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 counter oriented 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 { \cal E _ { B } } / { { \cal E } _ { k } } < 0.1 for the ratio of poloidal magnetic field energy-to-kinetic energy , corresponding to a maximum magnetic field strength B _ { c } \simeq 10 ^ { 16 } \mbox { G } \left ( { 7 M _ { \odot } } / { M _ { H } } \right ) \left ( { 6 M _ { H } } / { R } % \right ) ^ { 2 } \left ( { M _ { T } } / { 0.03 M _ { H } } \right ) ^ { 1 / 2 } .
The lifetime of rapid spin of the black hole is effectively defined by the timescale of dissipation of black hole-spin energy E _ { rot } in the horizon , and satisfies T \simeq 40 \mbox { s } ( M _ { H } / 7 M _ { \odot } ) ( R / 6 M _ { H } ) ^ { 4 } ( 0.03 M _ { H } / M _ { T } ) for a black hole of mass M _ { H } surrounded by a torus of mass M _ { T } and radius R . E _ { rot } of the black hole .
The torus converts a major fraction E _ { gw } / E _ { rot } \sim 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 100Mpc , these emissions over N = 2 \times 10 ^ { 4 } periods give rise to a characteristic strain amplitude \sqrt { N } h _ { char } \simeq 6 \times 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 } \simeq 10 ^ { -3 } in baryon-poor outflows to infinity .
We conjecture that these are not high-sigma outflows owing , in part , to magnetic reconnection in surrounding current sheets .
The fraction E _ { j } / E _ { rot } \sim ( 1 / 4 ) ( M _ { H } / R ) ^ { 4 } is standard for a universal horizon half-opening angle \theta _ { H } \simeq M _ { H } / R of the open flux-tube .
We identify this baryon poor output of tens of seconds with GRBs 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 .