No abstract

Radial and nonradial oscillations offer the opportunity to investigate the interior properties of stars. We use 2D stellar models and a 2D finite difference integration of the linearized pulsation equations to calculate non-radial oscillations. This approach allows us to directly calculate the pulsation modes for a distorted rotating star without treating the rotation as a perturbation. We are also able to express the finite difference solution in the horizontal direction as a sum of multiple spherical harmonics for any given mode. Using these methods, we have investigated the effects of increasing rotation and the number of spherical harmonics on the calculated eigenfrequencies and eigenfunctions and compared the results to perturbation theory. In slowly rotating stars, current methods work well, and we show that the eigenfunction can be accurately modelled using 2nd order perturbation theory and a single spherical harmonic. We use 10 Msun models with velocities ranging from 0 to 420 km/s (0.89 Omega_c) and examine low order p modes. We find that one spherical harmonic remains reasonable up to a rotation rate around 300km s^{-1} (0.69 Omega_c) for the radial fundamental mode, but can fail at rotation rates as low as 90 km/s (0.23 Omega_c) for the 2H mode or l = 2 p_2 mode, based on the eigenfrequencies alone. Depending on the mode in question, a single spherical harmonic may fail at lower rotation rates if the shape of the eigenfunction is taken into consideration. Perturbation theory, in contrast, remains valid up to relatively high rotation rates for most modes. We find the lowest failure surface equatorial velocity is 120 km/s (0.30 Omega_c) for the l = 2 p_2 mode, but failure velocities between 240 and 300 km/s (0.58-0.69 Omega_c)are more typical.Comment: accepted for publication in Ap

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 ( 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.

We have investigated the effects of uniform rotation and a specific model for differential rotation on the pulsation frequencies of 10 M ⊙ stellar models. Uniform rotation decreases the frequencies for all modes. Differential rotation does not appear to have a significant effect on the frequencies, except for the most extreme differentially rotating models. In all cases, the large and small separations show the effects of rotation at lower velocities than do the individual frequencies. Unfortunately, to a certain extent, differential rotation mimics the effects of more rapid rotation, and only the presence of some specific observed frequencies with well identified modes will be able to uniquely constrain the internal rotation of pulsating stars.