Surface trapping and leakage of low-frequency g-modes in rotating early-type stars -- I. Qualitative analysis

A qualitative study of the surface trapping of low-frequency non-radial g-modes in rotating early-type stars is undertaken within the Cowling, adiabatic and traditional approximations. It is demonstrated that, at frequencies below a cut-off, waves cannot be fully trapped within the star, and will leak through the surface. Expressions for the cut-off frequency are derived in both the non-rotating and rotating cases; it is found from these expressions that the cut-off frequency increases with the rotation rate for all but prograde sectoral modes. The results are of possible relevance to the 53 Per and SPB classes of variable star, which exhibit pulsation frequencies of the same order of magnitude as the cut-off frequencies found for the stellar model. It is suggested that observations either of an upper limit on variability periods (corresponding to the cut-off), or of line-profile variations due to leaking modes, may permit asteroseismological studies of the outer layers of these systems.Comment: 8 pages, 2 figures, to be published in MNRA

Excitation of g modes in Wolf-Rayet stars by a deep opacity bump

We examine the stability of l=1 and l=2 g modes in a pair of nitrogen-rich Wolf-Rayet stellar models characterized by differing hydrogen abundances. We find that modes with intermediate radial orders are destabilized by a kappa mechanism operating on an opacity bump at an envelope temperature log T ~ 6.25. This `deep opacity bump' is due primarily to L-shell bound-free transitions of iron. Periods of the unstable modes span ~ 11-21 hr in the model containing some hydrogen, and ~ 3-12 hr in the hydrogen-depleted model. Based on the latter finding, we suggest that self-excited g modes may be the source of the 9.8 hr-periodic variation of WR 123 recently reported by Lefevre et al. (2005).Comment: 5 pages, 3 figures, accepted by MNRAS letter

Centrifugal Breakout of Magnetically Confined Line-Driven Stellar Winds

We present 2D MHD simulations of the radiatively driven outflow from a rotating hot star with a dipole magnetic field aligned with the star's rotation axis. We focus primarily on a model with moderately rapid rotation (half the critical value), and also a large magnetic confinement parameter, $\eta_{\ast} \equiv B_{\ast}^2 R_{\ast}^{2} / \dot{M} V_{\infty} = 600$. The magnetic field channels and torques the wind outflow into an equatorial, rigidly rotating disk extending from near the Kepler corotation radius outwards. Even with fine-tuning at lower magnetic confinement, none of the MHD models produce a stable Keplerian disk. Instead, material below the Kepler radius falls back on to the stellar surface, while the strong centrifugal force on material beyond the corotation escape radius stretches the magnetic loops outwards, leading to episodic breakout of mass when the field reconnects. The associated dissipation of magnetic energy heats material to temperatures of nearly $10^{8}$K, high enough to emit hard (several keV) X-rays. Such \emph{centrifugal mass ejection} represents a novel mechanism for driving magnetic reconnection, and seems a very promising basis for modeling X-ray flares recently observed in rotating magnetic Bp stars like $\sigma$ Ori E.Comment: 5 pages, 3 figures, accepted by ApJ

Influence of the Coriolis force on the instability of slowly pulsating B stars

This paper explores the effect of rotation on the kappa-mechanism instability of slowly pulsating B stars. A new nonadiabatic code, that adopts the so-called `traditional approximation' to treat the Coriolis force, is used to investigate the influence exerted by rotation over the stability of stellar models covering the mass range 2.5 M_sun <= M_* <= 13.0 M_sun. The principal finding is that, for all modes considered apart from the prograde sectoral class, rotation shifts the kappa-mechanism instability toward higher luminosities and effective temperatures; these shifts are accompanied by broadenings in the extent of instability strips. Such behaviour is traced to the shortening of mode periods under the action of the Coriolis force. Instability strips associated with prograde sectoral modes behave rather differently, being shifted to marginally lower luminosities and effective temperatures under the influence of rotation. The implications of these results are discussed in the context of the observational scarcity of pulsation in B-type stars having significant rotation; various scenarios are explored to explain the apparent dichotomy between theory and observations. Furthermore, the possible significance of the findings to Be stars is briefly examined.Comment: 14 pages, 4 figures, to be published by MNRA

A Rigid-Field Hydrodynamics approach to modeling the magnetospheres of massive stars

We introduce a new Rigid-Field Hydrodynamics approach to modeling the magnetospheres of massive stars in the limit of very-strong magnetic fields. Treating the field lines as effectively rigid, we develop hydrodynamical equations describing the 1-dimensional flow along each, subject to pressure, radiative, gravitational, and centrifugal forces. We solve these equations numerically for a large ensemble of field lines, to build up a 3-dimensional time-dependent simulation of a model star with parameters similar to the archetypal Bp star sigma Ori E. Since the flow along each field line can be solved for independently of other field lines, the computational cost of this approach is a fraction of an equivalent magnetohydrodynamical treatment. The simulations confirm many of the predictions of previous analytical and numerical studies. Collisions between wind streams from opposing magnetic hemispheres lead to strong shock heating. The post-shock plasma cools initially via X-ray emission, and eventually accumulates into a warped, rigidly rotating disk defined by the locus of minima of the effective (gravitational plus centrifugal) potential. But a number of novel results also emerge. For field lines extending far from the star, the rapid area divergence enhances the radiative acceleration of the wind, resulting in high shock velocities (up to ~3,000 km/s) and hard X-rays. Moreover, the release of centrifugal potential energy continues to heat the wind plasma after the shocks, up to temperatures around twice those achieved at the shocks themselves. Finally, in some circumstances the cool plasma in the accumulating disk can oscillate about its equilibrium position, possibly due to radiative cooling instabilities in the adjacent post-shock regions.Comment: 21 pages, 12 figures w/ color, accepted by MNRA

The Rigidly Rotating Magnetosphere of Sigma Ori E

We attempt to characterize the observed variability of the magnetic helium-strong star sigma Ori E in terms of a recently developed rigidly rotating magnetosphere model. This model predicts the accumulation of circumstellar plasma in two co-rotating clouds, situated in magnetohydrostatic equilibrium at the intersection between magnetic and rotational equators. We find that the model can reproduce well the periodic modulations observed in the star's light curve, H alpha emission-line profile, and longitudinal field strength, confirming that it furnishes an essentially correct, quantitative description of the star's magnetically controlled circumstellar environment.Comment: 4 pages, 3 figures, accepted by Ap