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Title: Accretion-induced quasinormal mode excitation of a Schwarzschild black hole

Abstract

By combining the numerical solution of the nonlinear hydrodynamics equations with the solution of the linear inhomogeneous Zerilli-Moncrief and Regge-Wheeler equations, we investigate the properties of the gravitational radiation emitted during the axisymmetric accretion of matter onto a Schwarzschild black hole. The matter models considered include quadrupolar dust shells and thick accretion disks, permitting us to simulate situations which may be encountered at the end stages of stellar gravitational collapse or binary neutron star merger. We focus on the interference pattern appearing in the energy spectra of the emitted gravitational waves and on the amount of excitation of the quasinormal modes of the accreting black hole. We show that, quite generically in the presence of accretion, the black-hole ringdown is not a simple superposition of quasinormal modes, although the fundamental mode is usually present and often dominates the gravitational-wave signal. We interpret this as due to backscattering of waves off the nonexponentially decaying part of the black-hole potential and to the finite spatial extension of the accreting matter. Our results suggest that the black-hole QNM contributions to the full gravitational-wave signal should be extremely small and possibly not detectable in generic astrophysical scenarios involving the accretion of extended distributions ofmore » matter.« less

Authors:
 [1];  [2];  [3];  [2];  [4];  [5];  [6];  [7]
  1. Dipartimento di Fisica and INFN, Politecnico di Torino, Turin (Italy)
  2. (Spain)
  3. Dipartimento di Astronomia e Scienza dello Spazio Universita di Firenze, Florence (Italy)
  4. Departamento de Astronomia y Astrofisica, Universidad de Valencia, Valencia (Spain)
  5. Max-Planck-Institut fuer Gravitationsphysik, Albert-Einstein-Institut, Potsdam-Golm (Germany)
  6. (Italy)
  7. (United States)
Publication Date:
OSTI Identifier:
21011081
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevD.75.044016; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ACCRETION DISKS; AXIAL SYMMETRY; BACKSCATTERING; BLACK HOLES; COSMOLOGY; EMISSION; ENERGY SPECTRA; EXCITATION; GRAVITATIONAL COLLAPSE; GRAVITATIONAL RADIATION; GRAVITATIONAL WAVES; HYDRODYNAMICS; INTERFERENCE; NEUTRON STARS; NONLINEAR PROBLEMS; NUMERICAL SOLUTION; POTENTIALS

