What is a star? Colour and temperature
A star is a giant ball of hot gas, mostly hydrogen and helium, that makes its own light by nuclear fusion in its core. The Sun is our nearest star.
Hot objects glow. As they get hotter, the colour shifts from red to yellow to white to blue. Stars behave like this too (scientists call them black bodies).
Wien's law: the wavelength where a star is brightest gets shorter as it gets hotter:λmax × T = 2.9 × 10⁻³ m K
For the Sun, T ≈ 5,800 K, so λmax ≈ 500 nm (green-yellow light; the Sun looks white from space).
Spectra and spectral classes
Spreading starlight through a prism or grating gives a spectrum: a rainbow crossed by thin dark lines. Each element (hydrogen, helium, iron...) absorbs its own set of wavelengths, so the lines tell us what a star is made of.
The pattern of lines also depends on temperature. Stars are sorted into classes:
- O (above 30,000 K, blue) · B (10,000–30,000 K, blue-white) · A (7,500–10,000 K, white) · F (6,000–7,500 K, yellow-white) · G (5,200–6,000 K, yellow; the Sun) · K (3,700–5,200 K, orange) · M (below 3,700 K, red)
Each class is split 0–9 (the Sun is G2). A luminosity class (I supergiant ... V main sequence) is added from line widths: the Sun is G2 V.
Brightness, magnitude and distance
Luminosity and apparent brightness
Luminosity L is the total power a star gives out (watts). Apparent brightness b is the power reaching each square metre here: b = L / (4πd²). So brightness falls as 1/d².
Magnitudes
Astronomers also use magnitude. Smaller numbers mean brighter. A difference of 5 magnitudes = 100 times in brightness, so 1 magnitude ≈ 2.512 times.
- Apparent magnitude m: how bright it looks from Earth (Sirius −1.5; faintest naked-eye stars about +6).
- Absolute magnitude M: how bright it would look from 10 parsecs (Sun +4.8).
m − M = 5 log₁₀(d / 10 pc)
Distance by parallax
From two sides of Earth's orbit (6 months apart), a nearby star shifts against distant ones. The parallax angle p is half this shift. d (pc) = 1 / p (arcsec). 1 pc ≈ 3.26 light-years ≈ 3.09 × 10¹⁶ m. A light-year is the distance light travels in a year, about 9.46 × 10¹⁵ m. Parallax works well only for fairly near stars because far stars shift too little to measure.
Size and the H-R diagram
Size from temperature and luminosity
Stefan–Boltzmann law: L = 4πR²σT⁴, σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴. If a red star is much more luminous than the Sun even though it is cooler, it must be much bigger: a giant.
The Hertzsprung–Russell (H-R) diagram
A graph of luminosity (or absolute magnitude) up the side, and temperature (or spectral class) along the bottom, hot on the left.
- Main sequence: a diagonal band where about 90% of stars are, fusing hydrogen in their cores. Hot ones are big, bright and massive; cool ones are small and dim.
- Giants and supergiants (top right): cool but very luminous, so huge.
- White dwarfs (bottom left): hot but dim, so tiny (about Earth-sized).
A star's place on the diagram changes as it ages (see the lesson on stellar evolution).
Try it
On a clear night, find three bright stars of different colours. Rank them from hottest to coolest by colour, then check their spectral classes in a star app.
Key formulas and definitions
- Wien's law: λmax T = 2.9 × 10⁻³ m K
- Stefan–Boltzmann: L = 4πR²σT⁴, σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴
- Apparent brightness: b = L / (4πd²)
- Parallax: d (pc) = 1 / p (arcsec); 1 pc ≈ 3.26 ly
- Magnitude: 5 mag = 100× brightness; m − M = 5 log₁₀(d / 10 pc)
- Spectral classes, hot → cool: O B A F G K M
Worked examples
1. A star's light peaks at 290 nm. Find its surface temperature.
T = 2.9 × 10⁻³ ÷ λmax = 2.9 × 10⁻³ ÷ (290 × 10⁻⁹) = 10,000 K. It is a hot white or blue-white star (class A/B).
2. A star has a parallax of 0.25 arcseconds. How far is it in parsecs and light-years?
d = 1 / p = 1 / 0.25 = 4 pc. In light-years: 4 × 3.26 ≈ 13 ly.
3. Star A is 3 times farther away than star B, and both have the same luminosity. Compare their apparent brightness.
Brightness ∝ 1/d². A is 3² = 9 times fainter than B.
4. Star X has apparent magnitude +1 and star Y has +6. How many times brighter does X look?
The difference is 5 magnitudes, which is exactly 100 times. X looks 100 times brighter. (Smaller magnitude = brighter.)
5. A red giant has the same temperature as a red dwarf but is 10,000 times more luminous. How many times bigger is its radius?
L = 4πR²σT⁴. With T the same, L ∝ R². R ratio = √10,000 = 100. The giant's radius is 100 times larger.
6. A star at 100 pc has apparent magnitude m = +7. Find its absolute magnitude.
m − M = 5 log₁₀(d/10) = 5 log₁₀(10) = 5. So M = 7 − 5 = +2. It is more luminous than the Sun (M = +4.8).
Common mistakes
- Thinking a bigger magnitude number means brighter. It is the opposite: −1 is brighter than +6.
- Drawing the H-R diagram with hot stars on the right. Temperature increases to the LEFT.
- Thinking a star that looks bright must be powerful. It may just be close.
- Thinking red stars are hot because red means hot in daily life. In stars, red is the coolest and blue is the hottest.