ASTR 230 Lecture 02 Notes

Context and Why This Matters

Annie Jump Cannon and colleagues at Harvard classified hundreds of thousands of stellar spectra by eye in the early twentieth century, originally in an alphabetical sequence (A, B, C, ...) that seemed to track line strength. Only later did Cecilia Payne-Gaposchkin show, in her 1925 PhD thesis, that the sequence is really a temperature sequence and that stars are overwhelmingly hydrogen and helium — a result initially doubted because it contradicted the prevailing assumption that stars had roughly Earth-like compositions.

Learning Goals

Explain the OBAFGKM spectral sequence as a temperature sequence, not a composition sequence.
Describe why hydrogen absorption lines are strongest around spectral type A rather than in the hottest or coolest stars.
Use spectral type and luminosity class together to identify a star’s evolutionary state.

Opening Phenomenon

Vega (spectral type A0V, T_eff ≈ 9602 K) shows very strong hydrogen absorption lines. The Sun (G2V, T_eff ≈ 5778 K) shows much weaker hydrogen lines but strong lines of ionized calcium. Rigel (B8Ia, T_eff ≈ 12100 K) shows weaker hydrogen lines than Vega despite being hotter. All three stars are overwhelmingly hydrogen by mass.

Terms Developed in Context

These terms form the reasoning chain from observation to model, calculation, and interpretation. Each entry expands the corresponding term-explorer panel and should be read alongside the worked example.

spectral type (OBAFGKM)

Spectral type is set by surface temperature: which atomic transitions are visible depends on what fraction of atoms are in the right excitation and ionization state to absorb a given wavelength, and that fraction is a strong, non-monotonic function of temperature.

Use and relationship: Describe why hydrogen absorption lines are strongest around spectral type A rather than in the hottest or coolest stars. The lecture's quantitative connection is \( \text{line strength} = f(\text{ionization/excitation fraction}) = g(T_{\rm eff}),\ \text{non-monotonic in } T_{\rm eff} \), which shows how this term participates in the model rather than functioning as an isolated label.

Boundary or confusion: Assuming that strong hydrogen lines mean "more hydrogen" and weak hydrogen lines mean "less hydrogen." Line strength primarily reflects excitation/ionization state (i.e., temperature), not elemental abundance.

luminosity class (Ia-V)

Luminosity class (from line widths, sensitive to surface gravity) distinguishes a main-sequence dwarf from a giant or supergiant of the same temperature, resolving the ambiguity that temperature alone cannot fix size.

Use and relationship: Use spectral type and luminosity class together to identify a star’s evolutionary state. The lecture's quantitative connection is \( \text{line strength} = f(\text{ionization/excitation fraction}) = g(T_{\rm eff}),\ \text{non-monotonic in } T_{\rm eff} \), which shows how this term participates in the model rather than functioning as an isolated label.

ionization state

Use and relationship: Assuming that strong hydrogen lines mean "more hydrogen" and weak hydrogen lines mean "less hydrogen." Line strength primarily reflects excitation/ionization state (i.e., temperature), not elemental abundance. The lecture's quantitative connection is \( \text{line strength} = f(\text{ionization/excitation fraction}) = g(T_{\rm eff}),\ \text{non-monotonic in } T_{\rm eff} \), which shows how this term participates in the model rather than functioning as an isolated label.

absorption line

Describe why hydrogen absorption lines are strongest around spectral type A rather than in the hottest or coolest stars.

Use and relationship: Hydrogen (Balmer) absorption lines peak in strength around spectral type A (T_eff ≈ 9,000-10,000 K), not at the hottest O stars or the coolest M stars. The lecture's quantitative connection is \( \text{line strength} = f(\text{ionization/excitation fraction}) = g(T_{\rm eff}),\ \text{non-monotonic in } T_{\rm eff} \), which shows how this term participates in the model rather than functioning as an isolated label.

excitation temperature

Use and relationship: The OBAFGKM sequence orders stars by temperature, using ionization and excitation physics, not composition, to explain why line strengths rise and fall non-monotonically across it. The lecture's quantitative connection is \( \text{line strength} = f(\text{ionization/excitation fraction}) = g(T_{\rm eff}),\ \text{non-monotonic in } T_{\rm eff} \), which shows how this term participates in the model rather than functioning as an isolated label.

spectroscopic parallax

Evidence

Hydrogen (Balmer) absorption lines peak in strength around spectral type A (T_eff ≈ 9,000-10,000 K), not at the hottest O stars or the coolest M stars.
The hottest O and B stars show strong ionized helium lines instead, because their higher temperatures ionize most hydrogen atoms, removing the bound electron needed to produce a Balmer absorption line.
The coolest K and M stars show strong molecular bands (e.g., titanium oxide) because low temperatures allow molecules to survive without being dissociated by collisions.

Model

Spectral type is set by surface temperature: which atomic transitions are visible depends on what fraction of atoms are in the right excitation and ionization state to absorb a given wavelength, and that fraction is a strong, non-monotonic function of temperature.
A star’s line strengths therefore measure temperature (and, more weakly, pressure/density) even though essentially all stars share the same dominant composition (about 70% hydrogen, 28% helium by mass).
Luminosity class (from line widths, sensitive to surface gravity) distinguishes a main-sequence dwarf from a giant or supergiant of the same temperature, resolving the ambiguity that temperature alone cannot fix size.

Working Equation

\[ \text{line strength} = f(\text{ionization/excitation fraction}) = g(T_{\rm eff}),\ \text{non-monotonic in } T_{\rm eff} \]

Worked Example

Rank by T_eff: Rigel (12100 K, B8Ia) > Vega (9602 K, A0V) > Sun (5778 K, G2V) > Betelgeuse (3600 K, M1-2Ia).
Yet Balmer line strength peaks at Vega’s A0 type, not at hotter Rigel: above about 10,000 K, collisions with free electrons increasingly ionize hydrogen past neutral, removing the electron needed for a Balmer transition.
Below about 5,000-6,000 K (Sun and cooler), most hydrogen remains in its unexcited ground state, unable to absorb visible-light Balmer photons, so Balmer lines weaken again even though the gas is still overwhelmingly hydrogen.
This non-monotonic behavior is exactly why the historical alphabetical line-strength ordering (A, B, C, ...) had to be reshuffled into the temperature-ordered OBAFGKM sequence once the physics were understood.

Common Misconception

Assuming that strong hydrogen lines mean "more hydrogen" and weak hydrogen lines mean "less hydrogen." Line strength primarily reflects excitation/ionization state (i.e., temperature), not elemental abundance.

Active-Learning Guidance

Given three unlabeled spectra (strong Balmer lines; strong ionized helium lines; strong molecular bands), assign each to hot/intermediate/cool without additional information, and justify each assignment.

Lab Connection

Lab 01 uses each sample star’s spectral type and T_eff to place it correctly on the Hertzsprung-Russell diagram’s temperature axis.

Synthesis Questions

What was measured directly in this lecture’s worked example, and what was inferred from the model?
Which assumption would most change the interpretation if it were wrong?
How does this lecture’s technique connect to the lab and problem set that follow it?

References

OpenStax Astronomy 2e, Chapter 17.1-17.4 (the brightness/spectra of stars and spectral classification) and Chapter 5.5 (formation of spectral lines).
Local reference copy: references/openstax-astronomy-2e-extracted.txt.