Asymmetric neutrino production in strongly magnetized proto-neutron stars

We calculate the neutrino production cross-section through the direct URCA process in proto-neutron star matter in the presence of a strong magnetic field. We assume isoentropic conditions and introduce a new equation of state parameter set in the relativistic mean-field approach that can allow a neutron star mass up to $2.1M_{\odot }$ as required from observations. We find that the production process increases the flux of emitted neutrinos along the direction parallel to the magnetic field and decreases the flux in the opposite direction. This means that the neutrino flux asymmetry due to the neutrino absorption and scattering processes in a magnetic field becomes larger by the inclusion of the neutrino production process.

Figure 1

Upper panels (a) and (d): Density dependence of the total energy per baryon $E_T/A$ of neutron-star matter at a fixed lepton fraction $Y_L=0.4$ and for entropies $S/A=1$ (a) and 2 (d). Middle panels (b) and (e): Temperature profiles for entropies $S/A=1$ (b) and 2 (e). Solid and dashed lines represent results with and without $\mathrm{\Lambda }$ particles, respectively, in the EOS. Lower panels (c) and (f): Number fractions of protons $x_p$ and of $\mathrm{\Lambda }$ particles $x_{\mathrm{\Lambda }}$ for entropies $S/A=1$ (c) and 2 (f). Solid and dashed lines stand for $x_p$ with and without $\mathrm{\Lambda }$ particles, respectively. Dot-dashed lines show the $x_{\mathrm{\Lambda }}$ fraction.

Figure 2

Ratio of the magnetic part of the absorption cross-section $\mathrm{\Delta }{\sigma }_A$ to the cross-section without a magnetic-field ${\sigma }_A^0$. Lines are drawn for matter without $\mathrm{\Lambda }\mathrm{s}$ (a) and with $\mathrm{\Lambda }\mathrm{s}$ (b) at $T=20\mathrm{MeV}$. Solid, dot-dashed and dashed lines represent the results at ${\rho }_B={\rho }_0$, $3{\rho }_0$ and $5{\rho }_0$, respectively. Neutrino incident energies are taken to be equal to the neutrino chemical potentials.

Figure 3

Normalized magnetic part of the total production cross section, $\mathrm{\Delta }{\sigma }_{\text{pr}}/{\sigma }_{\text{pr}}^0$, as a function of final neutrino angle ${\theta }_f$ in a system without hyperons for the entropy $S/A=1$ (a) and $S/A=2$ (b), and with hyperons at $S/A=1$ (c) and $S/A=2$ (d). In each panel the solid, dash-dotted and dashed lines represent the results for ${\rho }_B={\rho }_0$, $3{\rho }_0$ and $5{\rho }_0$, respectively. A magnetic field strength of $B=10^{17}\mathrm{G}$ was used in this calculation.