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On Steady State Neutrino Heated Ultra-Relativistic Winds from Compact Objects

We study steady state winds from compact objects in the regime where the wind velocity at infinity is ultra-relativistic. This may have relevance to some models of Gamma-Ray-Bursts (GRB's). Particular attention is paid to the case where neutrinos provide the heating. Unless the neutrino luminosity is very large, L>10^{54} erg/s, the only allowed steady state solutions are those where energy deposition is dominated by neutrino-antineutrino annihilation at the sonic point. In this case, the matter temperature near the neutron star surface is low, less than 1MeV for typical neutrino luminosities. This is in contrast to the case for sub-relativistic winds discussed in the context of supernovae where the matter temperature near the neutron star approximates the temperature characterizing the neutrinos. We also investigate the setting of the neutron to proton ratio (n/p) in these winds and find that only for large (>10 MeV) electron neutrino or electron anti-neutrino temperatures is n/p entirely determined by neutrino capture. Otherwise, n/p retains an imprint of conditions in the neutron star.