Neutrino flavor evolution in neutron star mergers

We examine the flavor evolution of neutrinos emitted from the disklike remnant (hereafter called “neutrino disk”) of a binary neutron star (BNS) merger. We specifically follow the neutrinos emitted from the center of the disk, along the polar axis perpendicular to the equatorial plane. We carried out two-flavor simulations using a variety of different possible initial neutrino luminosities and energy spectra and, for comparison, three-flavor simulations in specific cases. In all simulations, the normal neutrino mass hierarchy was used. The flavor evolution was found to be highly dependent on the initial neutrino luminosities and energy spectra; in particular, we found two broad classes of results depending on the sign of the initial net electron neutrino lepton number (i.e., the number of neutrinos minus the number of antineutrinos). In the antineutrino-dominated case, we found that the matter-neutrino resonance effect dominates, consistent with previous results, whereas in the neutrino-dominated case, a bipolar spectral swap develops. The neutrino-dominated conditions required for this latter result have been realized, e.g., in a BNS merger simulation that employs the “DD2” equation of state for neutron star matter [Phys. Rev. D 93, 044019 (2016)]. For this case, in addition to the swap at low energies, a collective Mikheyev-Smirnov-Wolfenstein mechanism generates a high-energy electron neutrino tail. The enhanced population of high-energy electron neutrinos in this scenario could have implications for the prospects of $r$-process nucleosynthesis in the material ejected outside the plane of the neutrino disk.

Figure 1

These plots show the initial (magenta and black) and final (blue and green) energy spectra for neutrinos (left) and antineutrinos (right), for the simulation with parameters as described in Table 1. The final spectra were plotted at a distance $r=5000\mathrm{km}$ along the polar axis. As is evident, the MNR affected primarily the high-energy neutrinos. Neutrinos with energies below $E_{\nu }\lesssim 16\mathrm{MeV}$ and antineutrinos were not significantly affected.

Figure 2

These figures show the energy-averaged flavor evolution of a neutrino (left) and antineutrino (right), initially in the electron flavor state, for the simulation with parameters as described in Table 1. It is evident that the MNR begins early on at a distance of about $\approx 200\mathrm{km}$ and stabilizes at about $\approx 1200\mathrm{km}$. In each of these energy-averaged flavor evolution plots, the lines corresponding to different flavors (e.g., the blue and green lines in the left panel) sum to unity at each radius.

Figure 3

Same as Fig. 2, but for a neutrino (left) and antineutrino (right) initially in the $x$-flavor state. Mirroring the results of the initially electron flavor neutrinos, most of the flavor transformation occurs for the neutrinos, while the antineutrinos remain largely unaffected by the MNR.

Figure 4

Shown here is the 1-1 component of the matter, neutrino-neutrino, and the sum of the matter and neutrino-neutrino Hamiltonian experienced by our test neutrinos, for the simulation with parameters as described in Table 1. As we can see, the MNR develops early on at a radius of $\approx 200\mathrm{km}$. The nonlinear feedback of neutrino flavor transformations keep the total Hamiltonian near 0 for several hundred kilometers, thus giving rise to the MNR. In order to calculate the total Hamiltonian, an energy-dependent $(H_{\mathrm{vac}}{)}_{11}$ would have to be added. This vacuum term would manifest as an energy-dependent vertical offset (in the negative direction). Thus, not all neutrinos of all energies will go through the MNR, explaining the energy dependence of the MNR effect seen in Fig. 1.

Figure 5

These figures show some of the results from a three-flavor MNR calculation with the same parameters as in Table 1. (Left) Initial and final ($r=5000\mathrm{km}$) neutrino spectra for a three-flavor MNR calculation. (Right) Evolution of a neutrino initially in the electron flavor state.

Figure 6

Shown here are the initial ${\nu }_e$ (magenta) and ${\nu }_x$ (black) energy spectra, as well as the final ${\nu }_e$ (blue) and ${\nu }_x$ (green) spectra, at a distance of 5000 km from the neutrino disk along the polar-axis trajectory, for the simulation with parameters as described in Table 2. A flavor swap is seen to occur at an energy of approximately 8 MeV, and a high-energy electron neutrino tail is also seen to develop. This tail of high-energy electron neutrinos could potentially affect the electron fraction significantly.

Figure 7

Shown here are the initial ${\overline{\nu }}_e$ (magenta) and ${\overline{\nu }}_x$ (black) energy spectra, as well as the final ${\overline{\nu }}_e$ (blue) and ${\overline{\nu }}_x$ (green) spectra at a distance of 5000 km from the neutrino disk, along the polar-axis trajectory, for the same simulation as Fig. 6. Antineutrinos did not significantly convert from one flavor to another.

Figure 8

These plots show the energy-averaged neutrino flavor evolution for a neutrino (left) and an antineutrino (right) initially in the electron flavor state, for the simulation with the parameters listed in Table 2. We can see that significant flavor transformations begin to occur at a radius of approximately 600 km and these flavor oscillations stabilize at a radius of approximately 2000 km.

Figure 9

This is the energy-averaged evolution of neutrino flavors for a neutrino (left) and antineutrino (right) initially in the $x$-flavor state.

Figure 10

Results for a calculation run using the luminosities and average energies adopted from the DD2 equation-of-state simulation in Ref. [16]. This calculation also demonstrates a bipolar spectral swap, qualitatively very similar to the one shown in Fig. 6. (Left) Initial and final ($r=5000\mathrm{km}$) neutrino energy spectra. (Right) Energy-averaged flavor evolution of a neutrino initially emitted in the electron flavor state.

Figure 11

This is the final energy distribution spectra of neutrinos for a three-flavor simulation. Initial $\mu$ and $\tau$ neutrinos have the same energy spectra and so overlap on this graph. The red line represents both flavors.

Figure 12

Same as Fig. 11, but for antineutrinos.

Figure 13

Plots of the energy-averaged flavor evolution of neutrinos which start in the various initial states. We can see here that still interesting neutrino flavor transformations seem to occur at a radius of approximately 600 km. However, here, the neutrino flavor transformations do not seem to stabilize as much as in the two-flavor case. Although the antineutrinos mix more in the three-flavor case than the two-flavor case, it still does not convert as many $\mu$ and $\tau$ flavor antineutrinos into the electron flavor as in the neutrino sector.

Figure 14

These figures show the final energy spectra of neutrinos and antineutrinos, respectively, run with lowered luminosity and density conditions from those simulations shown in Secs. 3c and 3d. In the neutrino sector, we can see a very clear bipolar swap at an energy of $\approx 8\mathrm{MeV}$. This is perhaps the clearest bipolar swap result found in our simulations. In addition, the high-energy electron neutrino tail for neutrinos of energy $\gtrsim 38\mathrm{MeV}$ is very pronounced.

Figure 15

These figures show the energy-averaged flavor evolution of a neutrino and antineutrino, respectively, which started out in the electron flavor state for a simulation with a lowered neutrino luminosity and initial density. We can see that flavor evolution sets in much closer to the neutrino disk than the simulations shown with a higher luminosity and density in Secs. 3c and 3d. Here the flavor evolution begins around a radius of $\approx 100\mathrm{km}$.

Figure 16

This is the evolution of neutrino flavors for a neutrino and antineutrino initially in the $x$-flavor state in a simulation with a lowered luminosity and initial density.