🔭 Lecture 04 — Spectroscopy & Metallicity

Summary

Spectroscopy is the indispensable foundation of modern astrophysics: it reveals chemical composition, motion, and distance from how matter emits and absorbs radiation. This lecture traces the physics of spectral line formation and arrives at the [Fe/H] notation used across all of galactic archaeology to measure metallicity.

Lecture info

Course: Galactic Archaeology and Stellar Populations Institution: National Observatory (ON), Brazil Professor: Hélio Dotto Perottoni

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🌈 Modern spectroscopy

Spectroscopy links the properties observed in spectra (spectral lines and their intensities) to physical phenomena occurring in extraterrestrial environments — electronic transitions of different energies in stars, nebulae, planets, etc. This is the technique that let Cecilia Payne discover/interpret the Sun’s chemical composition (see below). The basic apparatus of a spectrograph is: source → slit → prism (today, a diffraction grating) → CCD.

🔎 The discovery of helium

A sequence of milestones in the early 19th/20th centuries:

• William Wollaston (1802): discovers dark lines in the Sun’s spectrum.
• Joseph Fraunhofer (1814): catalogs ~570 dark lines — the “Fraunhofer spectrum,” a term still used today.
• Henry Draper (1872): pioneer of stellar spectroscopy.
• Jules Janssen (1868): observes an unidentified dark line in the solar spectrum.
• Norman Lockyer (1868): identifies that same line and proposes it’s due to a previously unknown element — helium, named before it was ever isolated in a laboratory on Earth.

⚖️ Kirchhoff’s laws

1. Solids, liquids, or very dense gases, when heated, produce continuous spectra.
2. Low-density gases, when heated, produce emission spectra.
3. Low-density gases in front of a continuous-spectrum source produce absorption spectra — provided the gas is cooler than the source.

Every chemical element has a unique, characteristic set of lines — this is what allows an element to be identified through its spectrum.

⚛️ Spectral line formation

An electron bound to a nucleus has a ground state (minimum energy) and an ionization energy (above which it’s no longer bound — the atom becomes an ion). Between these two limits, the electron can only occupy discrete energy levels. The energy of the photon emitted/absorbed in a transition is:

$\Delta E=h\nu =\frac{hc}{\lambda }=E_0\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)$

where $E_0=-13.6$eV is hydrogen’s ionization potential (Rydberg’s formula).

The development of the Harvard Classification (~1910–1920) coincides with Bohr’s atomic model, which explains why hydrogen line intensity varies with stellar temperature:

• Low temperatures: the H atom typically stays in the ground state → weaker H lines (lower transition frequency).
• Intermediate temperatures: higher probability of the electron occupying the first excited state (level 2) → Balmer series transitions occur, detectable in the visible. This is why A-type stars have the strongest H lines of the entire spectral sequence.
• High temperatures: above $\sim$10,000 K, hydrogen ionizes rapidly → less neutral H → weaker lines again. That’s why O- and B-type stars have weaker H lines than A-type stars.

🧪 Stellar composition: Cecilia Payne

Understanding atomic excitation/ionization processes allowed the calculation of spectral line intensities as a function of temperature — work by Cecilia Payne, who demonstrated that the amounts of H and He are far greater than any other element in stars (and, by extension, in the Universe). In the early 20th century, data quality still didn’t allow distinguishing fine differences in chemical composition between stars; today, high-resolution spectra (more pixels per wavelength) allow detailed determinations — fundamental for understanding stellar evolution and the production of the periodic table’s elements.

Comparing spectra of stars with similar spectral type, an increase in the number/intensity of lines indicates a decrease in the amount of elements heavier than H and He — the metals, in the astronomical sense: literally any element besides hydrogen and helium. It’s generally assumed the observed surface composition reflects the original composition of the gas cloud the star formed from.

🔢 Metallicities and abundances

Early stellar evolution models considered only three abundance components: hydrogen ($X$), helium ($Y$), and metals ($Z$), with $X+Y+Z=1$. Spectroscopically, one assumes $Z\propto n(\text{Fe})$, giving rise to the standard notation:

$[\text{Fe/H}]={\log }_{10}\left(\frac{N_{Fe}/N_H}{(N_{Fe}/N_H{)}_{\odot }}\right)$

Equivalently, an abundance ratio between any two elements, $[X/Y]$, can be defined.

Interpreting [Fe/H]

Value	Interpretation
$[\text{Fe/H}]>0$	metal-rich — more metal-rich than the Sun
$[\text{Fe/H}]<0$	metal-poor — more metal-poor than the Sun
$[\text{Fe/H}]=-1$	10× less iron than the Sun
$[\text{Fe/H}]=-2$	100× less iron
$[\text{Fe/H}]=-3$	1000× less iron
$[\text{Fe/H}]=-4$	10000× less iron

[Beers & Christlieb 2005] is the classic reference for searching and characterizing extremely metal-poor stars — the oldest fossils accessible to galactic archaeology.

Photometric metallicity

Metallicity can also be estimated from photometry (colors) alone, without spectroscopy — a cheaper alternative for large surveys, though less precise [Babusiaux et al. 2018].

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📌 Key concepts

• Kirchhoff’s laws: continuous spectrum (dense hot source) vs. emission (hot rarefied gas) vs. absorption (cool rarefied gas in front of a continuous source).
• Balmer series: optical H transitions responsible for the peak in H line intensity in A-type stars.
• [Fe/H]: Sun-relative logarithmic notation; the quantitative basis of all of the Galaxy’s chemical archaeology.

🔗 References and related

• Beers & Christlieb (2005) — metal-poor stars
• Babusiaux et al. (2018) — photometric metallicity with Gaia data
• CursoON — overview
• Lecture 03 — Magnitudes, Colors & Spectral Classification
• Lecture 05 — Reddening, Extinction & IMF
• Winter School — Galactic Archaeology, Lecture 01 — [Fe/H] and [α/Fe] notation applied to population separation (Portuguese only)
• Anomaly Detection in Gaia Data — my research uses GALAH DR4 spectra processed with the same principles seen here