Stellar Temperatures and Spectra

Treat a star as an approximate black body: its continuum spectrum is mainly set by surface temperature. Raising temperature moves the wavelength peak to shorter wavelengths and increases the area under the spectral power curve. A hot blue star emits across a range of wavelengths; its colour does not mean it emits blue light only.

Wien’s law gives temperature from the wavelength of maximum emission. Stefan’s law gives total luminosity from surface area and temperature. For a spherical star use surface area $4\pi R^2$, not the area of its visible disc.

The sequence O B A F G K M runs from hottest to coolest. O and B stars are blue, A blue-white, F white, G yellow-white, K orange and M red. Approximate class boundaries in kelvin are O: 25000–50000, B: 11000–25000, A: 7500–11000, F: 6000–7500, G: 5000–6000, K: 3500–5000 and M: below 3500.

O spectra show ionised helium as well as helium and hydrogen; B show helium and hydrogen; A have strongest hydrogen Balmer lines and ionised metals; F mainly ionised metals; G both ionised and neutral metals; K neutral metals; M neutral atoms and titanium oxide molecular bands. The pattern measures excitation and ionisation as well as composition.

Balmer absorption needs electrons initially in hydrogen’s $n=2$ level. In a cool atmosphere most atoms have electrons in the ground level, so few can absorb Balmer photons. At moderate temperatures more atoms occupy $n=2$ and the lines strengthen. At very high temperatures hydrogen becomes ionised, reducing the population of neutral atoms that can absorb. This explains strong Balmer lines in A stars without claiming that they necessarily contain the most hydrogen.

Try each problem before opening the worked solution. State the physical model, show substitutions with consistent units, and explain what your answer means.