More than half of the Sun-like stars in the Milky Way belong to binary or multiple-star systems, and the catalogued variable stars now number over fifty-eight thousand (as of 2023). Binaries and variables transform stars from mere “points of light” into physical objects that can be studied quantitatively: the former provide almost the only means of directly measuring stellar mass, while among the latter the Cepheid variables and Type Ia supernovae form the key rungs of the cosmic distance ladder. This page distinguishes the criteria, physical mechanisms, and typical figures for the various classes of double and variable stars. Before reading, you may wish to review the fundamentals of stellar physics and the apparent magnitude system.
Two stars that appear very close together in the sky are called a double star. Their relationship has two possibilities:
Telling the two apart requires proper motion, parallax, or long-term orbital motion: the two members of a physical binary share a common proper motion and trace an orbital arc over time, whereas the members of an optical double each go their own way.
Physical binaries are divided into four classes according to how they are discovered and observed. The same system may belong to several classes at once—for example, many spectroscopic binaries are also eclipsing binaries.
| Type | English | Distinguishing criterion | Typical examples |
|---|---|---|---|
| Visual binary | visual binary | Resolvable by telescope into two separate stellar points | Sirius A/B, Mizar (Ursa Major) |
| Spectroscopic binary | spectroscopic binary | Spectral lines show periodic Doppler shifts due to orbital motion | Mizar A (Ursa Major) |
| Eclipsing binary | eclipsing binary | Orbit edge-on to Earth; members mutually eclipse, causing light variation | Algol (Perseus) |
| Astrometric binary | astrometric binary | Visible star wobbles about an empty point; companion invisible | Sirius B in the early days (before its discovery in 1862) |
A gravitationally bound system with three or more members is called a multiple-star system. Stable multiple-star systems are usually hierarchical: members pair up into tight subsystems, and the subsystems in turn orbit one another in larger orbits, ensuring long-term dynamical stability.
The central value of physical binaries is this: they provide almost the only means by which astronomers can directly weigh stellar masses. The two members orbit their common center of mass, and the distance from the barycenter to each star is inversely proportional to its mass:
r1 / r2 = m2 / m1r1 = a · m2 / (m1 + m2)Here a is the separation between the two stars, r1 and r2 are the distances of each star from the barycenter, and m1, m2 are the masses.
For a system with known orbital period P and semi-major axis a, Kepler’s third law gives the total mass of the system. In Solar System units, the formula takes its simplest form:
a^3 / P^2 = m1 + m2where a is in astronomical units (AU), P in years (yr), and mass in solar masses (M☉). To further separate the individual masses of the two stars, one also needs: for visual binaries, the true scale from parallax together with the ratio of the two stars’ distances from the barycenter; for spectroscopic binaries, the radial-velocity curves; and for eclipsing binaries, the light curve, which additionally constrains the orbital inclination and the members’ radii.
Orbital periods span an enormous range: from less than an hour (e.g. AM CVn–type cataclysmic binaries), to a few days (e.g. β Lyrae), to several hundred thousand years (the orbit of Proxima Centauri about α Centauri AB). Statistically, binary periods approximately follow a log-normal distribution, with a median on the order of 100 years.
A variable star is one whose brightness changes with time. By the cause of variation they fall into two broad classes:
Among catalogued variables, pulsating types make up about two-thirds (nearly thirty thousand), and eclipsing variables number over ten thousand. The following sections proceed mechanism by mechanism.
Eclipsing variables are the eclipsing binaries described above. The orbital planes of the two members lie close to the line of sight; when the fainter member obscures the brighter, the total brightness reaches a primary minimum, and conversely a shallower secondary minimum occurs. Algol (Perseus) is the prototype, with a light-variation period of about 2.87 days and a brightness varying between roughly magnitudes 2.1 and 3.4. The light variation of an eclipsing variable is entirely a geometric occultation effect, unrelated to the star’s internal physics, yet its light curve can be inverted to recover the members’ relative radii, brightness ratio, and orbital inclination.
The historically famous “Algol paradox” refers to the fact that the less massive member of the system has in fact evolved faster (it has become a subgiant); the cause is that early mass transfer redistributed the masses of the two stars.
When a member is flattened into an ellipsoid by rapid rotation, or its surface bears large dark spots or bright patches, rotation periodically changes the effective emitting area or brightness facing Earth, producing a rotating variable. Among these, a star tidally distorted into an ellipsoid by binary interaction, whose projected area varies with orbital phase, is called an ellipsoidal variable, with a light-variation period equal to half the orbital period.
The outer layers of a pulsating variable expand and contract periodically under an imbalance between gravity and pressure, so that radius, temperature, and luminosity vary periodically as well. The energy source of pulsation is the kappa mechanism: a certain ionization layer inside the star (typically the second-ionization zone of helium) increases in opacity when compressed, trapping radiation and accumulating energy that drives the outer layers to expand; after expansion the temperature drops, the opacity falls back, radiation escapes, and the outer layers fall back, thus forming a heat-engine cycle. The temperature range that can sustain this mechanism forms a nearly vertical band on the Hertzsprung–Russell diagram, called the instability strip.
