S E M I N A R IDepartament d'Astronomia i Astrofísica
Universitat de València
Gravitational wave emission from matter accretion onto Schwarzschild black holes: A perturbative approach
Departament d'Astronomia i Astrofísica, Universitat de València and Politecnico di Torino
Seminari del departament d'Astronomia i Astrofísica
Divendres 19 novembre 2004
In the first part of this talk I review in detail the theory of linear nonspherical metric perturbations of a Schwarzschild black holes, starting from the multipole expansion of the linearized metric and ending with the expressions that link the two gravitational wave (GW) polarization amplitudes to the odd and even-parity gauge-invariant master variables (i.e. solutions of the Regge-Wheeler and Zerilli-Moncrief master equations) in the presence of 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 hybrid procedure is adopted, in which I evolve numerically the inhomogeneous odd and even-parity master equations equation, coupled to a fully nonlinear, axisymmetric, hydrodynamics code that computes the dynamics of the accreting matter. Self-gravity of the accreting layers of fluid and radiation reaction effects are neglected. Different matter distributions 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 (QNM) of the hole; rather, it exhibits a complex pattern, with distinctive interference fringes related to the extended spatial distribution of the accreting matter. Qualitative similar results (but less pronounced) are found for runaway unstable accretion discs. For oscillating stable models, I compare waveforms computed using perturbation theory with waveforms extracted using the Standard Quadrupole Formula (SQF) and its variations present in the literature (the so-called stress-formula). I argue that the use of the SQF, in these regimes, is perfectly consistent with the perturbative approach. In addition, I show that the coupling between the torus and the black hole QNM 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 of the dynamics of the external distribution of matter, than by the QNM structure of the object.