Neutrino emissivity from Goldstone boson decay in magnetized neutron matter

Neutron matter at densities somewhat above nuclear densities is believed to be superfluid due to the condensation of neutron pairs in the ${}^3{P}_2$ channel. This condensate breaks rotational symmetry spontaneously and leads to the existence of Goldstone bosons (angulons). We show that the coupling to magnetic fields mediated by the magnetic moment of the neutron makes angulons massive and capable of decaying into a neutrino-antineutrino pair. We compute the rate for this process and argue they become competitive with other cooling processes for temperatures around ${10}^7$ K as long as the interior magnetic field of the star is in the $B\approx {10}^{15}$ G range or above.

Figure 1

Feynman diagram showing the massive angulon (dashed line) decay into a neutrino pair (solid line). The wavy line represents a $Z_0$.

Figure 2

$h\left(x\right)$ as a function of $x=\frac{e{g}_{N}B}{2MaT}$ (solid blue line) and its analytic approximation $h\left(x\right)\approx 0.000042x^7{e}^{-x}$ (dashed red line).

Figure 3

Neutrino emissivity as a function of temperature for different magnetic fields.