Supernova Matter at Subnuclear Densities as a Resonant Fermi Gas: Enhancement of Neutrino Rates

At low energies nucleon-nucleon interactions are resonant and therefore supernova matter at subnuclear densities has many similarities to atomic gases with interactions dominated by a Feshbach resonance. We calculate the rates of neutrino processes involving nucleon-nucleon collisions and show that these are enhanced in mixtures of neutrons and protons at subnuclear densities due to the large scattering lengths. As a result, the rate for neutrino pair bremsstrahlung and absorption is significantly larger below $10^{13}\mathrm{g}{\mathrm{cm}}^{-3}$ compared to rates used in supernova simulations.

Figure 1

Spin relaxation rate $1/{\tau }_A$ for $\omega =0$ as a function of density $\rho$ for different electron fractions $Y_e$. The temperature is taken along typical supernova conditions, Eq. (11). Results are shown for the OPE approximation, the approximation used in supernova simulations [OPE nn-only, Hannestad and Raffelt (HR)] [2], leading-order (LO) chiral EFT interactions, and including NN interactions at ${\mathrm{N}}^3\mathrm{LO}$ at the Born level. In addition, we show the results based on NN phase shifts ($T$ matrix). The color change from gray to orange indicates that the ${\mathrm{N}}^3\mathrm{LO}$ results should only be trusted at higher densities where the Born approximation works well. The $T$-matrix results are expected to be valid up to a fugacity of $z=1/2$, which is marked by the small bar.

Figure 2

Spin relaxation rate $1/{\tau }_A(\omega =0)$ as a function of temperature $T$ for $Y_e=0.3$ and $\rho =10^{13}\mathrm{g}{\mathrm{cm}}^{-3}$. Results are shown for the different cases as in Fig. 1.

Figure 3

$T$-matrix results for $1/{\tau }_A(\omega =0)$ as a function of density $\rho$ for $Y_e=0.3$, with temperature along supernova conditions (11). The full $T$-matrix results (solid line) are compared to only $S$ waves (dash-dotted line), only $S$-wave scattering lengths (dashed line), and, finally, also setting the ${}^1{S}_0$ scattering length to infinity (dotted line). For comparison, the ${\mathrm{N}}^3\mathrm{LO}$ results are also shown.

Figure 4

Top panel: Energy-averaged inverse mean-free path $⟨{\lambda }^{-1}⟩$ of a neutrino against pair absorption as a function of density $\rho$ for $Y_e=0.3$, with temperature along supernova conditions (11). We assume a Boltzmann distribution for the neutrino and antineutrino. Bottom panel: Same, but normalized to the approximation used in supernova simulations (OPE nn-only, HR) [2].