Spectra as Physical Evidence: Composition, Temperature, and Stellar Properties

Spectra as physical evidence

A spectrum is a measurement of how much light an object emits or absorbs as a function of wavelength (or frequency). Unlike a single brightness value, a spectrum contains many “channels” of information: broad trends (the continuum shape) and narrow features (spectral lines). In astronomy, spectra act like physical evidence because the same atomic and molecular processes that operate in laboratory gases also operate in stellar atmospheres, nebulae, and galaxies. When you see a line at a particular wavelength, you are seeing a specific transition between quantized energy levels. When you see a continuum that rises and falls smoothly, you are seeing thermal radiation shaped by temperature and opacity. When you see lines broadened or shifted, you are seeing motion, pressure, rotation, and magnetic fields imprinting themselves on the light.

This chapter focuses on how spectra constrain composition, temperature, and stellar properties. The goal is to connect what you see in a spectrum to physical parameters you can estimate, test, and refine.

What a spectrum is made of: continuum and lines

Most stellar spectra can be thought of as a continuum with absorption lines carved into it. The continuum is the baseline emission across wavelengths, often close to a thermal (blackbody-like) shape for stars. The absorption lines form when photons from deeper, hotter layers pass through cooler gas above; atoms and ions absorb photons at specific wavelengths, removing light and producing dips. In emission-line objects (planetary nebulae, H II regions, some active galaxies), the continuum may be weak and the spectrum is dominated by bright emission lines produced by excited gas.

Two practical ideas are used constantly:

• Line identification: matching observed line wavelengths to known transitions (e.g., hydrogen Balmer lines, Ca II H&K, Na I D, Mg b).
• Line strength and shape: measuring how deep/wide a line is and how its profile looks (narrow, broad, symmetric, asymmetric), which encodes abundance, temperature, pressure, rotation, and more.

Composition: why lines reveal elements and molecules

Each chemical species has a unique set of allowed transitions. In practice, you rarely rely on a single line; you look for a consistent pattern across multiple lines of the same element/ion and check that their relative strengths make sense for a plausible temperature and density. Composition inference in stars is often framed as “abundances” relative to hydrogen (or relative to the Sun), but the underlying evidence is the same: the presence and strength of lines.

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Key points that help interpret composition correctly:

• Ionization state matters: seeing Fe I versus Fe II is not just “iron present”; it also indicates how ionized the atmosphere is, which depends strongly on temperature and electron pressure.
• Molecules appear in cool atmospheres: at lower temperatures, molecules survive and produce broad band features (e.g., TiO in M-type stars, CN and CH bands in some giants). These bands can dominate the optical spectrum even when atomic lines are present.
• Line strength is not abundance alone: a line can be weak because the element is rare, but also because the relevant energy level is sparsely populated at that temperature, or because the line is saturated and no longer deepens linearly with abundance.

Temperature from the continuum: blackbody intuition and practical fitting

The continuum shape of a star is closely related to its effective temperature, the temperature a perfect blackbody would have to emit the same total flux per unit surface area. Real stellar atmospheres are not perfect blackbodies: opacity varies with wavelength, and line blanketing (many overlapping lines) can depress parts of the continuum. Still, the overall slope across a wide wavelength range is a powerful temperature indicator.

In practical work, you often estimate temperature by fitting a blackbody curve to the observed continuum after accounting for instrumental response and interstellar reddening. The fit does not need to be perfect to be useful; you are extracting a temperature scale from the broad trend.

Step-by-step: estimating effective temperature from a spectrum’s continuum

This workflow assumes you have a spectrum with wavelength and flux values and that you can mask out strong lines. The steps are conceptual and can be implemented in any analysis environment.

• 1) Choose a wavelength range: pick a region broad enough to show curvature or slope (for optical spectra, several hundred nanometers if available). Avoid regions with heavy telluric absorption or strong instrumental artifacts.
• 2) Identify and mask strong lines: create a mask that excludes known deep absorption features (e.g., Balmer lines, Ca II H&K) and obvious emission lines. The goal is to fit the continuum, not the lines.
• 3) Normalize or keep absolute scaling: if you only need temperature, you can fit a scaled blackbody: flux ≈ A × B(λ, T). The scale factor A absorbs distance and radius effects.
• 4) Fit a blackbody model: vary T and A to minimize residuals between the model and the masked spectrum. Use robust fitting if outliers remain.
• 5) Inspect residuals: systematic residuals (e.g., blue end too low) may indicate reddening or calibration issues. If reddening is significant, include a reddening parameter and refit.
• 6) Report T with context: call it an “effective temperature estimate from continuum slope,” and note the wavelength range used and whether reddening was modeled.