Citation Formats

Nagar, Alessandro, Departamento de Astronomia y Astrofisica, Universidad de Valencia, Valencia, Zanotti, Olindo, Departamento de Astronomia y Astrofisica, Universidad de Valencia, Valencia, Font, Jose A., Rezzolla, Luciano, SISSA, International School for Advanced Studies and INFN, Trieste, and Department of Physics, Louisiana State University, Baton Rouge, LA. Accretion-induced quasinormal mode excitation of a Schwarzschild black hole. United States: N. p., 2007. Web. doi:10.1103/PHYSREVD.75.044016.
Nagar, Alessandro, Departamento de Astronomia y Astrofisica, Universidad de Valencia, Valencia, Zanotti, Olindo, Departamento de Astronomia y Astrofisica, Universidad de Valencia, Valencia, Font, Jose A., Rezzolla, Luciano, SISSA, International School for Advanced Studies and INFN, Trieste, & Department of Physics, Louisiana State University, Baton Rouge, LA. Accretion-induced quasinormal mode excitation of a Schwarzschild black hole. United States. doi:10.1103/PHYSREVD.75.044016.
Nagar, Alessandro, Departamento de Astronomia y Astrofisica, Universidad de Valencia, Valencia, Zanotti, Olindo, Departamento de Astronomia y Astrofisica, Universidad de Valencia, Valencia, Font, Jose A., Rezzolla, Luciano, SISSA, International School for Advanced Studies and INFN, Trieste, and Department of Physics, Louisiana State University, Baton Rouge, LA. Thu . "Accretion-induced quasinormal mode excitation of a Schwarzschild black hole". United States. doi:10.1103/PHYSREVD.75.044016.
@article{osti_21011081,
title = {Accretion-induced quasinormal mode excitation of a Schwarzschild black hole},
author = {Nagar, Alessandro and Departamento de Astronomia y Astrofisica, Universidad de Valencia, Valencia and Zanotti, Olindo and Departamento de Astronomia y Astrofisica, Universidad de Valencia, Valencia and Font, Jose A. and Rezzolla, Luciano and SISSA, International School for Advanced Studies and INFN, Trieste and Department of Physics, Louisiana State University, Baton Rouge, LA},
abstractNote = {By combining the numerical solution of the nonlinear hydrodynamics equations with the solution of the linear inhomogeneous Zerilli-Moncrief and Regge-Wheeler equations, we investigate the properties of the gravitational radiation emitted during the axisymmetric accretion of matter onto a Schwarzschild black hole. The matter models considered include quadrupolar dust shells and thick accretion disks, permitting us to simulate situations which may be encountered at the end stages of stellar gravitational collapse or binary neutron star merger. We focus on the interference pattern appearing in the energy spectra of the emitted gravitational waves and on the amount of excitation of the quasinormal modes of the accreting black hole. We show that, quite generically in the presence of accretion, the black-hole ringdown is not a simple superposition of quasinormal modes, although the fundamental mode is usually present and often dominates the gravitational-wave signal. We interpret this as due to backscattering of waves off the nonexponentially decaying part of the black-hole potential and to the finite spatial extension of the accreting matter. Our results suggest that the black-hole QNM contributions to the full gravitational-wave signal should be extremely small and possibly not detectable in generic astrophysical scenarios involving the accretion of extended distributions of matter.},
doi = {10.1103/PHYSREVD.75.044016},
journal = {Physical Review. D, Particles Fields},
number = 4,
volume = 75,
place = {United States},
year = {Thu Feb 15 00:00:00 EST 2007},
month = {Thu Feb 15 00:00:00 EST 2007}
}
  • We formulate and calculate the second-order quasinormal modes (QNMs) of a Schwarzschild black hole (BH). Gravitational waves (GW) from a distorted BH, the so-called ringdowns, are well understood as QNMs in general relativity. Since QNMs from binary BH mergers will be detected with a high signal-to-noise ratio by GW detectors, it is also possible to detect the second perturbative order of QNMs, generated by nonlinear gravitational interaction near the BH. In the BH perturbation approach, we derive the master Zerilli equation for the metric perturbation to second order and explicitly regularize it at the horizon and spatial infinity. We numericallymore » solve the second-order Zerilli equation by implementing the modified Leaver continued fraction method. The second-order QNM frequencies are found to be twice the first-order ones, and the GW amplitude is up to {approx}10% that of the first order for the binary BH mergers. Since the second-order QNMs always exist, we can use their detections (i) to test the nonlinearity of general relativity, in particular, the no-hair theorem, (ii) to remove fake events in the data analysis of QNM GWs, and (iii) to measure the distance to the BH.« less
