Steady state equilibrium condition of npe gas and its application to astrophysics

The steady equilibrium conditions for a mixed gas of neutrons,protons,electrons,positrons and radiation fields(abbreviated as npe±gas)with or without external neutrino flux ate investigated,and a general chemical potential equilibrium equationμn=μp+Cμεis obtained to describe the steady equilibrium at high tem-peratures(T>109K).An analytic fitting formula of coefficient C is presented for the sake of simplicity,when neutrinos and antineutrinos are transparent.It is a sim-ple method to estimate the electron fraction for the steady equilibrium npe±gas that adopts the corresponding equilibrium condition.As an example,we apply this method to the GRB accretion disk and confirm that the composition in the inner region is ap-proximately in equilibrium when the accretion rate is low.For the case with external neutrino flux,we calculate the initial electron fraction of neutrino-driven wind from the proto-neutron star model M15-11-r1.The results show that the improved equilib-rium condition makes the electron fraction decrease significantly more than the caseμn=μp+μe when the time is less than 5s post bounce,which may be useful for r-process nucleosynthesis models.