Practical example: if the spectrum peaks in the blue/near-UV and declines toward red wavelengths, the star is hot (A/B type). If it rises toward red and shows molecular bands, it is cool (K/M type). The continuum alone can often place a star into a broad temperature class even before line analysis.

Temperature and pressure from lines: excitation and ionization balance

Lines provide temperature information in two complementary ways:

• Excitation: at higher temperatures, higher-energy levels are more populated, strengthening lines that originate from those levels. If you compare lines of the same species arising from different excitation energies, their relative strengths can constrain temperature.
• Ionization: hotter atmospheres have more ionized atoms. The ratio of neutral to ionized lines (e.g., Fe I vs Fe II) is sensitive to temperature and electron pressure. In stellar spectroscopy, “ionization balance” is a standard method: you adjust temperature and surface gravity until abundances inferred from Fe I and Fe II lines agree.

Pressure (and thus surface gravity) affects line formation through collisional broadening and through its role in ionization equilibrium. High surface gravity (dwarfs) tends to produce broader pressure-broadened wings in certain lines compared to low-gravity giants at similar temperature.

Step-by-step: using hydrogen Balmer lines to constrain temperature and gravity

Hydrogen Balmer lines (Hα, Hβ, Hγ, …) are prominent in many stellar spectra and are especially useful in A-type stars, where they reach maximum strength. Their line wings are sensitive to pressure broadening, which correlates with surface gravity.

• 1) Select Balmer lines with good signal: Hβ and Hγ are often cleaner than Hα in some setups due to telluric effects and emission contamination.
• 2) Normalize the local continuum: fit a smooth continuum on both sides of the line and divide the spectrum by it, so the continuum is near 1. This makes profile comparison easier.
• 3) Compare to a grid of synthetic profiles: use model spectra computed for a range of effective temperatures and surface gravities. Focus on matching the wings more than the core (the core can be affected by chromospheric activity or non-LTE effects).
• 4) Identify best-fit region: find the model that matches the wing shape and depth. If multiple models fit, note degeneracies (e.g., slightly different T and log g combinations).
• 5) Cross-check with metal lines: verify that the inferred temperature is consistent with the presence/absence of temperature-sensitive metal lines (e.g., strength of Ca II, Mg II, Fe lines).

This approach illustrates a general principle: some spectral features respond strongly to temperature, others to gravity, and combining them breaks degeneracies.

Stellar classification as a compressed summary of spectral physics

Spectral types (OBAFGKM and beyond) are not just labels; they summarize which lines and molecular bands dominate at different temperatures. You can treat classification as a practical shortcut: identify the dominant features, infer a temperature regime, then refine with quantitative fitting.

Examples of feature-temperature associations:

• Hot stars (O/B): strong ionized helium lines (He II in the hottest), weaker neutral metal lines; continuum very blue.
• A-type: Balmer lines very strong; metal lines moderate.
• F/G-type: Balmer lines weaken; metal lines (Fe, Ca, Mg) strengthen; G-type often shows strong CH (G band) around 430 nm.
• K-type: strong neutral metal lines; molecular features begin to appear.
• M-type: prominent molecular bands (TiO, VO) dominate optical; continuum very red.

Luminosity class (dwarf vs giant vs supergiant) is also encoded in spectra via gravity-sensitive lines and pressure broadening. For example, at similar temperature, giants tend to have narrower lines and different line ratios than dwarfs because their atmospheres are less dense.

Line strength as a measurement: equivalent width and what it means

A common way to quantify a line is its equivalent width (EW). Conceptually, EW is the width of a rectangle (at the continuum level) that contains the same “missing” flux as the absorption line. It compresses line depth and width into a single number and is widely used for abundance analysis and classification.

EW is useful because it is less sensitive to spectral resolution than line depth alone (within limits) and can be compared across spectra if continuum normalization is done consistently.

Step-by-step: measuring an equivalent width

• 1) Choose the line and define windows: specify a line window that covers the feature and two nearby continuum windows on either side that are relatively line-free.
• 2) Fit the local continuum: fit a straight line (or low-order polynomial) through the continuum windows to estimate the continuum level across the line window.
• 3) Normalize: divide the flux in the line window by the fitted continuum so the continuum is approximately 1.
• 4) Integrate the absorption: compute EW ≈ ∫(1 − normalized_flux) dλ over the line window. For emission lines, the sign flips (you integrate normalized_flux − 1).
• 5) Check sensitivity: slightly vary the continuum windows and line window to see how stable EW is. Blends with nearby lines can bias EW upward.

