The atmospheres of type II supernovae and the Expanding Photosphere Method

The Expanding Photosphere Method (EPM) determines distances to Type II supernova (SNe II) by comparing the photospheric angular size with the expansion velocity measured from spectral lines. The photospheres of SNe II are low density and are dominated by electron scattering, and consequently the photospheric flux is dilute relative to a Planck function at the best-fitting continuum color temperature. The reliability of EPM distances depends on understanding how the dilution is related to physical properties of the supernova atmosphere. To study this, we have calculated 63 different model atmospheres relevant to SNe II. The excitation, ionization, and thermal structure are described for the case of high effective temperature in which the atmosphere is completely ionized, and for the case of cooler effective temperatures in which the photosphere is formed in a region of recombining hydrogen. The general spectral features of both cases are discussed. We explore how the computed spectrum changes with density structure, helium abundance, metallicity, expansion rate, and luminosity or effective temperature. The most important variable in determining spectral appearance is the effective temperature. The amount by which the emergent flux is dilute relative to the best-fitting blackbody depends on a number of factors, most important of which are the temperature and, in short-wavelength bandpasses, density at the photosphere. For each of the models we derive distance correction factors for application in EPM, using the four filter combinations {BV}, {VI_c}, {BVI_c}, and {JHK}. The main differences may-be expressed in terms of the observable color temperature and a slowly varying dependence on density. Functional fits to the distance correction factor are provided which can be used to estimate the photospheric angular size from broadband photometry. The effect of uncertain dust extinction on angular size is shown to be small. This work places EPM on a firm theoretical foundation and substantiates the Hubble constant measurement by Schmidt et al. of H₀ = 73 ± 7.