Normal-mode excitation from stellar collapse to a black hole: Odd-parity perturbations

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Abstract
Odd-parity perturbations of stellar models are studied numerically, with an emphasis on the gravitational radiation produced during collapse to a black hole. The stellar models are produced by a May-White stellar collapse code using a polytropic equation of state. A wide range of collapse models are studied, ranging from stars without pressure (dust collapse) to stars which collapse and then bounce at radii near the Schwarzschild radius. For all collapse models studied, the quasinormal modes (QNM’s) of the black hole are excited to varying degrees after an initial, non-QNM transient wave form. Models with greater pressure collapse more slowly and generally emit a lower-amplitude ringing radiation. Furthermore, models with greater pressure are generally found to radiate less of their total gravitational energy from the normal-mode excitation than models with less pressure. Results are presented for some collapse models which show significantly damped and distorted wave forms. These models, which develop shocks that approach the surface of the star as it crosses the peak of the scattering potential, can produce an initial transient wave form unlike that which would be expected purely from quasinormal-mode excitation. Following this initial transient, the wave form settles into a more recognizable quasinormal wave form, although its amplitude may be enhanced or reduced (when compared to models which collapse without any significant hydrodynamic effect). This work indicates that while quasinormal ringing is a general feature of nonspherical collapse to a black hole, the details of the collapse can, in principle, affect both the amplitude and the shape of the emitted wave form.