Rotational Splitting of Pulsational Modes

Mode splittings produced by uniform rotation and a particular form of differential rotation are computed for two-dimensional rotating 10 Mo ZAMS stellar models. The change in the character of the mode splitting is traced as a function of uniform rotation rate, and it is found that only relatively slow rotation rates are required before the mode splitting becomes asymmetric about the azimuthally symmetric (m=0) mode. Increased rotation produces a progressively altered pattern of the individual modes with respect to each other. Large mode splittings begin to overlap with the mode splittings produced by different radial and latitudinal modes at relatively low rotation rates. The mode splitting pattern for the differentially rotating stars we model is different than that for uniformly rotating stars, making the mode splitting a possible discriminant of the internal angular momentum distribution if one assumes the formidable challenge of mode identification can be overcome.Comment: 6 journal pages, 7 Figures, accepted by Ap

Pulsations as a Driver for LBV Variability

Among the most spectacular variable stars are the Luminous Blue Variables (LBVs), which can show three types of variability. The LBV phase of evolution is poorly understood, and the driving mechanisms for the variability are not known. The most common type of variability, the S Dor instability, occurs on timescales of tens of years. During an S Dor outburst, the visual magnitude of the star increases, while the bolometric magnitude stays approximately constant. In this work, we investigate pulsation as a possible trigger for the S Dor type outbursts. We calculate the pulsations of envelope models using a nonlinear hydrodynamics code including a time-dependent convection treatment. We initialize the pulsation in the hydrodynamic model based on linear non-adiabatic calculations. Pulsation properties for a full grid of models from 20 to 85 M$_{\odot}$ were calculated, and in this paper we focus on the few models that show either long-period pulsations or outburst-like behaviour, with photospheric radial velocities reaching 70-80 km/s. At the present time, our models cannot follow mass loss, so once the outburst event begins, our simulations are terminated. Our results show that pulsations alone are not able to drive enough surface expansion to eject the outer layers. However, the outbursts and long-period pulsations discussed here produce large variations in effective temperature and luminosity, which are expected to produce large variations in the radiatively driven mass-loss rates.Comment: 9 pages, 10 figures, accepted for publication in MNRA

Radial and Nonradial Oscillation Modes in Rapidly Rotating 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.Comment: accepted for publication in Ap

Rotation and Convective Core Overshoot in theta Ophiuchi

(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 overshoot 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.Comment: 10 pages, 14 figures. Accepted for publication in A&A

Effects of Uniform and Differential Rotation on Stellar Pulsations

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 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 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.Comment: 33 pages, 16 figures. Accepted for publication in Ap