Neutrino scattering in supernovae and the universal spin correlations of a unitary gas

Core collapse supernova simulations can be sensitive to neutrino interactions near the neutrinosphere. This is the surface of last scattering. We model the neutrinosphere region as a warm unitary gas of neutrons. A unitary gas is a low density system of particles with large scattering lengths. We calculate modifications to neutrino scattering cross sections because of the universal spin and density correlations of a unitary gas. These correlations can be studied in laboratory cold atom experiments. We find significant reductions in cross sections, compared to free space interactions, even at relatively low densities. These reductions could reduce the delay time from core bounce to successful explosion in multidimensional supernova simulations.

Figure 1

Fourth-order virial calculations of the vector response $S_V$ (red heavy dashed line), axial response $S_A$ (heavy blue dashed-dotted line), and total response $S_{\mathrm{tot}}$ (heavy black line) versus Fermi energy over temperature ${\epsilon }_F/T$. The fugacity $z=exp(\mu /T)$ is shown as the heavy cyan dotted line. The dotted error bands show the effect of statistical and systematic errors in theoretical calculations of the fourth virial coefficient $b_4$. Finally the thin red dashed line shows $S_V$ calculated using an approximate virial expansion to tenth order [37].

Figure 2

Vector response $S_V$ (upper three curves) and axial response $S_A$ (lower four curves) versus Fermi energy over temperature ${\epsilon }_F/T$. Unitary gas fourth-order virial results from Fig. 1 are solid while second order virial results are dotted. Pure neutron gas results at a temperature of 10 MeV, to second order in the virial expansion, are dashed. Finally the dot-dashed curve shows the fit from Ref. [6] for pure neutron matter. This reproduces virial results at low density and RPA calculations [11] at high densities.