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Influence of the photon - neutrino processes on magnetar cooling

The photon-neutrino processes $γe^{\pm} \to e^{\pm} ν\bar ν$, $γ\to ν\bar ν$ and $γγ\to ν\bar ν$ are investigated in the presence of a strongly magnetized and dense electron-positron plasma. The amplitudes of the reactions $γe^{\pm} \to e^{\pm} ν\bar ν$ and $γγ\to ν\bar ν$ are obtained. In the case of a cold degenerate plasma contributions of the considering processes to neutrino emissivity are calculated. It is shown that contribution of the process $γγ\to ν\bar ν$ to neutrino emissivity is supressed in comparision with the contributions of the processes $γe^{\pm} \to e^{\pm} ν\bar ν$ and $γ\to ν\bar ν$. The constraint on the magnetic field strength in the magnetar outer crust is obtained.