NONLINEAR, NONRADIAL PULSATION IN RAPIDLY OSCILLATING AP STARS

The rapidly oscillating Ap stars pulsate in high-overtone, low degree p-modes with their pulsation axes aligned with their oblique magnetic axes. They show non-linearity in their pulsation in three ways: 1) The harmonics of the basic pulsation frequency are detectable. 2) The pul sation phase seems to vary stochastically on a time scale of days to y ears depending on the star. 3) The form of the nonradial surface disto rtion is not constant with time. These three effects are illustrated w ith HR 3831, the best studied of the roAp stars. HR 3831 pulsates in d istorted dipole mode which can be modelled as a linear sum of axisymme tric l = 0, 1, 2, and 3 spherical harmonics aligned with the magnetic axis. This gives rise to a 7-frequency multiplet split by exactly the rotation frequency. The form of the distortion shows small changes on a time-scale of years. HR 3831 shows a 5-frequency rotationally split first harmonic multiplet, a 3-frequency rotationally split second harm onic multiplet, and a single third harmonic frequency has probably bee n detected at an amplitude of 0.065 mmag. The first harmonic has chang ed its form significantly over the last 10 years. A technique for deco mposing the fundamental frequency septuplet into its component spheric al harmonics is used to fit the pulsation phase as a function of rotat ion phase. This allows a unique O-C to be defined for any length of li ght curve. The long term behaviour of the O-C diagram cannot be modell ed adequately with a combination of periodic (Doppler shift) and quadr atic (evolution) terms; there seems to be a significant stochastic com ponent. The direction of the pulsation phase reversal at rotational ph ase 0.747 is indeterminate; sometimes it is a positive-going reversal, sometimes negative-going. At present it is not known whether this is a numerical artifact, or a physical effect in the star. If it is a phy sical effect, it means that small non-periodic differences in pulsatio n amplitude between the bipolar hemispheres have been detected.