Pattern formation in rapidly oscillating peculiar A stars

Abstract

Peculiar A stars harbour pairs of antipodal spots, detectable in magnetic-field variation and chemical-abundance anomalies, and which are inclined from the axis of rotation. Many of the stars are observed to oscillate nonradially with frequencies of high-order acoustic modes. The oscillations appear to be dipolar, with axes that are almost always more-or-less aligned with the spots. It is known theoretically that when the spots produce the dominating aspherical influence on the dynamics of the oscillations, there is always an oscillation eigenmode that is constrained to be aligned with the spots, in accord with the observations. But under some circumstances the spots may not have complete dynamical dominance, and Coriolis precession can prevent a pure mode from remaining aligned. Yet, the oscillations appear to be aligned. Here I investigate the proposal that in such circumstances what is being observed is not a single oscillation eigenmode, stationary with respect to the rotating star, but an ensemble of precessing modes whose envelope is almost stationary, and almost aligned with the spots. I present a one-dimensional toy model of a slowly drifting (standing) acoustic mode in a medium with thermal “spots”, and show that under appropriate conditions stationary, non-precessing, mode envelopes are possible.

Keywords:

• roAp Stars
• Stellar oscillations
• Magnetic convection
• Starspots

Acknowledgements

I thank Luis Balona, Don Kurtz and Hiromoto Shibahashi for informative discussion, and Andrew Collier Cameron for correspondence; I thank Joy McSharry and Judith Moss for typing the manuscript, Amanda Smith for preparing figure 3, and Guenter Houdek for his help in preparing figures 4 and 5. I am grateful to the Leverhulme Trust for an Emeritus Fellowship.

Notes

†Strictly speaking, Ω is an appropriately weighted average of the angular velocity of the entire star, but the contribution from the differentially rotating outer convection zone, if indeed the convection zone does rotate differentially, is so small as to be negligible for the purposes of this discussion.

‡This is a perfectly valid procedure, and reflects how one defines the corresponding non-rotating, spot-free, spherically symmetrical equilibrium state (e.g. Gough and Thompson 1990, cf. Bigot and Dziembowski 2002).