LearnLight & spectraSome maths
Blackbody radiation
The characteristic spectrum any warm, opaque object emits, whose shape depends only on its temperature.
Why it matters
Stars are close enough to blackbodies that their colour tells you their surface temperature — which is the first rung of nearly everything else known about them.
The maths, in layers
1 · Intuition
Hotter means brighter at every wavelength and bluer at the peak. Both at once, which is why a hot star is not merely a brighter version of a cool one.
2 · The equation
L = 4π·R²·σ·T⁴
- R
- radius of the star
- σ
- Stefan–Boltzmann constant, 5.670 × 10⁻⁸ W m⁻² K⁻⁴
- T
- effective surface temperature, kelvin
3 · Where it comes from
The fourth power is brutal: a star twice as hot radiates sixteen times as much per unit area. It is why Betelgeuse, cool but enormous, and Rigel, hot but far smaller, end up comparably bright.
Rests on
Nothing. This is a starting point — you can begin here.
Leads to
- Wien's displacement lawThe wavelength at which a blackbody radiates most strongly is inversely proportional to its temperature.
- Spectral linesSharp bright or dark features in a spectrum, produced when electrons in atoms jump between fixed energy levels.
- The Hertzsprung–Russell diagramA plot of luminosity against temperature on which stars fall into a few narrow bands rather than scattering at random.
- Equilibrium temperatureThe temperature a world settles at when the sunlight it absorbs exactly balances the heat it radiates away.