the Leavitt law) was found by Henrietta Swan Leavitt in Cepheids of the Small Magellanic Cloud (published 1912): since all of them are at about the same distance, brighter ones had longer periods. Edwin Hubble used Cepheids in Andromeda (1923–25) to prove it is a separate galaxy. Confusing the two Cepheid types was why early distance estimates were off by about a factor of two (Walter Baade sorted this out in the 1950s, doubling the size of the universe).

Why the period depends on luminosity. A pulsation period is roughly the time for a sound wave to cross the star, which scales as $1/\sqrt{G\bar\rho}$. Bigger, more luminous stars have lower mean density, so they pulsate more slowly.

Prototypes and alternate names tests ask for: classical Cepheids are delta Cephei stars; Type II Cepheids are often called W Virginis variables after their best-known subclass; RR Lyrae stars are named after RR Lyrae; long-period variables are Mira variables after Mira (omicron Ceti), the first variable recognized as periodic (period about 332 days); luminous blue variables are also called S Doradus variables (P Cygni and eta Carinae are famous LBVs); ZZ Ceti stars are pulsating white dwarfs; W Ursae Majoris and Algol are the prototypes of contact (EW) and Algol-type (EA) eclipsing binaries.

Identifying a light curve

Variable stars are intrinsic (the star itself changes: pulsating, eruptive, cataclysmic) or extrinsic (geometry changes what we see: eclipsing binaries, rotating spotted stars). Tests often give a light curve and ask what it is.

Type Ia supernovae

A Type Ia supernova is the thermonuclear explosion of a carbon–oxygen white dwarf in a binary. Either it gains mass from a companion until it approaches the Chandrasekhar limit (the single-degenerate channel), or two white dwarfs spiral together, losing orbital energy to gravitational waves, and merge (the double-degenerate channel). Carbon fusion runs away through the whole star in seconds and unbinds it completely, so no remnant is left.

Type Ia supernovae are not perfectly identical, but their peak luminosity correlates with how fast they fade: brighter events decline more slowly (the Phillips relation). After that correction, the peak absolute magnitude is about $M_B \approx -19.3$, bright enough to see across billions of light-years. Their distances are calibrated using Cepheids in nearby host galaxies, which is exactly why NGC 4536 is on the list. Dust makes Type Ia events look fainter and redder, which matters for SN 2014J, which went off behind M82's dense dust.

Supernova types and light curves

Supernovae are classified by their spectra near peak, not by their mechanism. The physical split (thermonuclear versus core collapse) cuts across the letters:

The plateau of a II-P happens because the expanding hydrogen envelope recombines layer by layer, releasing its stored energy at a nearly constant rate. Afterwards, every type is powered by radioactivity: nickel-56 (half-life 6.1 days) decays to cobalt-56 (half-life 77 days), which decays to stable iron-56. A Type Ia makes roughly 0.6 $M_\odot$ of nickel-56, which is why it is brighter than core-collapse events that make far less. Decay gamma rays of cobalt-56 were detected directly from SN 2014J.

Type Ia supernovae were used in 1998 to show that the expansion of the universe is accelerating: distant ones looked fainter (farther) than a constant expansion rate allowed. That work earned the 2011 Nobel Prize in Physics. The cause of the acceleration is called dark energy, which makes up roughly 70% of the energy content of the universe.

Light echoes. When a supernova or outburst flashes, some light travels straight to us and some first hits dust clouds nearby and scatters toward us. The scattered light travels farther, so it arrives later, and we see rings or arcs that seem to expand faster than light (they are not moving; successive dust is lit up). The geometry of an echo gives the dust's distance from the source, and for well-observed cases a geometric distance to the source. SN 2014J produced light echoes in M82's dust.

Ejected mass: a Type Ia throws out about 1.4 $M_\odot$ (the whole white dwarf); a core-collapse supernova ejects most of the star outside the remnant, typically a few to over ten solar masses for a Type II, less for stripped Ib/Ic progenitors.

Supernova remnants

The ejected gas sweeps up the surrounding medium. A remnant passes through a free-expansion phase (a few hundred years, ejecta coasting at thousands of km/s), a Sedov–Taylor (blast-wave) phase lasting about ten thousand years, a radiative ("snowplow") phase once the shell cools, and finally merges with the ISM after about a million years. Its shock heats gas to millions of kelvin (X-rays) and accelerates electrons that spiral in magnetic fields and emit synchrotron radio; remnants are also where most galactic cosmic rays are thought to be accelerated. Shell-type remnants are bright rims; a pulsar wind nebula (plerion) is filled from the center by a young pulsar's wind of particles; composite remnants have both. A Type Ia remnant has no compact object at its center.

Neutron stars, ULXs and gravitational waves

Neutron stars and pulsars

A neutron star is the collapsed core of a massive star: typically about 1.2 to 2 solar masses (most near 1.4) packed into a sphere about 10–13 km in radius, supported by neutron degeneracy pressure and nuclear forces. Conservation of angular momentum makes a collapsing core spin up enormously, and magnetic flux conservation concentrates its field. A neutron star whose radiation beams sweep past Earth is a pulsar.

Isolated pulsars slow down as they radiate. A neutron star in a binary can be spun back up by accreting gas from its companion, which carries angular momentum; the result is a millisecond pulsar. Dense star clusters make many such binaries through close encounters, which is why Terzan 5 has more known millisecond pulsars than any other cluster.

Numbers to know. Density near the center exceeds that of an atomic nucleus (around 10¹⁷–10¹⁸ kg/m³): a teaspoon would weigh hundreds of millions of tonnes or more. Inside, an iron-rich crust sits over neutron-rich nuclei and then a superfluid of neutrons (a quantum fluid with zero viscosity), possibly with exotic matter in the core. Magnetic fields are typically 10⁸–10¹³ gauss (10⁴–10⁹ T). The maximum mass, the Tolman–Oppenheimer–Volkoff (TOV) limit, is uncertain, roughly 2–3 $M_\odot$; the heaviest well-measured pulsars are about 2 $M_\odot$ (some estimates a little higher), which rules out "soft" models of nuclear matter. Above the limit, nothing stops collapse to a black hole.

Why the maximum mass is uncertain: nobody knows the equation of state (how pressure rises with density) of matter denser than an atomic nucleus. Stiffer equations of state allow heavier, larger neutron stars; measured masses near 2 $M_\odot$, NICER radius measurements and the tidal deformation seen in GW170817 are the main constraints.

Pulsars. Jocelyn Bell Burnell and Antony Hewish discovered the first pulsar, CP 1919 (now PSR B1919+21, period 1.337 s), in 1967 (the 1974 Nobel Prize went to Hewish and Martin Ryle). In the lighthouse model, radio beams emerge along the magnetic axis, which is tilted relative to the spin axis, so the beams sweep around like a lighthouse and we see a pulse once per rotation if a beam crosses Earth. The emission is strongly polarized, as expected from charged particles moving along magnetic field lines. Periods run from about 1.4 milliseconds to tens of seconds.

The pulse argument for small size: a source cannot vary much faster than light can cross it, so a pulse lasting a few milliseconds means the emitting region is no larger than $c\,\Delta t$, a few hundred to a thousand kilometers. Only something as compact as a neutron star can also spin that fast without flying apart.

Pulsars do not shine forever. As a pulsar spins down, the voltage its rotating magnetic field can generate falls; once it is too slow to create the electron–positron pairs that power the radio beam, it crosses the death line on the period–period-derivative diagram and goes quiet, after roughly 10–100 million years. A dead pulsar in a binary can be spun back up ("recycled") by accretion from its companion into a millisecond pulsar.

A newborn neutron star (about 10¹¹ K) cools first and fastest by neutrino emission from its interior (Urca reactions, in which neutrons and protons convert back and forth emitting neutrinos, plus neutrino bremsstrahlung), dropping to around 10⁹ K within days to years; after about 100,000 years surface photon emission takes over.

Binary pulsars and gravitational waves. In 1974 Russell Hulse and Joseph Taylor found a pulsar orbiting another neutron star (PSR B1913+16). Its orbit shrinks at exactly the rate general relativity predicts for energy lost to gravitational waves, the first (indirect) evidence that gravitational waves exist (Nobel Prize 1993). Arrays of millisecond pulsars, timed to within tens of nanoseconds over years, act as a galaxy-sized detector: pulsar timing arrays such as NANOGrav reported evidence in 2023 for a background of nanohertz gravitational waves, most likely from supermassive black-hole binaries.

Black holes and X-ray binaries

A black hole is a region where gravity is so strong that nothing, not even light, escapes from inside its boundary, the event horizon. For a non-spinning black hole the horizon is at the Schwarzschild radius: any mass compressed inside its own Schwarzschild radius must collapse. A black hole is fully described by just three numbers, mass, spin and electric charge (the "no-hair" idea); in practice charge is negligible. The four exact solutions are named for what they include: Schwarzschild (mass only), Kerr (mass and spin, the realistic case), Reissner–Nordström (mass and charge) and Kerr–Newman (all three).

How we know they are there. Nothing comes from inside the horizon, so the evidence is from the surroundings: an X-ray binary whose invisible companion, weighed by the visible star's Doppler orbit, is above about 3 $M_\odot$ (too heavy to be a neutron star) and shows no surface; stars whipping around the Milky Way's center on orbits that require 4 million solar masses in a tiny volume (2020 Nobel Prize); the shadows imaged by the Event Horizon Telescope (M87's center in 2019, the Milky Way's in 2022); and gravitational waves from merging black holes. Hawking radiation, predicted by quantum theory, is far too weak to observe from any astrophysical black hole.

Accretion is the most efficient power source in astronomy. Gas spiraling through a disk toward a black hole can radiate roughly 6% (non-spinning) to over 30% (rapidly spinning) of its rest-mass energy, against 0.7% for hydrogen fusion. Tidal forces near a stellar-mass black hole stretch infalling objects ("spaghettification"). A star that wanders too close to a supermassive black hole is torn apart in a tidal disruption event, a flare that lasts months; for black holes above about 10⁸ $M_\odot$ the tidal radius lies inside the horizon, so a Sun-like star is swallowed whole without a flare.

X-ray binaries are a neutron star or black hole fed by a companion star:

In the Milky Way, high-mass X-ray binaries trace the young disk and spiral arms, so they lie close to the galactic plane; low-mass X-ray binaries are older and more spread out, concentrated toward the bulge and in globular clusters. At the center of a black hole, general relativity predicts a singularity, a point (or ring, if spinning) of infinite density where the theory breaks down; it is hidden behind the event horizon, and a quantum theory of gravity is expected to replace it.

Other X-ray binary labels: Be/X-ray binaries (a neutron star on an eccentric orbit flaring when it crosses a Be star's disk), supergiant X-ray binaries and supergiant fast X-ray transients, intermediate-mass X-ray binaries, soft X-ray transients (LMXBs that flare for weeks and then fade for years) and supersoft X-ray sources (white dwarfs burning accreted hydrogen steadily on their surfaces, a possible Type Ia route). Type I X-ray bursts, thermonuclear flashes of accreted helium or hydrogen lasting seconds to minutes, require a solid surface, so they prove the compact object is a neutron star, not a black hole.

Microquasars are X-ray binaries that launch relativistic jets, small-scale versions of quasars.

Accretion and the Eddington limit

Gas falling onto a compact object heats to millions of kelvin and shines in X-rays. There is a natural ceiling on how bright accretion can be: radiation pushing outward on the infalling gas eventually balances gravity pulling it in. That ceiling is the Eddington luminosity.

Ultra-luminous X-ray sources

A ULX is an X-ray source outside a galaxy's nucleus with luminosity above about $10^{39}$ erg/s ($10^{32}$ W). That is more than 5 times the Eddington limit of a 1.4 $M_\odot$ neutron star (about $1.8 \times 10^{38}$ erg/s) and equals the limit of a ~8 $M_\odot$ black hole (a 10 $M_\odot$ black hole's limit is about $1.3 \times 10^{39}$ erg/s). An ordinary stellar-mass object would have to run at or beyond its limit, so something unusual is going on. The candidate explanations, all tested with M82's two famous ULXs:

1. An intermediate-mass black hole (hundreds to thousands of solar masses) accreting below its own, higher Eddington limit. M82 X-1 is a leading candidate: the frequencies of its quasi-periodic X-ray oscillations suggest a mass of roughly 400 $M_\odot$.
2. Super-Eddington accretion onto a stellar-mass object, with the emission beamed toward us or the disk geometry letting radiation escape without stopping the inflow. M82 X-2 settled that this happens: NuSTAR found X-ray pulses every 1.37 s, so it is a neutron star, yet it shines at roughly 100 times its Eddington luminosity. It was the first known ULX pulsar.

ULXs cluster in star-forming regions. A starburst creates many massive stars, hence many black holes and neutron stars with massive companions feeding them. Chandra images of the Antennae, the Cartwheel ring, Arp 147 and M51 all show ULXs strung along zones of recent star formation.

Gravitational waves and multi-messenger astronomy

Accelerating masses ripple spacetime. Two compact objects in a tight orbit radiate gravitational waves, lose orbital energy, spiral inward and orbit faster. The signal is a chirp: frequency and amplitude both rise until the merger. The gravitational-wave frequency is twice the orbital frequency. Detectors such as LIGO, Virgo and KAGRA measure the stretching of space in kilometer-long laser interferometers, with fractional changes near $10^{-21}$.

What a gravitational wave is. Einstein's general relativity (1916) predicts that accelerating masses with a changing quadrupole shape, such as two stars orbiting each other, send out ripples in spacetime that travel at the speed of light. A passing wave stretches space in one direction while squeezing it in the perpendicular one, then reverses. One full stretch-and-squeeze cycle takes one wave period, which is half the orbital period, so the pattern repeats twice per orbit. It has two polarizations ("plus" and "cross"). Spherically symmetric events (a perfectly round collapse) and steadily spinning symmetric objects emit none. Like other waves, gravitational waves superpose: two signals add, and depending on their relative phase they can reinforce or partly cancel. They pass through matter almost unaffected, which is why they carry clean information from deep inside violent events, and also why they are so hard to detect.

Reading a chirp. A compact-binary signal has three parts. The inspiral: frequency and amplitude rise slowly, then faster (the chirp). The merger: the peak amplitude. The ringdown: the new, distorted black hole settles into a quiet sphere-like shape, the signal dying away at a frequency set by its mass and spin. Lighter systems chirp more slowly and stay in LIGO's band longer: a binary neutron star (GW170817) was tracked for about 100 seconds, a heavy binary black hole for only a fraction of a second.

In quantum terms gravity would be carried by a hypothetical massless particle, the graviton (as the photon carries electromagnetism); GW170817 showed gravitational waves travel at the speed of light to within about one part in 10¹⁵, consistent with a massless carrier. Gravitons have never been detected individually.

Merging black holes emit essentially no light, because there is no matter around them. Merging neutron stars do, because they shed neutron-rich debris; that is what made GW170817 a multi-messenger event. The glow is a kilonova, powered by radioactive decay of freshly made r-process nuclei. A fast "blue" component from lanthanide-poor ejecta fades within a day or two; a slower "red" and infrared component follows, because lanthanides are extremely opaque and trap blue light. A kilonova peaks roughly a thousand times brighter than a classical nova but much fainter than a supernova.

Three things follow directly from a chirp. The rate at which the frequency rises gives the chirp mass, a combination of the two masses. The amplitude falls as $1/d$, so knowing the masses gives the distance directly, with no distance ladder: a standard siren. If light from the same event is also seen, the host galaxy's redshift plus the siren distance give the Hubble constant.

Multi-messenger astronomy combines different carriers of information:

Neutrinos come in three flavors (electron, muon, tau), have tiny masses, and interact only through the weak force, so they stream out of the dense core of the Sun or a collapsing star where light is trapped. Detectors use huge volumes of water or ice and look for the faint Cherenkov light of the rare particles a neutrino knocks loose: Super-Kamiokande (Japan, 50,000 tonnes of water), IceCube (a cubic kilometer of Antarctic ice), and the Sudbury Neutrino Observatory, whose heavy water showed that solar neutrinos change flavor on the way to Earth. About two dozen neutrinos from SN 1987A, in the Large Magellanic Cloud, were caught by three detectors a few hours before the explosion was seen in light, confirming the core-collapse picture.

Cosmic rays are charged particles, mostly protons (about 90%) and helium nuclei (about 9%), with energies up to above 10²⁰ eV. Magnetic fields bend their paths, so their arrival directions do not point back to their sources. Supernova-remnant shocks are thought to accelerate most of those made in our galaxy. In a starburst like M82, cosmic rays from its many supernova remnants smash into the dense gas and make gamma rays (through decaying pions), which is why some starbursts glow in gamma rays.

GW170817, on the 2027 list, is the textbook case: a neutron-star merger heard in gravitational waves and seen across the spectrum.

Seeing in many wavelengths

Dust is the reason the infrared matters. It absorbs ultraviolet and blue light from young stars and re-emits it at tens of kelvin, so a dusty starburst can look unremarkable in visible light and blaze in the far infrared. JWST works mainly in the infrared for this reason.

Light basics. Light is an electromagnetic wave: oscillating electric and magnetic fields, perpendicular to each other and to the direction of travel, regenerating each other as they go. All electromagnetic radiation travels at $c = \lambda\nu$, and each photon carries $E = h\nu = hc/\lambda$. From longest wavelength (lowest frequency, lowest energy) to shortest: radio, microwave, infrared, visible (red → violet), ultraviolet, X-ray, gamma ray. Visible light spans only about 400–700 nm.

The windows in numbers: the optical window (about 300 nm to 1 μm), several near- and mid-infrared windows (about 1–5 μm, plus the thermal-infrared window near 8–14 μm), and the radio window (about 1 cm to 10–20 m; longer waves are reflected by the ionosphere, shorter ones absorbed by water and oxygen).

William Herschel discovered infrared radiation in 1800 by placing a thermometer beyond the red end of a sunlight spectrum and finding it warmed; Johann Ritter found ultraviolet beyond the violet end the next year.

Spitzer ran out of liquid-helium coolant in 2009; in its "warm mission" (to 2020) only the two shortest-wavelength IRAC channels, 3.6 and 4.5 μm, kept working.

How objects emit. Knowing the mechanism tells you what you are looking at:

Dust. Interstellar dust grains scatter and absorb blue light more than red, so starlight passing through dust is dimmed (extinction) and reddened. The same physics, scattering by particles smaller than the wavelength, makes Earth's sky blue (Rayleigh scattering). The absorbed energy warms the dust to tens of kelvin and is re-emitted in the far infrared. Starburst dust also shows strong infrared emission bands from polycyclic aromatic hydrocarbons (PAHs), carbon-rich molecules lit up by UV from young stars; the Cartwheel's red glow in JWST images is this emission. Infrared and radio see through dust; ultraviolet and visible do not.

Images. Astronomical images are almost always false color or representative color: each filter or band (including invisible ones like X-ray) is assigned a visible color, often in wavelength order (longest = red). Composite images combine telescopes: in a typical Chandra–Hubble–Spitzer composite, blue is X-ray hot gas, yellow/white is starlight and red is infrared dust. Detectors are mostly CCDs and similar arrays that count photons with high efficiency; photometry measures brightness through filters, spectroscopy spreads light by wavelength.

Telescope basics. Light-gathering power scales with the mirror area, $\propto D^2$: a 24 cm telescope gathers $(24/4)^2 = 36$ times as much light as a 4 cm one. Resolution (the smallest resolvable angle) is about $\theta \approx 1.22\,\lambda/D$ radians, so radio telescopes must be enormous, or be linked into interferometers whose baseline acts as $D$, to match optical sharpness. The VLA, for example, has 27 dishes of 25 m that can be spread along three 21 km arms, giving baselines up to about 36 km.

Galaxies: types, structure and populations

Morphological classification

Hubble's tuning fork sorts galaxies by appearance:

Despite the old labels "early type" (ellipticals) and "late type" (spirals), the sequence is not an evolutionary path. Mergers are the main route by which spirals become ellipticals. The ellipticity of an E galaxy is apparent, not intrinsic: a flattened elliptical seen end-on looks round.

What each type is made of. Ellipticals and lenticulars are dominated by old, red stars (textbooks describe them as mostly Population II, although the old stars of giant ellipticals are fairly metal-rich) with little cold gas, so they have few H II regions, almost no young stars and essentially no core-collapse supernovae. Their stars move on random orbits (the galaxy is supported by its velocity dispersion, not rotation). Spirals mix an old bulge and halo with a young, gas-rich disk where Population I stars form. Irregulars are usually gas-rich and actively forming stars. Giant ellipticals often hold millions-of-degrees, X-ray-emitting gas and many globular clusters; the largest (cD galaxies) sit at the centers of galaxy clusters, built by mergers.

Where they live. Ellipticals and lenticulars dominate dense galaxy clusters; spirals dominate the sparse field (the morphology–density relation). Mergers, harassment by fast encounters and stripping of gas inside clusters turn spirals into red, gas-poor galaxies. By number, the most common galaxies are dwarfs (dwarf ellipticals, dwarf spheroidals and dwarf irregulars such as NGC 1569); by stellar mass, big spirals and ellipticals dominate.

Colors: red sequence and blue cloud. Plot galaxy color against stellar mass and most galaxies fall into two groups: a blue cloud of star-forming (mostly spiral and irregular) galaxies and a red sequence of galaxies that have stopped forming stars (mostly ellipticals and lenticulars), with a thinly populated green valley between. Galaxies cross the valley when star formation is quenched: the gas is used up (as after a starburst), heated or expelled by supernova or AGN feedback, or stripped by the hot gas of a cluster (ram-pressure stripping, which leaves "jellyfish" tails of gas behind infalling spirals).

Spiral arms. Stars near the center orbit faster than those farther out, so arms made of the same stars would wind up tight within a few rotations (the winding problem). Density wave theory explains long-lived grand-design arms as a slowly rotating pattern of higher density: stars and gas move through the arms, gas is compressed as it enters, and stars form there. That is why arms are lined with blue O and B stars and pink H II regions, which die before drifting far downstream. Tidal interactions can drive strong two-armed patterns (M51). Patchy flocculent spirals instead come from star formation that propagates locally.

Galactic structure and stellar populations

A spiral like the Milky Way or M31 has a thin disk of gas, dust and young-to-middle-aged stars; a central bulge of mostly old stars; often a bar; a supermassive black hole at the center; a faint stellar halo of old stars and globular clusters; and a much larger, invisible dark matter halo.

(Population III, the hypothetical first metal-free stars, has never been observed directly.)

Globular clusters are dense, nearly spherical groups of $10^5$ to $10^6$ stars, typically old and metal-poor. The Milky Way has about 150–160; the Sombrero Galaxy has roughly 2,000. Their H-R diagrams show a low turnoff, a red-giant branch and a horizontal branch rich in RR Lyrae stars. Open clusters are the opposite: young, loose, in the disk. Terzan 5 is a reminder that not every "globular cluster" is simple: it holds stellar populations of different ages and iron content.

Globular clusters are also graded by how concentrated they look on the Shapley–Sawyer scale, from class I (most centrally concentrated) to XII (loosest).

Clusters and associations. Open clusters are gravitationally bound groups of tens to thousands of young-to-middle-aged disk stars (the Pleiades type); they slowly dissolve over hundreds of millions of years. OB associations are loose, gravitationally unbound groups of young O and B stars spread over tens of parsecs that drift apart within ~10 million years; their stars share a common motion and age. Globular clusters are dense, bound, old and spherical, mostly in the halo and bulge. Super star clusters in starbursts are young but as massive as globulars.

How disks form. Gas falling into a rotating dark matter halo keeps its angular momentum while radiating away energy, so it cannot collapse to the center but settles into a thin, rotating disk, where it forms Population I stars; stars that formed earlier, or arrived in mergers, stay on random halo orbits.

