stellar-spectroscopy

# Stellar Spectroscopy

A stellar spectrum is the single most information-dense observation in astronomy. From a dispersed beam of starlight you can read temperature, luminosity, surface gravity, chemical composition, radial velocity, rotation speed, magnetic field strength, and binary companionship. This skill covers the core techniques for turning a spectrum into astrophysics: how the continuum forms, how absorption lines are produced, how to classify a star on the OBAFGKM sequence, how to identify and measure lines, how to extract Doppler velocity, and how to run a curve-of-growth abundance analysis. Cecilia Payne-Gaposchkin's 1925 dissertation — the first analysis to show that stars are mostly hydrogen — is the worked example at the end.

**Agent affinity:** payne-gaposchkin (composition analysis), burbidge (nucleosynthesis signatures)

**Concept IDs:** astro-hr-diagram, astro-stellar-classification, astro-nuclear-fusion

## Where a Spectrum Comes From

A star's spectrum has three components, each produced by a different physical process:

1. **Continuous spectrum (continuum)** — thermal emission from the hot, dense gas below the photosphere, approximately a blackbody with small deviations.
2. **Absorption lines** — cooler gas in the photosphere absorbs specific wavelengths as electrons jump between bound energy levels.
3. **Emission lines** (less common in stars) — hot tenuous gas re-emits at specific wavelengths, most prominent in Be stars, Wolf-Rayets, and the solar chromosphere.

Kirchhoff's laws (1859) describe this: a hot dense gas produces a continuous spectrum; a hot diffuse gas produces emission lines; a cool gas in front of a continuum source produces absorption lines. The Sun shows all three depending on where you look.

## The Continuum and Temperature

The continuum is approximately blackbody, so the shape of the continuum encodes temperature through the Wien displacement law:

    lambda_max * T ~ 2.9 x 10^-3 m K

For the Sun (T ~ 5800 K), lambda_max ~ 500 nm, in the middle of the visible. For an O star (T ~ 30,000 K), lambda_max ~ 100 nm, in the far UV. For an M dwarf (T ~ 3000 K), lambda_max ~ 1 micron, in the near IR.

**Color as a temperature proxy.** Photometric indices like B-V (blue minus visual magnitude) map to temperature without requiring a full spectrum. A B-V of 0.0 corresponds to T ~ 10,000 K (A0V); a B-V of 1.5 corresponds to T ~ 3600 K (M0V). But color alone cannot separate temperature from reddening by interstellar dust, so photometric classification is always uncertain until you have a spectrum.

## The OBAFGKM Spectral Sequence

Stellar spectra are classified into seven primary types based on which absorption lines dominate:

| Type | T (K) | Color | Dominant features | Example |
|---|---|---|---|---|
| O | 30,000-50,000 | blue | He II, ionized metals, weak H | 10 Lac |
| B | 10,000-30,000 | blue-white | He I strong, H stronger | Rigel, Spica |
| A | 7,500-10,000 | white | H lines maximum, weak metals | Sirius, Vega |
| F | 6,000-7,500 | yellow-white | H weakening, Ca II H and K strong | Procyon |
| G | 5,200-6,000 | yellow | Metal lines strong, Ca II dominant, G-band (CH) | Sun |
| K | 3,700-5,200 | orange | Metal lines very strong, molecular bands appear | Arcturus |
| M | 2,400-3,700 | red | TiO molecular bands dominate | Betelgeuse, Proxima |

Each type subdivides 0-9, so the Sun is G2. Later additions extended the sequence to **L** (brown dwarfs, metal hydrides), **T** (methane brown dwarfs), **Y** (coolest brown dwarfs, below 500 K).

**Why the sequence is not temperature alphabetical.** Annie Jump Cannon, working at Harvard between 1896 and 1924, classified over 350,000 stellar spectra and discovered that the alphabetical ordering from Secchi's earlier system did not match temperature. She reordered the types as OBAFGKM (mnemonic: "Oh Be A Fine Girl/Guy, Kiss Me") — the sequence that has stood for a century.

**The ionization-excitation interpretation.** Cecilia Payne-Gaposchkin (1925) used Saha's ionization equation and Boltzmann's excitation equation to show that the spectral sequence reflects temperature through the physics of atomic excitation and ionization, not the abundances of elements. Hydrogen lines peak at type A not because A stars have more hydrogen but because A-star temperatures put the most hydrogen atoms in the n=2 level from which the Balmer lines are absorbed.

## Luminosity Classes (Morgan-Keenan)

Spectral type alone gives temperature. To separate a cool dwarf from a cool giant (very different luminosities but similar temperatures), the MK system adds a luminosity class:

| Class | Name | Example |
|---|---|---|
| Ia | Bright supergiant | Rigel (B8Ia) |
| Ib | Supergiant | Betelgeuse (M1-M2 Ia-Iab) |
| II | Bright giant | Polaris (F7Ib-II) |
| III | Giant | Arcturus (K1.5III) |
| IV | Subgiant | Procyon (F5IV-V) |
| V | Main sequence (dwarf) | Sun (G2V) |
| VI | Subdwarf | Kapteyn's Star |
| VII | White dwarf | Sirius B |

**How luminosity is read from a spectrum.** Giants have lower surface gravity than dwarfs. Low gravity means lower photospheric pressure, which narrows pressure-broadened lines and strengthens certain ionization stages relative to neutrals. Specific ratios (e.g., Sr II 4077 / Fe I 4045) are calibrated luminosity indicators. The analyst compares these to standard spectra to assign a class.

## Line Identification

Identifying which element produced which line is the first step in any quantitative analysis.

**Procedure:**

1. **Calibrate wavelength.** Use an arc lamp (Fe-Ar, Th-Ar) taken in the same instrument setting. Residuals after calibration should be under 0.01 A for high-resolution work.
2. **Correct for radial velocity.** Measure the Doppler shift from known stellar features (see next section) and transform the observed wavelengths to the rest frame.
3. **Match against a line list.** Standard references: the Moore Multiplet Tables, the VALD database (Vienna Atomic Line Database), NIST ASD.
4. **Che