12 - Spectrum analysis

Summary

The Balmer jump and the hydrogen lines

Hot stars

In Section 8.2 we saw that the Balmer discontinuity is determined by the ratio of the continuous absorption coefficients on both sides of this discontinuity. For hot stars we derived that the discontinuity is determined by the ratio of the number of hydrogen atoms in the second quantum level (absorbing shortward of 3647 Å) to the number of hydrogen atoms in the third quantum level (absorbing on the long wavelength side of 3647 Å). This ratio is completely determined by the temperature. For the B stars the temperature can in principle be determined from the Balmer discontinuity alone.

The pressure can be determined from the electron density n_e. For late B stars, for instance, the hydrogen is completely ionized, while the helium is not. Therefore, we know that n_e = H⁺ and N = n_e + H⁺ + He = n_e + H⁺ + 01H⁺ if the abundance of helium is 10% by number of atoms. With this we find

and, of course,

As we saw in the previous chapter, the number of free electrons can be determined from the hydrogen lines in two ways: either from the number of visible Balmer lines by means of the Inglis–Teller formula (equation 11.1), or by means of the hydrogen line wings. In Section 10.1 we saw that the line depth for optically thin lines is given by equation (10.8):

For the hot stars the continuous absorption coefficient K_c in the visual is due to the Paschen continuum, which means that it is due to absorption from the third level of the hydrogen atom.