The Milky Way as the reference galaxy

The Milky Way is a barred spiral (roughly SBbc) containing a few hundred billion stars.

We live inside the disk, so dust hides the center and the far side in visible light; infrared, radio and X-rays reveal them. The innermost few hundred parsecs, the Central Molecular Zone, hold a large reservoir of dense, warm, turbulent and strongly magnetized molecular gas (and long radio filaments) around Sagittarius A*; despite all that gas, it forms stars less efficiently than its density would suggest.

The Milky Way, Andromeda (M31) and the Triangulum Galaxy (M33) are the three spirals of the Local Group, which also holds dozens of dwarf galaxies, including the Large and Small Magellanic Clouds.

Rotation curves and galactic masses

Stars and gas in a disk orbit the center. If the galaxy's mass were concentrated where the light is, orbital speed would fall as $1/\sqrt{r}$ outside the bright region, as planets' speeds do. Instead, radio (21 cm) and optical measurements show flat rotation curves: speed stays roughly constant far beyond the visible disk. Since $M(<r) = v^2 r/G$, the enclosed mass keeps growing linearly with radius. That is the main evidence for dark matter halos; Vera Rubin's rotation curves of Andromeda were a key early case.

Mass-to-light ratio. Divide a mass (from rotation, velocity dispersion or lensing) by the luminosity, both in solar units: $M/L$. The Sun's is 1; young, blue populations are below 1; old stellar populations are about 2–10; whole galaxies measured out into their dark halos reach tens, and galaxy clusters a few hundred. For example, $1.0\times10^{11}\ M_\odot$ with a luminosity of $2\times10^{10}\ L_\odot$ gives $M/L = 5$. A value far above what old stars can supply is the dark-matter signal.

More evidence for dark matter. Fritz Zwicky first argued for unseen mass in the 1930s: galaxies in the Coma cluster move too fast for the cluster's visible mass to hold them. Later: flat rotation curves (Vera Rubin and Kent Ford, 1970s); the hot X-ray gas in clusters, which needs a deep gravitational well to stay bound; gravitational lensing masses of clusters; the Bullet Cluster, where lensing shows most of the mass has passed through a collision while the X-ray gas (most of the ordinary matter) lagged behind; and the pattern of fluctuations in the cosmic microwave background. Dark matter makes up about 85% of all matter. It is thought to be cold (slow-moving) particles that do not emit, absorb or reflect light; candidates include WIMPs and axions. Compact dark objects (MACHOs: faint stars, black holes) were searched for by microlensing and cannot account for most of it, and neutrinos are too fast ("hot") to build small structures. A minority view, MOND, modifies gravity instead.

Gravitational lensing. Mass bends light (general relativity), so a massive foreground galaxy or cluster acts as a lens for objects behind it. Strong lensing makes multiple images, arcs and, for exact alignment, Einstein rings; the images arrive with time delays because their paths differ in length, and they are magnified, which lets telescopes study galaxies too faint to see otherwise. Weak lensing slightly distorts the shapes of many background galaxies and maps dark matter statistically. Microlensing by a single star briefly brightens a background star without visibly splitting it. Lensing measures total mass, dark matter included, without any assumption about light.

Starbursts and galaxy interactions

What a starburst is

A starburst galaxy forms stars far faster than it could sustain over its lifetime. A useful test is the gas depletion time: the gas mass divided by the star-formation rate. The Milky Way forms roughly 1–2 solar masses of stars per year and would take a few billion years to use its gas; a starburst may form tens to hundreds of solar masses per year and exhaust its gas in some tens to hundreds of millions of years. A starburst can be galaxy-wide or concentrated in the nucleus.

Signatures of a starburst, and why each appears:

• Blue, UV-bright regions and super star clusters: many short-lived massive stars.
• Strong H-alpha emission: their UV ionizes surrounding hydrogen.
• Huge far-infrared luminosity: dust absorbs the UV and re-radiates it.
• Radio synchrotron: electrons accelerated in supernova remnants.
• A high core-collapse supernova rate and many ULXs and high-mass X-ray binaries.
• Galactic superwinds: supernovae and stellar winds together blow hot, metal-rich gas out of the disk, seen as X-ray-bright, H-alpha-bright plumes along the minor axis (M82 is the prototype).

The wind is feedback: it removes and heats the gas that fuels star formation, which is one reason starbursts end.

What triggers them: interactions

Most strong starbursts are triggered by gravity from a neighbor. Tidal forces, the difference in a companion's pull across a galaxy, stretch it, launch long tidal tails and bridges, and disturb gas orbits. Gas clouds collide, lose angular momentum and fall toward the center, where they are compressed into new stars. Bars do something similar internally. The stars themselves almost never collide during a galaxy collision; the space between them is enormous. Gas clouds, which fill far more volume, do collide.

The Roche limit idea, the distance inside which tides beat a body's self-gravity, applies at every scale: a moon near a planet, a star near a black hole, a globular cluster or dwarf galaxy near a large galaxy.

More interaction vocabulary.

• Major vs minor merger: comparable masses (ratio closer than about 1:3 or 1:4) versus a big galaxy eating a small one. Major mergers of two spirals can scramble the disks into an elliptical; minor mergers thicken disks and build stellar halos and streams. A big galaxy steadily absorbing small ones is galactic cannibalism.
• Wet vs dry merger: gas-rich (fuels a starburst and possibly an AGN) versus gas-poor (no starburst; grows ellipticals).
• Dynamical friction: a satellite moving through a halo of stars and dark matter pulls a wake behind it whose gravity slows it, so it spirals in.
• Tidal tails form from the far sides of disks during slow, prograde passes; bridges link the pair. New star clusters and even tidal dwarf galaxies can form in the tails.
• Ring galaxies (Cartwheel, Arp 147, Arp 143) need a nearly head-on, central passage; polar-ring galaxies form when captured gas settles into an orbit perpendicular to the disk.

• Galaxy harassment: repeated fast encounters in a cluster that heat and strip disks.
• The Toomre sequence orders merging pairs by stage, from separated disks with tails (the Antennae near the start) to a single remnant that looks like an elliptical with faint shells and ripples.
• Merger timescales are of order hundreds of millions to a billion years; a starburst lasts about 10–100 million years.
• Luminous and ultraluminous infrared galaxies (LIRGs above 10¹¹ $L_\odot$, ULIRGs above 10¹² $L_\odot$ in the infrared) are dusty galaxies powered mainly by starbursts; nearly all ULIRGs (and many LIRGs) are mergers, often with buried AGN too.

How star formation is measured. H-alpha (ionizing photons from stars younger than ~10 Myr), ultraviolet (stars younger than ~100 Myr), far-infrared (UV re-radiated by dust), radio continuum (supernova electrons), and X-ray binaries (high-mass X-ray binaries trace recent star formation). Each misses something: UV and H-alpha are hidden by dust, while the infrared misses unobscured stars, so careful estimates combine them. Tests may give a conversion such as Kennicutt's H-alpha calibration, $\text{SFR}\ (M_\odot/\text{yr}) \approx 7.9\times10^{-42}\,L(\text{H}\alpha)$ with $L$ in erg/s: $L(\text{H}\alpha) = 1.3\times10^{42}$ erg/s gives about 10 $M_\odot$ per year, an M82-like rate. Such conversions assume an initial mass function, usually Salpeter's $dN/dM \propto M^{-2.35}$: per unit mass range there are about $10^{2.35} \approx 220$ times as many 1 $M_\odot$ stars as 10 $M_\odot$ stars. The Kennicutt–Schmidt law, $\Sigma_\text{SFR} \propto \Sigma_\text{gas}^{1.4}$ (star formation and gas per unit area of disk), says that denser gas forms stars disproportionately faster, which is why gas driven into a galaxy's center ignites a starburst.

After the burst. When star formation stops abruptly, the O stars die within ~10 Myr and the B stars within a few hundred Myr, but A stars survive for ~1 Gyr. The galaxy then shows strong Balmer absorption lines from A stars but no emission lines: a post-starburst ("E+A" or "K+A") galaxy.

When two galaxies with central supermassive black holes merge, dynamical friction drags the black holes to the center, where they form a binary. Stars passing close by carry off energy and shrink the binary, but around a separation of about a parsec the supply of such stars can run out before gravitational waves become strong enough to finish the job: the final parsec problem. Gas, triaxial galaxy shapes or a third black hole probably solve it in practice; such binaries are thought to produce the nanohertz background seen by pulsar timing arrays.

Active galactic nuclei and how to tell them from starbursts

Nearly every large galaxy has a central supermassive black hole. When it is accreting heavily, the nucleus becomes an active galactic nucleus (AGN), which can outshine the rest of the galaxy from a region smaller than the solar system. The unified model says most AGN have the same parts, an accretion disk, fast-moving clouds near the black hole (the broad-line region), slower clouds farther out (the narrow-line region), a dusty torus and sometimes jets, and that what we see depends on viewing angle and power:

Quasar distances come from their redshifts through Hubble's law (or a cosmological model at high $z$), not from treating them as standard candles, because their luminosities vary enormously. Variability on timescales of days means the emitting region is light-days across or smaller, the same light-travel-time argument as for pulsars. Quasars were recognized in 1963 when the emission lines of 3C 273 turned out to be ordinary hydrogen lines at a redshift of 0.16.

Starburst or AGN? Both make a galaxy's center bright, both are fed by gas driven inward (often by an interaction), and many galaxies host both. The diagnostics:

The mass of the central black hole correlates with the velocity dispersion of the host's bulge (the M–σ relation), so black holes and galaxies grow together; AGN feedback (winds and jets heating or expelling gas) is thought to quench star formation in massive galaxies, just as supernova-driven superwinds regulate starbursts.

Magnitudes, distances and the distance ladder

Magnitudes and proper motion

Magnitudes are logarithmic and run backwards: smaller is brighter, and 5 magnitudes is a factor of 100 in flux. Apparent magnitude $m$ is what we see; absolute magnitude $M$ is what the object would show at 10 pc.

The scale goes back to Hipparchus, who ranked naked-eye stars from 1st magnitude (brightest) to 6th (faintest). In 1856 Norman Pogson made it exact: a difference of 5 magnitudes is a flux ratio of exactly 100, so 1 magnitude is $100^{1/5} \approx 2.512$. The zero point was historically set by Vega (magnitude about 0 in every band in the "Vega system"); Polaris was an early reference until it turned out to be variable. Anchors: the Sun $m = -26.7$, the full Moon about $-12.7$, Sirius $-1.46$, Vega $0.0$, the naked-eye limit about $+6$, the faintest Hubble and JWST detections around $+30$ and fainter.

Absolute magnitude and luminosity. The Sun has $M_V = +4.83$ and bolometric (all-wavelength) magnitude $M_\text{bol} = +4.74$. The bolometric correction $BC = M_\text{bol} - M_V$ is about zero for Sun-like stars and large and negative for very hot and very cool stars, which emit mostly outside the V band.

Where the parsec comes from. Picture a long, thin triangle: its base is the radius of Earth's orbit (1 AU) and its apex is the star. The small angle at the star is the parallax $p$. One parsec ("parallax of one arcsecond") is the distance at which 1 AU subtends exactly 1″, so $d = 1/p$ follows from the small-angle formula: $d = 1\ \text{AU}/p(\text{rad}) = 206{,}265\ \text{AU}/p(″)$.

1 pc = 206,265 AU = 3.086 × 10¹⁶ m = 3.26 light-years. Hipparcos measured parallaxes to about a milliarcsecond; Gaia reaches tens of microarcseconds for bright stars, which takes geometric distances across a large part of the Milky Way.

Proper motion $\mu$ is an object's angular drift across the sky, in arcseconds per year. Combined with distance it gives the tangential velocity; the Doppler shift gives the radial velocity; together they give the true space velocity.

Color indices such as B−V measure temperature (larger B−V means redder, cooler), but dust reddens and dims light too. An object that looks redder than its spectral class predicts is probably behind dust. This matters for M82, Terzan 5 and SN 2014J.

Dust changes the distance modulus. Extinction $A$ (in magnitudes) makes an object look fainter, so it must be subtracted:

The ladder, rung by rung

Other rungs you may meet: the tip of the red giant branch (old red giants all ignite helium at about the same luminosity, $M_I \approx -4.0$; this method revised NGC 1569's distance); Faber–Jackson for ellipticals ($L \propto \sigma^4$, the elliptical cousin of Tully–Fisher); surface brightness fluctuations; the brightest planetary nebulae and globular clusters; and masers orbiting a galaxy's central black hole, which give geometric distances. Each method is calibrated on the rung below it, so errors propagate upward; that is why NGC 4536's Cepheids, which link a Type Ia supernova (SN 1981B) to the Cepheid scale, matter.

The Tully–Fisher relation

In spiral galaxies, the maximum rotation speed and the luminosity are tightly linked: $L \propto v_\text{max}^{\,4}$ (roughly; the exponent depends on the waveband). The reason: a faster rotation speed means more mass ($M \propto v^2 r$), and more mass means more stars. Astronomers measure $v_\text{max}$ from the width of the 21 cm line (a spinning disk smears the line by its rotation, corrected for inclination), read $L$ or $M$ from the calibrated relation, and compare with $m$.

Hubble's law

Hubble's law is what an expanding universe looks like from inside if the universe is homogeneous and isotropic on large scales (the cosmological principle): if all distances scale up by the same factor, every observer sees every other galaxy receding at a speed proportional to its distance, so no galaxy is at the center. Georges Lemaître (1927) and Edwin Hubble (1929) found the relation, now often called the Hubble–Lemaître law; Hubble's first value, about 500 km/s/Mpc, was far too high, mostly because of the Cepheid mix-up. The actual age of the universe, about 13.8 billion years (from the cosmic microwave background plus a cosmological model), happens to be close to the Hubble time $1/H_0 \approx 14$ Gyr, but the two are different quantities. Today two precise methods disagree: about 67 km/s/Mpc from the cosmic microwave background and about 73 from Cepheids plus Type Ia supernovae (the Hubble tension).

The Hubble distance $c/H_0$ is the distance at which Hubble's law would give a recession speed equal to $c$: for $H_0 = 70$ km/s/Mpc, $c/H_0 = 3.00\times10^5/70 \approx 4{,}300$ Mpc $\approx 1.3\times10^{23}$ km (about 14 billion light-years). The Hubble time $1/H_0$: convert 1 Mpc $= 3.086\times10^{19}$ km, so $1/H_0 = 3.086\times10^{19}/70$ s $= 4.4\times10^{17}$ s $\approx 14$ Gyr.

Orbits in binary and galactic systems

Item 3b asks you to use Kepler's laws and circular motion for both binary stars and galaxies.

Kepler's three laws, stated the way tests ask for them:

1. Orbits are ellipses with the center of mass at one focus.
2. The line joining the bodies sweeps out equal areas in equal times, so a body moves fastest at closest approach (periapsis) and slowest at the farthest point (apoapsis). This is conservation of angular momentum.
3. $P^2 \propto a^3$ (the "harmonic law"); Newton's version adds the masses, below.

At periapsis and apoapsis the velocity is entirely perpendicular to the line joining the bodies, so the separation is momentarily not changing. Triple the orbit size and the period grows by $3^{3/2} \approx 5.2$.

Ellipse geometry. Semimajor axis $a$, semiminor axis $b$, eccentricity $e$: $b^2 = a^2(1 - e^2)$; the focus sits $ae$ from the center; periapsis $r_p = a(1-e)$, apoapsis $r_a = a(1+e)$, so $a = (r_p + r_a)/2$; the semi-latus rectum is $a(1 - e^2)$.

Deriving orbits from force balance. For a circular orbit, gravity supplies the centripetal force: $GMm/r^2 = mv^2/r$, so $v^2 = GM/r$; with $v = 2\pi r/P$ this gives Kepler's third law, $P^2 = 4\pi^2 r^3/(GM)$. The same method works for any force law a question invents: set the given force equal to $mv^2/r$ and solve for $v$ or $P$.

Kinds of binary star.

Spectroscopic binaries are the easiest to detect at large distances because they do not need to be resolved. Eclipsing spectroscopic binaries are the gold standard for stellar masses and radii.

Close binaries and mass transfer. Each star in a binary has a teardrop-shaped Roche lobe, the region where its gravity dominates; the lobes touch at the inner Lagrange point (L1). A star that swells past its lobe (as it becomes a giant) spills gas through L1 onto its companion. Detached binaries have both stars inside their lobes, semidetached have one filling it (Algols, cataclysmic variables, X-ray binaries), contact binaries share an envelope (W Ursae Majoris stars). Mass transfer explains the Algol paradox: the less massive star in an Algol system is the more evolved one, because it was originally the more massive and has given much of its mass away. Unstable transfer can engulf both stars in a common envelope, shrinking the orbit drastically; this is how compact double white dwarfs and double neutron stars, the progenitors of some Type Ia supernovae and of GW170817-like mergers, are made. Stripping by a companion is also the main way stars lose their hydrogen envelopes before exploding as Type Ib, Ic or IIb supernovae.

The five Lagrange points are where a small body can stay fixed relative to two orbiting masses. L1 lies between them (mass transfer), L2 beyond the smaller one (JWST orbits near the Sun–Earth L2, about 1.5 million km from Earth, where it can keep the Sun, Earth and Moon on one side of its sunshield), and L4 and L5, 60° ahead of and behind the smaller body, are the stable ones (provided the larger mass is more than about 25 times the smaller, as for the Sun and Jupiter).

Both bodies orbit the center of mass, and the heavier one sits closer to it.

For circular orbits, $v = \sqrt{GM/r}$, so orbital speed falls as $1/\sqrt{r}$ around a point mass, and escape speed is $\sqrt{2}$ times circular speed. Orbit shape follows eccentricity: $e = 0$ circle, $0 < e < 1$ ellipse, $e = 1$ parabola (exactly escape energy), $e > 1$ hyperbola (unbound). Galaxy encounters are usually on near-parabolic or bound orbits; the more slowly two galaxies pass, the stronger the tidal damage.

Binary stars give masses through eclipses and Doppler shifts: an eclipsing binary's light curve gives the period and the inclination, and with the orbital speed from spectroscopy it gives the radii; a spectroscopic binary's opposite-moving line sets give the velocity ratio, hence the mass ratio. Gravitational-wave binaries are the extreme case, with orbital periods of milliseconds just before merger.

The 2027 listed objects

Learn what each object is, which rules topic it illustrates, and which observation identifies it. Distances are approximate; published values vary by method, so quote a range or the value a question gives.

ReferenceListed objects at a glance· 16 rows

16 rows

Object	Type and location	Distance (approx.)	What tests ask about it
Andromeda Galaxy (M31)	Large spiral (Sb) in Andromeda; the nearest big galaxy and the largest member of the Local Group	~2.5 million ly (≈ 770 kpc)	Hubble's Cepheid V1 (1923–25) proved galaxies lie outside the Milky Way; Vera Rubin's rotation curve points to dark matter; blueshifted, approaching at roughly 110 km/s relative to the Milky Way, with a collision in roughly 5–10 billion years possible but not certain (recent estimates of the odds differ widely) (the merged galaxy is nicknamed "Milkomeda"); satellites M32 and M110; hundreds of globular clusters; a giant stellar stream and a dusty star-forming ring from past encounters; naked-eye visible; SN 1885A (S Andromedae) is the only supernova seen in it
Sombrero Galaxy (M104)	Bright, nearly edge-on galaxy in Virgo with a huge bulge and a dark dust lane	~30 million ly	Usually classed Sa (or S0/Sa); infrared data suggest a giant elliptical with a disk embedded in it; roughly 2,000 globular clusters; a central black hole near a billion $M_\odot$ and a low-luminosity active nucleus; little current star formation (a "normal" galaxy); one of the first galaxies whose large redshift (about 1,000 km/s) was measured, by Vesto Slipher
Whirlpool Galaxy (M51)	Grand-design spiral interacting with its small companion NGC 5195, in Canes Venatici	~25–30 million ly	Textbook tidal interaction: the encounter sharpened its two arms and triggered star formation along them; the first galaxy whose spiral shape was seen (Lord Rosse, 1845); several recent core-collapse supernovae; many X-ray binaries and ULXs
NGC 4536	Barred (intermediate) spiral in the Virgo cluster region	~50 million ly	Hubble measured Cepheids in it to calibrate the Type Ia supernova SN 1981B, a rung in the Hubble-constant ladder; star-forming inner ring and nucleus
MCG+07-33-027	Face-on spiral starburst galaxy imaged by Hubble	~300 million ly	Forms stars at an extraordinary rate, yet is an isolated field galaxy with no obvious partner, so its starburst was probably not triggered by a collision; the trigger is still debated
NGC 1569	Dwarf irregular starburst galaxy in Camelopardalis	~11 million ly	Starburst lasting ~100 million years; super star clusters of over a million stars each sitting in a central cavity blown out by supernovae; a galactic wind carrying metal-rich gas out of a small galaxy; Hubble's red-giant measurements put it about 1.5 times farther than thought, which made the starburst more intense
Antennae Galaxies (NGC 4038/4039)	Two colliding spirals partway through a merger, in Corvus	~45–65 million ly	Long tidal tails (the "antennae"); thousands of young star clusters and super star clusters, some likely to become globular clusters; Chandra found many ULXs and hot gas enriched with elements such as neon, magnesium, silicon and iron from supernovae; an early stage of the Toomre merger sequence
Arp 143	Interacting pair: NGC 2445 (distorted, star-forming) and NGC 2444 (older, gas-poor companion)	~190 million ly	A head-on passage set off a ring- or triangle-shaped burst of star formation in NGC 2445, bright in UV, infrared and X-rays (X-ray sources in the star-forming regions)
Arp 147	Pair shaped like the number "10": a relatively undisturbed galaxy (the "1") and a blue ring galaxy (the "0"), in Cetus	~400+ million ly	The "1" passed through the "0", sending out a density wave that formed a ring of star formation; a reddish knot in the ring probably marks the old nucleus; Chandra found ULXs in the ring, likely black holes in young binaries
Cartwheel Galaxy	Ring galaxy in Sculptor	~500 million ly	A smaller galaxy plunged through its disk a few hundred million years ago (estimates range from about 200 to 440 million years); a bright inner ring and a colorful outer ring expand like ripples, joined by "spokes"; JWST's infrared images show hydrocarbon-rich (PAH) dust and young star clusters; Chandra found many ULXs in the outer ring
M82 (Cigar Galaxy)	Prototype starburst, an edge-on disk in Ursa Major, disturbed by M81	~12 million ly	Star formation in the core roughly ten times the Milky Way's total rate, triggered by the M81 encounter; a bipolar superwind of million-degree gas seen in X-rays and H-alpha along the minor axis; very bright in the infrared; super star clusters; a high supernova rate; faint gamma-ray glow from cosmic rays
M82 X-1	ULX in M82	Same as M82	Intermediate-mass black hole candidate, about 400 $M_\odot$ from the frequencies of its X-ray oscillations
M82 X-2	ULX in M82	Same as M82	NuSTAR found 1.37 s pulsations in 2014: it is a neutron star, the first ULX pulsar, shining roughly 100 times its Eddington luminosity
SN 2014J	Type Ia supernova in M82, discovered January 2014	Same as M82	One of the nearest Type Ia events in decades; heavily reddened and dimmed by M82's dust (with unusual dust properties); gamma-ray lines from cobalt-56 decay were detected, confirming the radioactive power source; light echoes off dust
GW170817	Merger of two neutron stars, detected 17 August 2017	~130 million ly (≈ 40 Mpc), in the lenticular galaxy NGC 4993	First gravitational waves from neutron stars (LIGO/Virgo), followed about 1.7 s later by a short gamma-ray burst (Fermi, INTEGRAL) and within hours by a kilonova seen across the spectrum; showed that at least some short GRBs come from neutron-star mergers, saw heavy r-process elements forming, showed gravity travels at the speed of light, and gave the first standard-siren $H_0$ (about 70 km/s/Mpc)
Terzan 5	Globular-cluster-like stellar system in the Milky Way's bulge, in Sagittarius	~20,000 ly	Hidden behind heavy dust, so studied in infrared and X-rays; contains stellar populations of different ages and iron content, so it is probably a surviving building block of the bulge rather than an ordinary globular cluster; hosts more known millisecond pulsars (dozens) than any other cluster, including the fastest-spinning pulsar known (716 times per second)

Breadth reference

The chapters above teach the ideas. This section is the lookup shelf for the many short questions that test a single term, class, constant, instrument or name. Every table has a filter box: type a word to find the row.