Practical interpretation: if two stars have similar temperatures and gravities, a larger EW for an iron line generally indicates higher iron abundance. If temperatures differ, the same EW may correspond to different abundances because excitation/ionization changes the line’s formation.

Line broadening: rotation, pressure, turbulence, and instruments

Line profiles are not infinitely narrow. Several effects broaden lines, and disentangling them is part of extracting stellar properties.

• Instrumental broadening: finite spectral resolution spreads a line. This sets a baseline width you must account for when interpreting physical broadening.
• Thermal broadening: atoms moving due to temperature produce Doppler broadening; lighter elements broaden more at the same temperature.
• Pressure (collisional) broadening: collisions perturb energy levels, widening lines, especially in dense atmospheres (high gravity).
• Rotational broadening: a rotating star has one limb approaching and the other receding, spreading line wavelengths. This produces a characteristic “flattened” profile and allows estimation of projected rotation speed (v sin i).
• Microturbulence/macroturbulence: non-thermal motions in the atmosphere broaden lines and can mimic rotation in some regimes.

Broadening is not just a nuisance; it is evidence. For example, rapid rotators (many early-type stars) show noticeably broadened metal lines, while many giants show narrower lines but can have macroturbulent broadening.

Step-by-step: estimating projected rotation (v sin i) from line profiles

• 1) Pick suitable lines: choose isolated, moderately strong metal lines (not heavily pressure-broadened and not strongly blended). Avoid very deep saturated lines.
• 2) Determine instrumental resolution: obtain the spectrograph’s resolving power R or measure the width of narrow calibration lines. Convert this to an instrumental broadening kernel.
• 3) Create a template: use a slowly rotating star of similar spectral type or a synthetic spectrum as a narrow-lined reference.
• 4) Convolve the template: broaden the template with rotational kernels for a range of v sin i values, also including instrumental broadening.
• 5) Fit to the observed line: minimize residuals between observed and broadened template across the line profile. Use multiple lines and average results.
• 6) Report limitations: v sin i includes the unknown inclination i; low v sin i can be hard to distinguish from other broadening sources.

Surface gravity (log g): dwarfs vs giants in the spectrum

Surface gravity influences atmospheric pressure, which affects ionization balance and pressure broadening. Two stars with the same effective temperature but different radii (a dwarf and a giant) can show noticeably different spectra.

Gravity-sensitive indicators include:

• Pressure-broadened wings of certain strong lines (e.g., Balmer wings in A stars; some alkali lines in cooler stars).
• Line ratios where one line strengthens with pressure while another does not, providing a differential diagnostic.
• Molecular band behavior in cool stars, where gravity affects atmospheric structure and band strengths.

In quantitative analysis, log g is often constrained by fitting many lines simultaneously with model atmospheres. Conceptually, you are using the spectrum to infer how dense the line-forming region must be to produce the observed profiles.

Metallicity and chemical patterns: beyond “what elements are present”

In stellar astrophysics, “metallicity” usually means the overall abundance of elements heavier than helium, often summarized as [Fe/H]. Spectra allow you to go further: you can infer abundance patterns (e.g., alpha-elements like Mg, Si, Ca relative to Fe), which reflect nucleosynthesis and star formation environments. The physical evidence is again in line strengths, but interpretation requires controlling for temperature and gravity.

Two practical cautions:

• Blending increases in cool, metal-rich stars: many lines overlap, making continuum placement and individual EW measurements harder.
• Non-LTE and 3D effects: some lines form under conditions where simple assumptions break down, shifting inferred abundances. In many educational and introductory analyses, you can treat these as systematic uncertainties and prefer lines known to be robust.

Emission lines as diagnostics of temperature and density in gas

Not all spectra are stellar absorption spectra. In ionized nebulae, emission lines dominate and provide direct diagnostics of physical conditions. Different lines arise from different excitation mechanisms and energy levels. Ratios of certain lines can be sensitive to electron temperature and density because collisional excitation and radiative decay compete in predictable ways.

Examples of what emission lines can tell you:

• Composition: presence of lines from O, N, S, Ne, He indicates which elements are in the gas.
• Ionization state: relative strengths of lines from different ions (e.g., O II vs O III) indicate how hard the radiation field is.
• Physical conditions: some line ratios are temperature-sensitive, others density-sensitive, allowing you to estimate electron temperature and density in the emitting region.

