Hydrogen recombination at high optical depth and the spectrum of SN 1987A

A general theory is presented for hydrogen recombination line formation in an expanding medium in which some of the lines are optically thick. This theory is used to calculate the time evolution of the hydrogen lines of SN 1987A at t equal to or greater than 150 days, assuming that the supernova envelope is a homologously expanding uniform sphere. The theoretical luminosities and ratios of the recombination lines agree remarkably well with the observations. For the first 2 yr, the supernova envelope is optically thick to Balmer continuum. For t equal to or less than 400 days, hydrogen is ionized primarily from the n = 2 level by Balmer continuum photons, which are provided partly by the two-photon decay of the 2s state and partly by emission lines of heavy elements.