Possible effects of collective neutrino oscillations in three-flavor multiangle simulations of supernova $\nu p$ processes

We study the effects of collective neutrino oscillations on $\nu p$ process nucleosynthesis in proton-rich neutrino-driven winds by including both the multiangle $3\times 3$ flavor mixing and the nucleosynthesis network calculation. The number flux of energetic electron antineutrinos is raised by collective neutrino oscillations in a 1D supernova model for the $40M_{\odot }$ progenitor. When the gas temperature decreases down to $\sim 2–3\times {10}^9\mathrm{K}$, the increased flux of electron antineutrinos promotes the $\nu p$ process more actively, resulting in the enhancement of $p$-nuclei. In the early phase of neutrino-driven wind, blowing at 0.6 s after core bounce, oscillation effects are prominent in inverted mass hierarchy and $p$-nuclei are synthesized up to ${}^{106}\mathrm{Cd}$ and ${}^{108}\mathrm{Cd}$. On the other hand, in the later wind trajectory at 1.1 s after core bounce, abundances of $p$-nuclei are increased remarkably by $\sim 10–{10}^4$ times in normal mass hierarchy and even reaching heavier $p$-nuclei such as ${}^{124}\mathrm{Xe}$, ${}^{126}\mathrm{Xe}$ and ${}^{130}\mathrm{Ba}$. The averaged overproduction factor of $p$-nuclei is dominated by the later wind trajectories. Our results demonstrate that collective neutrino oscillations can strongly influence the $\nu p$ process, which indicates that they should be included in the network calculations in order to obtain precise abundances of $p$-nuclei. The conclusions of this paper depend on the difference of initial neutrino parameters between electron and nonelectron antineutrino flavors which is large in our case. Further systematic studies on input neutrino physics and wind trajectories are necessary to draw a robust conclusion. However, this finding would help understand the origin of solar-system isotopic abundances of $p$-nuclei such as ${}^{92,94}\mathrm{Mo}$ and ${}^{96,98}\mathrm{Ru}$.

Figure 1

The time evolution of neutrino luminosities $L_{\nu }$ (a), mean energies $⟨E_{\nu }⟩$ (b), and shape parameters $\gamma$ (c) in the 1D explosion model where ${\nu }_{\beta }={\nu }_{\mu }$, ${\nu }_{\tau }$, ${\overline{\nu }}_{\mu }$, ${\overline{\nu }}_{\tau }$.

Figure 2

This figure shows the evolution of angle averaged $⟨{\overline{\rho }}_{ee}(r,E)⟩$ in normal (a) and inverted (b) mass hierarchies in the early flow ($t=0.6\mathrm{s}$). $⟨{\overline{\rho }}_{ee}(r,E)⟩$ represents the ratio of ${\overline{\nu }}_e$ in an antineutrino whose energy is $E$ at $r$. The $\nu p$ process takes place during $T\sim 2–3\times {10}^9\mathrm{K}$ which corresponds to $r\sim 350–680\mathrm{km}$.

Figure 3

The evolution of energy spectra of antineutrinos from $r=40$ to 3300 km in both normal and inverted mass hierarchies using the early wind trajectory ($t=0.6\mathrm{s}$). Thin dashed curves display initial antineutrino spectra. There are two spectral crossing points in antineutrino spectra whose energies are $E_{c1}^{(e)}=7.1\mathrm{MeV}$ and $E_{c2}^{(e)}=22.3\mathrm{MeV}$.

Figure 4

The evolution of normalized $\lambda r^2$ in the early outflow model ($t=0.6\mathrm{s}$) where $\lambda$ represents the reaction rate of the charged current reaction ${\overline{\nu }}_e+p\to e^{+}+n$ or the neutral current reaction $\alpha +\nu \to {}^3\mathrm{He}+n+{\nu }^{\prime }$. The $\nu p$ process is active in the region $r\sim 350–680\mathrm{km}$.

Figure 5

The evolution of $⟨{\overline{\rho }}_{ee}(r,E)⟩$ in normal (a) and inverted (b) mass hierarchies using the later wind trajectory ($t=1.1\mathrm{s}$). The $\nu p$ process occurs during $r\sim 245–470\mathrm{km}$.

Figure 6

The evolution of energy spectra of antineutrinos for the later wind trajectory ($t=1.1\mathrm{s}$) as in Fig. 3. The spectral crossing points are $E_{c1}^{(l)}=8.2\mathrm{MeV}$ and $E_{c2}^{(l)}=17.8\mathrm{MeV}$.

Figure 7

The evolution of normalized $\lambda r^2$ in the later outflow model ($t=1.1\mathrm{s}$) as in Fig. 4. The $\nu p$ process occurs in the interval $r\sim 245-470\mathrm{km}$.

Figure 8

The overproduction factors of $p$-nuclei ${\mathrm{\Gamma }}_i$ in the early trajectory (a), later trajectory (b). The averaged value of overproduction factor (c) is obtained by using Eqs. (16) and (17).