Effects of neutrino oscillations on nucleosynthesis and neutrino signals for an $18M_{\odot }$ supernova model

In this paper, we explore the effects of neutrino flavor oscillations on supernova nucleosynthesis and on the neutrino signals. Our study is based on detailed information about the neutrino spectra and their time evolution from a spherically symmetric supernova model for an $18M_{\odot }$ progenitor. We find that collective neutrino oscillations are not only sensitive to the detailed neutrino energy and angular distributions at emission, but also to the time evolution of both the neutrino spectra and the electron density profile. We apply the results of neutrino oscillations to study the impact on supernova nucleosynthesis and on the neutrino signals from a Galactic supernova. We show that in our supernova model, collective neutrino oscillations enhance the production of rare isotopes ${}^{138}\mathrm{La}$ and ${}^{180}\mathrm{Ta}$ but have little impact on the $\nu \mathrm{p}$-process nucleosynthesis. In addition, the adiabatic Mikheyev-Smirnov-Wolfenstein flavor transformation, which occurs in the $\mathrm{C}/\mathrm{O}$ and He shells of the supernova, may affect the production of light nuclei such as ${}^7\mathrm{Li}$ and ${}^{11}\mathrm{B}$. For the neutrino signals, we calculate the rate of neutrino events in the Super-Kamiokande detector and in a hypothetical liquid argon detector. Our results suggest the possibility of using the time profiles of the events in both detectors, along with the spectral information of the detected neutrinos, to infer the neutrino mass hierarchy.

Figure 1

Sketch of neutrino emission and propagation.

Figure 2

Evolution of neutrino luminosities [panels (a)–(c)] and average energies [panels (d)–(f)] for the $18M_{\odot }$ supernova model as observed at infinity [37].

Figure 3

Evolution of (a) radius, (b) density, (c) temperature, and (d) electron fraction for four mass elements in the neutrino-driven wind of the $18M_{\odot }$ supernova model. The mass elements are labeled by their enclosed baryonic masses in units of $M_{\odot }$. The radius and density at which the temperature in units of GK reaches $T_9=10$, 7, 3, and 1 are marked in panels (a) and (b).

Figure 4

Neutrino decoupling in the $18M_{\odot }$ supernova model. (a) Comparison of ${\nu }_e$ angular distributions at the conventional neutrinosphere ($r=R_{\nu }$, blue dashed curve) and the decoupling sphere ($r=R_d$, red solid curve) for $t_{\mathrm{pb}}=1.025\mathrm{s}$. (b) Luminosities (corrected for gravitational redshift) of ${\nu }_e$ (black solid curve), ${\overline{\nu }}_e$ (red dashed curve), and ${\nu }_{\mu (\tau )}$ (blue dotted curve) as functions of radius for $t_{\mathrm{pb}}=1.025\mathrm{s}$, exhibiting constancy at $r>R_d$ to very good approximation. The luminosity of ${\overline{\nu }}_{\mu (\tau )}$ is essentially the same as that of ${\nu }_{\mu (\tau )}$.

Figure 5

Profiles of $n_e(r)$ (thin curves) and the net ${\nu }_e$ number density $n_{{\nu }_e}(r)-n_{{\overline{\nu }}_e}(r)$ in the absence of neutrino oscillations (thick curves) for $t_{\mathrm{pb}}\approx 0.6$ (green solid curve), 1.0 (blue dashed curve), and 3.0 s (red dotted curve), respectively, in the $18M_{\odot }$ supernova model.

Figure 6

The angle-averaged survival probabilities (a) $⟨P_{{\nu }_e{\nu }_e}{⟩}_v$ and (b) $⟨P_{{\overline{\nu }}_e{\overline{\nu }}_e}{⟩}_v$ as functions of $E$ and emission time $t_{\text{em}}$ (in terms of $t_{\mathrm{pb}}$) at $r=500\mathrm{km}$.

Figure 7

Angle-and-energy-averaged conversion probabilities ${⟨P_{{\nu }_e{\nu }_x}⟩}_{v,E}$ (thick black dotted curve), ${⟨P_{{\nu }_e{\nu }_y}⟩}_{v,E}$ (thick red solid curve), ${⟨P_{{\overline{\nu }}_e{\overline{\nu }}_x}⟩}_{v,E}$ (thick orange dash-dotted curve), and ${⟨P_{{\overline{\nu }}_e{\overline{\nu }}_y}⟩}_{v,E}$ (thick blue dashed curve) as functions of radius calculated from multi-angle simulations for $t_{\mathrm{pb}}=1.025$ (a), 3.007 (b), and 5.0 s (c). Similar quantities from single-angle calculations are shown as the corresponding thin curves.