Astronomy glossary

ReferenceAstronomy glossary· 378 rows

Filter by any word.

378 rows

Term	Definition	Topic
21-cm line	Radio line at 1420 MHz from the spin-flip of neutral hydrogen's electron; maps H I gas and galaxy rotation curves.	Spectra
Absolute bolometric magnitude	Absolute magnitude counting all wavelengths; the Sun's is +4.74.	Photometry
Absolute magnitude	Apparent magnitude an object would have at 10 pc; written $M$. The Sun's $M_V \approx +4.83$.	Photometry
Absorption line	Dark line where cooler gas in front of a hotter continuum source absorbs photons at one specific wavelength.	Spectra
Accretion	Growth of an object by infalling matter, which turns gravitational energy into heat and radiation.	Compact objects
Accretion disk	Flattened, rotating disk of gas spiralling onto a young star or compact object, heated by friction (viscosity) until it glows, up to X-rays near compact objects.	Compact objects
Accretion efficiency	Fraction of infalling rest-mass energy radiated: ~6% for a non-spinning black hole, up to ~42% for maximal spin, versus 0.7% for hydrogen fusion.	Compact objects
Adaptive optics	Deformable mirror and wavefront sensor that correct atmospheric blurring in real time, often using a laser guide star.	Instruments
Age of the universe	About 13.8 billion years (from the CMB); close to, but not the same quantity as, the Hubble time $1/H_0$.	Cosmology
Algol paradox	In Algol the less massive star is the more evolved one, explained by mass transfer from the originally more massive star.	Binaries
Algol variable	Eclipsing binary (EA type) with nearly constant light between sharp, distinct eclipses; prototype Algol (Beta Persei).	Binaries
ALMA	Atacama Large Millimeter/submillimeter Array: 66 antennas at ~5,000 m in Chile's Atacama Desert, imaging cold dust, molecular gas and protoplanetary disks.	Instruments
Alpha process	Successive helium-4 captures in massive stars building O, Ne, Mg, Si, S, Ar and Ca ("alpha elements").	Evolution
AM CVn star	Double-degenerate cataclysmic variable: a white dwarf accreting helium from a degenerate or semi-degenerate helium donor; orbital periods roughly 5–65 minutes, no hydrogen lines.	Binaries
Angular momentum	Rotational "quantity of motion" ($mvr$ for an orbit), conserved; why collapsing clouds spin up into disks and collapsing cores become fast pulsars.	Stars
Angular resolution	Smallest angular separation an instrument can distinguish; diffraction limit $\theta \approx 1.22\lambda/D$, or $\lambda/B$ for an interferometer of baseline $B$.	Instruments
Angular size	Angle an object subtends on the sky; physical size = distance × angle in radians (small-angle formula).	Distances
Apastron	Point of a binary orbit where the stars are farthest apart and moving slowest; velocity there is perpendicular to the line joining the stars.	Binaries
Apparent magnitude	Brightness as seen from Earth on a reversed logarithmic scale ($m$); smaller is brighter, 5 magnitudes = factor 100, 1 mag ≈ 2.512.	Photometry
Arcsecond	1/3,600 of a degree, about $4.85\times10^{-6}$ radian.	Distances
Astronomical unit	Roughly the mean Earth–Sun distance; since 2012 defined as exactly 149,597,870,700 m ≈ $1.496\times10^{8}$ km.	Distances
Asymptotic giant branch	Late stage of low and intermediate-mass stars: inert C–O core inside helium- and hydrogen-burning shells; very luminous, cool, pulsating, losing mass fast.	Evolution
Atmospheric window	Wavelength band that reaches the ground: visible/near-UV (~300–1,000 nm), parts of the near-IR, thermal IR ~8–14 µm, and radio (roughly 1 cm to 10–20 m, edges site- and ionosphere-dependent).	Instruments
Baade–Wesselink method	Combines a pulsating star's radial-velocity curve (change in radius) with its light and color curves to find its radius and distance.	Distances
Balmer series	Hydrogen lines from transitions to or from level $n=2$, mostly visible: H-alpha 656.3 nm, H-beta 486.1 nm; strongest in A stars (~10,000 K).	Spectra
Barred spiral galaxy	Spiral (type SB) whose arms start from the ends of a central bar of stars; the Milky Way is one.	Galaxies
Baryonic matter	Ordinary matter made of protons and neutrons (atoms, gas, stars); about 5% of the universe's energy density.	Cosmology
Be star	B star showing hydrogen emission lines from a gaseous decretion disk flung out by very fast rotation.	Stars
Be X-ray binary	High-mass X-ray binary in which a neutron star on an eccentric orbit accretes from a Be star's disk, giving periodic X-ray outbursts near periastron.	Binaries
Beta Cephei variable	Hot O8–B6 stars pulsating with periods ~0.1–0.6 days and small amplitudes, driven by the kappa mechanism in iron-group opacity.	Variables
Big Bang	Hot, dense early state from which the universe has expanded for ~13.8 Gyr; evidence: Hubble flow, CMB, light-element abundances.	Cosmology
Binary star	Two stars bound by gravity, orbiting their common center of mass with equal and opposite forces on each (Newton's third law).	Binaries
Bipolar outflow	Pair of oppositely directed jets or flows from a protostar along its disk's rotation axis.	Formation
Black dwarf	Hypothetical cold, dark end state of a white dwarf; none exist yet because cooling takes far longer than the universe's age.	Compact objects
Black hole	Region where gravity is so strong that nothing, not even light, escapes from inside its event horizon; the most compact end state of a massive star's core.	Compact objects
Blackbody	Ideal object that absorbs all radiation falling on it and emits a thermal spectrum set only by its temperature (Planck spectrum).	Radiation
Blazar	AGN whose relativistic jet points nearly at us; rapidly variable and highly polarized; includes BL Lac objects (nearly featureless spectra) and flat-spectrum radio quasars (broad lines).	AGN
Blue straggler	Cluster star lying above the turnoff that should already have evolved away; made by mass transfer or a merger in a binary.	Evolution
Blue supergiant	Hot (O–B), very luminous supergiant such as Rigel; SN 1987A's progenitor (Sk −69 202) was one.	Stars
Blueshift	Shift of spectral lines to shorter wavelengths because the source moves toward the observer.	Spectra
Bok globule	Small, isolated dark cloud, typically ~2–50 M☉ about a light-year across, seen as a silhouette against bright nebulae; forms one or a few stars.	Formation
Bolometric correction	BC = $M_\text{bol} - M_V$; converts a visual magnitude to an all-wavelength one; largest for very hot and very cool stars.	Photometry
Bolometric luminosity	A star's total power output at all wavelengths, as opposed to luminosity in one band.	Photometry
Bow shock	Curved shock front ahead of an object or jet moving supersonically through surrounding gas.	Formation
Bremsstrahlung	"Braking radiation" (free-free emission) from free electrons deflected by ions; thermal X-rays from hot cluster gas, radio from H II regions.	Radiation
Broad-line region	Fast-moving gas clouds close to an AGN's black hole producing emission lines thousands of km/s wide; hidden by the torus in type 2 AGN.	AGN
Brown dwarf	Substellar object of ~13 to ~75–80 Jupiter masses (below ~0.075–0.08 M☉): fuses deuterium briefly but never sustains hydrogen fusion; degeneracy-supported, cools forever.	Stars
Bulge	Central, roughly spheroidal concentration of mostly old stars in a spiral galaxy.	Galaxies
Carbon star	Cool giant, usually on the AGB, with more carbon than oxygen (C/O > 1) after dredge-up (or mass transfer from a companion); spectral class C, with C₂ and CN bands, no TiO.	Stars
Cataclysmic variable	Close binary in which a white dwarf accretes from a Roche-lobe-filling companion; includes novae, dwarf novae, polars and nova-likes.	Variables
Central Molecular Zone	Dense, turbulent, strongly magnetized molecular gas in the Milky Way's inner few hundred parsecs around Sgr A*.	Galaxies
Cepheid variable	Classical (Type I) Cepheid: young Population I yellow supergiant (~4–20 M☉) pulsating with periods ~1–100 days; longer period means more luminous.	Variables
Chandra X-ray Observatory	NASA X-ray telescope launched 1999 with ~0.5″ resolution, used to image X-ray binaries, ULXs, supernova remnants and hot gas.	Instruments
Chandrasekhar limit	Maximum mass a white dwarf can have while supported by electron degeneracy pressure, ≈ 1.4 M☉ (1.44 for a C–O composition).	Compact objects
Chirp	Rising frequency and amplitude of a gravitational-wave signal as a compact binary spirals in toward merger.	Gravitational waves
Chirp mass	Mass combination $(m_1m_2)^{3/5}/(m_1+m_2)^{1/5}$ that sets how fast a binary's GW frequency rises; the best-measured inspiral parameter.	Gravitational waves
Chromosphere	Thin layer above the photosphere where temperature rises; glows in H-alpha; very active in T Tauri and flare stars.	Stars
CNO cycle	Hydrogen-to-helium fusion using C, N and O as catalysts; dominates above ~1.3 M☉ (core above 17 MK), extremely temperature sensitive ($T^{16-20}$).	Stars
Color excess	E(B−V): observed minus intrinsic color, measuring dust reddening; visual extinction $A_V \approx 3.1\,E(B-V)$.	Photometry
Color index	Magnitude difference between two filters, e.g. B−V; smaller or negative means hotter. B−V ≈ 0 near 10,000 K, Sun ≈ 0.65.	Photometry
Color–magnitude diagram	Observational H-R diagram plotting apparent or absolute magnitude against color index, used for star clusters.	Photometry
Common envelope	Phase when a binary companion is engulfed by an expanding giant; drag shrinks the orbit, ejecting the envelope or merging the stars.	Binaries
Compact object	Collective term for white dwarfs, neutron stars and black holes, the stellar remnants supported by degeneracy or collapsed entirely.	Compact objects
Contact binary	Binary in which both stars overfill their Roche lobes and share a common envelope (W Ursae Majoris type); may end in a merger.	Binaries
Continuous spectrum	Unbroken spread of all wavelengths emitted by a hot, dense object (Kirchhoff's first law).	Spectra
Convection	Energy transport by rising hot and sinking cool gas; in cores of massive stars and envelopes of cool stars; stars below ~0.35 M☉ are fully convective.	Stars
Core collapse	Implosion of a massive star's iron core once it exceeds what degeneracy pressure can support, forming a neutron star or black hole.	Evolution
Core-collapse supernova	Explosion of a star above ~8 M☉ after core collapse (Types II, Ib, Ic); about 99% of the energy leaves as neutrinos.	Evolution
Corona	Hot (~1–2 million K), tenuous outer atmosphere of the Sun or a star, emitting X-rays.	Stars
Cosmic microwave background	Relic radiation from ~380,000 years after the Big Bang, now a 2.725 K blackbody peaking near 1 mm.	Cosmology
Cosmic rays	High-energy charged particles (mostly protons), many accelerated in supernova remnant shocks.	Radiation
Cosmological constant	Constant energy density of empty space (Λ) in Einstein's equations; simplest model of dark energy.	Cosmology
Cosmological principle	Assumption that the universe is homogeneous and isotropic on large scales; uniform expansion of such a universe yields Hubble's law.	Cosmology
Cosmological redshift	Stretching of light's wavelength by the expansion of space while it travels: $1+z$ = factor by which the universe expanded.	Cosmology
Coulomb barrier	Electrostatic repulsion between positive nuclei that fusion must overcome; at stellar temperatures it is crossed by quantum tunneling.	Stars
Dark energy	Unknown component (~68–70% of the energy density) driving the accelerating expansion discovered with distant Type Ia supernovae in 1998.	Cosmology
Dark matter	Matter detected only through gravity (flat rotation curves, lensing, cluster motions); emits and absorbs no radiation at any wavelength; ~85% of all matter.	Galaxies
Dark nebula	Dense cloud of gas and dust that blocks light behind it (e.g., Horsehead Nebula); a site of star formation.	Formation
De Vaucouleurs law	Surface-brightness profile $\log I \propto -r^{1/4}$ fitting elliptical galaxies and bulges; the Sérsic $n=4$ case.	Galaxies
Debris disk	Gas-poor dusty disk around a star, replenished by colliding planetesimals after the gas-rich protoplanetary disk has dispersed.	Formation
Degenerate matter	Matter so compressed that Pauli exclusion, not heat, supplies the pressure; pressure barely depends on temperature.	Compact objects
Delta Scuti variable	A0–F5 stars in the instability strip near the main sequence pulsating with periods ~0.01–0.2 days and small amplitudes.	Variables
Density wave theory	Spiral arms are slowly rotating compression waves; gas piles up as it passes through them, triggering star formation.	Galaxies
Deuterium burning	Fusion of deuterium with a proton into helium-3 at ~10⁶ K; occurs in protostars and in brown dwarfs above ~13 Jupiter masses.	Formation
Diffraction grating	Dispersing element with many fine, parallel lines that spreads light by wavelength through interference; standard in spectrographs.	Instruments
Distance ladder	Chain of distance methods, each calibrating the next: parallax → Cepheids/RR Lyrae → Tully–Fisher, Type Ia supernovae → Hubble's law.	Distances
Distance modulus	$m - M = 5\log_{10}(d/10\,\text{pc})$, plus extinction if dust is present; so $d = 10^{(m-M+5)/5}$ pc.	Distances
Doppler broadening	Line widening from random thermal or turbulent gas motions (and rotation); wider for hotter gas and faster rotators.	Spectra
Doppler effect	Wavelength shift from line-of-sight motion: $\Delta\lambda/\lambda = v_r/c$ for $v \ll c$; red if receding, blue if approaching.	Spectra
Double-lined spectroscopic binary	Spectroscopic binary in which both stars' lines are visible and shift in opposite directions, giving the mass ratio.	Binaries
Dwarf galaxy	Small, low-luminosity galaxy (dwarf elliptical, spheroidal or irregular); the most numerous galaxy type.	Galaxies
Dwarf nova	Cataclysmic variable (U Geminorum type) whose accretion disk periodically flares by several magnitudes for days to weeks via a disk instability, not fusion.	Variables
Dynamical friction	Gravitational drag on a massive body moving through a sea of stars and dark matter; makes merging galaxies and black holes sink together.	Galaxies
Eccentricity	Measure of an orbit's elongation, $e = c/a$; 0 is a circle, near 1 very elongated; $b = a\sqrt{1-e^2}$.	Binaries
Eclipsing binary	Binary seen nearly edge-on so the stars pass in front of each other, producing dips in the light curve; gives radii and inclination.	Binaries
Eddington luminosity	Luminosity at which radiation pressure on electrons balances gravity on infalling gas: ≈ $1.26\times10^{31}$ W ≈ $3.3\times10^4$ L☉ per solar mass.	Compact objects
Effective temperature	Temperature of a blackbody with the same radius and luminosity, from $L = 4\pi R^2\sigma T_\text{eff}^4$; the Sun's is 5,772 K.	Radiation
Electromagnetic wave	Self-sustaining oscillation of electric and magnetic fields, perpendicular to each other and to the direction of travel, moving at $c$.	Radiation
Electron capture	Proton plus electron → neutron plus neutrino; neutronizes a collapsing stellar core.	Evolution
Electron degeneracy pressure	Pressure from Pauli exclusion forcing electrons into high-momentum states; supports white dwarfs and brown dwarfs.	Compact objects
Elliptical galaxy	Smooth, featureless galaxy (E0–E7 by flattening) of mostly old stars with little gas, dust or star formation.	Galaxies
Emission line	Bright line at a specific wavelength emitted by hot, low-density gas (Kirchhoff's second law).	Spectra
Emission nebula	Glowing cloud of ionized gas, usually an H II region excited by hot young stars; red from H-alpha.	Formation
Energy flux	Power received per unit area, $F = L/4\pi d^2$ (W/m²); falls as the inverse square of distance.	Radiation
Equation of state	Relation between pressure, density and temperature; the unknown one for ultra-dense matter is why the neutron-star maximum mass is uncertain.	Compact objects
Erg	cgs energy unit, $10^{-7}$ J; 1 W/m² = 1,000 erg s⁻¹ cm⁻².	Radiation
Ergosphere	Region just outside a spinning (Kerr) black hole's horizon where spacetime drags everything around; nothing can stay still there.	Compact objects
Escape velocity	Minimum speed to escape a body's gravity, $v = \sqrt{2GM/r}$; equals $c$ at the Schwarzschild radius.	Compact objects
Event horizon	Boundary around a black hole from inside which nothing can escape; at the Schwarzschild radius for a non-spinning hole.	Compact objects
Extinction	Dimming of starlight by interstellar dust absorption and scattering, in magnitudes ($A_V$); stronger at shorter wavelengths.	Photometry
Faber–Jackson relation	For elliptical galaxies, luminosity grows as roughly the fourth power of stellar velocity dispersion ($L \propto \sigma^4$); a distance indicator.	Distances
Fermi Gamma-ray Space Telescope	NASA gamma-ray observatory (2008); its GBM detected GRB 170817A about 1.7 s after the GW170817 merger signal.	Instruments
Final parsec problem	Theoretical stall of a supermassive black-hole binary near ~1 pc separation, where star scattering runs out before gravitational waves take over.	Galaxies
Flare star	Red dwarf (UV Ceti type) that brightens suddenly by up to several magnitudes for minutes from magnetic flares.	Variables
Forbidden line	Emission line from a metastable level, seen only in very low-density gas, written in brackets: [O III] 500.7 nm, [N II] 658.4 nm.	Spectra
Fraunhofer lines	Dark absorption lines in the solar spectrum, e.g. sodium D (589.0/589.6 nm) and Ca II H and K (396.8/393.4 nm).	Spectra
Free-fall time	Time for a pressureless cloud to collapse, $t_\text{ff} = \sqrt{3\pi/32G\rho}$; independent of size, shorter for denser clouds.	Formation
FU Orionis object	Young star whose disk accretion surges, brightening ~5–6 mag in months and staying bright for decades; spectral type looks later in the IR.	Formation
Galactic halo	Roughly spherical outer component of a galaxy holding old Population II stars, globular clusters and the dark matter.	Galaxies
Galactic superwind	Outflow of hot, metal-rich gas driven by many supernovae and stellar winds in a starburst, seen along the minor axis (M82 is the prototype).	Galaxies
Galaxy cluster	Gravitationally bound group of hundreds to thousands of galaxies in hot, X-ray-emitting gas and dark matter.	Galaxies
Gamma-ray burst	Brief, intense gamma-ray flash: long (>2 s) from collapsing massive stars, short (<2 s) from neutron-star mergers.	Compact objects
Gamow peak	Narrow energy range where fusion actually happens: the falling Maxwell–Boltzmann tail times the rising tunneling probability.	Stars
General relativity	Einstein's 1915 theory of gravity as spacetime curvature; predicts black holes, gravitational lensing, redshift and gravitational waves.	Gravitational waves
Giant molecular cloud	Cold (~10–20 K) cloud of H₂ and dust, ~10⁴–10⁶ M☉ and tens of parsecs across; the main birthplace of stars ("stellar nursery").	Formation
Globular cluster	Dense, spherical cluster of ~10⁵–10⁶ old (~10–13 Gyr), metal-poor stars in a galaxy's halo or bulge; the Milky Way has ~150–160.	Galaxies
Grand-design spiral	Spiral galaxy with two prominent, well-defined arms (e.g., M51), as opposed to a patchy flocculent spiral.	Galaxies
Gravitational binding energy	Energy needed to disperse a body; $3GM^2/5R$ for a uniform sphere.	Stars
Gravitational lensing	Bending of light by mass, producing deflection, magnification, multiple images, arcs or Einstein rings, and time delays between images.	Galaxies
Gravitational redshift	Lengthening of light's wavelength as it climbs out of a gravitational well; extreme near neutron stars and black holes.	Compact objects
Gravitational wave	Ripple in spacetime curvature traveling at $c$, made by accelerating masses; transverse, with two polarizations (plus and cross).	Gravitational waves
Gravitational-wave interference	Waves from different sources superpose linearly, adding in phase or canceling out of phase, like other waves.	Gravitational waves
Graviton	Hypothetical massless quantum (force carrier) of gravity, analogous to the photon; never detected.	Gravitational waves
GW150914	First direct gravitational-wave detection (LIGO, 14 Sept 2015): two black holes of ~36 and ~29 M☉ merging ~410 Mpc away, radiating ~3 M☉c².	Gravitational waves
GW170817	Binary neutron-star merger (17 Aug 2017) in NGC 4993 ~40 Mpc away; GWs plus a short GRB 1.7 s later and a kilonova.	Gravitational waves
H I region	Cloud of cold neutral atomic hydrogen, mapped with the 21-cm line; surrounds the ionization front of H II regions.	Formation
H II region	Cloud of hydrogen ionized by UV from hot O and B stars; glows red in H-alpha (e.g., Orion Nebula); marks recent star formation.	Formation
H-alpha	Hydrogen's red Balmer line at 656.3 nm ($n=3 \leftrightarrow 2$); tracer of ionized gas and star formation.	Spectra
Hawking radiation	Predicted quantum thermal emission from black holes; negligibly weak for stellar-mass and larger holes.	Compact objects
Hayashi track	Nearly vertical pre-main-sequence path of a fully convective contracting star: luminosity falls at almost constant cool surface temperature.	Formation
Helium flash	Runaway ignition of helium in the degenerate core of a ~0.5–2 M☉ star at the red-giant-branch tip (~10⁸ K); a brief runaway (peak far shorter than a year), absorbed by the core and invisible outside.	Evolution
Henyey track	Nearly horizontal leftward pre-main-sequence path at roughly constant luminosity, once a radiative core forms (stars above ~0.5 M☉).	Formation
Herbig Ae/Be star	Pre-main-sequence star of ~2–8 M☉ with A or B spectral type, emission lines and infrared excess from a disk.	Formation
Herbig–Haro object	Small bright nebula where a protostellar jet shocks surrounding gas; glows in H-alpha and [S II], moves at hundreds of km/s.	Formation
Hertzsprung gap	Sparsely populated H-R diagram region between the main sequence and red giants, crossed quickly by intermediate and massive stars.	Evolution
Hertzsprung–Russell diagram	Plot of luminosity (or absolute magnitude) against temperature (or spectral type, color), hot on the left; shows main sequence, giants, white dwarfs.	Stars
High-mass X-ray binary	X-ray binary with an O or B donor (above ~10 M☉) feeding a neutron star or black hole, mostly by its wind; young, in the disk.	Binaries
Horizontal branch	Core-helium-burning stage of metal-poor low-mass stars, ~50–100 L☉; RR Lyrae stars lie where it crosses the instability strip.	Evolution
Hubble constant	Present expansion rate $H_0$, about 67–73 km/s/Mpc (CMB vs Cepheid–supernova values: the "Hubble tension"); often taken as 70.	Cosmology
Hubble distance	$c/H_0$, the distance where Hubble's law gives recession speed $c$: ≈ 4,300 Mpc ≈ $1.3\times10^{23}$ km for $H_0 = 70$.	Cosmology
Hubble flow	General recession of galaxies caused by cosmic expansion, apart from their own peculiar velocities.	Cosmology
Hubble Space Telescope	2.4 m NASA/ESA orbiting telescope launched 1990, observing in UV, visible and near-IR.	Instruments
Hubble time	$1/H_0$, about 14 Gyr for $H_0 = 70$; a rough expansion age, not exactly the age of the universe.	Cosmology
Hubble tuning fork	Hubble's galaxy scheme: ellipticals E0–E7, lenticulars S0 at the junction, then normal (Sa–Sc) and barred (SBa–SBc) spirals.	Galaxies
Hubble's law	Recession velocity is proportional to distance, $v = H_0 d$ (Hubble–Lemaître law); used to get distances to distant galaxies and quasars.	Cosmology
Hydrostatic equilibrium	Balance between inward gravity and outward pressure gradient, $dP/dr = -GM(r)\rho/r^2$, that keeps a star stable.	Stars
Hypergiant	Most luminous stars (class 0 or Ia⁺, up to ~10⁶ L☉) near the Eddington limit; unstable, heavy mass loss, P Cygni profiles.	Stars
Hypernova	Unusually energetic core-collapse supernova (broad-lined Type Ic) from a collapsar, linked to long gamma-ray bursts.	Evolution
Inclination	Tilt of an orbit's plane relative to the sky plane; 90° is edge-on (eclipses possible); spectroscopy alone gives binary masses only as $m\sin^3 i$ ($m\sin i$ for a planet).	Binaries
Infrared	Radiation from ~700 nm to ~1 mm; discovered by William Herschel in 1800; room-temperature objects peak near 10 µm.	Radiation
Infrared excess	More infrared light than a star's photosphere should emit, revealing warm dust in a disk or shell (young stars, AGB stars).	Formation
Initial mass function	Distribution of stellar masses at birth; Salpeter slope $dN/dM \propto M^{-2.35}$ above ~1 M☉; appears largely universal across environments.	Formation
Instability strip	Narrow, nearly vertical H-R diagram band where stars pulsate via the kappa mechanism: Cepheids, RR Lyrae, Delta Scuti, ZZ Ceti.	Variables
Interacting galaxies	Galaxies distorting each other gravitationally, producing tidal tails, bridges, rings and starbursts.	Galaxies
Interferometry	Combining signals from separated telescopes to reach the resolution of one as large as their baseline.	Instruments
Intermediate polar	Magnetic cataclysmic variable whose moderate field truncates the inner accretion disk; the white dwarf spins faster than the orbit.	Binaries
Intermediate-mass black hole	Black hole of ~10²–10⁵ M☉; candidates in dense clusters and some ULXs (e.g., M82 X-1).	Compact objects
Intermediate-mass X-ray binary	X-ray binary whose donor is of intermediate mass, roughly 1–10 M☉ (often quoted ~1.5–8), between LMXB and HMXB donors.	Binaries
Interstellar medium	Gas (~99% by mass) and dust (~1%) between stars, in phases from cold molecular clouds to million-kelvin gas.	Formation
Interstellar reddening	Stars look redder than their spectral type because dust scatters and absorbs blue light more than red.	Photometry
Inverse-square law	Flux from a point source falls as $1/d^2$: double the distance, one-quarter the brightness.	Radiation
Ionization	Removal of electrons from atoms; Roman numerals mark the state (H I neutral, H II ionized hydrogen; He II singly ionized helium).	Spectra
Iron core	End product of silicon burning; iron-group nuclei have nearly the highest binding energy per nucleon, so fusing them yields no energy.	Evolution
Irradiance	Power received per unit area (W/m²); falls as $1/d^2$ from a point source.	Radiation
Irregular galaxy	Galaxy with no regular shape (Irr), usually gas-rich and actively forming stars, e.g. the Magellanic Clouds.	Galaxies
James Webb Space Telescope	6.5 m infrared telescope (0.6–28 µm) launched December 2021, at Sun–Earth L2.	Instruments
Jeans mass	Minimum mass a cloud needs for gravity to beat thermal pressure and collapse; grows as $T^{3/2}\rho^{-1/2}$.	Formation
Jet	Narrow, collimated outflow along a rotation axis, from protostars, X-ray binaries or AGN; AGN jets are relativistic plasma.	AGN
Kappa mechanism	Pulsation driver: a partially ionized layer (He II in Cepheids, iron-group in Beta Cephei stars) becomes more opaque when compressed, trapping heat that pushes it outward, then cycles.	Variables
Kelvin–Helmholtz timescale	Time a star could shine on gravitational contraction alone, $GM^2/RL$; ~30 million years for the Sun.	Stars
Kepler's third law	$P^2 = a^3/(M_1+M_2)$ with $P$ in years, $a$ in AU, masses in M☉; gives binary and galaxy masses.	Binaries
