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Seminario
"Gravitational wave interference from matter accretion onto Schwarzschild black holes"

Relatore: Alessandro Nagar- Departament d'Astronomia i Astrofìsica, Universitat de València

Sala Feynman
14 Ottobre 2004 ore 15.30

Abstract
This talk is divided in two parts. In the first one, I review in detail the theory of linear nonspherical metric perturbations of Schwarzschild black holes, starting from the multipole expansion of the linearized metric and ending with the expressions that link the gravitational wave (GW) amplitudes $h_ imes$ and $h_+$ to the odd and even-parity gauge-invariant master variables (i.e. solutions of the Regge-Wheeler and Zerilli-Moncrief master equations). The formalism discussed is intrinsically gauge-invariant and the odd and even-parity master equations are written in the time domain for general matter sources. In the second part, I discuss the applications of this formalism to the study of the GWs emission driven by matter accretion onto the black hole. A {it hybrid} procedure is adopted, in which I evolve numerically the inhomogeneous odd and even-parity master equations equation, coupled to a fully nonlinear hydrodynamics code that computes the dynamics of the accreting matter. In this approach, self-gravity of the accreting layers of fluid as well as radiation reaction effects are neglected. Different matter distributions, in axisymmetry, are considered: quadrupolar shells of dust or thick (non--keplerian) perfect fluid (no viscosity) accretion discs. The shells are unstable, so that they immediately plunge into the hole. The discs can be unstable (runaway instability) or can just oscillate around their equilibrium position, emitting GWs. In the case of dust shells plunging from a finite distance $r_0$, our results show that the energy spectrum of GWs is far from having only one clear, monochromatic peak at the frequency of the fundamental quasi-normal mode; rather, it exhibits a complex pattern, with distinctive interference fringes related to the extended spatial distribution of the accreting matter. Depending on the parameters characterizing the shells (i.e. its radial extension and its initial position), the energy is mainly emitted at frequencies lower than that of the fundamental mode. In addition, due to destructive interference among the parts of the extended objects, the specific energy emitted in GWs is roughly two order of magnitude smaller than the point-particle values, in quantitative agreement with findings of Shapiro and Wasserman for shells plunging from infinity. However, in this case, as $r_0 ightarrowinfty$, no interference modulations are present in the spectrum. Qualitative similar results are found for runaway unstable accretion discs. In this case the specific energy released in GWs is around one order of magnitude smaller than the point-particle limit. For oscillating stable models, I compare waveforms computed using perturbation theory with waveforms extracted by the (relativistic) quadrupole formula: I argue that the latter approach (already followed in the literature) slightly overestimates the amplitudes of the signals and that the coupling between the torus and the black hole oscillation is practically absent. The analysis presented here illustrates that the gravitational wave signal driven by accretion onto a Schwarzschild black hole is influenced more by the details and dynamics of the external distribution of matter, than by the quasi-normal mode structure of the object.