Figure 8

Angle-averaged survival probabilities $⟨P_{{\nu }_e{\nu }_e}{⟩}_v$ ($\omega >0$) and $⟨P_{{\overline{\nu }}_e{\overline{\nu }}_e}{⟩}_v$ ($\omega <0$) at $r=500\mathrm{km}$ as functions of $\omega$ calculated from multi-angle simulations (red solid curve) for $t_{\mathrm{pb}}=1.025$ (a), 3.007 (b), and 5.0 s (c). The corresponding single-angle results for $1-P_{{\nu }_e{\nu }_y}$ and $1-P_{{\overline{\nu }}_e{\overline{\nu }}_y}$ are shown as blue dashed curves. The green dotted curves give the function $g(\omega )/15+0.5$.

Figure 9

Angle-averaged survival probabilities $⟨P_{{\nu }_e{\nu }_e}{⟩}_v$ ($\omega >0$) and $⟨P_{{\overline{\nu }}_e{\overline{\nu }}_e}{⟩}_v$ ($\omega <0$) as functions of $\omega$ at $r=500\mathrm{km}$ for $t_{\mathrm{pb}}=1.025\mathrm{s}$ obtained from multi-angle simulations assuming isotropic neutrino emission (blue dashed curve). The red solid curve [same as in Fig. 8] is calculated with the forward-peaked neutrino angular distributions in our supernova model and is shown for comparison.

Figure 10

(a) Onset radii $r_{\text{on}}$ for two flavor instabilities as functions of time. (b) Corresponding ${\lambda }_{\text{on}}=\lambda (r_{\text{on}})$ (thin curves) and ${\mu }_{\text{on}}=\mu (r_{\text{on}})$ (thick curves) as functions of time. The instability occurring at smaller radii (solid curves) only exists for $t_{\mathrm{pb}}\sim 1\mathrm{s}$ while that occurring at larger radii (dashed curves) exists for $t_{\mathrm{pb}}\gtrsim 1\mathrm{s}$.

Figure 11

Comparison of $⟨P_{{\nu }_e{\nu }_y}{⟩}_{v,E}$ calculated for $n_e(r)$ in our supernova model (red solid curves), $n_e^{\prime }(r)=0.5n_e(r)$ (blue dashed curves), and $n_e^{\prime \prime }(r)=0.2n_e(r)$ (black dotted curves) for $t_{\mathrm{pb}}=1.025$ (a) and 5.0 s (b), respectively.

Figure 12

Comparison of $⟨P_{{\nu }_e{\nu }_e}{⟩}_v$ ($\omega >0$) and $⟨P_{{\overline{\nu }}_e{\overline{\nu }}_e}{⟩}_v$ ($\omega <0$) at $r=500\mathrm{km}$ calculated for $n_e(r)$ in our supernova model (red solid curves), $n_e^{\prime }(r)=0.5n_e(r)$ (blue dashed curves), and $n_e^{\prime \prime }(r)=0.2n_e(r)$ (black dotted curves) for $t_{\mathrm{pb}}=1.025$ (a) and 5.0 s (b), respectively. Note that in (b), the ${\overline{\nu }}_e$ flavor conversion for $\omega \lesssim -1{\mathrm{km}}^{-1}$ is due to the MSW effect for the reduced $n_e^{\prime \prime }(r)$.

Figure 13

(a) Comparison of $⟨P_{{\nu }_e{\nu }_y}{⟩}_{v,E}$ for ${\theta }_{13}=0.15$ (red solid curve) and 0.1 (black dashed curve) as functions of radius for $t_{\mathrm{pb}}=3.007\mathrm{s}$. (b) Difference in survival probability $\mathrm{\Delta }⟨P_{{\nu }_e{\nu }_e}{⟩}_v\equiv ⟨P_{{\nu }_e{\nu }_e}({\theta }_{13}=0.15){⟩}_v-⟨P_{{\nu }_e{\nu }_e}({\theta }_{13}=0.1){⟩}_v$ at $r=500\mathrm{km}$ as functions of neutrino energy for $t_{\mathrm{pb}}=1.025$ (blue solid curve), 1.401 (red dashed curve), 3.007 (black dotted curve), and 5.0 s (green dot-dashed curve), respectively.