Kerr black hole	Black hole solution with spin and no charge; Kerr–Newman adds charge, Reissner–Nordström is charged but non-spinning.	Compact objects
Kilonova	Optical/IR glow from radioactive decay of r-process elements ejected in a neutron-star merger; ~1,000 times a nova (AT 2017gfo).	Gravitational waves
Kirchhoff's laws	Hot dense body → continuous spectrum; hot thin gas → emission lines; cool thin gas before a hot source → absorption lines.	Spectra
L dwarf	Spectral class below M (~1,300–2,400 K): TiO and VO fade into dust clouds; metal hydrides and Na, K lines strong.	Stars
Leavitt law	Cepheid period–luminosity relation, found by Henrietta Leavitt (1912) from Cepheids in the Small Magellanic Cloud.	Distances
Lenticular galaxy	Disk galaxy with a bulge but no spiral arms and little gas (S0); between ellipticals and spirals on the tuning fork.	Galaxies
Light curve	Graph of brightness (magnitude) versus time for a variable star, binary or supernova.	Variables
Light echo	Light from an outburst scattered off dust and arriving later; the delay and geometry give the dust's distance (e.g., V838 Mon).	Distances
Light-travel-time argument	A source varying in time Δt can be no larger than ~$c\Delta t$; sets sizes of pulsars and quasars.	AGN
Light-year	Distance light travels in one year, ≈ $9.46\times10^{12}$ km ≈ 0.307 pc.	Distances
LIGO	Laser Interferometer Gravitational-Wave Observatory: two 4 km L-shaped detectors (Hanford, WA; Livingston, LA) sensing strain ~10⁻²¹.	Gravitational waves
Limb darkening	A star's disk looks darker toward its edge because there we see cooler, higher layers.	Stars
Line blanketing	Many metal absorption lines removing blue and UV flux, making metal-rich stars redder than metal-poor ones of equal temperature.	Photometry
LINER	Low-ionization nuclear emission-line region: a galaxy center with weak, low-ionization lines, from low-power AGN or shocks.	AGN
LISA	Planned ESA space gravitational-wave detector (launch ~2035) with ~2.5 million km arms, sensitive to millihertz waves.	Gravitational waves
Lithium test	Lithium (670.8 nm) in a cool object means it is young or substellar; stars and brown dwarfs above ~65 Jupiter masses destroy it.	Stars
Local Group	Gravitationally bound group of ~80+ galaxies (Milky Way, Andromeda, M33 and dwarfs) spanning about 3 Mpc.	Galaxies
Long-period variable	Cool red giant or AGB star varying over ~100–1,000 days; Miras and semiregulars.	Variables
Lookback time	How long ago light left an object; equals its distance in light-years only for nearby objects.	Cosmology
Low-mass X-ray binary	X-ray binary with a donor of about 1 M☉ or less overflowing its Roche lobe onto a neutron star or black hole; old.	Binaries
Luminosity	Total power an object emits, in watts; $L = 4\pi R^2\sigma T^4$; the Sun's is $3.828\times10^{26}$ W.	Stars
Luminosity class	MK Roman numeral for size: 0/Ia⁺ hypergiant, I supergiant, II bright giant, III giant, IV subgiant, V dwarf, VI subdwarf, VII white dwarf.	Spectra
Luminous blue variable	Very massive, unstable star near the Eddington limit (S Doradus variable) with irregular eruptions; e.g., Eta Carinae, P Cygni.	Variables
Lyman series	Hydrogen lines from transitions to or from $n=1$, in the ultraviolet; Lyman-alpha at 121.6 nm.	Spectra
Magellanic Clouds	Two irregular satellite galaxies of the Milky Way (~50 and ~60 kpc); Leavitt's Cepheids and SN 1987A were found there.	Galaxies
Magnetar	Neutron star with a field ~10¹⁴–10¹⁵ G, spin periods ~2–12 s, powered by field decay; soft gamma repeaters, anomalous X-ray pulsars.	Compact objects
Magnitude	Logarithmic brightness scale in which 5 magnitudes is a factor of 100 and smaller numbers are brighter.	Photometry
Main sequence	Diagonal H-R band from hot, luminous upper left to cool, dim lower right where stars fuse hydrogen in their cores; ~90% of stars.	Stars
Main-sequence fitting	Cluster distance by sliding its color–magnitude diagram vertically to match a calibrated main sequence; the cluster form of spectroscopic parallax.	Distances
Main-sequence lifetime	Time spent fusing core hydrogen, roughly $10^{10}\,\text{yr}\,(M/M_\odot)^{-2.5}$; massive stars live only millions of years.	Stars
Maser	Microwave amplification by stimulated emission (e.g., water, OH); bright spots mapping star-forming regions and orbits around galactic nuclei.	Spectra
Mass function	For a single-lined binary, $PK^3/2\pi G = M_2^3\sin^3 i/(M_1+M_2)^2$; a minimum mass for an unseen companion.	Binaries
Mass loss	Shedding of a star's outer layers in winds or eruptions; the Sun loses ~10⁻¹⁴ M☉/yr, O and Wolf–Rayet stars 10⁻⁶–10⁻⁵.	Evolution
Mass transfer	Flow of gas from one binary star to the other, mainly by Roche-lobe overflow through the inner Lagrange point or by winds.	Binaries
Mass–luminosity relation	For main-sequence stars $L \propto M^{a}$ with $a$ ≈ 3–4 (3.5 typical; some keys use 4).	Stars
Metallicity	Fraction of a star's mass in elements heavier than helium (all called "metals"); often [Fe/H], log ratio to the Sun.	Stars
Microlensing	Brightening of a background star as a foreground compact mass passes in front, without resolved separate images.	Galaxies
Microquasar	X-ray binary with relativistic radio jets, a small-scale analog of a quasar (e.g., SS 433, GRS 1915+105).	Binaries
Millisecond pulsar	Old neutron star spun up to periods of ~1–10 ms by accretion in an LMXB; very stable; common in globular clusters like Terzan 5.	Compact objects
Mira variable	Pulsating AGB star with periods ~100–1,000 days (GCVS: 80–1,000) and visual amplitudes over 2.5 mag; radius and temperature both change; prototype Mira (omicron Ceti, ~332 d).	Variables
MK system	Morgan–Keenan (Yerkes) two-dimensional spectral classification (1943): temperature type plus luminosity class, e.g. G2 V.	Spectra
Molecular cloud	Cold, dense interstellar cloud where hydrogen is mostly H₂, traced by CO emission; where stars form.	Formation
Mount Wilson prefixes	Older luminosity notation placing d (dwarf), sg (subgiant), g (giant) or c (supergiant) before the spectral type.	Spectra
M–sigma relation	Correlation between a galaxy's central black-hole mass and its bulge's stellar velocity dispersion.	AGN
Multi-messenger astronomy	Studying one event through different carriers: light, gravitational waves, neutrinos and cosmic rays (e.g., GW170817, SN 1987A).	Gravitational waves
Narrow-line region	Slower gas clouds farther from an AGN's black hole producing narrower emission lines (hundreds of km/s); seen in both Seyfert types.	AGN
Neutrino	Nearly massless, neutral particle barely interacting with matter; made in fusion and core collapse; ~two dozen detected from SN 1987A.	Radiation
Neutron degeneracy pressure	Pauli-exclusion pressure of neutrons, with nuclear forces, that supports neutron stars.	Compact objects
Neutron star	Collapsed core of ~1.2–2 M☉ in ~10–13 km radius, near nuclear density (~10¹⁷ kg/m³); neutron degeneracy plus nuclear forces support it.	Compact objects
Neutron-star cooling	Young neutron stars cool first by neutrino emission (Urca processes, bremsstrahlung), later by surface photons.	Compact objects
No-hair theorem	An isolated black hole is fully described by only mass, spin and electric charge.	Compact objects
Nova	Thermonuclear runaway in hydrogen accreted onto a white dwarf's surface; brightens ~7–19 mag, ejects the layer, white dwarf survives.	Variables
OB association	Loose, gravitationally unbound group of young O and B stars spread over tens of parsecs, drifting apart within ~10 Myr.	Formation
Opacity	How strongly gas absorbs or scatters radiation; ionized gas is opaque because free electrons scatter (Thomson) and free-free absorb photons.	Stars
Open cluster	Loosely bound group of ~10²–10⁴ young-to-middle-aged Population I stars in a galaxy's disk (e.g., Pleiades).	Galaxies
Optical depth	Number of photon mean free paths through a medium; intensity drops as $e^{-\tau}$; the photosphere is near $\tau \approx 2/3$.	Radiation
Optical double	Two stars that look close on the sky only by chance alignment; they lie at different distances and are not bound.	Binaries
P Cygni profile	Emission line with a blueshifted absorption trough, the signature of an expanding wind or shell.	Spectra
Pair-instability supernova	Explosion of a very massive, low-metallicity star (~140–260 M☉) when pair production softens core pressure; leaves no remnant.	Evolution
Parallax	Apparent shift of a nearby star against background stars as Earth orbits; $d\,(\text{pc}) = 1/p\,(\text{arcsec})$.	Distances
Parsec	Distance at which 1 AU subtends 1 arcsecond: 3.26 ly, 206,265 AU, $3.086\times10^{13}$ km.	Distances
Pauli blocking	In degenerate matter, beta decay of neutrons is blocked because all low-energy electron states are filled, so neutrons stay stable.	Compact objects
Pauli exclusion principle	No two identical fermions (electrons, neutrons) can share a quantum state; source of degeneracy pressure and of Pauli blocking.	Compact objects
Peculiar velocity	A galaxy's motion relative to the Hubble flow, from local gravity; dominates for nearby galaxies (Andromeda approaches).	Cosmology
Peculiarity codes	Suffixes on spectral types: e emission, p peculiar, m metallic, n nebulous (fast rotation), s sharp, sh shell, var variable, : uncertain.	Spectra
Periastron	Point of a binary orbit where the stars are closest and moving fastest; velocity there is perpendicular to the line joining the stars.	Binaries
Period–luminosity relation	For Cepheids and RR Lyrae-like pulsators, pulsation period fixes luminosity, so period plus apparent magnitude gives distance.	Distances
Phillips relation	Brighter Type Ia supernovae fade more slowly; peak $M_B \approx -21.73 + 2.70\,\Delta m_{15}(B)$ standardizes them.	Distances
Photodisintegration	Gamma rays breaking iron nuclei into helium and nucleons in a collapsing core, absorbing energy and speeding collapse.	Evolution
Photometry	Measurement of brightness through standard filters.	Photometry
Photon	Quantum of light with energy $E = hf = hc/\lambda$; $hc \approx 1240$ eV nm.	Radiation
Photosphere	Visible "surface" of a star where light escapes (optical depth ~2/3); no fusion occurs there; Sun 5,772 K.	Stars
Planckian locus	Path a blackbody's color traces with temperature: red → orange → white → blue-white as $T$ rises.	Radiation
Planck's law	Spectrum of blackbody intensity versus wavelength at temperature $T$; integrating over wavelength and angles gives $\sigma T^4$.	Radiation
Planetary nebula	Glowing shell ejected by an AGB star and ionized by its hot exposed core; lasts ~10⁴ years, unrelated to planets.	Evolution
Polar	Magnetic cataclysmic variable (AM Herculis type): a strong white-dwarf field (~10 to ~230 MG) prevents a disk, funnels gas, locks spin to orbit; polarized light.	Binaries
Population I	Young, metal-rich stars in the disk and spiral arms: O and B stars, classical Cepheids, open clusters.	Galaxies
Population II	Old (>10 Gyr), metal-poor halo, bulge and globular-cluster stars; old (though often metal-rich) stars also dominate elliptical galaxies.	Galaxies
Population III	Hypothetical first, metal-free stars, thought very massive (tens to hundreds of M☉), hot, luminous and short-lived; never observed directly.	Galaxies
Pre-main-sequence star	Young star still contracting toward the main sequence, more luminous than a main-sequence star of the same mass.	Formation
Pressure broadening	Line widening from collisions in dense atmospheres; broad lines mean dwarfs, narrow lines mean giants (luminosity class).	Spectra
Prism	Dispersing element that spreads light by refraction because glass bends blue light more than red.	Instruments
Proper motion	A star's angular motion across the sky, in arcseconds per year; tangential speed $v_t = 4.74\,\mu d$ km/s.	Distances
Proton–proton chain	Main hydrogen fusion route in the Sun and lower-mass stars; branches ppI, ppII (lithium-7 destroyed by proton capture) and ppIII.	Stars
Protoplanetary disk	Gas-rich dusty disk around a young star from which planets form; lasts a few million years.	Formation
Protostar	Collapsing core still gaining mass from its envelope, powered by gravitational contraction and seen in the infrared (Class 0/I).	Formation
Pulsar	Rapidly spinning, magnetized neutron star whose beams sweep past Earth; first found 1967 by Jocelyn Bell (CP 1919, now PSR B1919+21).	Compact objects
Pulsar death line	Boundary in the period–spin-down diagram beyond which a slowed pulsar can no longer make pairs and its radio emission stops.	Compact objects
Pulsar timing array	Network of millisecond pulsars whose arrival times reveal nanohertz gravitational waves; evidence for a background reported in 2023.	Gravitational waves
Pulsar wind nebula	Nebula of relativistic particles and magnetic field blown by a young pulsar, glowing by synchrotron (e.g., Crab Nebula).	Compact objects
Quasar	Most luminous AGN, star-like with broad emission lines at large redshift; distances from redshift and Hubble's law (3C 273, $z$ = 0.158).	AGN
R Coronae Borealis star	Hydrogen-poor, carbon-rich supergiant that fades irregularly by 1–9 mag when carbon soot forms.	Variables
Radial velocity	Line-of-sight component of a star's velocity, from Doppler shifts; positive (redshift) when receding.	Spectra
Radiance	Power per area per steradian (W m⁻² sr⁻¹); surface brightness, independent of distance for resolved objects.	Radiation
Radiant exitance	Power emitted per unit surface area (W/m²), also called emittance; $\sigma T^4$ for a blackbody.	Radiation
Radiation pressure	Pressure from photon momentum; supports massive stars, sets the Eddington limit and helps disperse H II region gas.	Radiation
Radiative zone	Stellar layer where energy moves outward by photons slowly diffusing; Sun's inner ~70% of radius.	Stars
Radio galaxy	AGN host with huge radio lobes fed by jets lying near the plane of the sky (e.g., Cygnus A).	AGN
Radio-mode feedback	Low-accretion AGN putting energy into jets that inflate X-ray cavities in cluster gas and stop cooling; contrast with radiative quasar mode.	AGN
Rayleigh–Jeans law	Long-wavelength limit of Planck's law ($hc/\lambda \ll kT$): intensity ∝ $T/\lambda^4$.	Radiation
Recurrent nova	Nova seen to erupt more than once, 10–80 years apart (e.g., T CrB, RS Oph).	Variables
Red clump	Metal-rich core-helium-burning giants forming a compact clump on the H-R diagram; a standard candle.	Evolution
Red dwarf	Main-sequence M star of ~0.08–0.6 M☉; the most common stars (~3/4) and the longest-lived.	Stars
Red giant	Star that has exhausted core hydrogen, burning hydrogen in a shell around a contracting helium core; envelope swells and cools.	Evolution
Red giant branch	H-R path of shell-hydrogen-burning stars rising up and to the right, ending at helium ignition.	Evolution
Red supergiant	Cool (K or M) Ia/Ib supergiant, roughly 10–30 M☉, such as Betelgeuse; typical Type II-P supernova progenitor.	Stars
Redshift	Fractional wavelength increase, $z = \Delta\lambda/\lambda_0$; $v \approx cz$ for $z \ll 1$.	Spectra
Reflection nebula	Dust cloud scattering light from nearby stars, looking blue (e.g., around the Pleiades).	Formation
Relativistic beaming	Light from matter moving near $c$ is concentrated forward, so jets aimed at us look far brighter.	AGN
Resolving power	Spectral resolution $R = \lambda/\Delta\lambda$: ability to separate closely spaced wavelengths.	Instruments
Ring galaxy	Galaxy with a ring of new stars made when a smaller galaxy plunged through its disk (e.g., Cartwheel, Arp 147).	Galaxies
Ringdown	Final gravitational-wave phase as the merged black hole settles to a stable shape, after inspiral and merger.	Gravitational waves
Roche lobe	Teardrop-shaped region around a binary star inside which matter is bound to it; lobes meet at the inner Lagrange point L1.	Binaries
Roche-lobe overflow	Mass transfer when a star expands past its Roche lobe; can strip envelopes, leading to Type Ib/Ic progenitors.	Binaries
Rotation curve	Orbital speed versus radius in a galaxy; flat curves far out reveal dark matter.	Galaxies
r-process	Rapid neutron capture making the heaviest elements (gold, platinum, uranium); observed in a neutron-star merger via GW170817's kilonova (other sites possible).	Evolution
RR Lyrae variable	Old Population II horizontal-branch pulsators, periods ~0.2–1.2 days, $M_V \approx +0.6$; subtypes RRab, RRc, RRd.	Variables
RRab, RRc and RRd	RR Lyrae subtypes: RRab fundamental mode (asymmetric, 0.3–1.2 d), RRc first overtone (sinusoidal, 0.2–0.5 d), RRd both modes.	Variables
RV Tauri variable	Pulsating supergiants (F–G at maximum, K–M at minimum) with alternating deep and shallow minima, formal periods ~30–150 days; post-AGB stars.	Variables
Sagittarius A*	Milky Way's central supermassive black hole, ~4×10⁶ M☉, imaged by the Event Horizon Telescope (2022).	Galaxies
Saha equation	Gives the fraction of atoms in each ionization stage versus temperature and density; explains why Balmer lines peak in A stars.	Spectra
Schwarzschild radius	Event-horizon radius of a non-spinning black hole, $R_s = 2GM/c^2 \approx 2.95$ km per M☉; any mass inside it must collapse.	Compact objects
Seeing	Blurring of star images by atmospheric turbulence, typically ~0.5–2″ at good sites.	Instruments
Semi-latus rectum	Ellipse parameter $p = a(1-e^2)$, the distance from focus to orbit measured perpendicular to the major axis.	Binaries
Semi-major axis	Half the longest diameter of an elliptical orbit; for a binary, the sum $a = a_1 + a_2$ with $m_1a_1 = m_2a_2$.	Binaries
Semiregular variable	Red giant or AGB star (SR) with partly regular periods of ~20–2,000 days and smaller amplitudes than Miras.	Variables
Seyfert galaxy	Spiral with a bright compact AGN; Seyfert 1 shows broad and narrow lines, Seyfert 2 only narrow (torus hides the broad-line region).	AGN
Shapley–Sawyer class	Globular-cluster concentration scale from I (most centrally concentrated) to XII (loosest).	Galaxies
Shell burning	Fusion in a thin shell around an inert core, as in red giants and AGB stars; fusion never happens at the photosphere.	Evolution
Singularity	Point (or ring, if spinning) of predicted infinite density at a black hole's center, where general relativity breaks down.	Compact objects
Soft X-ray transient	Low-mass X-ray binary, often hosting a black hole, that is usually quiet but erupts in X-rays for weeks to months, years or decades apart.	Binaries
Solar luminosity	L☉ = $3.828\times10^{26}$ W (IAU nominal).	Stars
Solar mass	M☉ = $1.989\times10^{30}$ kg; standard unit for stellar and galaxy masses.	Stars
Spectral class	Temperature sequence O, B, A, F, G, K, M (hot to cool), each split 0–9, plus L, T, Y brown dwarfs.	Spectra
Spectrograph	Instrument that disperses light with a prism or grating and records the spectrum on a detector.	Instruments
Spectroscopic binary	Binary detected by periodic Doppler shifts of spectral lines, even when unresolved.	Binaries
Spectroscopic parallax	Distance from spectral type and luminosity class (giving $M$) compared with $m$; involves no parallax.	Distances
Spiral arms	Bright, star-forming lanes in a disk, lit by young O and B stars and H II regions.	Galaxies
Spiral galaxy	Disk galaxy with a bulge and spiral arms (Sa–Sc, tighter arms and larger bulge for Sa).	Galaxies
Spitzer Space Telescope	NASA infrared telescope (2003–2020); after its cryogen ran out in 2009 its warm mission kept IRAC's 3.6 and 4.5 µm channels.	Instruments
s-process	Slow neutron capture in AGB stars making elements such as Sr, Ba and technetium, which marks S stars as active.	Evolution
Sérsic profile	Galaxy surface-brightness law $\log I \propto -r^{1/n}$; $n = 4$ for ellipticals (de Vaucouleurs), $n = 1$ exponential disks.	Galaxies
Standard candle	Object of known luminosity (Cepheids, RR Lyrae, Type Ia supernovae) whose apparent brightness gives distance.	Distances
Standard siren	Compact-binary merger whose gravitational waveform gives its distance directly; with a host redshift it measures $H_0$.	Gravitational waves
Star formation rate	Mass of new stars formed per year in a galaxy (M☉/yr), estimated from H-alpha, UV or far-infrared light.	Galaxies
Starburst galaxy	Galaxy forming stars far faster than it can sustain, often tens to hundreds of M☉/yr versus the Milky Way's ~1–2; gas lasts only ~10⁷–10⁸ years.	Galaxies
Starspot	Cool, dark, magnetically active region on a star's surface; rotating spots make periodic variability, as in T Tauri stars.	Stars
Stefan–Boltzmann law	Blackbody flux $F = \sigma T^4$, so $L = 4\pi R^2\sigma T^4$; $\sigma = 5.67\times10^{-8}$ W m⁻² K⁻⁴.	Radiation
Stellar nursery	Informal name for a star-forming molecular cloud or region.	Formation
Stellar wind	Outflow from a star's surface: Sun ~10⁻¹⁴ M☉/yr; O stars ~10⁻⁶ M☉/yr at ~2,000 km/s; cool giants slow (10–30 km/s) but dense.	Stars
Steradian	SI unit of solid angle; a full sphere is $4\pi$ sr.	Radiation
Strain	Fractional change of length $\Delta L/L$ caused by a gravitational wave; ~10⁻²¹ for detected events.	Gravitational waves
Subdwarf	Luminosity class VI: metal-poor stars lying slightly below the main sequence.	Stars
Subgiant	Luminosity class IV star leaving the main sequence after core-hydrogen exhaustion.	Evolution
Super star cluster	Very massive young cluster (up to ~10⁶ M☉) formed in starbursts; possible young globular clusters.	Galaxies
Supergiant	Luminosity class I (Ia, Iab, Ib), ~10⁴–10⁵ L☉ or more; evolved massive stars.	Stars
Supergiant fast X-ray transient	HMXB with an OB supergiant donor showing hours-long X-ray flares roughly 10²–10⁵ times its quiescent level.	Binaries
Superluminal motion	Apparent faster-than-light motion of jet blobs moving near $c$ almost toward us; an illusion of light-travel time.	AGN
Supermassive black hole	Black hole of ~10⁶–10¹⁰ M☉ at a galaxy's center; powers AGN when accreting.	AGN
Supernova remnant	Expanding shell of ejecta (≈1.4 M☉ for Ia, up to ~10 M☉ for core collapse) and swept-up gas; radio synchrotron and X-rays for ~10⁴–10⁵ yr.	Evolution
Supersoft X-ray source	White dwarf steadily burning accreted hydrogen on its surface, emitting very soft X-rays (photon energies below ~0.5 keV).	Binaries
Symbiotic star	Binary of a red giant and a hot white dwarf in a shared nebula (Z Andromedae type), showing combined cool and hot spectra.	Variables
Synchrotron radiation	Nonthermal, polarized radiation from relativistic electrons spiralling in magnetic fields; in pulsar nebulae, supernova remnants and AGN jets.	Radiation
T dwarf	Brown-dwarf class (~500–1,300 K) defined by methane absorption in the near-infrared, plus strong water bands.	Stars
T Tauri star	Pre-main-sequence star below ~2 M☉: irregular variability (accretion, spots, flares), emission lines, lithium, IR excess, strong magnetic fields, outflows ~10⁻⁸–10⁻⁷ M☉/yr.	Formation
Thermal pulse	Periodic runaway ignition of the helium shell in an AGB star; drives dredge-up and mass loss.	Evolution
Thomson scattering	Wavelength-independent scattering of photons off free electrons, cross section $6.65\times10^{-29}$ m²; sets the Eddington limit.	Radiation
Tidal acceleration	Difference in gravity across a body of size $L$ at distance $r$, ≈ $2GML/r^3$; grows sharply as $r$ shrinks.	Galaxies
Tidal disruption event	Flare when a star passing too close to a supermassive black hole is torn apart and partly accreted.	AGN
Tidal tails	Long streams of stars and gas pulled out of interacting galaxies by tides (e.g., the Antennae).	Galaxies
TOV limit	Tolman–Oppenheimer–Volkoff maximum neutron-star mass, roughly 2–3 M☉; heaviest measured pulsars are ~2 M☉.	Compact objects
Triple-alpha process	Fusion of three helium-4 nuclei into carbon-12 via unstable beryllium-8, at ~10⁸ K.	Evolution
Tully–Fisher relation	Spiral galaxies' luminosity scales with rotation speed (~$v^4$), measured from 21-cm line width; gives distances to ~100+ Mpc.	Distances
Turnoff point	Point where a cluster's main sequence bends toward the giants; its stars' lifetime equals the cluster's age.	Evolution
Type I X-ray burst	Thermonuclear flash of accreted helium/hydrogen on a neutron-star surface lasting seconds to minutes; proves a surface, ruling out a black hole.	Compact objects
Type Ia supernova	Thermonuclear explosion of a white dwarf near 1.4 M☉; no hydrogen, strong Si II; peak $M_B \approx -19.3$; occurs in all galaxy types.	Evolution
Type Ib supernova	Core collapse of a star stripped of hydrogen (not helium); helium lines, no hydrogen; Wolf–Rayet or binary-stripped progenitor.	Evolution
Type Ic supernova	Core collapse of a star stripped of both hydrogen and helium; neither line in its spectrum.	Evolution
Type II Cepheid	Old, low-mass Population II pulsators (W Virginis and BL Herculis variables), ~1–35 days; fainter than classical Cepheids of equal period by ~0.7–2 mag.	Variables
Type II supernova	Core collapse of a massive star that kept its hydrogen; hydrogen lines; subtypes II-P (plateau), II-L, IIn, IIb.	Evolution
UBVRI system	Johnson–Cousins filters: U ~365 nm, B ~440 nm, V (visual) ~550 nm, R ~650 nm, I (near-IR) ~800–900 nm.	Photometry
Ultraluminous X-ray source	Off-nuclear X-ray source above ~10³⁹ erg/s, beyond a stellar black hole's Eddington limit; some are neutron stars (M82 X-2).	Compact objects
Unified model	Idea that AGN types are the same engine (disk, broad and narrow-line regions, torus, jets) seen at different angles and powers.	AGN
Urca process	Neutrino-emitting cycle of beta decay and electron capture that rapidly cools young neutron stars.	Compact objects
Very Large Array	27 radio dishes (25 m) on a Y in New Mexico; largest configuration has a ~36 km maximum baseline.	Instruments
Virial theorem	For a bound, steady system, $2K + U = 0$: half of released gravitational energy heats it, half is radiated.	Stars
Visual binary	Binary whose two stars are resolved in a telescope, with orbital motion seen over time.	Binaries
White dwarf	Earth-sized remnant (~0.6 M☉ typical) of a low-mass star, held up by electron degeneracy; radius shrinks with mass ($R \propto M^{-1/3}$).	Compact objects
Wien approximation	Short-wavelength limit of Planck's law ($hc/\lambda \gg kT$), where intensity falls exponentially.	Radiation
Wien's law	Peak wavelength of a blackbody, $\lambda_\text{max} = 2.898\times10^{-3}\,\text{m K}/T$; hotter means bluer peak.	Radiation
WN and WC stars	Wolf–Rayet subtypes: WN show nitrogen (CNO-processed) layers; WC, later, expose carbon and oxygen from helium burning.	Stars
Wolf–Rayet star	Hot, stripped massive star with broad He, N or C emission lines; ~10⁵–10⁶ L☉, winds ~10⁻⁵ M☉/yr at 1,000–3,000 km/s.	Stars
X-ray binary	Binary in which a neutron star or black hole accretes from a companion, emitting X-rays; concentrated toward the galactic plane.	Binaries
Y dwarf	Coolest brown-dwarf class, below ~500 K, with ammonia, methane and water bands; found mainly by infrared surveys (WISE, JWST).	Stars
Zeeman effect	Splitting of spectral lines by a magnetic field; measures stellar and starspot field strengths.	Spectra
Zero-age main sequence	Position on the H-R diagram where a newly formed star begins steady core hydrogen fusion.	Formation
ZZ Ceti variable	Pulsating hydrogen-atmosphere (DA) white dwarf near ~11,000–12,500 K with periods ~30 s to 25 min.	Variables

