Variable Star
A variable star is any star whose observed brightness (apparent magnitude) changes over time, whether due to intrinsic physical changes in the star itself or due to geometric effects such as eclipses or rotation. Intrinsic variables include pulsating stars (Cepheids, RR Lyrae, Mira), eruptive variables (novae, flare stars), and cataclysmic variables (dwarf novae, Type Ia supernovae). Of particular cosmological importance are Cepheid variable stars, whose pulsation period is directly related to their intrinsic luminosity (the period–luminosity relation), making them crucial standard candles for measuring distances to nearby galaxies.
Key Formula
log(L/L_sun) = 1.15 × log(P/days) + 2.47
LaTeX: \log L = 1.15 \log P + 2.47 \quad (\text{Leavitt Law, approx.})
| Symbol | Meaning | Unit |
|---|---|---|
| L | Absolute luminosity of Cepheid | solar luminosities (L☉) |
| P | Pulsation period | days |
Worked Example
Problem
A Classical Cepheid variable has a pulsation period of 10 days. Using the Leavitt Law, estimate its luminosity in solar units.
Solution
Step 1 — Apply Leavitt Law: log(L/L☉) = 1.15 × log(P) + 2.47. Step 2 — log(10) = 1.000. Step 3 — log(L/L☉) = 1.15 × 1.000 + 2.47 = 3.62. Step 4 — L/L☉ = 10^3.62 ≈ 4,169 L☉.
Answer
Luminosity ≈ 4,169 L☉ (approximately 4,200 times the Sun's luminosity)
Major Classes of Variable Stars
| Class | Type | Period Range | Amplitude (mag) | Cosmological Use |
|---|---|---|---|---|
| Classical Cepheid | Pulsating (intrinsic) | 1–100 days | 0.5–2.0 | Extragalactic distances |
| RR Lyrae | Pulsating (intrinsic) | 0.2–1 day | 0.3–2.0 | Globular cluster distances |
| Mira (Long-Period) | Pulsating (intrinsic) | 100–1,000 days | 2.5–11 | AGB star evolution tracer |
| Eclipsing Binary | Geometric (extrinsic) | Hours–years | 0.1–3.0 | Stellar radii and masses |
| Nova | Eruptive (cataclysmic) | Irregular | 6–19 | Thermonuclear eruption study |
| Type Ia Supernova | Catastrophic (cataclysmic) | Days–weeks (rise) | ~19 | Cosmological distances, dark energy |
Interactive Tools
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Related Terms
Absolute Magnitude
Absolute magnitude is the intrinsic brightness of a celestial object expressed as the apparent magnitude it would have if placed at a standard distance of 10 parsecs (32.6 light-years) from the observer. It provides a true measure of luminosity independent of the object's actual distance, allowing direct comparison between stars. Astronomers use absolute magnitude to classify stellar populations, construct the Hertzsprung–Russell diagram, and estimate distances via the distance modulus.
Binary Star System
A binary star system consists of two stars gravitationally bound to each other, orbiting their common centre of mass (barycentre) under mutual gravitational attraction. Binary systems are remarkably common, accounting for roughly half of all star systems in the Milky Way, and are the primary means of directly measuring stellar masses through application of Kepler's third law. Depending on orbital geometry, binaries may be classified as visual, spectroscopic, eclipsing, or astrometric, each revealing complementary information about the stellar components.
Quasar
A quasar (quasi-stellar object) is an extremely luminous active galactic nucleus (AGN) powered by a supermassive black hole (10⁶–10¹⁰ M☉) accreting material at the centre of a distant galaxy, producing energy output that can exceed the combined light of an entire galaxy by factors of 100–1,000. Quasars were among the first objects identified at cosmological redshifts (z > 0.1), appearing star-like in early optical surveys despite being billions of light-years away, and their spectra showed enormous redshifted emission lines confirming their cosmological distances. Because quasar light has travelled billions of years to reach us, they serve as luminous probes of the early universe, intergalactic medium, and the history of black hole growth throughout cosmic time.
From Latin "variabilis" (changeable) and Latin "stella" (star). The term was formally established in astronomical catalogues in the 19th century; the period–luminosity relation for Cepheids was discovered by Henrietta Swan Leavitt in 1908.