We have calculated the pulsations of massive stars using a nonlinear hydrodynamic code including time-dependent convection. The basic structure models are based on a standard grid published by Meynet et al. (1994). Using the basic structure, we calcu
lated envelope models, which include the outer few percent of the star. These models go down to depths of at least 2 million K. These models, which range from 40 to 85 solar masses, show a range of pulsation behaviours. We find models with very long period pulsations ( $>$ 100 d), resulting in high amplitude changes in the surface properties. We also find a few models that show outburst-like behaviour. The details of this behaviour are discussed, including calculations of the resulting wind mass-loss rates.
A large number of massive stars are known to rotate, resulting in significant distortion and variation in surface temperature from the pole to the equator. Radiatively driven mass loss is temperature dependent, so rapid rotation produces variation in
mass loss and angular momentum loss rates across the surface of the star, which is expected to affect the evolution of rapidly rotating massive stars. In this work, we investigate the two dimensional effects of rotation on radiatively driven mass loss and the associated loss of angular momentum in ZAMS models with solar metallicity. Using 2D stellar models, which give the variation in surface parameters as a function of co-latitude, we implement two different mass loss prescriptions describing radiatively driven mass loss. We find a significant variation in mass loss rates and angular momentum loss as a function of co-latitude. We find that the mass loss rate decreases as the rotation rate increases for models at constant initial mass, and derive scaling relations based on these models. When comparing 2D to 1D mass loss rates, we find that although the total angle integrated mass loss does not differ significantly, the 2D models predict less mass loss from the equator and more mass loss from the pole than the 1D predictions using von Zeipels law. As a result, rotating models lose less angular momentum in 2D than in 1D, which will change the subsequent evolution of the star. The evolution of these models will be investigated in future work.
(abridged) Recent work on several beta Cephei stars has succeeded in constraining both their interior rotation profile and their convective core overshoot. In particular, a recent study focusing on theta$ Oph has shown that a convective core overshoo
t parameter of alpha = 0.44 is required to model the observed pulsation frequencies, significantly higher than for other stars of this type. We investigate the effects of rotation and overshoot in early type main sequence pulsators, and attempt to use the low order pulsation frequencies to constrain these parameters. This will be applied to a few test models and theta Oph. We use a 2D stellar evolution code and a 2D linear adiabatic pulsation code to calculate pulsation frequencies for 9.5 Msun models. We calculate low order p-modes for models with a range of rotation rates and convective core overshoot parameters. Using these models, we find that the convective core overshoot has a larger effect on the pulsation frequencies than the rotation, except in the most rapidly rotating models considered. When the differences in radii are accounted for by scaling the frequencies, the effects of rotation diminish, but are not entirely accounted for. We find that increasing the convective core overshoot decreases the large separation, while producing a slight increase in the small separations. We created a model frequency grid which spanned several rotation rates and convective core overshoot values. Using a modified chi^2 statistic, we are able to recover the rotation velocity and core overshoot for a few test models. Finally, we discuss the case of the beta Cephei star theta Oph. Using the observed frequencies and a fixed mass and metallicity, we find a lower overshoot than previously determined, with alpha = 0.28 +/- 0.05. Our determination of the rotation rate agrees well with both previous work and observations, around 30 km/s.
We have investigated the effects of uniform rotation and a specific model for differential rotation on the pulsation frequencies of 10 Msun stellar models. Uniform rotation decreases the frequencies for all modes. Differential rotation does not appea
r 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 o f 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.
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.
