The effect of tidal interactions on hot subdwarf B stars and their pulsations

Hot subdwarf B (sdB) stars are evolved core He-burning stars. The sdBs are formed by binary interactions on the red giant branch (RGB) which cause the stars to lose most of their H envelopes. Over half of all observed hot subdwarf B stars are found in binaries, many of which are found in close configurations with orbital periods of $10\,$d or less. These short period systems are formed by common envelope evolution. In order to estimate the companion masses in these predominantly single-lined systems, tidal locking has frequently been assumed for sdB binaries with periods less than half a day. Observed non-synchronicity of a number of close sdB binaries challenges that assumption and hence provides an ideal testbed for tidal theory. The stars have convective cores and radiative envelopes. Tidal dissipation in such systems is not particularly well understood. We solve the second-order differential equations for detailed 1D stellar models of sdB stars to obtain the tidal dissipation strength and hence to estimate the tidal synchronization time-scale owing to Zahn's dynamical tide and the equilibrium tide. The results indicate synchronization time-scales longer than the sdB lifetime in all observed cases using standard input physics. Asteroseismological analysis of NY Vir suggests that at least the outer 55 per cent of the star (in radius) rotates as a solid body and is tidally synchronized to the orbit. Detailed calculation of tidal dissipation rates in NY Vir fails to account for this synchronization. Recent observations of He core burning stars suggest that the extent of the convective core may be substantially larger than that predicted with theoretical models. We conduct a parametric investigation of sdB models generated with the Cambridge STARS code to artificially extend the radial extent of the convective core. These models with extended cores still fail to account for the synchronization. Tidal synchronization may be achievable with a non-MLT treatment of convection. Several sdB stars have been both predicted and observed to pulsate with multiple frequencies. Asteroseismological analysis of the observed pulsations shows that they do not quite fit with the theoretical models, especially in the close binary systems. We present a method for computing tidal distortion and associated frequency shifts. Validation is by application to polytropes and comparison with previous work. For typical sdB stars, a tidal distortion of less than 1% is obtained for orbital periods greater than 0.1\,d. Application to numerical helium core-burning stars identifies the period and mass-ratio domain where tidal frequency shifts become significant and quantifies those shifts in terms of binary properties and pulsation modes. Tidal shifts disrupt the symmetric form of rotationally split multiplets by introducing an asymmetric offset to modes. Tides do not affect the total spread of a rotationally split mode unless the stars are rotating sufficiently slowly that the rotational splitting is smaller than the tidal splitting.