Direct Urca process in strong magnetic fields and neutron star cooling

TL;DR

This paper investigates how magnetic fields influence the neutrino emission in neutron star cooling, deriving a general expression for the process and analyzing the effects of different magnetic field strengths on star cooling rates.

Contribution

It provides a new general formula for neutrino emissivity in magnetic fields and explores the impact of magnetic field strength on neutron star cooling, including cases with many Landau levels and superstrong fields.

Findings

Magnetic fields can extend the operative range of the direct Urca process.

Magnetic fields near the star's center can accelerate cooling for certain stellar masses.

The study offers insights into interpreting thermal radiation observations of neutron stars.

Abstract

The effect of the magnetic field on the energy loss rate in the direct Urca reactions is studied. The general expression for the neutrino emissivity at arbitrary magnetic field B is derived. The main emphasis is laid on a case, in which the field is not superstrong, and charged reacting particles (e and p) populate many Landau levels. The magnetic field keeps the process operative if Delta k / k_{Fn} < N_{Fp}^{-2/3} (N_{Fp} is the number of the Landau levels populated by protons and Delta k = k_{Fn}-k_{Fp}-k_{Fe}), that is beyond the well-known switch-on limit in the absence of the field, Delta k < 0. Cooling of magnetized neutron stars with strong neutron superfluid in the outer cores and nonsuperfluid inner cores is simulated. The magnetic field near the stellar center speeds up the cooling if the stellar mass M is slightly less than the minimum mass M_c at which the direct Urca reaction becomes allowed for B=0. If B=3x10^{16} G the affected mass range is M_c-M < 0.1M_c, while for B=3x10^{15} G the range is M_c-M < 0.015M_c. This may influence a theoretical interpretation of the observed thermal radiation as illustrated for the Geminga pulsar. The case of superstrong magnetic fields (B>10^{18} G), such that e and p populate only the lowest Landau levels is briefly outlined.