Surface Temperature and Synthetic Spectral Energy Distributions for Rotationally Deformed Stars

Extreme deformation of a stellar surface, such as that produced by rapid rotation, causes the surface temperature and gravity to vary significantly with latitude. Thus, the spectral energy distribution (SED) of a nonspherical star could differ significantly from the SED of a spherical star with the same average temperature and luminosity. Calculation of the SED of a deformed star is often approximated as a composite of several spectra, each produced by a plane-parallel model of given effective temperature and gravity. The weighting of these spectra over the stellar surface, and hence the inferred effective temperature and luminosity, will be dependent on the inclination of the rotation axis of the star with respect to the observer, as well as the temperature and gravity distribution on the stellar surface. Here we calculate the surface conditions of rapidly rotating stars with a two-dimensional stellar structure and evolution code and compare the effective temperature distribution to that predicted by von Zeipel's law. We calculate the composite spectrum for a deformed star by interpolating within a grid of intensity spectra of plane-parallel model atmospheres and integrating over the surface of the star. This allows us to examine the SED for effects of inclination and degree of deformation based on the two-dimensional models. Using this method, we find that the deduced variation of effective temperature with inclination can be as much as 3000 K for an early B star, depending on the details of the underlying model. As a test case for our models, we examine the rapidly rotating star Achernar (a Eri, HD 10144). Recent interferometric observations have determined the star to be quite oblate. Combined with the ultraviolet SED measured by the OAO 2 satellite, we are able to make direct comparisons with observations.