Figure 14

Rates ${\lambda }_{\nu N}^0$ of ${\nu }_e$ (thin solid red curve) and ${\overline{\nu }}_e$ (thin dashed blue curve) absorption on free nucleons in the absence of neutrino oscillations as functions of time $t-t_0$ during expansion of four mass elements ejected from the proto-neutron star at $t_0=0.840$ (a), 1.253 (b), 1.726 (c), and 2.526 s (d), respectively (both $t$ and $t_0$ are in terms of $t_{\mathrm{pb}}$). The corresponding thick curves show the ratios ${\lambda }_{\nu N}^{\text{osc}}/{\lambda }_{\nu N}^0$ of absorption rates with and without neutrino oscillations. The times at which the temperature of a mass element reaches $T=10$, 7, 3, 2, and 1 GK, respectively, are also indicated.

Figure 15

Snapshots of the electron number density $n_e$ as a function of radius for $t_{\mathrm{pb}}=1.0$ (black solid curve), 3.0 (red dashed curve), and 5.0 s (blue dotted curve), respectively. The gray and yellow bands indicate the range of $n_{\mathrm{e},\mathrm{MSW}}^{13}$ and $n_{\mathrm{e},\mathrm{MSW}}^{12}$ for $5<E<100\mathrm{MeV}$, respectively. The positions of the $\mathrm{O}/\mathrm{Ne}$, $\mathrm{C}/\mathrm{O}$, and He layers are marked by the vertical lines. The bump in $n_e$ at $r\sim 10^3–{10}^4\mathrm{km}$ corresponds to matter that has been shocked recently.

Figure 16

Effective probabilities $P_{{\nu }_e{\nu }_e}^{\prime }$ [(a) and (c)] and $P_{{\overline{\nu }}_e{\overline{\nu }}_e}^{\prime }$ [(b) and (d)] following adiabatic MSW flavor conversion as functions of $r$ and $E$ for both the NH and IH.

Figure 17

(a) The ratio ${\lambda }^{\text{osc}}/{\lambda }^0$ (thick curves) and the rate ${\lambda }^0$ without neutrino oscillations (thin curves) for charged-current ${\nu }_e$ (red solid curves) and ${\overline{\nu }}_e$ (blue dashed curves) interactions on ${}^4\mathrm{He}$ at $r=10^5\mathrm{km}$ as functions of $t_{\mathrm{pb}}$ for the NH. (b) Same as (a) but for the IH. The thickest curves are for the full case including both collective neutrino oscillations and MSW flavor transformation while the thicker curves are for the case of pure MSW flavor transformation.

Figure 18

(a) The ratio $\mathrm{\Delta }{n}^{\text{osc}}/\mathrm{\Delta }{n}^0$ (thick curves) and the time-integrated rate $\mathrm{\Delta }{n}^0$ without neutrino oscillations (thin curves) as functions of $r$ for charged-current ${\nu }_e$ (red solid curves) and ${\overline{\nu }}_e$ (blue dashed curves) interactions on ${}^4\mathrm{He}$ for the NH. (b) Same as (a) but for the IH. The thickest curves are for the full case including both collective neutrino oscillations and MSW flavor transformation while the thicker curves are for the case of pure MSW flavor transformation.

Figure 19

The ratios ${\lambda }^{\text{osc}}/{\lambda }^0$ for charged-current interactions of ${\nu }_e$ on ${}^{138}\mathrm{Ba}$ (red solid curves) and ${}^{180}\mathrm{Hf}$ (blue dashed curves) as functions of $t_{\mathrm{pb}}$ for the IH. The rates ${\lambda }^0$ at $r=10^4\mathrm{km}$ without oscillations (thin curves) are also shown.

Figure 20

The number of all neutrino events per time bin as a function of time for an LArTPC detector and the Super-K detector, respectively, during (a) the neutronization burst, (b) the accretion phase, and (c) the proto-neutron star cooling phase of a Galactic supernova at a distance of 10 kpc.

Figure 21

Time-integrated energy spectra of neutrino events during the first 0.5 s for the LArTPC and Super-K detectors.