The Stability of an Isentropic Model for a Gaseous Relativistic Star

We show that the isentropic subclass of Buchdahl's exact solution for a gaseous relativistic star is stable and gravitationally bound for all values of the compactness ratio $u [\equiv (M/R)$, where $M$ is the total mass and $R$ is the radius of the configuration in geometrized units] in the range, $0 < u \leq 0.20$, corresponding to the {\em regular} behaviour of the solution. This result is in agreement with the expectation and opposite to the earlier claim found in the literature.Comment: 9 pages (including 1 table); accepted for publication in GR

Excitation of the odd-parity quasi-normal modes of compact objects

The gravitational radiation generated by a particle in a close unbounded orbit around a neutron star is computed as a means to study the importance of the $w$ modes of the neutron star. For simplicity, attention is restricted to odd parity (``axial'') modes which do not couple to the neutron star's fluid modes. We find that for realistic neutron star models, particles in unbounded orbits only weakly excite the $w$ modes; we conjecture that this is also the case for astrophysically interesting sources of neutron star perturbations. We also find that for cases in which there is significant excitation of quadrupole $w$ modes, there is comparable excitation of higher multipole modes.Comment: 18 pages, 21 figures, submitted to Phys. Rev.