Variable stars and special stellar classes

ReferenceVariable-star and special stellar-class catalog· 68 rows

Ranges follow the General Catalogue of Variable Stars (GCVS) definitions where it gives them; "typical" values are rounded; amplitudes are in V unless stated.

68 rows

Class	Prototype	Type (pulsating / eruptive / cataclysmic / eclipsing / rotating / spectral)	Period or timescale	Amplitude	Physical cause and where on the H-R diagram
Classical (Type I) Cepheid	δ Cephei (5.37 d)	Pulsating (radial)	About 1–100 d (GCVS allows up to 135 d)	0.1–2 mag (Polaris only a few hundredths); fast rise, slow decline	κ mechanism in the He II ionization zone; young Population I F–K supergiants (about 4–20 $M_\odot$) crossing the instability strip on blue loops; longer period = brighter (Leavitt law)
Type II Cepheid, W Vir subclass	W Virginis	Pulsating (radial)	GCVS: above 8 d (all Type II: 0.8–35 d); modern split about 4–20 d	0.3–1.2 mag; often a hump on the decline	Old, low-mass (about 0.5–0.6 $M_\odot$) Population II stars after the horizontal branch; fainter than classical Cepheids of the same period; globular clusters and halo
BL Herculis star	BL Herculis	Pulsating (radial)	1–4 d (GCVS: shorter than 8 d)	0.3–1.2 mag	Shortest-period Type II Cepheids: low-mass stars leaving the blue horizontal branch toward the AGB, crossing the strip above the RR Lyrae stars
RV Tauri star	RV Tauri (RVb); AC Her (RVa)	Pulsating (radial)	Formal period (deep minimum to deep minimum) 30–150 d, so about 15–75 d between successive minima; RVb also varies in mean light over 600–1,500 d	Up to 3–4 mag; alternating deep and shallow minima	Post-AGB yellow supergiants (F–G at maximum, K–M at minimum), the longest-period Type II Cepheids, crossing the strip at high luminosity on the way to becoming white dwarfs
RR Lyrae RRab	RR Lyrae (0.567 d)	Pulsating (radial, fundamental mode)	0.3–1.2 d (typically 0.4–1 d)	0.5–2 mag; sawtooth curve with steep rise	Old Population II horizontal-branch A–F giants inside the instability strip; $M_V \approx +0.6$, about 50 $L_\odot$; globular clusters and halo
RR Lyrae RRc	SX UMa	Pulsating (radial, first overtone)	0.2–0.5 d (typically 0.2–0.4 d)	At most 0.8 mag; nearly sinusoidal	Same stars as RRab, on the hotter (bluer) side of the horizontal-branch part of the strip
RR Lyrae RRd (double-mode)	AQ Leonis	Pulsating (fundamental + first overtone at once)	$P_1/P_0 \approx 0.745$	Smaller than RRab; beating light curve	Horizontal-branch stars in the zone where both modes are unstable; the period ratio constrains mass and metallicity
Delta Scuti star	δ Scuti	Pulsating (radial and non-radial p modes)	About 0.01–0.3 d (GCVS 0.01–0.2 d), i.e. under 1 h to several h	0.003–0.9 mag, usually a few hundredths; high-amplitude subgroup (HADS) above 0.3 mag	κ mechanism (He II zone) in A0–F5 stars on or just above the main sequence where the strip crosses it; Population I; asteroseismology targets
SX Phoenicis star	SX Phoenicis	Pulsating	0.04–0.08 d	Up to 0.7 mag	Population II analog of delta Scuti stars: metal-poor A2–F5 stars, mostly blue stragglers in globular clusters; obey a period–luminosity relation
Gamma Doradus star	γ Doradus	Pulsating (non-radial g modes)	About 0.3–3 d (GCVS: few tenths of a day to just over 1 d)	Usually under 0.1 mag	F-type (about A7–F5) main-sequence stars at the cool edge of the strip; driven by convective blocking at the base of the outer convection zone
Beta Cephei star	β Cephei (also called β CMa stars)	Pulsating (mostly p modes, some radial)	0.1–0.6 d	0.01–0.3 mag; much larger in UV	κ mechanism on the iron-group opacity bump (≈ 200,000 K layer); early B (GCVS O8–B6) stars of 8–20 $M_\odot$ near the upper main sequence; brightest at minimum radius
Slowly pulsating B (SPB) star	53 Persei	Pulsating (non-radial g modes)	About 0.5–5 d, multiperiodic	Usually under 0.1 mag	Same iron-bump κ mechanism in mid-to-late B (about B3–B9 V, 3–8 $M_\odot$) main-sequence stars, below the β Cephei region
Mira (long-period variable)	Mira = ο Ceti (about 332 d)	Pulsating (radial)	About 100–1,000 d (GCVS 80–1,000 d)	Above 2.5 mag (up to 11) in V; under 1 mag in K band	Large-amplitude pulsation of cool AGB giants (Me, Ce, Se emission spectra); visual swing amplified by TiO forming at cool phases; upper right of the H-R diagram; heavy dusty mass loss; infrared period–luminosity law
Semiregular SRa	Z Aquarii	Pulsating	35–1,200 d, persistent periodicity	Usually under 2.5 mag; shape varies	M, C or S giants that differ from Miras mainly by smaller amplitude; upper red giant and AGB region
Semiregular SRb	AF Cygni; RR CrB	Pulsating	Mean cycles 20–2,300 d, poorly defined; periodic spells alternate with irregular or constant spells	Usually 1–2 mag	M, C or S giants on the red giant branch and AGB, often with two or more periods at once
Semiregular SRc and SRd	μ Cephei (SRc); SX Her, SV UMa (SRd)	Pulsating	SRc 30 d to several thousand d; SRd 30–1,100 d	SRc about 1 mag; SRd 0.1–4 mag	SRc: late-type red supergiants (Betelgeuse is usually listed here); SRd: F, G, K giants and supergiants, sometimes with emission lines
Slow irregular (L, LB, LC)	CO Cygni (LB); TZ Cassiopeiae (LC)	Pulsating (poorly periodic)	No clear period; changes over weeks to years	Up to about 1 mag (LC); often small	LB: late-type (K, M, C, S) giants; LC: late-type supergiants; many turn out to be poorly studied semiregulars
ZZ Ceti (DAV)	ZZ Ceti (= R548)	Pulsating (non-radial g modes)	30 s to 25 min (typically 100–1,200 s)	0.001–0.2 mag	Hydrogen-atmosphere (DA) white dwarfs at about 11,000–12,500 K, driven where hydrogen is partly ionized; the white-dwarf cooling track crossing the instability strip, bottom left
DBV (V777 Her star)	V777 Herculis (= GD 358)	Pulsating (non-radial g modes)	Several minutes (about 100–1,000 s)	Up to about 0.1–0.2 mag	Helium-atmosphere (DB) white dwarfs at roughly 22,000–30,000 K, driven by partial helium ionization; hotter part of the white-dwarf track
GW Virginis (DOV / PG 1159 star)	GW Virginis (= PG 1159−035)	Pulsating (non-radial g modes)	About 5–80 min	Hundredths of a magnitude	Very hot (about 80,000–180,000 K) hydrogen-deficient pre-white dwarfs rich in He, C, O; driven by partial ionization of carbon and oxygen; at the "knee" where post-AGB stars join the white-dwarf track; some are planetary-nebula nuclei
Rapidly oscillating Ap (roAp)	DO Eridani (= HR 1217); first found in HD 101065	Pulsating (high-overtone p modes) on top of rotational variation	About 5–25 min	About 0.01 mag or less	Cool, strongly magnetic Ap stars on the main sequence; pulsation axis aligned with the magnetic axis, so amplitude varies with rotation (oblique pulsator model)
T Tauri star: classical (CTTS) and weak-line (WTTS)	T Tauri	Eruptive (Orion variables; irregular plus spot-modulated)	Hours to years; spot periods of a few days	Up to several magnitudes (CTTS); WTTS mostly a few tenths from spots	Pre-main-sequence stars below about 2 $M_\odot$ (F–M) on Hayashi tracks, above the main sequence; CTTS are accreting from a disk (H-alpha equivalent width above about 10 Å, UV and IR excess); WTTS have weak H-alpha and little inner disk; both show lithium 670.8 nm and X-ray flares
FU Orionis star (FUor)	FU Orionis (1937 outburst)	Eruptive	Rise over months to a year; stays bright for decades	About 5–6 mag	Disk accretion rate jumps about a thousandfold onto a young low-mass star; the hot inner disk outshines the star (F–G supergiant-like optical spectrum, cooler in the IR); associated with reflection nebulae
EX Lupi star (EXor)	EX Lupi	Eruptive	Outbursts lasting weeks to months, recurring every few years	About 1–5 mag	Smaller, shorter accretion bursts on T Tauri stars; spectrum keeps T Tauri emission lines (unlike FUors)
Herbig Ae/Be star	AB Aurigae (example); UX Orionis for the deep-fading subgroup	Eruptive (Orion type, INA)	Irregular; days to years	Up to about 2–3 mag in UX Ori-type dust dimmings	Pre-main-sequence A–B stars of about 2–8 $M_\odot$ with emission lines and IR excess from disks; on Henyey tracks above the upper main sequence
UV Ceti flare star	UV Ceti (Proxima Cen is one)	Eruptive (flares)	Rise in seconds to tens of seconds; decay in minutes to tens of minutes	Several tenths up to 6 mag in V; larger in UV	Magnetic reconnection in the coronae of K Ve–M Ve dwarfs with deep convection zones; lower right of the main sequence; often also BY Dra spotted stars
BY Draconis star	BY Draconis	Rotating (starspots)	Fraction of a day to 120 d (the rotation period); quasi-periodic	Several hundredths to 0.5 mag	Large cool starspots and chromospheric activity on rapidly rotating dKe–dMe dwarfs; lower main sequence
RS Canum Venaticorum star	RS Canum Venaticorum	Eruptive in GCVS; really rotating (spots) in close binaries	Close to the orbital period (days to weeks); spot "distortion wave" migrates slowly	Up to 0.2 mag	Tidally locked, fast-rotating G–K subgiant or giant in a close detached binary, with strong Ca II H and K emission, radio and X-ray emission; just above the main sequence and lower giant branch
R Coronae Borealis star	R Coronae Borealis	Eruptive (plus small pulsations)	Sudden fades lasting a month to several hundred days, at irregular intervals; pulsations 30–100 d	Fades of 1–9 mag; pulsations a few tenths	Carbon (soot) dust condensing in clouds ejected toward us from a hydrogen-poor, carbon- and helium-rich supergiant (spectral types Bpe–R, mostly F–G); possibly a merged double white dwarf; upper H-R diagram
Luminous blue variable (S Doradus variable)	S Doradus (also P Cygni, η Carinae)	Eruptive	S Dor cycles over years to decades; rare giant eruptions (η Car in the 1840s)	1–2 mag at nearly constant bolometric luminosity in S Dor cycles; GCVS full range 1–7 mag	Very massive stars near the Eddington limit at the top left of the H-R diagram (near the Humphreys–Davidson limit); radius and temperature swing so the spectral type changes; heavy mass loss and nebulae
Wolf–Rayet variable	γ² Velorum (brightest; example)	Eruptive (also spectral class W)	Irregular, hours to days	Up to about 0.1 mag	Clumpy, unsteady winds of hot, stripped massive-star cores (WN, WC, WO; broad He, N, C, O emission lines); far upper left of the H-R diagram; progenitors of Type Ib/Ic supernovae
Gamma Cassiopeiae (Be) variable	γ Cassiopeiae	Eruptive	Days to decades, irregular	Up to 1.5 mag	Rapidly rotating B III–Ve stars losing mass into an equatorial decretion disk; disk building and dispersal changes light and emission lines; upper main sequence
Classical nova	GK Persei (fast, 1901); RR Pictoris (slow)	Cataclysmic (explosive)	Rise in days; fades 3 mag within 100 d (fast) or 150+ d (slow), then months to years; orbit typically hours	Typically 8–15 mag (GCVS full range 7–19)	Thermonuclear (CNO) runaway in hydrogen accreted onto a white dwarf from a Roche-lobe-filling companion; ejects about $10^{-5}$–$10^{-4}\ M_\odot$; the white dwarf survives
Recurrent nova	T Coronae Borealis (1866, 1946); RS Oph, U Sco	Cataclysmic (explosive)	Repeat outbursts every 10–80 yr; each fades within weeks	About 6–10 mag (T CrB from about 10 to 2)	Same runaway on a massive white dwarf (near the Chandrasekhar limit) with a high accretion rate; T CrB and RS Oph have red-giant donors (symbiotic recurrent novae)
Dwarf nova, U Gem (SS Cyg) type	U Geminorum; SS Cygni	Cataclysmic (novalike)	Rise in 1–2 d, outburst lasts days; mean cycle 10 d to thousands of days; orbits 0.05–0.5 d	2–6 mag	Thermal–viscous instability in the accretion disk around a white dwarf (no fusion); longer cycles give bigger outbursts
Dwarf nova, Z Cam type	Z Camelopardalis	Cataclysmic (novalike)	Cycles 10–40 d, interrupted by standstills lasting months or longer	2–5 mag; standstills sit between maximum and minimum	Mass-transfer rate near the critical value for disk stability, so the disk sometimes stays in a steady, partly bright state
Dwarf nova, SU UMa type	SU Ursae Majoris (WZ Sge is an extreme subtype)	Cataclysmic (novalike)	Normal outbursts plus rarer superoutbursts about 5× longer (about 2 weeks); orbits under 0.1 d (about 2.4 h)	Superoutbursts brighter than normal ones (usually by about 0.5–1 mag; GCVS says 2 mag); superhumps 0.2–0.3 mag	Short-period systems with low-mass M-dwarf donors; the disk grows to the 3:1 resonance and precesses, giving superhumps a few percent longer than the orbital period
Polar (AM Her star)	AM Herculis	Cataclysmic (magnetic; X-ray)	Orbits about 1–4 h; high and low states over months to years	Total range up to 4–5 mag	White dwarf field about $10^{7}$–$10^{8}$ G prevents a disk; gas flows along field lines onto the poles; the white dwarf spins in step with the orbit; strong circular polarization (cyclotron light), X-rays
Intermediate polar (DQ Her star)	DQ Herculis (Nova Her 1934; spin 71 s)	Cataclysmic (magnetic; X-ray)	White-dwarf spin seconds to about an hour, much shorter than the orbit (hours)	Small pulsations at the spin period; nova or dwarf-nova outbursts possible	Weaker field (roughly $10^{6}$–$10^{7}$ G) truncates the inner disk; accretion curtains onto the poles give X-ray pulses at the spin period
AM CVn star	AM Canum Venaticorum (orbit 17.1 min)	Cataclysmic	Orbits about 5–65 min; some show dwarf-nova outbursts	Outbursts a few magnitudes in longer-period systems	White dwarf accreting helium from a degenerate or semi-degenerate helium donor; no hydrogen lines; ultracompact; gravitational-wave sources for LISA
Symbiotic star	Z Andromedae	Cataclysmic (Z And type)	Orbits hundreds to thousands of days; outbursts last years	Irregular, up to 4 mag	Red giant (often a Mira) losing mass to a hot white dwarf inside a shared ionized nebula; spectrum combines cool TiO absorption with high-ionization emission (He II)
Type Ia supernova	SN 1572 (Tycho) and SN 2014J are well-known examples	Cataclysmic (explosive, thermonuclear)	Rise about 2–3 weeks; fades about 3 mag in blue in the first month, then a radioactive tail (⁵⁶Ni → ⁵⁶Co, half-life 6.1 d → ⁵⁶Fe, 77 d)	Peak $M_B \approx -19.3$; no plateau	Carbon–oxygen white dwarf near the Chandrasekhar limit explodes completely (single- or double-degenerate); no H, strong Si II; occurs in all galaxy types; standard candle after Phillips correction
Type II supernova (II-P, II-L, IIn, IIb)	SN 1987A (peculiar II); SN 1999em (II-P example)	Cataclysmic (explosive, core collapse)	II-P: plateau about 100 d then a drop; II-L: steady linear decline; IIn: slow decline	Peaks typically $M \approx -16$ to $-18$ (II-P plateau about −16 to −17)	Iron-core collapse of a star above about 8 $M_\odot$ that kept its hydrogen; hydrogen lines; leaves a neutron star or black hole; only where massive stars formed recently (spirals, starbursts)
Type Ib and Ic supernova	SN 2008D (Ib) and SN 1998bw (broad-lined Ic with GRB 980425)	Cataclysmic (explosive, core collapse)	Rise 2–3 weeks; faster decline than II-P	Peak about −17 to −18	Core collapse of a massive star stripped of hydrogen (Ib, helium lines) or of hydrogen and helium (Ic) by winds (Wolf–Rayet) or a binary companion; broad-lined Ic linked to long gamma-ray bursts
Kilonova	AT 2017gfo (with GW170817)	Explosive transient (compact-object merger)	Blue component peaks within about a day; red/infrared component lasts about a week or more	Peak luminosity of order $10^{41}$–$10^{42}$ erg/s (the name means roughly 1,000× a nova); well below a supernova	Radioactive decay of r-process nuclei in neutron-rich ejecta from a neutron-star merger; lanthanides make the red, long-lived component
Algol-type eclipsing binary (EA)	Algol = β Persei (2.87 d)	Eclipsing	0.2 to over 10,000 d	Anywhere from tiny to several magnitudes (Algol 2.1 → 3.4)	Nearly spherical stars; light nearly constant between eclipses, so eclipse start and end are clear; secondary minimum may be absent; Algol paradox (less massive star is the more evolved) from mass transfer
Beta Lyrae-type eclipsing binary (EB)	β Lyrae (12.94 d)	Eclipsing	Mostly longer than 1 d	Usually under 2 mag; secondary minimum always seen, shallower	Tidally distorted (ellipsoidal) early-type (B–A) stars, often semidetached with mass transfer; light changes continuously, so eclipse edges cannot be timed
W UMa-type eclipsing binary (EW)	W Ursae Majoris (0.33 d)	Eclipsing	Shorter than 1 d (typically 0.2–0.8 d)	Usually under 0.8 mag; nearly equal minima	Contact binary: two F–K main-sequence stars sharing a common envelope, so both have about the same temperature
Ellipsoidal variable (ELL)	b Persei; Spica (α Virginis)	Rotating (non-eclipsing binary)	Two equal-ish dips per orbit (light period = orbital period with a double wave)	Under 0.1 mag	Tidally stretched star in a close binary shows changing projected area as it orbits; no eclipses
Pulsar	CP 1919 (PSR B1919+21, 1.337 s); Crab pulsar (33 ms)	Rotating (GCVS PSR)	About 1.4 ms to tens of seconds; very steady, slowly lengthening	Pulsed; optical pulses up to 0.8 mag for the few seen optically	Rotating, magnetized ($\sim10^{12}$ G; millisecond pulsars $10^{8}$–$10^{9}$ G) neutron star whose beams along the tilted magnetic axis sweep past Earth (lighthouse model); not on the H-R diagram proper
Magnetar (SGR / AXP)	SGR 0526−66 (1979 burst); SGR 1806−20 (2004 giant flare)	Eruptive (X-ray and gamma-ray bursts) and rotating	Spin periods about 2–12 s; bursts last milliseconds to seconds; giant flares very rare	Bursts reach huge X-ray/gamma luminosities; little optical light	Neutron stars with $10^{14}$–$10^{15}$ G fields powered by field decay; crustal "starquakes" release bursts; linked to some fast radio bursts
X-ray burster	V801 Ara and V926 Sco (GCVS examples); Rapid Burster for Type II	X-ray binary (GCVS class of its own)	Type I: rise about 1–10 s, decay 10–100 s, repeat every hours to days	X-ray flux rises many times; optical about 0.1 mag	Type I: thermonuclear flash of accreted H/He on a neutron star's surface in a low-mass X-ray binary (can reach the Eddington limit); Type II: accretion instability
Of star	ζ Puppis (O4 I(n)fp; example)	Spectral	Not a variable class; strong, variable winds	Not applicable (spectral class)	O stars with N III (463–464 nm) and He II (468.6 nm) emission from dense winds; very luminous, top left of the H-R diagram; a step toward Wolf–Rayet
Be star	γ Cassiopeiae	Spectral (often γ Cas variable)	Disk changes over days to decades	Up to 1.5 mag when variable	Non-supergiant B star that shows (or has shown) Balmer emission from an equatorial decretion disk; rotates near breakup; "shell star" when seen edge-on
Ap / Bp star	α² Canum Venaticorum	Spectral; rotating (α² CVn variable)	Rotation period 0.5–160 d or more	0.01–0.1 mag; line strengths and field vary with rotation	Main-sequence B8p–A7p stars with strong (kilogauss) ordered magnetic fields; Si, Sr, Cr, Eu and rare earths concentrated in surface patches; oblique-rotator model; slow rotators
Am star (metallic-line)	Sirius A (A1 Vm; example)	Spectral	Not a variable class	Not applicable (spectral class)	Slowly rotating A and early F main-sequence stars, often in close tidally locked binaries; weak Ca and Sc but strong iron-group and heavy-element lines; atomic diffusion in calm atmospheres; no strong field
Carbon star C-R (old R type)	No single prototype (former Harvard class R)	Spectral	Usually not strongly variable	Not applicable (spectral class)	Warmer carbon stars (about 4,000–5,000 K, overlapping K) with C₂ and CN bands but little s-process enhancement; many are red-clump giants, not AGB stars; possibly merger products
Carbon star C-N (old N type)	Y Canum Venaticorum (La Superba; example)	Spectral (often SR, L or Mira variable)	Often semiregular or Mira-type, hundreds of days	Not applicable as a class; follows its variable type	Cool AGB stars where dredge-up made C/O above 1: strong C₂ Swan bands and CN, no TiO, blue light strongly suppressed, s-process elements and technetium; upper right of the H-R diagram
S star	χ Cygni (an S-type Mira; example)	Spectral (often Mira or SR variable)	Follows its variable type	Not applicable as a class	AGB stars with C/O close to 1: ZrO (also LaO, YO) bands in place of or beside TiO; s-process enhanced; "intrinsic" S stars show technetium (self-made), "extrinsic" ones lack it (binary mass transfer)
MS star	No single prototype (transitional)	Spectral	Follows its variable type	Not applicable (spectral class)	Intermediate between M and S: TiO bands with weak ZrO; AGB stars just beginning to show dredged-up s-process material
Barium star	ζ Capricorni (example)	Spectral	Orbits of years in a binary; not intrinsically variable	Not applicable (spectral class)	G–K giants with very strong Ba II (455.4 nm) and Sr II lines and enhanced carbon, but no technetium; the s-process material came from a former AGB companion that is now a white dwarf (all are binaries); Population I disk
CH star	No single prototype (Keenan's metal-poor high-velocity class)	Spectral	Orbits of years in a binary	Not applicable (spectral class)	Population II (halo) analog of barium stars: metal-poor giants with strong CH G band (430 nm) and s-process lines from mass transfer by a former AGB companion
Hot subdwarf sdB / sdO	Examples: V361 Hya (pulsating sdB); class VI cool subdwarfs are a different group	Spectral (some pulsating)	sdB pulsators: p modes of minutes (V361 Hya type), g modes of about 1–2 h (V1093 Her type)	Pulsations of hundredths of a magnitude	sdB: helium-core-burning stars of about 0.5 $M_\odot$ with almost no hydrogen envelope (extreme horizontal branch), about 20,000–40,000 K; sdO hotter; between the main sequence and white dwarfs, lower left; most lost their envelopes to a binary companion. Cool subdwarfs (class VI) are metal-poor stars just below the main sequence
White dwarfs DA, DB, DO	Sirius B (DA); GD 358 (DB)	Spectral (some pulsate: ZZ Ceti, DBV, GW Vir)	Cooling over billions of years	Not applicable (spectral class)	DA: hydrogen Balmer lines only (the majority, about 80%); DB: neutral helium (He I) lines, about 12,000–30,000 K; DO: ionized helium (He II), hotter than about 45,000 K; all at the bottom left of the H-R diagram
White dwarfs DC, DQ, DZ	van Maanen's star (DZ); Procyon B (DQ-type)	Spectral	Cooling over billions of years	Not applicable (spectral class)	DC: no lines (too cool to show them: helium atmospheres below about 11,000 K, hydrogen atmospheres below about 5,000 K); DQ: carbon features (C₂ bands or atomic C) dredged from the core; DZ: only metal lines (Ca, Mg, Fe) from accreted planetary debris; lower left, cooler end of the track
L dwarf	GD 165B (first recognized; example)	Spectral	Not a variable class (weather can cause small changes over hours)	Not applicable (spectral class)	About 1,300–2,400 K; TiO and VO fade as they condense into dust; metal hydrides (FeH, CrH) and alkali lines (Na, K, Rb, Cs) strong; lowest-mass stars and young/massive brown dwarfs; far lower right, off the visible H-R diagram
T dwarf	Gliese 229B (first; example)	Spectral	Not a variable class	Not applicable (spectral class)	About 500–1,300 K; methane (CH₄) and strong water absorption in the near-infrared; brown dwarfs only
Y dwarf	WISE 0855−0714 (coldest known; example)	Spectral	Not a variable class	Not applicable (spectral class)	Below about 500 K; ammonia (NH₃) features, water-ice clouds predicted in the coolest; discovered by WISE, characterized with JWST

