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 evenparity gaugeinvariant master variables
(i.e. solutions of the ReggeWheeler and ZerilliMoncrief master equations). The formalism discussed
is intrinsically gaugeinvariant and the odd and evenparity 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 evenparity master equations equation, coupled to a fully nonlinear hydrodynamics
code that computes the dynamics of the accreting matter. In this approach, selfgravity 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 (nonkeplerian) 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
quasinormal 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 pointparticle 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 pointparticle 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 quasinormal mode
structure of the object.


