Off‐Axis Neutrino Scattering in Gamma‐Ray Burst Central Engines

The search for an understanding of an energy source great enough to explainthe gamma-ray burst (GRB) phenomena has attracted much attention from theastrophysical community since its discovery. In this paper we extend the workof K. Asano and T. Fukuyama, and J. D. Salmonson and J. R. Wilson, and analyzethe off-axis contributions to the energy-momentum deposition rate (MDR) fromthe neutrino anti-neutrino collisions above a rotating black hole/thinaccretion disk system. Our calculations are performed by imaging the accretiondisk at a specified observer using the full geodesic equations, and calculatingthe cumulative MDR from the scattering of all pairs of neutrinos andanti-neutrinos arriving at the observer. Our results shed light on the beamingefficiency of GRB models of this kind. Although we confirm Asano and Fukuyama'sconjecture as to the constancy of the beaming for small angles away from theaxis; nevertheless, we find the dominant contribution to the MDR comes fromnear the surface of the disk with a tilt of approximately \pi/4 in thedirection of the disk's rotation. We find that the MDR at large radii isdirected outward in a conic section centered around the symmetry axis and islarger, by a factor of 10 to 20, than the on-axis values. By including thisoff-axis disk source, we find a linear dependence of the MDR on the black holeangular momentum (a). In addition, we find that scattering is directed backonto the black hole in regions just above the horizon of the black hole. Thisgravitational ``in scatter'' may provide an observable high energy signature ofthe central engine, or at least another channel for accretion.Comment: 21 pages, 9 figures, (Author Contact: wam@lanl.gov