Theory and astrophysical consequences of a magnetized torus around a rapidly rotating black hole

We analyze the topology, lifetime, and emissions of a torus around a black hole formed in hypernovae and black hole-neutron star coalescence. The torus is ab initio uniformly magnetized, represented by two counteroriented current rings, and develops a state of suspended accretion against a "magnetic wall" around the black hole. Magnetic stability of the torus gives rise to a new fundamental limit ℰ_ℬ/_k < 0.1 for the ratio of poloidal magnetic field energy to kinetic energy, corresponding to a maximum magnetic field strength B_c ≃ (10¹⁶ G)(7 M_⊙/M_H)(6M_H/R)²(M _T/0.03M_H)^1/2. The lifetime of rapid spin of the black hole, effectively defined by the timescale of dissipation of spin energy E_rot in the horizon, hereby satisfies T ≃ (40 s) (M _H/7 M⊙)(R/6M_H)⁴(0.03M_H/M _T) for a black hole of mass M_H surrounded by a torus of mass M_T and radius R. The torus converts a major fraction E _gw/E_rot ∼ 10% into gravitational radiation through a finite number of multipole mass moments and a smaller fraction into MeV neutrinos and baryon-rich winds. At a source distance of 100 Mpc, these emissions over N = 2 × 10⁴ periods give rise to a characteristic strain amplitude N^1/2h_char ≃ 6 × 10^-21. We argue that torus winds create an open magnetic flux tube on the black hole, which carries a minor fraction E_j/E _rot ≃ 10^-3 in baryon-poor outflows to infinity. We conjecture that these are not high-σ outflows, owing, in part, to magnetic reconnection in surrounding current sheets. The fraction E _j/E_rot ∼ 1/4 (M_H/R)⁴ is standard for a universal horizon half-opening angle θ_H ≃ M_H/R of the open flux tube. We identify this baryon-poor output of tens of seconds with gamma-ray bursts with contemporaneous and strongly correlated emissions in gravitational radiation, conceivably at multiple frequencies. Ultimately, this leaves a black hole binary surrounded by a supernova remnant.