3.2 Blackbody radiation and stellar spectra

Blackbody Radiation and Stellar Spectra

Blackbody radiation describes how objects emit light based on their temperature, and stellar spectra reveal what stars are made of and how hot they are. Together, these concepts give us the tools to classify stars and trace their evolution using nothing but the light they send our way.

Blackbody Radiation

Properties of blackbody radiation

A blackbody is an idealized object that absorbs all incoming electromagnetic radiation and re-emits it across the full spectrum. No real object is a perfect blackbody, but stars (including the Sun) come remarkably close, making this model extremely useful.

The Planck function describes the spectral radiance of a blackbody at a given temperature:

$B_\lambda(T) = \frac{2hc^2}{\lambda^5} \frac{1}{e^{hc/\lambda kT} - 1}$

This tells you how much energy a blackbody emits at each wavelength $\lambda$ for a given temperature $T$. The shape of the resulting curve is smooth and continuous, rising to a peak and then falling off on either side.

Wien's displacement law connects the peak wavelength of that curve to the object's temperature:

$\lambda_{\text{peak}} = \frac{b}{T}$

where $b = 2.898 \times 10^{-3}$ m·K. Because temperature is in the denominator, hotter objects peak at shorter (bluer) wavelengths and cooler objects peak at longer (redder) wavelengths. For example, the Sun at ~5,800 K peaks around 500 nm (visible green-yellow), while a cooler red dwarf at ~3,000 K peaks in the near-infrared.

Thermal equilibrium and radiation

Thermal equilibrium means a system's temperature stays constant over time because there's no net energy flow in or out. A blackbody in thermal equilibrium absorbs and emits radiation at equal rates, maintaining a stable energy balance.

Kirchhoff's law of thermal radiation states that at each wavelength, a body's emissivity equals its absorptivity when the body is in thermal equilibrium. In practical terms: a good absorber at some wavelength is also a good emitter at that wavelength.

Stellar atmospheres aren't perfect blackbodies, but they can be approximated as being in local thermodynamic equilibrium (LTE). In LTE, each small region of the atmosphere behaves as though it's in thermal equilibrium at a local temperature, even though the star as a whole has a temperature gradient. This approximation is what lets us apply the Planck function and Wien's law to real stars.

Stellar Spectra

Formation of stellar spectra

A star's spectrum has three components layered on top of each other:

• Continuous spectrum: The dense, hot photosphere emits a smooth blackbody-like curve across all wavelengths. This is the baseline.
• Absorption lines: Cooler gas in the star's outer atmosphere absorbs photons at specific wavelengths corresponding to electron transitions in atoms and ions. These show up as dark lines superimposed on the continuous spectrum. The dark lines in the solar spectrum, first cataloged in the early 1800s, are called Fraunhofer lines.
• Emission lines: When excited atoms release photons, bright lines appear at specific wavelengths. These are less common in ordinary stellar spectra but show up prominently in nebulae and certain types of active stars.

Which lines appear, and how strong they are, depends on the atmospheric temperature, chemical composition, pressure, and density. Temperature matters most because it controls which atoms are ionized and which electron energy levels are populated.

Classification of stellar types

The Harvard spectral classification sorts stars into types based on the pattern and strength of their absorption lines:

O – B – A – F – G – K – M

A classic mnemonic: Oh Be A Fine Girl/Guy, Kiss Me.

Temperature decreases across this sequence:

• O-type: > 30,000 K, blue, strong ionized helium lines
• B-type: ~10,000–30,000 K, blue-white, strong neutral helium lines
• A-type: ~7,500–10,000 K, white, strongest hydrogen (Balmer) lines
• F-type: ~6,000–7,500 K, yellow-white, weakening hydrogen, stronger metal lines
• G-type: ~5,200–6,000 K, yellow (the Sun is G2), prominent calcium and iron lines
• K-type: ~3,700–5,200 K, orange, strong molecular bands beginning to appear
• M-type: < 3,500 K, red, dominated by molecular bands (especially TiO)

Each letter class is subdivided 0–9 for finer resolution (e.g., the Sun is G2).

Luminosity classes add a second dimension, accounting for differences in surface gravity and physical size among stars of the same temperature:

• I – Supergiants
• II – Bright giants
• III – Giants
• IV – Subgiants
• V – Main-sequence (dwarf) stars

So the Sun's full classification is G2V.

The Hertzsprung-Russell (H-R) diagram plots luminosity (vertical axis) against temperature or spectral type (horizontal axis, with hotter stars on the left). Main-sequence stars form a diagonal band running from hot, luminous O-types in the upper left to cool, dim M-types in the lower right. Giants and supergiants sit above the main sequence, and white dwarfs sit below it. The H-R diagram is one of the most important tools in astrophysics for visualizing how mass, temperature, and luminosity relate to each other and how stars evolve over time.