Stellar Classification
Stellar Classification
Stars are classified by their surface temperature, luminosity, size, and spectral characteristics. The Hertzsprung-Russell (HR) diagram is the primary tool for understanding stellar populations and evolution.
Luminosity and Apparent Magnitude
Luminosity, L: The total power radiated by a star in all directions (watts). The Sun's luminosity L☉ = 3.85 × 10²⁶ W.
Apparent magnitude, m: How bright a star appears from Earth. The scale is logarithmic and inverted — lower numbers are brighter.
- A difference of 5 magnitudes = a factor of 100 in brightness
- Each magnitude step = a factor of 100^(1/5) ≈ 2.512
Absolute magnitude, M: The apparent magnitude a star would have if placed at a distance of 10 parsecs (32.6 light-years). This allows fair comparison of intrinsic brightness.
The Inverse Square Law for Stars
The intensity (power per unit area) received from a star:
I = L / (4πd²)
where d = distance to the star.
Stefan-Boltzmann Law
The total power radiated by a star (assuming it is a black body):
L = 4πr²σT⁴
where:
- r = radius of the star (m)
- σ = Stefan-Boltzmann constant = 5.67 × 10⁻⁸ W m⁻² K⁻⁴
- T = surface temperature (K)
This shows that luminosity depends on both size and temperature. A cool red giant can outshine the Sun because of its enormous surface area.
Wien's Displacement Law
The peak wavelength of emission from a black body:
λ_max T = 2.898 × 10⁻³ m K
Hotter stars peak at shorter (bluer) wavelengths; cooler stars peak at longer (redder) wavelengths.
Worked Example
A star has surface temperature 6000 K and radius 2R☉ (R☉ = 6.96 × 10⁸ m). Find its luminosity relative to the Sun (T☉ = 5778 K).
L/L☉ = (r/R☉)² × (T/T☉)⁴ = 2² × (6000/5778)⁴ = 4 × (1.0384)⁴ = 4 × 1.163 = 4.65 L☉
Spectral Classes
Stars are classified by spectral type based on surface temperature:
| Class | Colour | Temperature (K) | Key spectral features | Example |
|---|---|---|---|---|
| O | Blue | >30,000 | Ionised helium lines | 10 Lacertae |
| B | Blue-white | 10,000–30,000 | Neutral helium, hydrogen | Rigel |
| A | White | 7,500–10,000 | Strong hydrogen (Balmer) | Sirius |
| F | Yellow-white | 6,000–7,500 | Ionised metals, weak H | Procyon |
| G | Yellow | 5,200–6,000 | Ionised and neutral metals | Sun |
| K | Orange | 3,700–5,200 | Neutral metals, some molecules | Arcturus |
| M | Red | 2,400–3,700 | Molecular bands (TiO) | Betelgeuse |
Mnemonic: Oh Be A Fine Girl/Guy, Kiss Me
Each class is subdivided 0–9 (e.g., the Sun is G2).
The Hertzsprung-Russell Diagram
The HR diagram plots luminosity (or absolute magnitude) on the y-axis against temperature (or spectral class) on the x-axis. Temperature increases to the left (a historical convention).
Regions of the HR Diagram
Main sequence: A diagonal band from hot/luminous (upper left) to cool/dim (lower right). ~90% of stars are on the main sequence, where they fuse hydrogen to helium.
- Upper main sequence: massive, hot, luminous O and B stars (short lives, ~millions of years)
- Lower main sequence: low-mass, cool, dim K and M stars (long lives, ~trillions of years)
- The Sun is roughly in the middle (G2, ~10 billion year lifespan)
Red giants and supergiants: Upper right — cool but very luminous (large radius). Stars expand to this region when hydrogen fuel in the core is exhausted.
White dwarfs: Lower left — hot but very dim (tiny radius, about Earth-sized). The remnant cores of low/medium-mass stars after they shed their outer layers.
Stellar Evolution on the HR Diagram
Low-mass stars (< ~8 M☉):
1. Main sequence (hydrogen fusion) →
2. Red giant (helium fusion in core, hydrogen shell burning) →
3. Planetary nebula (outer layers ejected) →
4. White dwarf (core remnant, no fusion, slowly cools)
High-mass stars (> ~8 M☉):
1. Main sequence →
2. Red supergiant (fuses progressively heavier elements up to iron) →
3. Supernova (core collapse when iron core cannot fuse further) →
4. Neutron star or black hole (depending on remnant mass)
Chandrasekhar Limit
The maximum mass of a white dwarf: ~1.4 M☉ (the Chandrasekhar limit). Above this, electron degeneracy pressure cannot support the star, and it collapses further to become a neutron star.
Measuring Stellar Distances
Stellar parallax: The apparent shift of a nearby star against distant background stars as Earth orbits the Sun.
p (arcseconds) = 1/d (parsecs) → d = 1/p
1 parsec = 3.26 light-years = 3.09 × 10¹⁶ m
Parallax is reliable for stars within ~100 pc (Hipparcos) or ~10,000 pc (Gaia satellite).
Standard candles: Objects of known luminosity (e.g., Cepheid variables, Type Ia supernovae) allow distance measurement via the inverse square law.