| Type | English | Period range | Visual amplitude | Population / characteristics |
|---|---|---|---|---|
| Classical Cepheid | classical Cepheid | 1–100+ days | about 0.1–2 mag | Population I, yellow supergiants, 4–20 M☉ |
| W Virginis (Type II Cepheid) | Type II Cepheid | about 1–50 days | about 0.3–1.2 mag | Population II, old, about 0.5–0.6 M☉ |
| RR Lyrae | RR Lyrae | about 0.2–1 day | about 0.2–2 mag | Population II, old horizontal-branch stars |
| Mira (long-period) | Mira / long-period | about 100–1000+ days | up to 8 mag or more | red giants / asymptotic giant branch |
| Semiregular | semiregular | tens to hundreds of days | usually < 2.5 mag | red giants / supergiants, period not strict |
Classical Cepheids are high-luminosity yellow supergiants of 4–20 M☉, with luminosities up to one hundred thousand times that of the Sun. Their central rule is the period–luminosity relation (also known as Leavitt’s law): the longer the light-variation period, the higher the mean absolute luminosity, the two being approximately linear on a logarithmic scale. The relation was discovered by Henrietta Leavitt in 1908–1912 among the Cepheids of the Small Magellanic Cloud—because they belong to the same galaxy and lie at the same distance, the correspondence between period and apparent brightness directly reflects differences in true luminosity.
M = a · log10(P) + bHere M is the absolute magnitude, P is the light-variation period (days), and a, b are empirical calibration constants (a is negative, so a longer period gives a smaller magnitude, i.e. brighter). Delta Cephei is the prototype of the classical Cepheids.
A cataclysmic variable is a close binary containing a white dwarf: the white dwarf accretes material from a companion that fills its Roche lobe, and erupts under various conditions. Unlike supernovae, these eruptions do not destroy the progenitor star and can recur.
| Type | English | Mechanism | Brightening / recurrence |
|---|---|---|---|
| Nova | nova | Thermonuclear flash once the hydrogen layer accreted on the white dwarf’s surface reaches a critical point | Brightens thousands to tens of thousands of times; long recurrence period |
| Recurrent nova | recurrent nova | Same as the nova mechanism; high accretion rate causes frequent eruptions | Multiple recorded eruptions within decades |
| Dwarf nova | dwarf nova | Accretion-disk instability releases gravitational energy; non-thermonuclear eruption | Brightens about 2–6 mag; recurs over weeks to months |
Dwarf novae are further divided into three types by their light-variation behavior:
A supernova is the most violent of stellar-scale eruptions; its peak can brighten by more than 20 magnitudes within a few days, and for a short time its luminosity can rival that of an entire galaxy. They are classified by the presence or absence of hydrogen lines in the spectrum and further features, combined with the physical mechanism, as follows:
| Type | Hydrogen lines | Key spectral features | Physical mechanism | Peak absolute magnitude (approx.) |
|---|---|---|---|---|
| Type Ia | absent | 615 nm singly ionized silicon (Si II) line | Thermonuclear detonation of a white dwarf | −19 |
| Type Ib | absent | No silicon; 587.6 nm neutral helium (He I) line present | Core collapse (hydrogen envelope already lost) | about −17 |
| Type Ic | absent | No silicon; helium weak or absent | Core collapse (hydrogen and helium envelopes already lost) | about −16 |
| Type II | present | Balmer-series hydrogen emission lines | Core collapse (hydrogen envelope retained) | about −16 to −17 |
Type Ia supernovae
A white dwarf in a close binary accretes material; as its mass approaches the Chandrasekhar limit (about 1.44 M☉), carbon burning ignites in a runaway, and the entire white dwarf undergoes thermonuclear detonation and is completely disrupted. The spectrum has no hydrogen but shows silicon lines. The energy released is about 1–2×10⁴⁴ joules, and the ejecta travel at about 5000–20000 km/s.
Core-collapse supernovae (II / Ib / Ic)
A massive star of about 8 M☉ or more evolves to an iron core; nuclear fusion can no longer resist its own gravity, the iron core collapses and violently rebounds in an explosion. Depending on whether the hydrogen and helium outer layers are retained before the eruption, it appears as Type II, Ib, or Ic. After the explosion a neutron star or black hole usually remains at the core.
Because their detonation conditions (near the Chandrasekhar limit) are highly uniform, Type Ia supernovae have a nearly standardized peak luminosity (about −19 mag), and after correction for light-curve shape they can serve as standard candles at extreme distances. In 1998, it was precisely by using high-redshift Type Ia supernovae that two independent teams discovered the universe to be in a state of accelerating expansion, on the basis of which dark energy was proposed.
The material ejected by the explosion expands at thousands to tens of thousands of kilometers per second, colliding with the interstellar medium, being heated by the shock wave, and emitting light to form a supernova remnant. The Crab Nebula (M1) in Taurus is the remnant of the supernova of AD 1054 (SN 1054), and at its center remains a rapidly rotating neutron star (a pulsar).
Within a single constellation, variable stars are labeled in order of discovery using the Bayer-style variable-star nomenclature (stars that already have a Bayer Greek-letter name keep their original name):
For example, Algol’s variable-star name is “β Persei” (keeping its Bayer name), while RR Lyrae, ο Ceti (Mira), and others are each named according to the rules.
A curve recording the change in brightness over time is called a light curve, with magnitude on the vertical axis (brighter upward) and time on the horizontal axis. For a variable of known period, the time can be folded by the period and a magnitude–phase diagram plotted with phase (0–1) on the horizontal axis, superposing data from many periods onto a single curve, which makes it easier to precisely measure the period, amplitude, and times of minimum.
Globular clusters are ideal places for practicing variable-star observation (especially RR Lyrae): the members within a cluster lie at essentially the same distance, making it easy to compare brightness side by side. Observing methods can be combined with this site’s hemisphere visibility and observing conditions to plan targets.
