Initial neutrino loss in neutron star formation

The nonlinear diffusion equation which describes the initial loss of neutrinos from the inner core of a newly formed neutron star is solved numerically. The diffusion coefficient used is that appropriate to degenerate neutrinos in dense matter taking into account both absorption and scattering of neutrinos by nucleons. It is found that the time for the neutrinos to escape cannot be less than approx.1 s. This time is primarily determined by the transport processes in the core and is insensitive to the boundary conditions. Energy dissipation due to neutrino loss is calculated and is found to be rather insensitive to the diffusion coefficient. Maximum dissipation occur in the outer regions of the core where the diffusion coefficient is largest and the heat capacity the smallest. The resultant temperature increase is modest and so not sufficient to significantly increase the pressure. The loss times are too long for neutrino escape to be dynamically useful in matter ejectio processes which occur on millisecond time scales. The loss of these neutrinos can therefore be neglected in determining the dynamical processes of neutron star formation.