  • Processes near the event horizon of a black hole excite a ringing of fields (electromagnetic, gravitational perturbation, etc.) at certain complex frequencies, called quasinormal frequencies, characteristic of the hole. Evidence for such oscillations consists almost entirely of their appearance in detailed numerical solutions of specific problems. Despite the importance of quasinormal ringing in the generation of gravitational radiation, little work has been done on clarifying the way in which the ringing is excited, or in estimating the strength of the excitation, without a detailed computer solution. We formulate here the theory of the excitation of ringing of Schwarzschild holes frommore » Cauchy data, in which a coefficient C/sub q/ seems to describe the excitation, but is given by a formally divergent integral. The meaning of C/sub q/ is shown actually to be an analytic continuation of the integral in the complex frequency plane, and this idea is used as the basis of computational techniques for finding C/sub q/. We then demonstrate that C/sub q/ does not in general describe the astrophysically interesting quantity, the near-horizon stimulation of the ringing. We introduce two approaches to the correct description. The first uses a modified C/sub q/ based on an ad hoc modification of the Cauchy data. The second is based on a series representation of C/sub q/; a truncation of this series automatically selects the astrophysically interesting part of C/sub q/.« less
  • We investigate the Dirac quasinormal modes (QNMs) of a Schwarzschild black hole using continued fraction and Hill-determinant approaches. For large angular quantum number, we find that the fundamental quasinormal frequencies become evenly spaced and the spacing is given by {omega}{sub {lambda}}{sub +1}-{omega}{sub {lambda}}=0.38490-0.00000i, where {lambda}={+-}(l+1/2) (l is the angular quantum number). We show that the angular quantum number has a surprising effect of increasing real part but almost does not affect imaginary part of the quasinormal frequencies, especially for the lowest lying mode. We also find that the spacing for imaginary part of the quasinormal frequencies at high overtones ismore » equidistant and equals to -i/4M, as it takes place for scalar, electromagnetic and gravitational perturbations.« less
  • The computation of the gravitational radiation emitted by a particle falling into a Schwarzschild black hole is a classic problem that was already studied in the 1970s. Here we present a detailed numerical analysis of the case of radial infall starting at infinity with no initial velocity. We compute the radiated waveforms, spectra, and energies for multipoles up to l=6, improving significantly on the numerical accuracy of existing results. This is done by integrating the Zerilli equation in the frequency domain using the Green's function method. The resulting wave exhibits a ''ring-down'' phase whose dominant contribution is a superposition ofmore » the quasinormal modes of the black hole. The numerical accuracy allows us to recover the frequencies of these modes through a fit of that part of the wave. Comparing with direct computations of the quasinormal modes, we reach a {approx}10{sup -4} to {approx}10{sup -2} accuracy for the first two overtones of each multipole. Our numerical accuracy also allows us to display the power-law tail that the wave develops after the ring-down has been exponentially cut off. The amplitude of this contribution is {approx}10{sup 2} to {approx}10{sup 3} times smaller than the typical scale of the wave.« less
  • Three-dimensional simulations for the merger of binary neutron stars are performed in the framework of full general relativity. We pay particular attention to the black hole formation case and to the resulting mass of the surrounding disk for exploring the possibility for formation of the central engine of short-duration gamma-ray bursts (SGRBs). Hybrid equations of state are adopted mimicking realistic, stiff nuclear equations of state (EOSs), for which the maximum allowed gravitational mass of cold and spherical neutron stars, M{sub sph}, is larger than 2M{sub {center_dot}}. Such stiff EOSs are adopted motivated by the recent possible discovery of a heavymore » neutron star of mass {approx}2.1{+-}0.2M{sub {center_dot}}. For the simulations, we focus on binary neutron stars of the ADM mass M > or approx. 2.6M{sub {center_dot}}. For an ADM mass larger than the threshold mass M{sub thr}, the merger results in prompt formation of a black hole irrespective of the mass ratio Q{sub M} with 0.65 < or approx. Q{sub M}{<=}1. The value of M{sub thr} depends on the EOSs and is approximately written as 1.3-1.35M{sub sph} for the chosen EOSs. For the black hole formation case, we evolve the space-time using a black hole excision technique and determine the mass of a quasistationary disk surrounding the black hole. The disk mass steeply increases with decreasing the value of Q{sub M} for given ADM mass and EOS. This suggests that a merger with small value of Q{sub M} is a candidate for producing central engine of SGRBs. For M<M{sub thr}, the outcome is a hypermassive neutron star of a large ellipticity. Because of the nonaxisymmetry, angular momentum is transported outward. If the hypermassive neutron star collapses to a black hole after the long-term angular momentum transport, the disk mass may be (> or approx. 0.01M{sub {center_dot}} irrespective of Q{sub M}. Gravitational waves are computed in terms of a gauge-invariant wave extraction technique. In the formation of the hypermassive neutron star, quasiperiodic gravitational waves of frequency between 3 and 3.5 kHz are emitted irrespective of EOSs. The effective amplitude of gravitational waves can be > or approx. 5x10{sup -21} at a distance of 50 Mpc, and hence, it may be detected by advanced laser-interferometers. For the black hole formation case, the black hole excision technique enables a long-term computation and extraction of ring-down gravitational waves associated with a black hole quasinormal mode. It is found that the frequency and amplitude are {approx_equal}6.5-7 kHz and {approx}10{sup -22} at a distance of 50 Mpc for the binary of mass M{approx_equal}2.7-2.9M{sub {center_dot}}.« less