Rotational Modes of Nonisentropic 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 theCoriolis force and the centrifugal force. For the non-isentropic models weconsider only two cases, that is, the models with the stable fluidstratification 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 modelsfrom isentropic structure is small. Examining the dissipation timescales due tothe gravitational radiation and several viscous processes for the polytropicneutron star models, we find that the gravitational radiation driveninstability of the r-modes remains strong even in the non-isentropic models.Calculating the rotational modes of the radiative models as functions of theangular rotation frequency $\Omega$, we find that the inertial modes arestrongly modified by the buoyant force at small $\Omega$, where the buoyantforce as a dominant restoring force becomes comparable with or stronger thanthe Coriolis force. Because of this property we obtain the mode sequences inwhich the inertial modes at large $\Omega$ are identified as g-modes or ther-modes with l=|m| at small $\Omega$. We also note that as $\Omega$ increasesfrom $\Omega=0$ the retrograde g-modes become retrograde inertial modes, whichare unstable against the gravitational radiation reaction.Comment: 22 pages, 16 figures, to appear in ApJ supplemen