Pairing effects on neutrino transport in low-density stellar matter

We investigate the impact of pairing correlations on neutrino transport in stellar matter. Our analysis is extended to nuclear matter conditions where large density fluctuations may develop, associated with the onset of the liquid-vapor phase transition, and where clustering phenomena occur. Within a thermodynamical treatment, we show that at moderate temperatures, where pairing effects are still active, the scattering of neutrinos in the nuclear medium is significantly affected by pairing correlations, which increase the neutrino trapping, thus modifying the cooling mechanism, by neutrino emission, of protoneutron stars.

Figure 1

Left panel: The critical temperature for the transition from superfluid to normal matter, as a function of the reduced neutron density ${\rho }_n/{\rho }_0$, as obtained in the strong pairing (full line) and weak pairing (dot-dashed line) cases. Right panel: The spinodal border (full line), in the $(\rho ,y_p)$ plane, associated with temperature $T=0.5$ MeV and momentum transfer $q=30$ MeV. The inset shows a zoom of the low-density region. The dashed lines are curves of constant neutron density, corresponding to the values associated with the circles in the left panel (see text for more details).

Figure 2

Left panels: Neutrino differential cross sections, ${\sigma }_{VE}$ (see text), as a function of the neutrino energy $E_{\nu }$, obtained in the full calculation (strong pairing case, full lines) or neglecting the pairing interaction (dashed lines). Right panels: Ratio $R$ between the full calculation and the results obtained neglecting the pairing interaction, as a function of the cosine of the neutrino scattering angle $\theta$, for selected neutrino energies. Results are shown for the following conditions: $\rho ={\rho }_0/100-T=0.5$ MeV [panels (a) and (c)] and $\rho ={\rho }_0/4-T=1.4$ MeV [(b) and (d)]. The proton fractions considered are indicated inside the figure.

Figure 3

Left panels: Neutrino differential cross sections, ${\sigma }_{VE}$ (see text), as a function of the neutrino energy $E_{\nu }$, obtained for the full calculation, in the strong pairing (full lines) or weak pairing (dashed-dotted line) case, or neglecting the pairing interaction (dashed lines). Right panels: Ratio $R$ between the full calculation and the results obtained neglecting the pairing interaction, as a function of the cosine of the neutrino scattering angle $\theta$, for selected neutrino energies. Results are shown for $\rho ={\rho }_0/100-T=0.4$ MeV. The proton fractions considered are indicated inside the figure.

Figure 4

Top panels: Neutrino differential cross section ${\sigma }_{VE}$ (see text) as a function of the temperature T, obtained in the full calculation (strong pairing case, full lines) or neglecting the pairing interaction (dashed lines). Bottom panels: Ratio $R$ between the full calculation and the results obtained neglecting the pairing interaction, as a function of T. Results are shown for the following conditions: $\rho ={\rho }_0/100$ [panels (a) and (c)] and $\rho ={\rho }_0/4$ [(b) and (d)]. The proton fractions considered are indicated inside the figure.