Gravitational radiation from gamma-ray burst-supernovae as observational opportunities for LIGO and VIRGO

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Abstract

Gamma-ray bursts are believed to originate in the core collapse of massive stars. This produces an active MeV-nucleus containing a rapidly rotating Kerr black hole of mass ${M}_{H}$ and angular velocity ${\ensuremath{\Omega}}_{H}\ensuremath{\simeq}{1/2M}_{H},$ surrounded by a uniformly magnetized torus of angular velocity ${\ensuremath{\Omega}}_{T}=\ensuremath{\eta}{\ensuremath{\Omega}}_{H}$ represented by two counteroriented current rings. We quantify black-hole--spin interactions with the torus and charged particles along open magnetic flux tubes subtended by the event horizon at a finite half-opening angle ${\ensuremath{\theta}}_{H}.$ A major output of ${E}_{\mathrm{gw}}\ensuremath{\simeq}4\ifmmode\times\else\texttimes\fi{}{10}^{53}(\ensuremath{\eta}{/0.1)(M}_{H}{/7M}_{\ensuremath{\bigodot}})\mathrm{erg}$ is radiated in gravitational waves of frequency ${f}_{\mathrm{gw}}\ensuremath{\simeq}500(\ensuremath{\eta}{/0.1)(7M}_{\ensuremath{\bigodot}}{/M}_{H})$ Hz by a quadrupole mass moment in the torus when its minor-to-major radius is less than 0.3260. The durations correspond to the lifetime ${T}_{s}$ of black hole spin, determined by a stability condition of poloidal magnetic field energy-to-kinetic energy $<1/15$ in the torus. Consistent with observations of GRB-SNe, we find (i) ${T}_{s}\ensuremath{\simeq}90\mathrm{s}$ (tens of s), (ii) aspherical SNe of kinetic energy ${E}_{\mathrm{SN}}\ensuremath{\simeq}2\ifmmode\times\else\texttimes\fi{}{10}^{51}\mathrm{erg}$ $(2\ifmmode\times\else\texttimes\fi{}{10}^{51}\mathrm{erg}$ in SN1998bw), and (iii) GRB-energies ${E}_{\ensuremath{\gamma}}\ensuremath{\simeq}2\ifmmode\times\else\texttimes\fi{}{10}^{50}\mathrm{erg}(3\ifmmode\times\else\texttimes\fi{}{10}^{50}\mathrm{erg}),$ upon associating ${\ensuremath{\theta}}_{H}$ with poloidal curvature of the magnetosphere. GRB-SNe occur perhaps about once a year within $D=100\mathrm{Mpc}.$ Correlating LIGO-VIRGO detectors enables searches for nearby events and their spectral closure density $6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ around 250 Hz in the stochastic background radiation in gravitational waves. At current sensitivity, LIGO-Hanford may place an upper bound around ${150M}_{\ensuremath{\bigodot}}$ in GRB030329. Upcoming all-sky supernovae surveys may provide distances to GRB-SNe, conceivably coincident with weak wide-angle GRB emissions similar to the nearby event GRB980425/SN1998bw. Detection of ${E}_{\mathrm{gw}}$ thus provides a method for identifying Kerr black holes by calorimetry.

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