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

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 ${\Omega }_H\simeq {1/2M}_H,$ surrounded by a uniformly magnetized torus of angular velocity ${\Omega }_T=\eta {\Omega }_H$ 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 ${\theta }_H.$ A major output of $E_{\mathrm{gw}}\simeq 4\times {10}^{53}\left(\eta {/0.1\left)\right(M}_H{/7M}_{\odot }\right)\mathrm{erg}$ is radiated in gravitational waves of frequency $f_{\mathrm{gw}}\simeq 500\left(\eta {/0.1\left)\right(7M}_{\odot }{/M}_H\right)$ 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 $<1/15\mathrm{}$ in the torus. Consistent with observations of GRB-SNe, we find (i) $T_s\simeq 90\mathrm{s}$ (tens of s), (ii) aspherical SNe of kinetic energy $E_{\mathrm{SN}}\simeq 2\times {10}^{51}\mathrm{erg}$ $(2\mathrm{}\times {10}^{51}\mathrm{erg}$ in SN1998bw), and (iii) GRB-energies $E_{\gamma }\simeq 2\times {10}^{50}\mathrm{erg}(3\mathrm{}\times {10}^{50}\mathrm{erg}),$ upon associating ${\theta }_H$ with poloidal curvature of the magnetosphere. GRB-SNe occur perhaps about once a year within $D=100\mathrm{}\mathrm{Mpc}.$ Correlating LIGO-VIRGO detectors enables searches for nearby events and their spectral closure density $6\times {10}^{-9}$ around 250 Hz in the stochastic background radiation in gravitational waves. At current sensitivity, LIGO-Hanford may place an upper bound around ${150M}_{\odot }$ 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.