Improved neutrino-nucleon interactions in dense and hot matter for numerical simulations

Neutrinos play an important role in compact star astrophysics: neutrino heating is one of the main ingredients in core-collapse supernovae, neutrino-matter interactions determine the composition of matter in binary neutron star mergers and have among others a strong impact on conditions for heavy element nucleosynthesis, and neutron star cooling is dominated by neutrino emission except for very old stars. Many works in the last decades have shown that in dense matter medium effects considerably change the neutrino-matter interaction rates, whereas many astrophysical simulations use analytic approximations which are often far from reproducing more complete calculations. In this work we present a scheme which allows to incorporate improved rates for charged current interactions into simulations and show as an example some results for core-collapse supernovae, where a noticeable difference is found in the location of the neutrinospheres of the low-energy neutrinos in the early post-bounce phase.

Figure 1

Example of the interpolation procedure and distribution of the energy domains in the case of a pronounced reaction threshold for $T=6$ MeV, $n_B=0.025 {\mathrm{fm}}^{-3}, Y_e=0.53$ with RG(SLy4) EoS and RPA in the Landau approximation. The crosses indicate the calculated points using five domains in energy, and the solid line corresponds to the interpolation. On the left-hand side oscillations due to the Gibbs phenomenon in the interpolation function are clearly visible, whereas a better choice of the energy domains and thus a better distribution of the interpolated data points on the right-hand side avoids them.

Figure 2

Neutrino (left) and antineutrino (right) opacities for $T=8$ MeV, $n_B=0.11 {\mathrm{fm}}^{-3}$, and $Y_e=0.05$ (upper panels), and $T=5$ MeV, $n_B=0.01 {\mathrm{fm}}^{-3}$, and $Y_e=0.15$ (lower panels). These correspond to typical conditions for the decoupling of neutrinos in the merger remnant [59], the former are more relevant for lower neutrino energies than the latter. The different line types distinguish the different approximations and results with HS(DD2) are indicated in red, whereas those with RG(SLy4) are in blue, see Sec. 2b for details. The dominant processes contributing to the opacities in a certain energy domain are mentioned in the figure, too.

Figure 3

Neutrino (left) and antineutrino (right) opacities for $T=12$ MeV, $n_B=0.01 {\mathrm{fm}}^{-3}$, and $Y_e=0.1$ (upper panels), $T=19$ MeV, $n_B=5\times {10}^{-3} {\mathrm{fm}}^{-3}$, and $Y_e=0.1$ (middle panels) and $T=5$ MeV, $n_B={10}^{-4}{\mathrm{fm}}^{-3}$, and $Y_e=0.1$ (lower panels). These correspond to typical conditions close to the neutrinosphere in a CCSN from our fiducial simulation, see Sec. 3. The different line types which distinguish the different approximations and results with HS(DD2) are indicated in red, whereas those with RG(SLy4) are in blue. The dominant processes contributing to the opacities in a certain energy domain are mentioned in the figure, too.

Figure 4

Profiles of the electron fraction at bounce as a function of the enclosed baryon mass, employing different approximation schemes to compute charged-current neutrino-nucleon interaction rates.

Figure 5

Total neutrino luminosities as a function of time after bounce.

Figure 6

Neutrinospheres radius as a function of time after bounce, for two different neutrinos energies. (a) Electron neutrino ${\nu }_e$, energy $E_{\nu }=2\mathrm{MeV}$, (b) Electron antineutrino ${\overline{\nu }}_e$, energy $E_{\nu }=2\mathrm{MeV}$, (c) Electron neutrino ${\nu }_e$, energy $E_{\nu }=14\mathrm{MeV}$, and (d) Electron antineutrino ${\overline{\nu }}_e$, energy $E_{\nu }=14\mathrm{MeV}$.