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 $6.7 \times 10^{-5}$ 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 $\approx35\,\%$ 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$\bar{X} - 1.92\bar{X}^2 $MeV/nucleon, where $\bar{X}$ is the average hydrogen mass fraction of the ignition column, with an RMS error of $0.052\,$Mev/nucleon. 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.