Constants and unit conversions

ReferenceConstants and unit conversions· 49 rows

Values from CODATA 2018 and the IAU 2015 nominal solar values, rounded to what a test needs; cgs equivalents in the last column.

49 rows

Quantity	Symbol	Value (SI)	Other units / handy form
Speed of light	$c$	$2.998\times10^{8}$ m/s (exactly 299,792,458)	$3.00\times10^{10}$ cm/s; 1 light-second ≈ 300,000 km
Gravitational constant	$G$	$6.674\times10^{-11}$ m³ kg⁻¹ s⁻²	$6.674\times10^{-8}$ cm³ g⁻¹ s⁻²
Planck constant	$h$	$6.626\times10^{-34}$ J s	$6.626\times10^{-27}$ erg s; $4.136\times10^{-15}$ eV s; $hc = 1240$ eV nm
Boltzmann constant	$k$	$1.381\times10^{-23}$ J/K	$1.381\times10^{-16}$ erg/K; $8.617\times10^{-5}$ eV/K; 1 eV ↔ 11,600 K
Stefan–Boltzmann constant	$\sigma$	$5.670\times10^{-8}$ W m⁻² K⁻⁴	$5.670\times10^{-5}$ erg s⁻¹ cm⁻² K⁻⁴; $L = 4\pi R^2\sigma T^4$
Radiation constant	$a = 4\sigma/c$	$7.566\times10^{-16}$ J m⁻³ K⁻⁴	$7.566\times10^{-15}$ erg cm⁻³ K⁻⁴; radiation pressure $P = aT^4/3$
Wien displacement constant	$b$	$2.898\times10^{-3}$ m K	$\lambda_\text{max}(\text{nm}) \approx 2.898\times10^{6}/T(\text{K})$; Sun 5,772 K → 502 nm
Proton mass	$m_p$	$1.6726\times10^{-27}$ kg	$1.6726\times10^{-24}$ g; 1.00728 u; $m_pc^2 = 938.3$ MeV
Neutron mass	$m_n$	$1.6749\times10^{-27}$ kg	1.00866 u; $m_nc^2 = 939.6$ MeV
Electron mass	$m_e$	$9.109\times10^{-31}$ kg	$9.109\times10^{-28}$ g; $m_ec^2 = 0.511$ MeV; $m_p/m_e = 1836$
Atomic mass unit	u (amu)	$1.6605\times10^{-27}$ kg	1/12 of a carbon-12 atom; $uc^2 = 931.5$ MeV; ¹H atom = 1.00783 u
Elementary charge	$e$	$1.602\times10^{-19}$ C	Sets the electron-volt: 1 eV = $1.602\times10^{-19}$ J
Thomson cross-section	$\sigma_T$	$6.652\times10^{-29}$ m²	$6.652\times10^{-25}$ cm²; electron scattering in the Eddington limit
Rydberg constant	$R_\infty$	$1.0974\times10^{7}$ m⁻¹	Hydrogen ($R_H$) $1.0968\times10^{7}$ m⁻¹; $1/\lambda = R_H(1/n_1^2 - 1/n_2^2)$; ionization 13.6 eV; H-alpha 656.3 nm, Lyman-alpha 121.6 nm
Hubble constant	$H_0$	≈ 70 km s⁻¹ Mpc⁻¹ (measurements 67–73)	$1/H_0 \approx 14$ Gyr for 70; $v = H_0 d$
Solar mass	$M_\odot$	$1.989\times10^{30}$ kg	$1.989\times10^{33}$ g; $GM_\odot = 1.327\times10^{20}$ m³/s² (known far better than $M_\odot$ itself)
Solar luminosity	$L_\odot$	$3.828\times10^{26}$ W	$3.828\times10^{33}$ erg/s; $L/L_\odot = (R/R_\odot)^2(T/5772)^4$
Solar radius	$R_\odot$	$6.957\times10^{8}$ m	$6.957\times10^{10}$ cm; 109 Earth radii; 0.00465 AU (1 AU = 215 $R_\odot$)
Solar effective temperature	$T_\odot$	5,772 K	Spectral type G2 V; core about $1.57\times10^{7}$ K
Solar magnitudes	$M_V$, $M_\text{bol}$, $m_V$	$M_V = +4.83$; $M_\text{bol} = +4.74$	Apparent $m_V \approx -26.74$; color $B-V \approx 0.65$; $M_\text{bol} = 4.74 - 2.5\log(L/L_\odot)$
Other solar values	$\bar\rho_\odot$, $g_\odot$, $v_\text{esc}$	Mean density 1,410 kg/m³; surface gravity 274 m/s²	Escape speed from the surface 617.7 km/s; solar constant at 1 AU 1,361 W/m²; $M_\odot c^2 = 1.79\times10^{47}$ J
Earth mass	$M_\oplus$	$5.972\times10^{24}$ kg	$GM_\oplus = 3.986\times10^{14}$ m³/s²; $3.00\times10^{-6}\ M_\odot$ (≈ 1/333,000)
Earth radius	$R_\oplus$	6,378 km (equatorial); 6,371 km (mean)	Surface $g = 9.81$ m/s²; escape speed 11.2 km/s; orbital speed around the Sun 29.8 km/s
Moon	$M_\text{Moon}$, $d$	$7.342\times10^{22}$ kg; mean distance $3.844\times10^{8}$ m	1/81.3 of Earth's mass; radius 1,737 km; sidereal month 27.32 d, synodic month 29.53 d
Jupiter mass	$M_\text{Jup}$	$1.898\times10^{27}$ kg	317.8 $M_\oplus$; $9.55\times10^{-4}\ M_\odot$ (≈ 1/1,048); brown dwarfs ≈ 13–80 $M_\text{Jup}$
Astronomical unit	AU	$1.496\times10^{11}$ m (exactly 149,597,870,700 m)	$1.496\times10^{13}$ cm; light takes 499 s (8.3 min); Earth's mean distance from the Sun
Light-year	ly	$9.461\times10^{15}$ m	Distance light travels in a Julian year; 63,241 AU; 0.3066 pc
Parsec	pc	$3.086\times10^{16}$ m	$3.086\times10^{18}$ cm; 206,265 AU; 3.262 ly; distance at which 1 AU subtends 1″; $d(\text{pc}) = 1/p(″)$
Kiloparsec, megaparsec	kpc, Mpc	1 kpc = $3.086\times10^{19}$ m; 1 Mpc = $3.086\times10^{22}$ m	1 kpc = 3,262 ly; 1 Mpc = $3.262\times10^{6}$ ly; Gpc = $10^9$ pc
Kilometer, speed handy forms	km	$10^{3}$ m = $10^{5}$ cm	1 km/s ≈ 1.02 pc/Myr; 1 AU/yr = 4.74 km/s, so $v_t = 4.74\,\mu d$ (km/s, ″/yr, pc)
Year	yr	Julian year = 365.25 d = $3.156\times10^{7}$ s	≈ $\pi\times10^{7}$ s; sidereal year 365.256 d; tropical year 365.242 d
Day	d	Mean solar day = 86,400 s	Sidereal day = 23 h 56 m 4.1 s = 86,164 s (one spin relative to the stars)
Radian, degree	rad, °	1 rad = 57.30°	$\pi$ rad = 180°; small-angle rule: size = distance × angle (in rad)
Arcminute, arcsecond	′, ″	1″ = $4.848\times10^{-6}$ rad	1° = 60′ = 3,600″; 1 rad = 206,265″; size (AU) = angle (″) × distance (pc)
Milli- and micro-arcsecond	mas, μas	1 mas = $10^{-3}$″; 1 μas = $10^{-6}$″	Gaia DR3 parallax errors ≈ 0.02–0.03 mas (G < 15) to ≈ 0.5 mas (G = 20); parallax 1 mas ↔ 1 kpc
Steradian	sr	Solid angle subtended by area $r^2$ on a sphere of radius $r$	Whole sky 4π sr = 41,253 deg²; 1 sr = 3,283 deg²; 1 deg² = $3.05\times10^{-4}$ sr
Joule, erg	J, erg	1 erg = $10^{-7}$ J	1 W = 1 J/s = $10^{7}$ erg/s
Electron-volt	eV, keV, MeV	1 eV = $1.602\times10^{-19}$ J = $1.602\times10^{-12}$ erg	1 MeV = $1.602\times10^{-13}$ J; photon $\lambda(\text{nm}) = 1240/E(\text{eV})$, so 1 keV ↔ 1.24 nm (X-ray), 2 eV ↔ 620 nm; $T = E/k$: 1 keV ↔ $1.16\times10^{7}$ K
Flux (energy)	$F$	W/m²	1 W/m² = $10^{3}$ erg s⁻¹ cm⁻²; $F = L/(4\pi d^2)$
Jansky (flux density)	Jy	$10^{-26}$ W m⁻² Hz⁻¹	$10^{-23}$ erg s⁻¹ cm⁻² Hz⁻¹; mJy = $10^{-3}$ Jy; AB magnitude zero point = 3,631 Jy; $L_\nu = 4\pi d^2 F_\nu$
Ångström	Å	$10^{-10}$ m	0.1 nm; H-alpha = 6,563 Å = 656.3 nm
Nanometer, micrometer	nm, μm	1 nm = $10^{-9}$ m; 1 μm = $10^{-6}$ m	1 μm = 1,000 nm = 10,000 Å; visible ≈ 400–700 nm; near-IR ≈ 0.7–5 μm
Temperature scales	K, °C, °F	K = °C + 273.15	°F = 1.8 °C + 32; −40 °C = −40 °F; 0 K = −273.15 °C; Wien and Stefan–Boltzmann need kelvin
Magnitude ↔ flux ratio	$\Delta m$	$m_1 - m_2 = -2.5\log_{10}(F_1/F_2)$	$F_1/F_2 = 10^{0.4(m_2 - m_1)}$: 1 mag = 2.512×, 2.5 mag = 10×, 5 mag = 100× (exact), 10 mag = $10^4$×, 15 mag = $10^6$×
Distance modulus	$m - M$	$m - M = 5\log_{10}d - 5$ ($d$ in pc)	$d = 10^{(m - M + 5)/5}$ pc; $m - M = 0$ at 10 pc, 10 at 1 kpc, 25 at 1 Mpc, 30 at 10 Mpc
Eddington luminosity per solar mass	$L_\text{Edd}$	$1.26\times10^{31}$ W × $(M/M_\odot)$	$1.26\times10^{38}$ erg/s × $(M/M_\odot)$ ≈ $3.3\times10^{4}\ L_\odot$ × $(M/M_\odot)$; $L_\text{Edd} = 4\pi GMm_pc/\sigma_T$
Chandrasekhar limit	$M_\text{Ch}$	≈ 1.4 $M_\odot$ ($2.8\times10^{30}$ kg)	1.44 $M_\odot$ is the figure usually quoted; maximum mass of a white dwarf (and of a collapsing iron core)
Schwarzschild radius per solar mass	$R_s = 2GM/c^2$	2.95 km × $(M/M_\odot)$	Earth's mass → 8.9 mm; $4\times10^{6}\ M_\odot$ → $1.2\times10^{7}$ km ≈ 0.08 AU
Neutron-star scale	$M_\text{NS}$, $R_\text{NS}$	Typically 1.2–2 $M_\odot$ (most near 1.4); radius 10–13 km	Heaviest measured pulsars ≈ 2 $M_\odot$; white dwarf ≈ 0.6 $M_\odot$ at about Earth's size

Orbital mechanics formulas and worked examples

ReferenceOrbital mechanics and binaries: formulas with worked examples· 23 rows

SI units unless the row says "solar units" (AU, years, $M_\odot$); every example was recomputed with $GM_\odot = 1.327\times10^{20}$ m³/s² and $GM_\oplus = 3.986\times10^{14}$ m³/s².

