Rotational modes of non-isentropic stars and the gravitational radiation driven instability

We investigate the properties of r-mode and inertial mode of slowly rotating, non-isentropic, Newtonian stars, by taking account of the effects of the Coriolis force and the centrifugal force. For the non-isentropic models we consider only two cases, that is, the models with the stable fluid stratification in the whole interior and the models that are fully convective. For simplicity we call these two kinds of models "radiative" and "convective" models in this paper. For both cases, we assume the deviation of the models from isentropic structure is small. Examining the dissipation timescales due to the gravitational radiation and several viscous processes for the polytropic neutron star models, we find that the gravitational radiation driven instability of the r-modes remains strong even in the non-isentropic models. Calculating the rotational modes of the radiative models as functions of the angular rotation frequency $\Omega$, we find that the inertial modes are strongly modified by the buoyant force at small $\Omega$, where the buoyant force as a dominant restoring force becomes comparable with or stronger than the Coriolis force. Because of this property we obtain the mode sequences in which the inertial modes at large $\Omega$ are identified as g-modes or the r-modes with l=|m| at small $\Omega$. We also note that as $\Omega$ increases from $\Omega=0$ the retrograde g-modes become retrograde inertial modes, which are unstable against the gravitational radiation reaction.