Uncertainty quantification for neutrino opacities in core-collapse supernovae and neutron star mergers

We perform an extensive study of the correlations between the neutrino-nucleon inverse mean free paths (IMFPs) and the underlying equation of states (EoSs). Strong interaction uncertainties in the neutrino mean free path are investigated in different density regimes. The nucleon effective mass, the nucleon chemical potentials, and the residual interactions in the medium play an important role in determining neutrino-nucleon interactions in a density-dependent manner. We study how the above quantities are constrained by an EoS consistent with (i) nuclear mass measurements, (ii) proton-proton scattering phase shifts, and (iii) neutron star observations. We then study the uncertainties of both the charged current and the neutral current neutrino-nucleon inverse mean free paths due to the variation of these quantities, using the $\text{Hartree-Fock}+\text{random}$ phase approximation method. Finally, we calculate the Pearson correlation coefficients between (i) the EoS-based quantities and the EoS-based quantities; (ii) the EoS-based quantities and the IMFPs; (iii) the IMFPs and the IMFPs. We find a strong impact of residual interactions on neutrino opacity in the spin and spin-isospin channels, which are not well constrained by current nuclear modelings.

Figure 1

Residual interactions as function of density. In the left column, residual interactions in vector current channel are shown. In the right column, residual interactions in axial vector current channel are shown. The colored solid curves stand for residual interactions derived from Skyrme-type interactions. The black dashed curves stand for residual interactions derived from MC EoSs, see Sec. 2 for detailed description of the underlying EoSs used to derive the residual interactions. The detailed formula expressions of the residual interactions in NC(CC) channel are provided in the Appendices [see Eqs. (A35), (A38), (A42), and (A43) for NC residual interaction, and Eqs. (A45) and (A46) for CC residual interactions].

Figure 2

CC [(a) and (b)] and NC [(c) and (d)] IMFPs in vector current [(a) and (c)] and axial-vector current [(b) and (d)] channel at $T=10$ MeV. The colored solid curves stand for IMFPs derived from Skyrme-type interactions. The black dashed curves stand for IMFPs derived from MC EoSs, see Sec. 2 for detailed description of the underlying EoSs used to derive the residual interactions.

Figure 3

Ferromagnetic instability density $n_{\mathrm{crit}}$ as a function of $Y_p$ in different EoSs.

Figure 4

CC [(a) and (b)] and NC [(c) and (d)] IMFPs with and without RPA corrections in vector [(a) and (c)] and axial vector [(b) and (d)] channel at $T=10$ MeV. The colored solid curves stand for IMFPs derived from Skyrme and MC EoSs without RPA corrections. The colored dashed curves stand for IMFPs derived from Skyrme and MC EoSs with RPA corrections. The small peaks observed in a few MC curves are due to the numerical noise.

Figure 5

This figure shows the CC [(a) and (b)] and NC [(c) and (d)] uncertainties of IMFPs in vector [(a) and (c)] and axial vector [(b) and (d)]. The points labeled “mb” show the uncertainty due to many-body methods by showing the difference between the RPA and mean-field estimates for pure Skyrme models. The points labeled “EOS-Skyrme” show the uncertainty due to the constraints used in obtaining the Skyrme-type EOSs. This was computed by comparing the variation across pure Skyrme models which were generated with fits to different sets of nuclear data. Finally, the points labeled “EOS-MC” show just the uncertainties in the mean free path across the Monte Carlo EOSs, which shows the variation due to the inability of the Skyrme model to precisely reproduce the experimental data from McDonnell et al. [30]. See Sec. 3 for detailed discussion of the classification of IMFP uncertainties.

Figure 6

CC dynamic response based on MC EoSs in axial-vector current channel at $T=10$ MeV, with $q=3T=30\mathrm{MeV}$. (a), (b), and (c) are the dynamic response functions at $n=0.15$, 0.005, ${10}^{-4}{\mathrm{fm}}^{-3}$, respectively.

Figure 7

NC dynamic response based on MC EoSs in axial-vector current channel at $T=10$ MeV, with $q=3T=30\mathrm{MeV}$. (a), (b), and (c) are the dynamic response functions at $n=0.15$, 0.005, ${10}^{-4}{\mathrm{fm}}^{-3}$, respectively.

Figure 8

Pearson coefficients between Skyrme parameters $t_i, x_i$, and $\gamma$.

Figure 9

Pearson coefficients between residual interactions at $n=0.15{\mathrm{fm}}^{-3}$ (a), $n=0.005{\mathrm{fm}}^{-3}$ (b), and $n={10}^{-4}{\mathrm{fm}}^{-3}$ (c).

Figure 10

Pearson coefficients between EoS-based quantities and CC IMFPs in vector channel (a) and in axial vector channel (b).

Figure 11

Pearson coefficients between EoS-based quantities and NC IMFPs in vector channel (a) and in axial vector channel (b).

Figure 12

Pearson coefficients between IMFPs at $n=0.15{\mathrm{fm}}^{-3}$ (a), $n=0.005{\mathrm{fm}}^{-3}$ (b), and $n={10}^{-4}{\mathrm{fm}}^{-3}$ (c).