Spectra & Composition

Section 6 of 8

Spectrum Inference

Part 5: Putting It Together — Reading a Real Stellar Spectrum

You now have a complete spectroscopic toolkit. A single stellar spectrum gives you three independent pieces of information:

Observable	What we measure	What we infer
Which lines appear (wavelength positions)	Line wavelengths matched to lab data	Composition — which elements are present
How strong lines are (depth and pattern)	Relative strengths of different species	Temperature (spectral type) — which states are populated
Where lines are shifted (offset from lab)	Doppler shift $\Delta\lambda$	Radial velocity — motion toward/away

Additional information comes from line widths (pressure, rotation, turbulence) and line splitting (Zeeman effect from magnetic fields), but the three inferences above are the workhorses.

Spectra are powerful but limited. Spectroscopy alone does not directly give luminosity (need distance + photometry), mass (need binary orbits or asteroseismology), radius (need Stefan-Boltzmann with $L$ and $T$ ), distance (need parallax or standard candles), or transverse velocity (need astrometric tracking).

Connection: The Module 2 Inference Chain

Each lecture in Module 2 adds one link:

Lecture	New Tool	What It Unlocks
1	Parallax → distance	Distance, then luminosity ( $L = 4\pi d^2 F$ )
2	Color → temperature; Stefan-Boltzmann	Radius ( $R$ from $L$ and $T$ )
3	Spectral lines → composition, $T$ , $v_r$	Chemical inventory; refined temperature; radial velocity
4	Binary orbits + Doppler	Mass
5–6	Magnitudes + HR diagram	Full stellar classification

Combined with distance (Lecture 1) and Stefan-Boltzmann (Lecture 2), we can now characterize five fundamental stellar properties — distance, luminosity, temperature, radius, and composition — from photons alone. Mass requires one more tool: binary orbits (Lecture 4).

Now let’s use all three clues simultaneously on a real problem.

Worked Example 4Multi-Clue Stellar Diagnosis

Problem

You observe a star and measure: a blackbody continuum fit of $T_{\text{eff}} \approx 9{,}500\ \text{K}$ ; strong Hα, Hβ, Hγ absorption; weak metal lines; and the Hα center at 656.1 nm (rest 656.3 nm). What can you infer?

Step(a) Spectral type

The temperature ( $\sim 9{,}500\ \text{K}$ ) and strong Balmer lines point to spectral type A — the Goldilocks temperature for hydrogen absorption. Weak metal lines are consistent.

Step(b) Radial velocity

$\Delta\lambda = 656.1 - 656.3 = -0.2\ \text{nm}\ (\text{blueshift, approaching})$ $v_r = c\,\frac{\Delta\lambda}{\lambda_0} = (3.0 \times 10^5\ \text{km/s})\frac{-0.2\ \text{nm}}{656.3\ \text{nm}} \approx -91\ \text{km/s}$

Dimensional check

$(\text{km/s}) \times (\text{nm}/\text{nm}) = \text{km/s}$ ✓; the sign carries the direction.

Result

A hot A-type star, made mostly of hydrogen (like all stars), approaching at $\sim 91\ \text{km/s}$ . To complete the picture you’d still need distance (parallax → luminosity), luminosity + temperature (→ radius via Stefan-Boltzmann), and time-series Doppler (→ binary companion → mass). Spectroscopy confirms and sharpens what color alone suggested.