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

TL;DR

This paper presents a detailed calculation of neutrino losses in Type I X-ray bursts, showing they are significantly lower than previously assumed, and provides an improved approximation formula for the nuclear energy released during these bursts.

Contribution

It introduces the first detailed neutrino flux estimates for Type I X-ray bursts using a comprehensive nuclear reaction network and offers a new approximation formula for burst energy output.

Findings

Neutrino losses range from 6.7e-5 to 0.14 of total energy, depending on hydrogen fraction.

Previous estimates of 35% neutrino losses are significantly higher than the new findings.

An approximation formula for burst energy release as a function of hydrogen fraction is provided.

Abstract

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.