Even if your main focus is stars, it is useful to recognize that spectra are a general-purpose physics probe: the same principles apply, but the environment (photosphere vs diffuse gas) changes which features dominate.

Putting it together: a practical spectral “evidence checklist” for a star

When you receive an unknown stellar spectrum, you can treat the analysis like a structured investigation. The aim is to extract temperature, composition indicators, and key stellar properties without relying on a single feature.

• 1) Continuum shape: is it blue, flat, or red? Are there broad depressions from line blanketing or molecular bands? This gives a first temperature estimate.
• 2) Dominant features: identify the strongest lines/bands (Balmer series, Ca II H&K, Na I D, Mg b, TiO bands). This narrows spectral type.
• 3) Gravity clues: look for pressure-broadened wings and gravity-sensitive line ratios to distinguish dwarf vs giant.
• 4) Metallicity impression: are metal lines generally weak or strong compared to a reference of similar type? This suggests low or high [Fe/H].
• 5) Broadening and rotation: are lines sharp or smeared? If broadened, consider v sin i and other broadening sources.
• 6) Consistency checks: verify that temperature inferred from continuum agrees with temperature implied by ionization/excitation (e.g., presence of ionized lines, strength of Balmer lines).

This checklist is intentionally redundant: spectra are rich, and robust inference comes from multiple, consistent pieces of evidence.

Worked mini-example: interpreting two simplified spectra

Spectrum A: blue continuum; very strong, broad Balmer absorption lines; relatively weak metal lines; lines moderately broadened. Interpretation: effective temperature likely around the A-star regime; Balmer strength suggests near the peak of Balmer-line strength; broad wings indicate significant pressure broadening consistent with a main-sequence star (higher gravity) unless other evidence suggests otherwise; moderate broadening could indicate rotation.

Spectrum B: red continuum; deep molecular bands (TiO-like) across the optical; strong neutral metal lines; very weak Balmer lines. Interpretation: cool atmosphere (late K to M type); molecules indicate low temperature; Balmer weakness consistent with cool photosphere; gravity assessment would use specific gravity-sensitive features, but the overall appearance is consistent with a cool dwarf or giant depending on band shapes and line widths.

Even without computing exact parameters, these spectra already constrain physical properties strongly. Quantitative fitting refines the estimates, but the physical evidence is visible directly in the spectral structure.

Practical pitfalls and how to avoid them

• Confusing reddening with temperature: dust can make a hot star look cooler by reddening the continuum. Use line-based temperature indicators (Balmer profiles, ionization ratios) as cross-checks.
• Misplacing the continuum: in crowded spectra (cool or metal-rich stars), the “true” continuum may be hard to find. Use local pseudo-continuum regions consistently and compare to templates.
• Line blending: an apparent single line may be multiple blended lines. Prefer isolated lines for EW and rotation measurements or use full-spectrum fitting.
• Resolution limits: low resolution can wash out narrow lines and mimic broadening. Always interpret line widths relative to instrumental resolution.
• Over-interpreting one feature: robust inference uses multiple lines and the continuum together, because many parameters (T, log g, [Fe/H]) interact.

Full-spectrum fitting as a unified approach

Instead of measuring individual lines, you can fit the entire observed spectrum with a grid of model spectra or empirical templates. The fit adjusts parameters such as effective temperature, surface gravity, metallicity, radial velocity shift, and broadening to minimize differences across many wavelengths at once. This approach naturally uses all available information and handles blending better than isolated-line methods.

A practical workflow for full-spectrum fitting:

• 1) Prepare the spectrum: ensure wavelength solution is consistent; mask bad pixels and strong telluric regions; optionally normalize or fit with a flexible continuum polynomial.
• 2) Choose a model grid: select synthetic spectra spanning plausible ranges of T, log g, and [Fe/H], or use a library of observed templates.
• 3) Include nuisance parameters: allow for a radial-velocity shift and a broadening kernel (instrumental plus rotation/turbulence).
• 4) Fit and inspect: examine residuals to see which regions drive mismatches (e.g., molecular bands, Balmer cores). Adjust masks or model choices if needed.
• 5) Validate with feature checks: confirm that key diagnostic lines are matched, not just the overall shape.

Full-spectrum fitting does not replace physical understanding; it operationalizes it. Knowing which features constrain which parameters helps you diagnose why a fit succeeds or fails and prevents you from accepting a numerically “good” fit that is physically inconsistent.