Spectra & Composition

Part 1: Kirchhoff’s Laws — Why Stars Show Absorption Spectra

Three Types of Spectra

In Lecture 4 (Module 1), you saw a preview of spectral types. Now we formalize the physics. Light sources produce three distinct spectral signatures, depending on their structure:

Continuous spectrum (blackbody continuum): a hot, dense source — a solid, liquid, or dense gas — emits light at all wavelengths, producing a smooth rainbow. The shape follows the Planck function $B_\lambda(T)$ you studied in Lecture 4 (Module 1). Examples: the Sun’s photosphere, an incandescent filament, the interior of a kiln.

Emission spectrum (bright lines on a dark background): a hot, low-density gas emits photons only at specific wavelengths — those corresponding to transitions between its atoms’ energy levels. The background is dark; you see isolated bright lines. Examples: nebulae excited by nearby hot stars, neon signs, gas discharge tubes.

Absorption spectrum (dark lines in a continuous rainbow): a cooler gas in front of a hotter continuum source absorbs photons from the continuum at exactly the wavelengths it would emit if heated. You see the rainbow interrupted by dark lines — a photographic negative of the emission spectrum. Examples: stellar spectra, the solar spectrum (Fraunhofer lines).

Kirchhoff’s Laws of Spectroscopy

These three observations codify into Kirchhoff’s laws:

1. A hot, dense object emits a continuous spectrum — all wavelengths, shaped by $B_\lambda(T)$.
2. A hot, low-density gas emits an emission-line spectrum — bright lines at wavelengths determined by its atomic composition.
3. A cooler gas in front of a hot continuum source produces an absorption-line spectrum — the continuum minus specific wavelengths, at the same positions the gas would emit if heated.

Why Stars Show Absorption Spectra: The Two-Layer Model

A star has a steep temperature gradient. Deep in the interior, temperatures reach millions of kelvin. The photosphere — the visible “surface,” meaning the depth where the star becomes opaque (optical depth $\tau \approx 1$) — sits at thousands of kelvin (about 5,800 K for the Sun). Just above it lies the stellar atmosphere, a thin layer of gas slightly cooler than the photosphere below it.

The light we observe is emitted by the photosphere (Kirchhoff’s law 1, a continuous spectrum). As this light travels outward through the cooler atmosphere, atoms there absorb photons at their characteristic wavelengths (Kirchhoff’s law 3, dark absorption lines appear). The result: a continuous spectrum scored by dark absorption lines.

Part 1 takeaway: Kirchhoff’s three laws connect the appearance of a spectrum to the physical conditions of the source. Stars produce absorption spectra because their cooler atmospheres absorb from the hotter photosphere — and those dark lines are the key to everything that follows.