Detectability of collective neutrino oscillation signatures in the supernova explosion of a $8.8M_{\odot }$ star

In order to investigate the impact of collective neutrino oscillations (CNOs) on the neutrino signal from a nearby supernova, we perform three-flavor neutrino oscillation simulations employing the multiangle effect. The background hydrodynamic model is based on the neutrino hydrodynamic simulation of a $8.8M_{\odot }$ progenitor star. We find that CNO commences after some 100 ms post bounce. Before this, CNO is suppressed by matter-induced decoherence. In the inverted mass hierarchy, the spectrum of ${\overline{\nu }}_e$ becomes softer after the onset of CNO. To evaluate the detectability of this modification, we define a hardness ratio between the number of high energy neutrino events and low energy neutrino events adopting a fixed critical energy. We show that Hyper-Kamiokande (HK) can distinguish the effect of CNO for supernova distances out to $\sim 10\mathrm{kpc}$. On the other hand, for the normal mass hierarchy, the spectrum of ${\nu }_e$ becomes softer after the onset of CNO, and we show that DUNE can distinguish this feature for supernova distances out to $\sim 10\mathrm{kpc}$. More work is necessary to optimize the best value of critical energy for maximum sensitivity. We also show that if the spectrum of ${\overline{\nu }}_e$ in HK becomes softer due to CNO, the spectrum of ${\nu }_e$ in DUNE becomes harder, and vice versa. These synergistic observations in ${\overline{\nu }}_e$ and ${\nu }_e$, by HK and DUNE, respectively, will be an intriguing opportunity to test the occurrence of CNO.

Figure 1

The black curve is the time evolution of the shock radius. The colored areas show the time evolution of the logarithmic density profile $[\mathrm{g}/{\mathrm{cm}}^3]$. The horizontal axis is the time after bounce in ms, and the vertical axis shows the radial coordinates in km.

Figure 2

Time evolution of the neutrino luminosity (top panel), the neutrino average energy (central panel), and the neutrino number luminosity (bottom panel). In all panels, the green, red, and blue curves correspond to ${\nu }_e$, ${\overline{\nu }}_e$, and ${\nu }_X$, respectively. In the middle panel, the solid line denotes the mean energy, and the dotted line is the rms energy. We evaluate the luminosities and energies at 500 km and assume the bulb model; i.e., those luminosities and energies are set to the neutrinosphere in the oscillation simulations.

Figure 3

The survival probabilities of an electron antineutrino at a radius of 1500 km as a function of neutrino energy and emission time. Top panel: The probability for the inverted mass hierarchy. Bottom panel: The probability for the normal mass hierarchy. In both panels, we employ the multiangle method to calculate neutrino oscillations, and the Gamma function [Eq. (1)] is used for the neutrino spectrum.

Figure 4

The radial profiles of conversion probabilities of ${\overline{\nu }}_e$ at 231 ms postbounce. The inverted mass hierarchy is assumed, and the multiangle scheme (labeled MA) is used. The different colors show the profile at different energies of the neutrino: Red, green, and violet correspond to 2.4, 12.0, and 40.0 MeV, respectively.

Figure 5

Flux spectra of electron antineutrinos in the inverted mass hierarchy (red solid line). For comparison, the original electron neutrino (green dotted line) and heavy lepton neutrino (blue dotted line) are shown. The time snapshot of 231 ms is used. Top panel: CNO with the MA scheme (1500 km from the center; note that the vertical axis has been rescaled to a source distance of 10 kpc). Bottom panel: Flux spectrum at the Earth, including all oscillation effects (CNO, MSW, vacuum). Note that in both panels, the horizontal axis is logarithmic for $E<20\mathrm{MeV}$ and linear for $E>20\mathrm{MeV}$ in the both panels (indicated by the vertical dashed line).

Figure 6

The radial profiles of conversion probabilities of ${\overline{\nu }}_e$ at 81 ms postbounce. The normal mass hierarchy is assumed, and the multiangle scheme (labeled MA) is used. The different colors show the profile at different energies of the neutrino: Red, green, and violet correspond to 2.4, 12.0, and 40.0 MeV, respectively.

Figure 7

The time snapshots of matter potential ${\lambda }_r=\sqrt{2}{G}_F{n}_e$ for 81 and 281 ms postbounce. The horizontal band shows the values of atmospheric vacuum frequencies ${\omega }_{\mathrm{atm}}=|\mathrm{\Delta }{m}_{32}^2|/2E$ for $E[\mathrm{MeV}]\in [1.2,60]$. The upper line corresponds to that of the lowest energy. The MSW resonance occurs when the matter potential enters the band of ${\omega }_{\mathrm{atm}}$.

Figure 8

The radial profiles of conversion probabilities of electron antineutrinos at 281 ms postbounce in the normal mass hierarchy. The different colors show the profiles of different conversion probabilities of ${\overline{\nu }}_e$: $P_{e\alpha }=P({\overline{\nu }}_e\to {\overline{\nu }}_{\alpha })(\alpha =e,x,y)$ whose energy is 40 MeV. The red, green, and violet lines correspond to $P_{ee}$, $P_{ex}$, and $P_{ey}$, respectively.

Figure 9

Evolution of event number in 50 ms bins (solid lines, left axis) and the hardness ratio (dotted lines, right axis). Top: That of HK in the inverted mass hierarchy. A volume of 220 kton is adopted. Middle: That of HK in the normal mass hierarchy. Bottom: That of JUNO in the inverted mass hierarchy. See the text for adopted detector parameters.

Figure 10

Same as Fig. 5 but for the normal mass hierarchy. The time snapshot of 81 ms is used.

Figure 11

Same as Fig. 5, but for electron neutrinos. Note that in both panels, the horizontal axis is logarithmic for $E<15\mathrm{MeV}$ and linear for $E>15\mathrm{MeV}$ in the both panels (indicated by the vertical dashed line).

Figure 12

Event number and hardness ratio in 50 ms bins, both for ${\nu }_e$ detected by DUNE. Note that a lower $E_c$ is adopted than that in Fig. 9. Top panel: The case of inverted mass hierarchy and a source distance of 2 kpc. Bottom panel: The case of normal mass hierarchy and a source distance of 8 kpc.

Figure 13

The comparison of conversion probabilities of ${\overline{\nu }}_e$ in the inverted mass hierarchy at 181 ms postbounce. The solid (dashed) lines represent radial profiles of conversion probabilities in the bulb model assuming $R=30(50)\mathrm{km}$.

Figure 14

Comparison of ${\overline{\nu }}_e$ spectra after CNO. The red (magenta) line represents ${\overline{\nu }}_e$ spectra after CNO in the $R=30(50)\mathrm{km}$ model. As in Fig. 5, the flux is scaled to that for the 10 kpc source.

Figure 15

Same as Fig. 3 but with nondegenerate Fermi-Dirac distributions for the initial neutrino spectra.

Figure 16

Same as Fig. 9 but for the FD initial spectra. Different from Fig. 9, the result for JUNO is omitted. Note that the source distance is assumed to be 10 kpc, while 20 kpc is used in Fig. 9.

Figure 17

Same as Fig. 12 but for the FD initial spectra.