Thermalization of Neutrinos in a Neutron Star Merger Simulation

Abstract

We study the neutrino distributions that arise in a simulation of a neutron star merger that uses a Monte Carlo (MC) neutrino transport scheme. In a snapshot taken 1 ms after merger, we calculate relevant observables to test when neutrinos behave like a thermalized gas, and when a free-streaming picture is more appropriate. We find that in hot, dense regions where neutrino-matter interactions are frequent, MC neutrino and antineutrino distributions are consistent with thermalized neutrinos. In moderately warm regions, where neither approximation is expected to hold, we find significant departures from the predictions of the thermalized-neutrino approximation, particularly for the (anti)neutrino average opacity and net rate of absorption per baryon, even when average energies appear approximately thermal. At lower temperatures, MC results approach the free-streaming limit. Our results demonstrate that energy-averaged agreement with thermalized-neutrino assumptions does not guarantee accurate weak interaction rates. Non-equilibrium aspects of the neutrino distribution are therefore crucial for neutrino-mediated microphysics such as composition evolution in the early post-merger phase.

Figures (8)

• Figure 1: Each contour encloses the range of temperature and baryon number density of fluid cells with a proton fraction within $\pm\,5\%$ of the specified NuLib proton fractions $x_p$, in our 1 ms time slice.
• Figure 2: Top: Side cross-sectional view of the thermal profile for the merger simulation $1\,\text{ms}$ after merger showing all fluid cells with $n_B\geq1\,n_{0}$, where the rotation axis is in the $z$-direction. The black dots show the location of a subset of the fluid cells we analyze in Sec. \ref{['sec: compare_mc_fd_warm']}. Bottom: Same as the top panel but showing an equatorial cross-sectional view.
• Figure 3: The (anti)neutrino mean net displacement between thermalizing collisions (Eq. \ref{['eq:lambda-d']}) (in meters) for $n_B=2.34\,n_{0}$ and $x_p=0.081$. The black dotted lines show the average energy $\langle E_{\nu,{\bar{\nu}}} \rangle=3 T$ of nondegenerate thermalized (anti)neutrinos. The qualitative behavior of both panels does not change if the proton fraction or the baryon density take the other values considered in this paper, i.e., $x_p=0.057$ and $n_B=1.78\,n_{0}$.
• Figure 4: Top: Neutrino number density as a function of energy. The energy-binned Monte Carlo (MC) distribution in pink is from a representative fluid cell with parameters $T = 62.5\,\text{MeV}$, $n_B = 2.34\,n_{0}$, $x_p = 0.081$, $x_L = 0.048$ ($x_\nu=0.002$, $x_{\bar{\nu}}=0.035$). The Fermi--Dirac (FD) distribution, where $\mu_\nu$ is fixed by the fluid cell's neutrino number density, is in black. Bottom: Antineutrino number density as a function of energy in purple from the same fluid cell as the top panel, where $\mu_{\bar{\nu}}$ is fixed by the fluid cell's antineutrino number density.
• Figure 5: Properties of hot ($T=62.5\,\text{MeV}$) fluid cells with baryon density $n_B=2.34\,n_{0}$ and proton fraction $x_p=0.081$, comparing Monte Carlo (MC) simulation data with predictions from thermalized-neutrino (FD) and free-streaming-neutrino (Free) approximations. (a) Top row: Average neutrino (left panel, pink) and antineutrino (right panel, purple) energy as a function of the (anti)neutrino fraction, showing individual MC fluid cells (pale dots), averages over cells in (anti)neutrino fraction deciles, and the thermalized-neutrino approximation (solid pink/purple lines). (b) Middle row: Average (anti)neutrino opacity, following the same conventions as the top row, except the diamonds correspond to decile medians. (c) Bottom row: Net rate of (anti)neutrino absorption per baryon as a function of (anti)neutrino fraction and the corresponding chemical potentials in the thermalized-neutrino approximation, following the same conventions as the top row, except the diamonds correspond to decile medians. Blue lines are the predictions of the free-streaming-neutrino approximation.