Neutrino oscillation signatures of oxygen-neon-magnesium supernovae

We discuss the flavor conversion of neutrinos from core-collapse supernovae that have oxygen-neon-magnesium (ONeMg) cores. Using the numerically calculated evolution of the star up to 650 ms post bounce, we find that, for the normal mass hierarchy, the electron neutrino flux in a detector shows signatures of two typical features of an ONeMg-core supernova: a sharp step in the density profile at the base of the He shell and a faster shock wave propagation compared to iron core supernovae. Before the shock hits the density step ($t\lesssim 150\mathrm{ms}$), the survival probability of electron neutrinos above $\sim 20\mathrm{MeV}$ of energy is about $\sim 0.68$, in contrast to values of $\sim 0.32$ or less for an iron core supernova. The passage of the shock through the step and its subsequent propagation cause a decrease of the survival probability and a decrease of the amplitude of oscillations in the Earth, reflecting the transition to a more adiabatic propagation inside the star. These changes affect the lower energy neutrinos first; they are faster and more sizable for larger ${\theta }_{13}$. They are unique of ONeMg-core supernovae, and give the possibility to test the speed of the shock wave. The time modulation of the Earth effect and its negative sign at the neutronization peak are the most robust signatures in a detector.

Figure 1

Snapshots of the electron density profile at $t=0,50,100,\dots ,700\mathrm{ms}$ (lines from top to bottom at their left end, except for the inverted curves for $t=0$ and $t=50\mathrm{ms}$). The positions of the supernova shock for $t\ge 200\mathrm{ms}$ coincide essentially with the lower right footprints of the profiles. For $t=300\mathrm{ms}$ we also plot the effective number density of neutrinos [dashed curve, see Eq. (4)], which is responsible for the effects of neutrino-neutrino forward scattering. The two horizontal lines represent the densities corresponding to the two MSW resonances for a neutrino of 20 MeV energy.

Figure 2

Neutrino luminosities (top) and average energies (bottom) before oscillations. The ${\nu }_x$ (${\nu }_x={\nu }_{\mu }$, ${\nu }_{\tau }$, ${\overline{\nu }}_{\mu }$, ${\overline{\nu }}_{\tau }$) luminosity is per species, so the total luminosity in the nonelectron flavors is 4 times the one plotted here. The average energy is defined as the ratio of energy flux to number flux.

Figure 3

The jumping probability $P_H$ for $t=60$, 450, 700 ms (solid curves, from upper to lower) as a function of ${sin}^2{\theta }_{13}$ for energy $E=20\mathrm{MeV}$. The dashed line shows the same probability for a Fe supernova with the parameters in Ref. 3.

Figure 4

The electron neutrino survival probability for $t=60$, 450, 700 ms (solid line, short-dashed line, and long-dashed line, respectively) and ${sin}^2{\theta }_{13}=6\times {10}^{-4}$. $p=0$ for a Fe-core supernova over the same time interval.

Figure 5

The ${\nu }_e$ survival probability as a function of time for $E=20\mathrm{MeV}$ and ${sin}^2{\theta }_{13}=0.01$, $6·{10}^{-4}$, ${10}^{-5}$ (solid line, short-dashed line, and long-dashed line, respectively). The steplike structure reflects the fact that the oscillation effects were evaluated for density profiles in steps of 50 ms ($t=0,50,100,\dots \mathrm{ms}$, middle points of the steps, see profiles of Fig. 1). For $t\sim 150–300\mathrm{ms}$ the figure is only schematic: it does not capture the full complexity of the conversion in accelerating matter when the shock passes through the density step (see Sec. 3b).

Figure 6

The relative Earth matter effect in the neutrino channel, at 60 degrees nadir angle, for $t=60$, 450, 700 ms (solid line, short-dashed line, and long-dashed line, respectively) and ${sin}^2{\theta }_{13}=6\times {10}^{-4}$. For a Fe supernova and the same value of ${\theta }_{13}$, the Earth effect is zero.

Figure 7

Same as Fig. 6 for ${sin}^2{\theta }_{13}={10}^{-5}$. The conversion is nonadiabatic at all times, and so the oscillations in the Earth never vanish. They differ from the case of a Fe-core supernova in the sign at early times ($t\sim 60\mathrm{ms}$, around the neutronization peak): negative for ONeMg-core supernovae and positive for Fe-core ones.

Figure 8

Same as Fig. 6 for ${sin}^2{\theta }_{13}={10}^{-2}$. After the shock reaches the He shell, the conversion is essentially adiabatic and the Earth effect disappears. In a Fe supernova the effect would be zero at all times.

Figure 9

Summary of the oscillation signatures of ONeMg-core supernovae compared to Fe-core supernovae at different times. They refer to the ${\nu }_e$ channel for the normal mass hierarchy; $p$ is the ${\nu }_e$ survival probability. The shaded areas represent the preshock phase, defined as the time interval before the shock front reaches the location of the MSW resonances, while the white regions (“shocked”) indicate the later times.

Figure 10

Left column: predicted spectra of the ${\nu }_e$ flux in a detector for a ONeMg-core supernova, inclusive of oscillations in the star and in the Earth (nadir angle 60 degrees). Right column: the same spectra, but with the oscillation effects that are characteristic of a Fe-core supernova. From the upper to lower panel: ${sin}^2{\theta }_{13}=0.01$, $6\times {10}^{-4}$, ${10}^{-5}$. The thick curves refer to different times: $t=60$, 450, 700 ms (solid line, short-dashed line, and long-dashed line, respectively). For $t=60\mathrm{ms}$ we also show the spectrum in absence of Earth shielding (thin solid line). The vertical axis has units of ${\mathrm{MeV}}^{-1}{\mathrm{s}}^{-1}$.