23 rows

Relation	Formula ($math$)	Units / notes	Worked example
Kepler's first and second laws	Orbit is an ellipse with the central mass at one focus; $dA/dt = h/2$ = constant	Equal areas in equal times means fastest at periapsis, slowest at apoapsis; at both apsides the velocity is purely sideways (radial velocity zero)	For $e = 0.5$: $v_p/v_a = r_a/r_p = (1+e)/(1-e) = 3$
Kepler's third law, solar units	$P^2 = a^3/(M_1 + M_2)$	$P$ in years, $a$ in AU, masses in $M_\odot$; with a planet, $M \approx$ star's mass	Jupiter, $a = 5.20$ AU: $P = 5.20^{1.5} = 11.9$ yr. Visual binary with separation 2.0″ at parallax 0.10″: $a = 2.0/0.10 = 20$ AU; with $P = 50$ yr, $M_1 + M_2 = 20^3/50^2 = 3.2\ M_\odot$
Kepler's third law, Newton's SI form	$P^2 = \dfrac{4\pi^2 a^3}{G(M_1 + M_2)}$	$a$ in m, $P$ in s, $M$ in kg; tripling $a$ multiplies $P$ by $3^{1.5} = 5.2$	Earth: $a = 1.496\times10^{11}$ m, $P = 3.156\times10^{7}$ s gives $M = 4\pi^2a^3/(GP^2) = 1.99\times10^{30}$ kg
Centripetal balance, circular speed	$\dfrac{GMm}{r^2} = \dfrac{mv^2}{r}$, so $v_c = \sqrt{GM/r}$ and $M(<r) = v^2 r/G$	$M$ is the mass inside the orbit; works for galaxies (rotation curves)	Earth: $v_c = \sqrt{1.327\times10^{20}/1.496\times10^{11}} = 29.8$ km/s. Galaxy: $v = 220$ km/s at $r = 8$ kpc gives $M(<r) = 9.0\times10^{10}\ M_\odot$
Period from speed and radius	$P = 2\pi r/v$	Circular orbits; keep units consistent	Sun around the Galaxy: $r = 8$ kpc $= 2.47\times10^{20}$ m, $v = 220$ km/s, $P = 7.05\times10^{15}$ s ≈ 223 Myr
Vis-viva equation	$v^2 = GM\left(\dfrac{2}{r} - \dfrac{1}{a}\right)$	Speed anywhere on an orbit; reduces to $v_c$ when $r = a$ and to $v_\text{esc}$ when $a \to \infty$	Comet with $a = 10$ AU passing $r = 1$ AU: $v = 29.8 \times \sqrt{2 - 0.1} = 41.1$ km/s
Escape speed	$v_\text{esc} = \sqrt{2GM/r} = \sqrt{2}\,v_c$	Independent of the escaping mass and of direction (ignoring drag)	Earth's surface: $\sqrt{2 \times 3.986\times10^{14}/6.378\times10^{6}} = 11.2$ km/s. Sun's surface: 617.7 km/s
Center of mass	$m_1 r_1 = m_2 r_2$, $r_1 + r_2 = a$, so $r_1 = a\,\dfrac{m_2}{m_1 + m_2}$	Both bodies orbit the barycenter with the same period; speeds also scale as $v_1/v_2 = m_2/m_1$	Sun–Jupiter: $r_\odot = 5.20\text{ AU} \times 9.54\times10^{-4} = 7.4\times10^{8}$ m ≈ 1.07 $R_\odot$ (just outside the Sun); the Sun moves at about 12.5 m/s
Reduced mass	$\mu = \dfrac{m_1 m_2}{m_1 + m_2}$	Turns a two-body problem into one body of mass $\mu$ orbiting the total mass at the separation $a$	Two 1 $M_\odot$ stars: $\mu = 0.5\ M_\odot$. Earth–Moon: $\mu = 7.25\times10^{22}$ kg (just under the Moon's mass)
Mass ratio from velocity amplitudes	$\dfrac{M_1}{M_2} = \dfrac{K_2}{K_1} = \dfrac{a_2}{a_1}$	Needs both stars' spectra (SB2); independent of inclination	$K_1 = 20$ km/s, $K_2 = 60$ km/s: $M_1/M_2 = 3$ (star 1 is heavier and moves less)
Total mass, double-lined binary	$(M_1 + M_2)\sin^3 i = \dfrac{P(K_1 + K_2)^3}{2\pi G}$	Circular orbit; only $\sin^3 i$ times the mass unless eclipsing ($i \approx 90°$)	$P = 10$ d, $K_1 + K_2 = 150$ km/s: $(M_1 + M_2)\sin^3 i = 3.5\ M_\odot$
Mass function, single-lined binary	$f(M) = \dfrac{PK_1^3}{2\pi G} = \dfrac{M_2^3\sin^3 i}{(M_1 + M_2)^2}$	A strict lower limit on the unseen companion's mass; above about 3 $M_\odot$ suggests a black hole	$P = 5.6$ d $= 4.84\times10^{5}$ s, $K_1 = 75$ km/s: $f = 4.84\times10^{5} \times (7.5\times10^{4})^3/(2\pi \times 6.674\times10^{-11}) = 4.9\times10^{29}$ kg ≈ 0.245 $M_\odot$
Projected orbit size	$a_1\sin i = \dfrac{K_1 P}{2\pi}$	Circular orbit; for the separation use $a\sin i = (K_1 + K_2)P/(2\pi)$	$K_1 = 30$ km/s, $P = 10$ d: $a_1\sin i = 4.1\times10^{9}$ m ≈ 5.9 $R_\odot$ ≈ 0.028 AU
Ellipse geometry	$b = a\sqrt{1 - e^2}$; $r_p = a(1 - e)$; $r_a = a(1 + e)$; semi-latus rectum $p = a(1 - e^2)$	Focus lies $ae$ from the center; $a = (r_p + r_a)/2$; $e = (r_a - r_p)/(r_a + r_p)$	Halley-like orbit, $a = 17.8$ AU, $e = 0.967$: $r_p = 0.59$ AU, $r_a = 35.0$ AU, $b = 4.5$ AU, $p = 1.16$ AU, $P = 17.8^{1.5} = 75$ yr
Specific orbital energy	$\varepsilon = \dfrac{v^2}{2} - \dfrac{GM}{r} = -\dfrac{GM}{2a}$	J/kg; negative = bound, zero = parabolic escape, positive = unbound	400 km orbit ($r = 6.778\times10^{6}$ m): $\varepsilon = -3.986\times10^{14}/(2 \times 6.778\times10^{6}) = -2.94\times10^{7}$ J/kg
Specific angular momentum	$h = r v_\perp = \sqrt{GMa(1 - e^2)}$	m²/s; conserved, which gives Kepler's second law and $r_p v_p = r_a v_a$	Circular 400 km orbit: $h = 6.778\times10^{6} \times 7.67\times10^{3} = 5.2\times10^{10}$ m²/s
Roche lobe (Eggleton approximation)	$\dfrac{r_L}{a} = \dfrac{0.49\,q^{2/3}}{0.6\,q^{2/3} + \ln(1 + q^{1/3})}$	$q = M_\text{star}/M_\text{companion}$; $r_L$ is the radius of a sphere with the lobe's volume; accurate to about 1%	$q = 1$: $r_L = 0.38\,a$. $q = 0.5$: $0.32\,a$. $q = 2$: $0.44\,a$. A star swelling past $r_L$ transfers mass through L1
Hill sphere	$r_H \approx a(1 - e)\left(\dfrac{m}{3M}\right)^{1/3}$	Region where a small body's gravity controls satellites against the larger body's tides	Earth: $r_H = 1\text{ AU} \times (3.00\times10^{-6}/3)^{1/3} = 0.0100$ AU ≈ $1.5\times10^{6}$ km (the Moon at $3.8\times10^{5}$ km is well inside)
Tidal acceleration	$\Delta g \approx \dfrac{2GM\,\Delta r}{d^3}$	Difference in pull across a body of size $\Delta r$ at distance $d$; falls as $1/d^3$	Moon across Earth's radius: $2 \times 4.90\times10^{12} \times 6.371\times10^{6}/(3.844\times10^{8})^3 = 1.1\times10^{-6}$ m/s²; the Sun's is $5.1\times10^{-7}$, about 0.46 of the Moon's
Roche limit	Fluid: $d \approx 2.44\,R_M\left(\dfrac{\rho_M}{\rho_m}\right)^{1/3}$; rigid: $d \approx 1.26\,R_M\left(\dfrac{\rho_M}{\rho_m}\right)^{1/3}$	$R_M$, $\rho_M$: primary's radius and density; $\rho_m$: satellite's density; inside it tides tear apart a self-gravitating body	Moon-like satellite (3,344 kg/m³) near Earth (6,371 km, 5,514 kg/m³): fluid limit $2.44 \times 6{,}371 \times 1.18 = 18{,}400$ km; rigid 9,500 km
Synodic vs sidereal period	$\dfrac{1}{S} = \left\lvert\dfrac{1}{P_1} - \dfrac{1}{P_2}\right\rvert$	Sidereal = relative to the stars; synodic = between repeat alignments as seen from a moving body	Mars ($P = 1.881$ yr) from Earth: $S = 1/(1 - 1/1.881) = 2.135$ yr = 780 d. Solar day from the sidereal day: $1/(1/86{,}164 - 1/3.156\times10^{7}) = 86{,}400$ s
Geostationary orbit	$r = \left(\dfrac{GM_\oplus T^2}{4\pi^2}\right)^{1/3}$ with $T$ = sidereal day	Must be circular, prograde and over the equator (a polar orbit cannot stay over one spot)	$T = 86{,}164$ s: $r = 42{,}164$ km from Earth's center, altitude 35,786 km, speed 3.07 km/s
Low Earth orbit	$P = 2\pi\sqrt{r^3/(GM_\oplus)}$, $v = \sqrt{GM_\oplus/r}$	$r = R_\oplus$ + altitude, not altitude alone	400 km altitude: $r = 6{,}778$ km, $P = 5{,}554$ s ≈ 92.6 min, $v = 7.67$ km/s

Missions, telescopes and instruments

ReferenceMissions, telescopes and instruments· 83 rows

Grouped by band from gamma rays to radio, then CMB, gravitational-wave, neutrino and cosmic-ray facilities, then detector and instrument terms. Status is as of October 2026; LEO = low Earth orbit, L2 = the Sun–Earth L2 point about 1.5 million km from Earth.

83 rows

Name	Type / band	Launched or first light (status)	Location or orbit	Known for
Compton Gamma Ray Observatory (CGRO)	Space, gamma ray (BATSE, OSSE, COMPTEL, EGRET)	1991 (deorbited 2000)	LEO	Second of NASA's four Great Observatories; BATSE showed gamma-ray bursts come evenly from all directions, so they are far outside the Milky Way; EGRET found gamma-ray pulsars and blazars
Fermi Gamma-ray Space Telescope	Space, gamma ray (LAT about 20 MeV to over 300 GeV; GBM for bursts)	2008 (operating)	LEO	Mostly surveys the whole sky every few hours; GBM caught GRB 170817A 1.7 s after GW170817; gamma-ray glow of starbursts M82 and NGC 253; pulsars; the Fermi bubbles
Neil Gehrels Swift Observatory	Space, gamma ray + X-ray + UV/optical	2004 (orbit decaying; 2026 commercial reboost attempt failed, reentry expected)	LEO	Fast gamma-ray burst response: BAT finds the burst, the craft slews within minutes, XRT and UVOT catch the X-ray and UV/optical afterglow; pointed follow-up rather than survey
INTEGRAL	Space, gamma ray and hard X-ray (ESA)	2002 (science ended February 2025)	Highly elliptical orbit	Gamma-ray spectroscopy: the 511 keV positron line from the Galactic center, cobalt-56 decay lines from SN 2014J; also saw GRB 170817A
H.E.S.S.	Ground, very-high-energy gamma ray (Cherenkov array; four 12 m + one 28 m)	2002–2003 (operating)	Khomas Highland, Namibia	Survey of TeV sources along the southern Galactic plane; TeV gamma rays from starburst NGC 253 (2009)
VERITAS	Ground, very-high-energy gamma ray (four 12 m Cherenkov telescopes)	2007 (operating)	Fred Lawrence Whipple Observatory, Arizona	Northern TeV sky; TeV gamma rays from starburst M82 (2009), evidence for dense cosmic rays
MAGIC	Ground, very-high-energy gamma ray (two 17 m Cherenkov telescopes)	2004 (second telescope 2009; operating)	Roque de los Muchachos, La Palma, Canary Islands	Low energy threshold; first TeV photons from a gamma-ray burst (GRB 190114C, 2019)
CTAO (Cherenkov Telescope Array Observatory)	Ground, gamma ray (next-generation Cherenkov arrays)	— (under construction)	La Palma (north) and Paranal, Chile (south)	Planned to be about ten times more sensitive than H.E.S.S., VERITAS and MAGIC
Uhuru (SAS-A, Explorer 42)	Space, X-ray	1970 (ended 1973)	LEO; launched from the San Marco platform off Kenya	First X-ray survey satellite (339 sources); Cen X-3 shown to be a pulsing neutron star in a binary; helped make Cyg X-1 a black-hole candidate
Einstein Observatory (HEAO-2)	Space, X-ray	1978 (ended 1981)	LEO	First fully imaging (focusing) X-ray telescope in orbit; showed ordinary stars, galaxies and clusters emit X-rays
ROSAT	Space, soft X-ray (Germany, US, UK)	1990 (ended 1999)	LEO	First all-sky survey with an imaging X-ray telescope, over 100,000 sources
RXTE (Rossi X-ray Timing Explorer)	Space, X-ray timing	1995 (ended 2012)	LEO	Microsecond timing of X-ray binaries: first accreting millisecond X-ray pulsar (1998), kilohertz oscillations from neutron stars
Chandra X-ray Observatory	Space, X-ray (Wolter grazing-incidence mirrors; ACIS, HRC, gratings)	1999 (operating on a reduced budget)	Highly elliptical orbit reaching about a third of the way to the Moon	Sharpest X-ray images (about 0.5″); ULXs in the Antennae, Cartwheel and M82; hot gas and remnants; third Great Observatory; named for Chandrasekhar
XMM-Newton	Space, X-ray (ESA)	1999 (operating)	Highly elliptical 48-hour orbit	Largest X-ray collecting area (three mirror modules); X-ray spectra of hot gas, ULXs and AGN
NuSTAR	Space, high-energy (hard) X-ray, 3–79 keV	2012 (operating)	LEO	First focusing hard-X-ray telescope; found 1.37 s pulses from M82 X-2 (2014), so that ULX is a neutron star
NICER	Space, X-ray timing	2017 (light leak patched January 2025; science paused since June 2025 by a pointing-motor fault)	International Space Station	Neutron-star radii and masses from the shape of X-ray pulses (e.g., PSR J0030+0451)
eROSITA (on Spektr-RG)	Space, X-ray all-sky survey (German telescope on a Russian–German craft)	2019 (eROSITA idle since February 2022)	L2	Deepest all-sky X-ray survey; first data release 2024; the eROSITA bubbles above and below the Galactic center
XRISM	Space, X-ray spectroscopy (JAXA with NASA)	2023 (operating; detector's protective gate valve stuck closed)	LEO	Resolve microcalorimeter gives very high-resolution X-ray spectra (gas motions, element abundances); replaces Hitomi (lost 2016)
IUE (International Ultraviolet Explorer)	Space, UV spectroscopy (NASA, ESA, UK)	1978 (ended 1996)	Geosynchronous orbit	Long-lived UV spectrograph: hot-star winds; UV data showing SN 1987A's progenitor was a blue supergiant
FUSE	Space, far-UV spectroscopy (about 90–120 nm)	1999 (ended 2007)	LEO	Deuterium abundance; O VI lines tracing hot gas in the Galactic halo
GALEX	Space, UV imaging survey	2003 (ended 2013)	LEO	UV maps of recent star formation (young O and B stars) in nearby galaxies; UV star-formation rates
Hubble Space Telescope	Space, UV–visible–near-IR, 2.4 m mirror	1990 (operating; one-gyro mode since 2024)	LEO, now below 500 km and slowly decaying	First Great Observatory; 1993 servicing fixed the flawed mirror (five shuttle servicing missions, last 2009); Cepheid distances and H₀; deep fields; WFC3, ACS, COS, STIS
James Webb Space Telescope (JWST)	Space, infrared 0.6–28 μm, 6.5 m mirror of 18 gold-coated beryllium segments	2021 (Dec 25; science from July 2022; operating)	Halo orbit around L2	Earliest galaxies; protostars and dust-buried star formation (Cartwheel); sunshield keeps it cold; NIRCam, NIRSpec, MIRI, NIRISS
Spitzer Space Telescope	Space, infrared about 3.6–160 μm, 0.85 m	2003 (liquid helium ran out 2009; ended January 2020)	Earth-trailing solar orbit	Fourth and last Great Observatory; IRAC, IRS, MIPS; dusty star formation, protostars, Herbig-Haro objects; warm mission kept only the 3.6 and 4.5 μm channels
Herschel Space Observatory	Space, far-IR/submillimeter 55–672 μm, 3.5 m (ESA)	2009 (helium ran out 2013)	L2	Largest infrared mirror in space before JWST; cold dust, filaments in molecular clouds where stars form; PACS, SPIRE, HIFI
IRAS	Space, infrared all-sky survey at 12, 25, 60, 100 μm (US, UK, Netherlands)	1983 (about 10 months)	LEO	First infrared all-sky survey; discovered ultraluminous infrared galaxies, the dust disk around Vega and infrared cirrus
WISE / NEOWISE	Space, mid-infrared all-sky survey at 3.4, 4.6, 12, 22 μm	2009 (coolant ran out 2010; NEOWISE asteroid mission 2013–2024)	LEO, Sun-synchronous polar orbit	Coldest brown dwarfs (Y dwarfs, WISE 0855−0714); all-sky dusty galaxies and AGN
SOFIA	Airborne infrared, 2.5 m telescope in a Boeing 747SP	2010 (ended 2022)	Stratosphere, about 12–14 km up	Flew above most atmospheric water vapor to see far-infrared light
Kepler / K2	Space photometry (transit light curves), 0.95 m	2009 (March; K2 from 2014 after reaction-wheel failures; retired 2018)	Earth-trailing solar orbit; managed by NASA Ames	Thousands of transiting exoplanets; ultra-precise light curves for asteroseismology and eclipsing binaries
TESS	Space photometry, nearly all-sky	2018 (operating)	13.7-day elliptical orbit in 2:1 resonance with the Moon	Transits around bright nearby stars; light curves of variable stars
Hipparcos	Space astrometry (ESA)	1989 (ended 1993)	Stranded in a highly elliptical transfer orbit after its apogee motor failed	Parallaxes of about 118,000 stars to about 1 milliarcsecond (catalogue 1997)
Gaia	Space astrometry and photometry (ESA)	2013 (observations ended January 2025; Data Release 4 due December 2026)	L2	Parallaxes, proper motions and colors of nearly 2 billion stars; finely detailed H-R diagrams (DR2, 2018; DR3, 2022)
Euclid	Space, visible and near-IR wide survey (ESA)	2023 (operating)	L2	Shapes and redshifts of over a billion galaxies to map dark matter and dark energy
Nancy Grace Roman Space Telescope	Space, near-IR wide field, 2.4 m	2026 (launched August 30; science after commissioning)	L2	Hubble-like sharpness over a field about 100 times larger (300-megapixel Wide Field Instrument); dark energy, microlensing planets
Mount Wilson Observatory	Ground, optical: 60-inch (1908) and 100-inch Hooker (1917)	1904 (founded)	San Gabriel Mountains near Pasadena, California	Hubble's Cepheids in M31 and the expansion law; Shapley's globular-cluster distances; Mount Wilson luminosity prefixes (d, sg, g, c)
Yerkes Observatory	Ground, optical; 40-inch (1.02 m) refractor	1897	Williams Bay, Wisconsin	Largest refractor ever used for research; Morgan–Keenan (Yerkes) spectral classification, 1943
Palomar Observatory	Ground, optical: 200-inch (5.1 m) Hale and 48-inch Oschin Schmidt	1949 (Hale first light; dedicated 1948)	Palomar Mountain, California	World's leading large telescope for decades; Palomar Sky Survey; Maarten Schmidt's quasar redshift (1963); Zwicky's supernova searches
W. M. Keck Observatory	Ground, optical/IR; twin 10 m mirrors of 36 hexagonal segments	1993 (Keck I), 1996 (Keck II)	Mauna Kea, Hawaii	Pioneered segmented mirrors and laser adaptive optics; Ghez's stellar orbits around Sgr A*
Very Large Telescope (VLT)	Ground, optical/IR; four 8.2 m telescopes, combinable as VLTI (ESO)	1998 (first unit)	Cerro Paranal, Atacama Desert, Chile	Genzel's group tracked stars around Sgr A* (GRAVITY instrument); MUSE spectroscopy of galaxies
Gemini Observatory	Ground, optical/IR; twin 8.1 m	1999 (North), 2000 (South)	Mauna Kea, Hawaii, and Cerro Pachón, Chile	One identical telescope in each hemisphere covering the whole sky
Subaru Telescope	Ground, optical/IR, 8.2 m (Japan)	1999	Mauna Kea, Hawaii	Very wide-field imaging (Hyper Suprime-Cam)
Gran Telescopio Canarias (GTC)	Ground, optical/IR, 10.4 m segmented (Spain)	2007	Roque de los Muchachos, La Palma	Largest single-aperture optical telescope
Sloan Digital Sky Survey (SDSS)	Ground, optical imaging + spectroscopic survey with a 2.5 m wide-field telescope	2000 (survey start; SDSS-V ongoing)	Apache Point Observatory, New Mexico	3-D map of millions of galaxies and quasars; ugriz filters; galaxy color–type statistics
Vera C. Rubin Observatory (LSST)	Ground, optical survey; 8.4 m telescope with a 3.2-gigapixel camera	2025 (first images); 10-year LSST began the night of June 29, 2026 (announced June 30)	Cerro Pachón, Chile	Images the whole southern sky every few nights: supernovae, variable stars, transients, asteroids
Extremely Large Telescope (ELT)	Ground, optical/IR, 39 m mirror of 798 segments (ESO)	— (under construction; first light planned 2029)	Cerro Armazones, Chile	Will be the largest optical/IR telescope
Giant Magellan Telescope (GMT)	Ground, optical/IR, seven 8.4 m mirrors (25.4 m effective)	— (under construction; first light planned 2030s)	Las Campanas Observatory, Chile	US-led extremely large telescope chosen by NSF for final design (2025)
Thirty Meter Telescope (TMT)	Ground, optical/IR, 30 m segmented	— (proposed; stalled)	Mauna Kea, Hawaii (La Palma as alternative)	Delayed by site opposition; NSF's 2026 budget request did not advance it
Parkes (Murriyang)	Ground, radio, 64 m dish	1961	New South Wales, Australia	Many pulsars, including the double pulsar (2003); first fast radio burst (reported 2007); received Apollo 11 TV
Arecibo Observatory	Ground, radio, 305 m fixed dish	1963 (collapsed 2020)	Puerto Rico	Hulse–Taylor binary pulsar (1974); first exoplanets, around a pulsar (1992); radar astronomy
Green Bank Telescope	Ground, radio, 100 × 110 m fully steerable dish	2000	Green Bank, West Virginia (National Radio Quiet Zone)	Largest fully steerable dish; pulsar timing for NANOGrav; a 2 M☉ pulsar (PSR J1614−2230, 2010)
Very Large Array (VLA)	Ground, radio interferometer; 27 dishes of 25 m on a Y	1980 (completed)	Plains of San Agustin near Socorro, New Mexico	Configurations A (widest, baselines to about 36 km) to D (most compact); 21 cm gas, jets, CO in distant galaxies
Very Long Baseline Array (VLBA)	Ground, radio VLBI; ten 25 m dishes	1993	Hawaii to St. Croix (U.S. Virgin Islands), baselines to about 8,600 km	Milliarcsecond images; parallaxes of masers and pulsars
ALMA (Atacama Large Millimeter/submillimeter Array)	Ground, millimeter/submillimeter interferometer; 66 antennas	2011 (early science; inaugurated 2013)	Chajnantor plateau, Atacama Desert, Chile, about 5,000 m	Cold dust and molecular gas (CO); gaps in protoplanetary disks (HL Tauri, 2014); partners ESO, NRAO/NSF, NAOJ with Chile
LOFAR (Low-Frequency Array)	Ground, low-frequency radio, about 10–240 MHz	2010	Core in the Netherlands, stations across Europe	Fixed antennas steered electronically; old synchrotron-emitting electrons, the early universe
FAST	Ground, radio, 500 m fixed dish	2016 (completed; full operations 2020)	Guizhou, China	Largest single-dish radio telescope; over 1,000 new pulsars, fast radio bursts
Square Kilometer Array (SKA)	Ground, radio arrays: SKA-Low (antennas) and SKA-Mid (dishes)	— (under construction; SKA-Low first image 2025)	Western Australia (Low) and Karoo, South Africa (Mid); headquarters Jodrell Bank, UK	Will be the largest radio telescope; neutral hydrogen across cosmic time, pulsars
Event Horizon Telescope (EHT)	Ground, VLBI at 1.3 mm (230 GHz) linking dishes worldwide (including ALMA)	Images released 2019 (M87*) and 2022 (Sgr A*)	Earth-sized virtual dish	About 20 microarcsecond resolution; first images of black-hole shadows
COBE	Space, microwave/IR (CMB)	1989 (ended 1993)	LEO	CMB is a near-perfect 2.725 K blackbody (FIRAS) with tiny anisotropies (DMR); 2006 Nobel (Mather, Smoot)
WMAP	Space, microwave (CMB)	2001 (ended 2010)	L2	Precise CMB maps: age about 13.7 Gyr, flat geometry
Planck	Space, microwave/submillimeter (CMB, ESA)	2009 (ended 2013)	L2	Best CMB maps: age 13.8 Gyr, H₀ ≈ 67 km/s/Mpc (low side of the Hubble tension)
LIGO	Ground, gravitational waves; two laser interferometers with 4 km arms	2002 (initial); Advanced LIGO 2015	Hanford, Washington, and Livingston, Louisiana	First direct detection, GW150914 (September 14, 2015; announced February 2016); GW170817; 2017 Nobel
Virgo	Ground, gravitational waves, 3 km arms	2007 (first science run; Advanced Virgo joined August 2017)	Cascina near Pisa, Italy	Third site sharpened sky positions (GW170814, GW170817)
KAGRA	Ground, gravitational waves, 3 km, underground and cryogenic	2020 (first observing run)	Kamioka mine, Gifu, Japan	First large detector underground with cooled sapphire mirrors
LISA	Space, gravitational waves (ESA with NASA); three craft with 2.5 million km arms	— (adopted 2024; launch planned about 2035)	Earth-trailing solar orbit	Millihertz waves: supermassive black-hole mergers, white-dwarf binaries
Pulsar timing arrays (NANOGrav, EPTA, PPTA and others)	Radio timing of dozens of millisecond pulsars	Evidence for a nanohertz background announced June 2023	Galaxy-sized detector timed with GBT, VLA, CHIME and other dishes	Correlated timing shifts (Hellings–Downs pattern), likely from supermassive black-hole binaries
Kamiokande(-II)	Underground water Cherenkov detector, about 3,000 tonnes	1983	Kamioka mine, Japan	11 neutrinos from SN 1987A; solar neutrinos; 2002 Nobel (Koshiba)
IMB (Irvine–Michigan–Brookhaven)	Underground water Cherenkov detector	1982 (ended 1991)	Salt mine near Cleveland, Ohio, under Lake Erie	8 neutrinos from SN 1987A
Super-Kamiokande	Underground water Cherenkov detector, 50,000 tonnes	1996	Kamioka mine, Japan	Neutrino oscillation (1998; 2015 Nobel, Kajita); would see thousands of neutrinos from a Galactic supernova
Sudbury Neutrino Observatory (SNO)	Underground heavy-water detector, 1,000 tonnes	1999 (ended 2006; now SNO+)	Creighton mine, Sudbury, Ontario, 2 km down	Showed solar neutrinos change flavor (2001–2002), solving the solar neutrino problem; 2015 Nobel (McDonald)
IceCube Neutrino Observatory	Ice Cherenkov detector, 1 km³ with 5,160 sensors	2010 (completed)	South Pole	High-energy astrophysical neutrinos (2013); blazar TXS 0506+056 (2017); Seyfert NGC 1068 (2022); Milky Way plane (2023)
Pierre Auger Observatory	Cosmic-ray air showers: about 1,600 water-Cherenkov tanks + fluorescence telescopes over 3,000 km²	2008 (completed)	Near Malargüe, Argentina	Highest-energy cosmic rays come from outside the Milky Way (2017)
CCD (charge-coupled device)	Silicon pixel detector	1969 (invented at Bell Labs; 2009 Nobel)	Focal plane of nearly every optical telescope	Up to about 90% quantum efficiency vs a few percent for photographic plates; linear response, digital output
Photometer	Measures brightness through a filter	—	—	Magnitudes, colors and light curves; early ones used photomultiplier tubes, now CCDs
Spectrograph	Slit + dispersing element + detector	—	—	Splits light by wavelength: composition, temperature, radial velocity; resolving power R = λ/Δλ
Prism vs diffraction grating	Dispersing elements	—	—	Prism refracts and bends blue most (uneven spread); grating diffracts, bends red most, spreads nearly evenly and gives several orders
Bolometer	Thermal detector of total absorbed power	1878 (Langley)	—	Measures heating, not individual photons; cooled versions used for far-IR, submillimeter and CMB (Herschel, Planck)
Coronagraph	Mask blocking a bright central source	1930 (Lyot, for the Sun)	—	Solar corona without an eclipse; faint disks and planets next to bright stars
Adaptive optics	Deformable mirror reshaped hundreds of times a second	1953 (proposed by Babcock); routine from the 1990s	Ground telescopes	Corrects atmospheric twinkling using a bright guide star or a laser guide star (sodium layer about 90 km up); near-diffraction-limited infrared images
Interferometer / VLBI	Combines light or signals from separated telescopes	—	—	Resolution set by baseline B: θ ≈ λ/B; VLBI records each dish with atomic clocks and correlates later (VLBA, EHT)
Imaging atmospheric Cherenkov telescope	Ground, very-high-energy gamma ray	—	—	A gamma ray makes a particle shower in the air; particles faster than light in air give a nanosecond blue Cherenkov flash that mirrors image
Wolter (grazing-incidence) mirror	X-ray optics	1952 (Wolter design)	—	X-rays reflect only at shallow angles, so nested paraboloid–hyperboloid shells focus them (Chandra, XMM-Newton, NuSTAR)
Schmidt camera	Wide-field telescope with a thin corrector plate	1930 (Bernhard Schmidt)	—	Wide sky surveys (Palomar 48-inch Schmidt); Kepler's optics are a Schmidt design
Photometric filters UBVRI and JHK	Broadband filters	UBV system 1953 (Johnson and Morgan)	—	U ~365 nm, B ~445 nm, V ~551 nm ("visual"), R ~658 nm, I ~806 nm; J ~1.2 μm, H ~1.6 μm, K ~2.2 μm; B−V color index

