Direct Urca process in strong magnetic fields and neutron star cooling

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 ∆k/kFn . N−2/3 Fp (NFp is the number of the Landau levels populated by protons and ∆k ≡ kFn − kFp − kFe), that is beyond the well–known switch–on limit in the absence of the field, ∆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 Mc, at which the direct Urca reaction becomes allowed for B = 0. If B = 3 · 1016 G, the affected mass range isMc −M . 0.1Mc, while forB = 3 · 1015 G the range is Mc −M . 0.015Mc. This may influence a theoretical interpretation of the observed thermal radiation as illustrated for the Geminga pulsar. The case of superstrong magnetic fields (B & 1018 G), such that e andppopulate only the lowest Landau levels is briefly outlined.