OSCILLATIONS OF RED DWARFS IN EVOLVED LOW-MASS BINARIES WITH NEUTRON-STARS

We investigate a novel aspect of a problem related to the properties o f low-mass binaries (LMBs) with millisecond pulsars: the pulsations of the red dwarf (donor) companion of the neutron star (NS). The illumin ation of the donor star by the pulsar's high-energy nonthermal radiati on and relativistic wind may substantially affect its structure. We pr esent a quantitative analysis of the oscillation spectrum of a red dwa rf which has evolved in an LMB and has undergone the stage of evaporat ion. We calculate the p- and g-modes for red dwarfs with masses in the interval (0.2-0.6) M.. For comparison, similar calculations are prese nted for zero age main-sequence (ZAMS) stars of the same masses. For l ess massive donor stars (almost-equal-to 0.2 M.), the oscillation spec trum becomes qualitatively different from that of their ZAMS counterpa rts. The difference is due to the fact that a ZAMS star of 0.2 M. is f ully convective, while the donor star in an LMB is expected to be far from thermal equilibrium and not fully convective. As a result, in con trast to a low-mass ZAMS star, a red dwarf of the same mass in an LMB allows the existence of g-modes. We also consider tidally forced g-mod es, and perform a linear analysis of these oscillations for different degrees of nonsynchronism between the orbital and spin rotation of the red dwarf component. We demonstrate the existence of a series of reso nances for the low-order g-modes which may occur in LMBs at a late sta ge of their evolution. We discuss the possibility that these oscillati ons may trigger Roche lobe overflow and sudden mass loss by the donor star. Further implications of this effect for and X-ray burst phenomen a are outlined.