Neutrino Losses in Type I Thermonuclear X-Ray Bursts: An Improved Nuclear Energy Generation Approximation

Type I X-ray bursts are thermonuclear explosions on the surface of accreting neutron stars. Hydrogen rich X-ray bursts burn protons far from the line of stability and can release energy in the form of neutrinos from beta-decays. We have estimated, for the first time, the neutrino fluxes of Type I bursts for a range of initial conditions based on the predictions of a 1D implicit hydrodynamics code, Kepler, which calculates the complete nuclear reaction network. We find that neutrino losses are between 6.7 x 10(-5) and 0.14 of the total energy per nucleon, Q(nuc), depending upon the hydrogen fraction in the fuel. These values are significantly below the 35% value for neutrino losses often adopted in recent literature for the rp-process. The discrepancy arises because it is only at beta-decays that approximate to 35% of energy is lost due to neutrino emission, whereas there are no neutrino losses in (p, gamma) and (alpha, p) reactions. Using the total measured burst energies from Kepler for a range of initial conditions, we have determined an approximation formula for the total energy per nucleon released during an X-ray burst, Q(nuc) = (1.31 + 6.95 (X) over bar - 1.92 (X) over bar (2)) MeV nucleon(-1), where (X) over bar is the average hydrogen mass fraction of the ignition column, with an rms error of 0.052 MeV nucleon(-1). We provide a detailed analysis of the nuclear energy output of a burst and find an incomplete extraction of mass excess in the burst fuel, with 14% of the mass excess in the fuel not being extracted.