Spectra & Composition

Part 3: The OBAFGKM Sequence — Temperature, Not Composition

A Temperature Sequence in Disguise

In the early 1900s, astronomers at Harvard Observatory — led by Annie Jump Cannon and Williamina Fleming — classified hundreds of thousands of stellar spectra by eye, sorting them by the appearance and strength of their spectral lines. After much rearranging, the sequence settled into O, B, A, F, G, K, M — from strongest helium lines to strongest molecular bands. The classic mnemonic: “Oh Be A Fine Guy/Girl, Kiss Me.”

The breakthrough came when Cecilia Payne-Gaposchkin showed in her 1925 PhD thesis — arguably the most important doctoral dissertation in the history of astronomy — that stars are overwhelmingly hydrogen and helium, and that the spectral sequence is fundamentally a temperature sequence, not a composition sequence. This was so radical that her advisor, Henry Norris Russell, initially urged caution (he later acknowledged she was right). Stellar composition is remarkably uniform (about 74% hydrogen, 25% helium, 1–2% heavier elements by mass). What changes along the sequence is not what atoms are present but which quantum states those atoms occupy — and that depends on temperature.

Before you read the sequence as letters in a table, look at the sky the way an observer does first: stars already announce that they are not thermally identical. A real star field shows blue-white, yellow, and orange-red stars sharing the same patch of sky. Spectroscopy explains why those colors differ, but the diversity is visible before any prism enters the story.

Several examples are giants or supergiants rather than main-sequence dwarfs — those are the ones bright enough to have names. The prevalence column refers to main-sequence stars only.

Look at the prevalence column: M dwarfs make up over three-quarters of all main-sequence stars, yet they’re too faint to see with the naked eye. The bright stars that fill constellations — Rigel (B supergiant), Sirius (A dwarf), Arcturus (K giant) — are the rare luminous ones. The galaxy is dominated by cool, dim, long-lived M dwarfs.

Why Temperature Controls Line Strength

This is a critical conceptual point that trips up beginners: spectral type does NOT directly reflect composition. All main-sequence stars have roughly the same composition. What changes is which atomic transitions are active — and that depends on temperature through the Boltzmann distribution.

For an atom to absorb a photon at a given wavelength, an electron must already be in the right starting energy level. The fraction of atoms in any given level depends on temperature through the Boltzmann distribution:

$\text{fraction in level } n \propto e^{-\chi_n / k_B T}$

where $\chi_n$ is the excitation energy — the energy above the ground state needed to reach level $n$ (always positive) — and $k_B = 8.617 \times 10^{-5}\ \text{eV/K}$ is Boltzmann’s constant. For hydrogen, $\chi_2 = 10.2\ \text{eV}$ (the energy to excite from $n = 1$ to $n = 2$). Note $\chi_n$ is not the Bohr energy $E_n$ used earlier — it’s the gap $\chi_n = E_n - E_1$, which is always positive.

The exponential is ruthless: even modest temperature changes dramatically shift which levels are populated. Higher excitation energy $\chi_n$ demands higher temperature for significant population. As a rough guide, every factor-of-two increase in temperature can boost high-energy level populations by orders of magnitude.

(More precisely, the full Boltzmann expression includes degeneracy factors $g_n$ and a partition function in the denominator, but the key physics — exponential sensitivity to $\chi_n/k_BT$ — is captured above.)

How this creates the spectral sequence:

O stars (30,000+ K): so hot that collisions ionize most hydrogen — electrons are stripped free. No neutral hydrogen means weak Balmer lines. Instead we see lines of ionized helium (He II), which requires extreme temperatures. (The governing physics is the Saha equation, which we won’t derive — but the idea is simple: hot enough collisions knock electrons free entirely.)

A stars (7,500–10,000 K): the Goldilocks temperature for hydrogen Balmer absorption. Balmer strength reflects a competition between excitation and ionization: the Boltzmann factor sets what fraction of neutral atoms are in $n = 2$, while the Saha equation sets what fraction are neutral at all. At A-star temperatures, enough hydrogen stays neutral and enough of it is excited to $n = 2$ that Balmer absorption is maximally efficient. H lines are strongest here.

G stars (5,800 K, like the Sun): Balmer lines are weaker — fewer atoms sit in $n = 2$. Metal absorption lines become prominent: ionized calcium (Ca II H & K at 393.4 and 396.8 nm), neutral iron, sodium (the D lines at 589.0 and 589.6 nm). The spectrum looks like a forest of metallic lines.

M stars (below 3,700 K): so cool that atoms stay neutral and even molecules form. Titanium oxide (TiO) produces broad absorption bands dominating the red and infrared. Balmer lines are very weak because almost no atoms are in $n = 2$.

Metallicity: A Secondary Effect

Metallicity ($Z$) is the mass fraction of elements heavier than helium. The Sun has $Z_\odot \approx 0.014$ — about 1.4% of its mass is “metals” (everything heavier than He, in astronomical parlance; older references cite 0.02, since revised downward). High-metallicity stars show more and stronger metal absorption lines; low-metallicity stars appear “cleaner.” But metallicity is a second-order effect for classification: two stars at the same temperature with different metallicities have the same spectral type — the metal-line strengths differ, but the overall pattern is set by temperature.

Part 3 takeaway: OBAFGKM is a temperature sequence. Composition is nearly uniform across stars — what changes is which energy levels are populated, exponentially sensitive to temperature. Spectral type tells you temperature; metallicity and luminosity class add refinement.