Questions: Stellar Photometry, Colors, and Spectral Classification

Question 1

Two stars are measured. Star X has a B−V color index of −0.3. Star Y has a B−V color index of +1.6. Which star has a higher surface temperature?

• A. Star Y — a larger color index means more total luminosity, which indicates greater energy output and temperature
• B. Star X — a smaller or negative B−V means the star is relatively brighter in blue light, indicating higher temperature
• C. Neither — B−V measures chemical composition, not temperature
• D. Star Y — positive B−V values indicate ultraviolet emission characteristic of hot stars

Answer: (B)

B−V is the difference in magnitude between blue and visual filters. Because magnitudes are on a reversed scale (smaller magnitude = brighter), a small or negative B−V means the star is brighter in blue than in visual — indicating its emission peaks toward shorter wavelengths and therefore a higher surface temperature. Star X with B−V = −0.3 is blue-white and hot (like an O or B star). Star Y with B−V = +1.6 is relatively brighter in visual light, indicating a cool red star. Option D has the relationship backwards — O-type stars (hot, blue) have negative or very small B−V values.

Question 2

O-type stars have surprisingly weak hydrogen absorption lines despite hydrogen being by far their most abundant element. What is the correct explanation?

• A. O-type stars have fused most of their hydrogen into helium through nuclear burning
• B. At extremely high temperatures (above ~30,000 K), hydrogen is mostly ionized and has no bound electrons available to absorb photons at visible wavelengths
• C. O-type stars rotate so rapidly that spectral lines are broadened beyond detectability
• D. Hydrogen absorption only occurs in cool stars where molecules can form

Answer: (B)

Spectral line strengths depend on both the abundance of an element and the physical state of its atoms at the star's surface temperature. In O-type stars, temperatures exceed 30,000 K, which is hot enough to strip electrons from most hydrogen atoms — the hydrogen is ionized. Ionized hydrogen (a bare proton) cannot absorb photons at hydrogen's characteristic wavelengths because those absorption transitions require a bound electron. The hydrogen is present in enormous quantities, but it's in the wrong physical state to produce absorption lines. A-type stars (~10,000 K) show the strongest hydrogen lines because the temperature is 'just right' to populate the energy levels involved in visible-light absorption transitions.

Question 3

A star with a large positive B−V color index is hotter than a star with a small or negative B−V color index.

• T. True
• F. False

Answer: False

This reverses the relationship. A large positive B−V means the star is relatively fainter in blue light compared to visual — its emission peaks at longer (redder) wavelengths, indicating a lower surface temperature. Cool M-type stars have large positive B−V values. Hot O- and B-type stars have small or negative B−V values because they emit proportionally more blue light. The intuition is that hotter objects (like a blue flame) appear bluer, which means relatively more blue light — a smaller B−V. Cooler objects (like a red ember) appear redder — a larger B−V.

Question 4

A star's spectral type provides information about both its surface temperature and the chemical composition of its atmosphere.

• T. True
• F. False

Answer: True

Spectral classification does reveal both. The spectral sequence O–B–A–F–G–K–M is primarily a temperature sequence, but the specific pattern of absorption lines encodes chemical information as well. The presence and strength of lines from calcium, sodium, titanium oxide, iron, and other species tells astronomers which elements are present and in what ionization states in the star's photosphere. The Sun's G2 classification signals not just its temperature (~5,800 K) but also that it displays prominent ionized calcium H and K lines and neutral metal lines — chemical fingerprints. Deviations from expected line strengths for a given temperature class can reveal unusual abundances.

Question 5

Why do A-type stars show the strongest hydrogen absorption lines even though many other star types also contain large amounts of hydrogen?

Model answer: Hydrogen absorption line strength depends not just on how much hydrogen is present but on how many hydrogen atoms are in the right energy state to absorb visible light. In very hot O- and B-type stars, hydrogen is mostly ionized — no bound electrons, no absorption. In very cool K- and M-type stars, hydrogen atoms are in their lowest energy state (ground state) and require ultraviolet, not visible, photons to be excited — so visible absorption lines are weak. A-type stars (~10,000 K) hit the temperature 'sweet spot' where a significant fraction of hydrogen atoms have electrons in the first excited state (n=2), which is exactly the configuration needed to absorb visible-wavelength photons (the Balmer series). Temperature determines the population of that energy level.

This is the key insight that explains why spectral classification reflects temperature: absorption lines are 'thermometers' for the stellar photosphere. The same principle applies to other elements — calcium lines peak in G/K stars, titanium oxide only appears in cool M stars because molecules are destroyed at higher temperatures. Astronomers reading a spectrum aren't just cataloging what elements are present; they're reading the temperature from which quantum transitions are populated. This is what makes spectroscopy so powerful: a single spectrum encodes temperature, composition, and surface gravity.