People and discoveries

ReferencePeople and discoveries· 61 rows

Roughly chronological by key work. Years are birth–death (b. = living); the last column gives the year of the work named.

61 rows

Person	Years	Discovery or contribution	Year of key work
Hipparchus	c. 190–c. 120 BCE	Star catalogue ranking naked-eye stars from 1st (brightest) to 6th magnitude; discovered precession	2nd century BCE
Charles Messier	1730–1817	Catalogue of fuzzy objects (M1 Crab, M31, M51, M82…) listed so comet hunters would not mistake them for comets	1774 (first list); 1781 (final)
William Herschel	1738–1822	Discovered Uranus; mapped the Milky Way's shape by star counts; showed some double stars orbit each other (true binaries); discovered infrared with a thermometer beyond the red	1781; 1785; 1802–1803; 1800
Caroline Herschel	1750–1848	Discovered eight comets and several nebulae; first woman paid as an astronomer	1786 (first comet)
John Herschel	1792–1871	Charted the southern sky from the Cape of Good Hope; General Catalogue of nebulae and clusters, the basis of the NGC	1834–1838; 1864
John Goodricke	1764–1786	Measured Algol's period and suggested eclipses; discovered δ Cephei's variability	1782–1783; 1784
Joseph von Fraunhofer	1787–1826	Mapped hundreds of dark lines in the solar spectrum, labeling the strongest A–K (D = sodium); pioneered diffraction gratings	1814
Friedrich Bessel	1784–1846	First stellar parallax (61 Cygni); predicted Sirius's unseen companion (Sirius B) from its wobbling motion	1838; 1844
Norman Pogson	1829–1891	Made magnitudes exact: 5 magnitudes = factor of 100 in brightness (1 mag ≈ 2.512×)	1856
Gustav Kirchhoff & Robert Bunsen	1824–1887 & 1811–1899	Each element has its own set of spectral lines; solar dark lines are absorption by elements in the Sun; Kirchhoff's three laws of spectra	1859–1860
William Huggins	1824–1910	Stars contain Earth's elements; a planetary nebula's bright-line spectrum showed some nebulae are glowing gas, not unresolved stars; first attempt at a stellar radial velocity (Sirius)	1864; 1868
Charles Wolf & Georges Rayet	1827–1918 & 1839–1906	Found hot stars with broad emission lines, now Wolf–Rayet stars	1867
Edward C. Pickering	1846–1919	Harvard College Observatory director; organized the Henry Draper Catalogue and the "Harvard computers"; first spectroscopic binary (Mizar)	1889
Williamina Fleming	1857–1911	Classified over 10,000 stars in an A–Q letter scheme; found the Horsehead Nebula, 310 variables and 10 novae; noted 40 Eridani B's oddly hot spectrum (first white dwarf recognized)	1888; 1890; 1910
Antonia Maury	1866–1952	Classification adding line sharpness; her narrow-line "c" stars proved to be giants, which Hertzsprung used; orbit of the spectroscopic binary β Aurigae	1897; 1889
Annie Jump Cannon	1863–1941	Reordered the classes into the temperature sequence O B A F G K M; classified about 350,000 stars (Henry Draper Catalogue)	1901; 1918–1924
James Jeans	1877–1946	Jeans criterion: a gas cloud collapses if its mass exceeds the Jeans mass	1902
Henrietta Swan Leavitt	1868–1921	Found 1,777 variables in the Magellanic Clouds; Cepheid period–luminosity relation (Leavitt law) from SMC Cepheids	1908; 1912
Ejnar Hertzsprung	1873–1967	Separated giants from dwarfs; first color–magnitude diagrams (Pleiades, Hyades); first Cepheid distance calibration	1905–1911; 1913
Henry Norris Russell	1877–1957	Absolute magnitude vs spectral type plot (H-R diagram); confirmed the Sun is mostly hydrogen	1913–1914; 1929
Vesto Slipher	1875–1969	First spiral-nebula radial velocities at Lowell Observatory: Andromeda approaching (~300 km/s), most spirals receding	1912; 1917
Karl Schwarzschild	1873–1916	First exact solution of general relativity, for a point mass; Schwarzschild radius R = 2GM/c² (event horizon of a non-rotating black hole)	1916
Albert Einstein	1879–1955	General relativity; predicted gravitational waves and gravitational lensing	1915–1916; 1936
Harlow Shapley	1885–1972	Distances to globular clusters put the Sun far from the Galactic center; argued spirals lie inside the Milky Way in the Great Debate; Shapley–Sawyer cluster concentration classes	1918; 1920; 1927
Heber Curtis	1872–1942	Great Debate: argued spiral nebulae are separate "island universes" (correct)	1920
Arthur Eddington	1882–1944	Proposed hydrogen-to-helium fusion powers stars; mass–luminosity relation; radiation-pressure (Eddington) limit; valve mechanism for Cepheids; 1919 eclipse test of relativity	1920; 1924; 1926
Meghnad Saha	1893–1956	Ionization equation linking line strengths to temperature	1920
Cecilia Payne-Gaposchkin	1900–1979	Thesis: spectral types reflect temperature, and stars are made mostly of hydrogen and helium	1925
Edwin Hubble	1889–1953	Cepheid V1 in M31 proved spirals are galaxies outside the Milky Way; galaxy classification (tuning fork); velocity–distance law	1923–1925; 1926/1936; 1929
Georges Lemaître	1894–1966	Expanding-universe solution with a velocity–distance relation, before Hubble; "primeval atom" (Big Bang) idea	1927; 1931
Milton Humason	1891–1972	Measured faint galaxy redshifts extending Hubble's law; began at Mount Wilson as a mule driver and janitor	1929–1931
Subrahmanyan Chandrasekhar	1910–1995	Maximum white-dwarf mass ≈ 1.4 M☉ (Chandrasekhar limit); 1983 Nobel	1930–1931
Fritz Zwicky	1898–1974	Coma cluster needs unseen mass (dark matter); with Baade named supernovae and proposed neutron stars and cosmic-ray origin; predicted galaxy lensing	1933; 1934; 1937
Walter Baade	1893–1960	Stellar Populations I and II (from M31 during wartime blackouts); two Cepheid types, which doubled the distance scale	1944; 1952
Hans Bethe	1906–2005	pp chain (with Critchfield) and CNO cycle as the energy sources of stars; 1967 Nobel	1938–1939
J. Robert Oppenheimer & George Volkoff	1904–1967 & 1914–2000	With Tolman, maximum neutron-star mass (TOV limit; their ideal-gas value ~0.7 M☉, modern ~2–3 M☉); Oppenheimer–Snyder collapse to a black hole	1939
Rudolph Minkowski	1895–1976	Split supernovae into Type I (no hydrogen lines) and Type II (hydrogen lines)	1941
William W. Morgan & Philip Keenan	1906–1994 & 1908–2000	With Edith Kellman, the MK (Yerkes) system: spectral type plus luminosity class (0/Ia to V); Morgan later traced the Milky Way's spiral arms with OB stars	1943
Carl Seyfert	1911–1960	Spirals with bright, star-like nuclei and broad emission lines (Seyfert galaxies)	1943
Alfred Joy	1882–1973	Defined T Tauri stars: irregular variables with emission lines in dark clouds	1945
Lyman Spitzer Jr.	1914–1997	Proposed a large space telescope (led to Hubble); physics of interstellar gas and dust; Spitzer Space Telescope named for him	1946
George Herbig	1920–2013	Herbig–Haro objects (with Haro); Herbig Ae/Be stars, intermediate-mass pre-main-sequence stars	1951; 1960
Guillermo Haro	1913–1988	Herbig–Haro objects found independently; flare stars; compact blue (Haro) galaxies	1952; 1956
Fred Hoyle	1915–2001	Predicted the carbon-12 energy level (7.65 MeV) that makes triple-alpha fusion work; coined "Big Bang"; steady-state theory	1953; 1949; 1948
Louis Henyey	1910–1970	Henyey track: nearly horizontal leftward pre-main-sequence path once a radiative core forms; Henyey method for computing stellar models	1955; 1959
B²FH: Margaret & Geoffrey Burbidge, William Fowler, Fred Hoyle	1919–2020, 1925–2010, 1911–1995, 1915–2001	How stars build the elements: hydrogen and helium burning, alpha, s-, r- and p-processes; Fowler shared the 1983 Nobel	1957
Chushiro Hayashi	1920–2010	Hayashi track: fully convective pre-main-sequence stars drop almost straight down at nearly constant cool temperature; forbidden zone to its right	1961
Riccardo Giacconi	1931–2018	Rocket found Sco X-1, the first X-ray source beyond the Sun; led Uhuru and Einstein; 2002 Nobel	1962
Maarten Schmidt	1929–2022	Redshift of 3C 273 (z = 0.158) showed quasars are distant and enormously luminous; Schmidt law of star formation vs gas density	1963; 1959
Roy Kerr	b. 1934	Exact solution for a rotating black hole (Kerr metric)	1963
Jocelyn Bell Burnell & Antony Hewish	b. 1943 & 1924–2021	First pulsar, CP 1919 (period 1.337 s); the 1974 Nobel went to Hewish (with Ryle), not Bell Burnell	1967
Vera Rubin & Kent Ford	1928–2016 & 1931–2023	Flat rotation curves of M31 and many spirals: evidence for dark-matter halos	1970; 1978–1980
Alar & Juri Toomre	Alar b. 1937; Juri (his brother)	Simulations showing tidal tails and bridges (Antennae, Mice) come from close encounters; Toomre merger sequence; Toomre Q disk-stability criterion (Alar)	1972; 1977; 1964
Halton Arp	1927–2013	Atlas of Peculiar Galaxies (338 objects, including Arp 143 and Arp 147)	1966
J. L. E. Dreyer	1852–1926	New General Catalogue (NGC, 7,840 objects) and Index Catalogues (IC)	1888; 1895, 1908
Stephen Hawking	1942–2018	Black holes emit thermal (Hawking) radiation; horizon area theorem; singularity theorems with Penrose	1974; 1971; 1970
Russell Hulse & Joseph Taylor	b. 1950 & b. 1941	Binary pulsar PSR B1913+16 (Arecibo); its orbital decay matches gravitational-wave losses; 1993 Nobel	1974
R. Brent Tully & J. Richard Fisher	b. 1943 & b. 1943	Spiral luminosity rises with rotation speed (L ∝ v⁴) measured from 21 cm line widths: a distance method	1977
Saul Perlmutter, Brian Schmidt & Adam Riess	b. 1959, b. 1967, b. 1969	Type Ia supernovae show the expansion is accelerating (dark energy); 2011 Nobel	1998
Reinhard Genzel & Andrea Ghez	b. 1952 & b. 1965	Orbits of stars such as S2 around Sgr A* reveal a ~4 million M☉ black hole; 2020 Nobel (with Penrose)	1990s–2000s
Rainer Weiss, Barry Barish & Kip Thorne	1932–2025, b. 1936, b. 1940	Conceived, built and led LIGO; first direct detection of gravitational waves; 2017 Nobel	2015

Common pitfalls

How tournaments test this

Our archive of public tournament tests holds 7,046 Astronomy questions, of which 6,977 are tagged Division C. The practice bank holds 21,370 Astronomy questions (18,692 Division C): about 8,300 match questions in the archive, and most of the rest come from older tournament tests the archive does not have. Most archived questions come from seasons that emphasized single-star evolution, so the archive under-represents galaxies; use it for the stellar physics and calculation skills, and expect 2027 tests to shift weight toward the galaxy material above.

Format. Free-response questions dominate, which suits an event built on explaining and calculating.

Subtopics. Questions may carry several tags. Stars (4,201 questions, 59.6%) and stellar evolution (3,026, 42.9%) dominate; deep-sky objects follow at 8.2%, galaxies 5.8%, instruments 4.7%, solar system 2.1% and cosmology 0.7%. Earlier galaxy-themed seasons supply most of the galaxy questions, and those are the ones to seek out for practice.

Task profile. Task labels cover about 27% of questions, so treat these as minimums: explain-or-why prompts lead at 9.8%, then which-of-the-following items (5.2%), calculations (4.8%), interpreting a graph, table or curve (3.5%) and compare-and-contrast (1.6%). Most tasks ask for reasoning; calculation is a substantial minority.

Recurring vocabulary. The most frequent words in prompts are "star" (in 7,060 documents), "mass" (2,256), "distance" (1,560), "temperature" (1,439), "radius" (1,204), "magnitude" (1,126), "luminosity" (1,059) and "supernova" (1,034). The commonest phrases are main sequence, apparent magnitude, white dwarf, solar masses, absolute magnitude, black hole, neutron star and binary system.

Most common correct answers. White dwarf (101 questions), hydrogen (66), infrared (56), mass (55), iron (49), temperature (46), red giant (43), electron degeneracy pressure (41), neutron star (37), luminosity (34), planetary nebula (30), main sequence (29), radio (28), carbon and helium (27 each). The pattern still applies in 2027: tests reward the endpoint of a process, the element that dominates a stage, and the wavelength that reveals a structure (infrared for dust-buried starbursts, radio for gas disks, X-rays for ULXs).

Quizzes. Of the archived questions, 2,959 meet the site's trust rule (answer from an official key, not flagged). The quizzes below use only questions inside the 2027 scope, each re-solved before inclusion.

Strategy

Split by skill, then check each other. One partner owns stars and spectra (classification, H-R diagrams, variables, remnants, ULXs, gravitational waves); the other owns galaxies and calculations (morphology, populations, interactions, rotation curves, the distance ladder). Both should know every formula, and each should check the other's units.

Build the resources around formulas and objects. One formula page with a worked example each: magnitude difference, distance modulus, parallax, proper motion, Wien, Stefan–Boltzmann, Doppler, Kepler, enclosed mass from rotation, Tully–Fisher, Hubble's law and Eddington luminosity. One page per listed object with its images in several wavelengths, its distance, its classification and its "story". A tuning-fork diagram, a population I/II table and a ladder diagram round it out. Binder pages can be removed during the event, so tab them by topic.

If you use computers, prepare offline. Download every image, paper and press release you might need. No internet, and no AI tools under any circumstances.

Practice reading data. Expect light curves (identify a Type Ia decline or a Cepheid period), spectra (identify lines, measure a shift), H-R diagrams (find the turnoff), rotation curves, X-ray images and gravitational-wave chirps. Read the axes and units first, every time.

Manage time in two passes. Answer the short items first, mark long calculations and multi-part data sets, and return to them. Tiebreakers are preselected questions, so do not skip anything entirely.

Show work a grader can follow. Formula, substitution with units, answer with units. For explain-or-why answers, one clear cause-and-effect sentence, such as "the encounter compressed the gas, so the star-formation rate rose".

Rehearse on your actual calculator. Logarithms and powers of ten drive almost every distance question.

Test yourself

These questions come from public tournament tests in our archive. Choose an answer to check it; each link goes to the full test.

Test yourselfStars and stellar evolution

0 / 0 correct

1. 1

   What is the upper mass limit of a white dwarf known as?

   Question 1 options

   AChandrasekhar limitBCore accretion limitCTOV limitDSupercritical mass threshold

   From: Greenbrier Invitational, 2025-26, Division C

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Test yourselfDistances, magnitudes and orbits

0 / 0 correct

1. 1

   A star with an apparent magnitude of 2 and absolute magnitude of –3 is

   Question 1 options

   Acloser than 10 pcBfarther than 10 pcCExactly 10 pc awayDimpossible to determine

   From: University of Michigan Invitational - MI, 2025-26, Division C

1 question from this set is no longer available.

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Test yourselfSupernovae, galaxies and multi-wavelength data

0 / 0 correct

1. 1

   In what kind of galaxy[ies] would you be able to observe a Type 1a supernova?

   Question 1 options

   ASpiralBEllipticalCIrregularDAll of the aboveENone of the above

   From: Jordan Invitational, 2024-25, Division C

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Test yourselfStar formation, spectra, galaxies and instruments

0 / 0 correct

1. 1

   Which observational feature distinguishes Mira variables from other red giants?

   Question 1 options

   ALonger pulsation periods exceeding 100 daysBHigher surface temperatureCLack of infrared excessDStable luminosity

   From: Monta Vista Invitational, 2025-26, Division C

1 question from this set is no longer available.

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Condensed facts

References and further reading

• Science Olympiad, event pages and the 2027 rules manual: https://www.soinc.org
• SciOly Wiki, Astronomy event page (for orientation only): https://scioly.org/wiki/index.php/Astronomy
• OpenStax, Astronomy 2e (stellar evolution, galaxies, the distance ladder, active galaxies): https://openstax.org/details/books/astronomy-2e
• NASA Science, Universe section (galaxies, stars, black holes): https://science.nasa.gov/universe/
• ESA/Hubble picture releases (M82, NGC 1569, the Antennae, Arp 147, MCG+07-33-027): https://esahubble.org
• NASA Chandra X-ray Observatory (ULXs, the Antennae, the Cartwheel, M82): https://chandra.harvard.edu
• NASA Webb Space Telescope (the Cartwheel and dusty star formation): https://webb.nasa.gov
• LIGO Caltech, GW170817 overview: https://www.ligo.caltech.edu/page/press-release-gw170817
• NuSTAR, M82 X-2 pulsar discovery: https://www.nustar.caltech.edu
• ESA Gaia mission (parallax and proper motion): https://www.cosmos.esa.int/web/gaia