Neutrino luminosity and matter-induced modification of collective neutrino flavor oscillations in supernovae

We present the first calculations of self-coupled neutrino flavor oscillations with time integrated luminosities and energy spectra for the neutronization burst of an $\mathrm{O}-\mathrm{Ne}-\mathrm{Mg}$ core-collapse supernova. These calculations allow us to gauge the effects of time varying neutrino luminosity and of the bump in the electron number density profile at the base of the hydrogen envelope in $\mathrm{O}-\mathrm{Ne}-\mathrm{Mg}$ core-collapse supernovae. The bump allows a significant fraction of the low-energy ${\nu }_e$ to survive by rendering their flavor-evolution nonadiabatic. Increasing the luminosity of the neutronization burst shifts the bump-affected ${\nu }_e$ to lower energy with reduced survival probability. Similarly, lowering the luminosity shifts the bump-affected neutrinos to higher energies. While these low-energy neutrinos lie near the edge of detectability, the population of bump-affected neutrinos has direct influence on the spectral swap formation in the neutrino signal at higher energies.

Figure 1

The final emission angle averaged neutrino mass state energy spectra for calculations of the flavor transformation in the neutronization neutrino burst of an $\mathrm{O}-\mathrm{Ne}-\mathrm{Mg}$ core-collapse supernova. Each panel shows the results for a different possible burst luminosity, ranging from $L_{\nu }={10}^{54}–{10}^{52}\mathrm{erg}{\mathrm{s}}^{-1}$, with identical Fermi-Dirac energy distributions.

Figure 2

The emission angle averaged probability for electron neutrinos in the neutronization neutrino burst of an $\mathrm{O}-\mathrm{Ne}-\mathrm{Mg}$ core-collapse supernova to hop out of the (initial) heavy mass eigenstate, $1-P_{\mathrm{H}}$, plotted as a function of inverse neutrino energy. Each panel shows the results for a different possible burst luminosity, ranging from $L_{\nu }={10}^{54}–{10}^{52}\mathrm{erg}{\mathrm{s}}^{-1}$, with identical Fermi-Dirac energy distributions.

Figure 3

High luminosity evolution ($L_0={10}^{53}\mathrm{erg}{\mathrm{s}}^{-1}$): The opening angle $\alpha$ between the collective NFIS ${\mathbf{S}}^{(0)}$ and ${\mathbf{H}}_{\mathrm{MSW}}$, plotted as a function of $|{\mathbf{H}}_{\mathrm{MSW}}|/|{\mathbf{H}}_{\mathrm{v}}|$ as the system moves through resonance. The idealized NFIS (solid line) shows the evolution of ${\mathbf{S}}^{(0)}$ in the ideal, strong neutrino self-coupling case. The dashed line, dot-dashed line, and dotted line show the evolution of $\mathbf{S}$ as calculated for neutrino luminosities $10L_0$, $10L_0$, and $L_0$, respectively.

Figure 4

Moderate luminosity evolution ($L_0={10}^{53}\mathrm{erg}{\mathrm{s}}^{-1}$): The opening angle $\alpha$ between the collective NFIS ${\mathbf{S}}^{(0)}$ and ${\mathbf{H}}_{\mathrm{MSW}}$, plotted as a function of $|{\mathbf{H}}_{\mathrm{MSW}}|/|{\mathbf{H}}_{\mathrm{v}}|$ as the system moves through resonance. The idealized NFIS (solid line) shows the evolution of ${\mathbf{S}}^{(0)}$ in the ideal, strong neutrino self-coupling case. The dashed line, dotted-dashed line, and dotted line show the evolution of $\mathbf{S}$ as calculated for neutrino luminosities $L_0$, $0.8L_0$, and $0.6L_0$, respectively.

Figure 5

Low luminosity evolution ($L_0={10}^{53}\mathrm{erg}{\mathrm{s}}^{-1}$): The opening angle $\alpha$ between the collective NFIS ${\mathbf{S}}^{(0)}$ and ${\mathbf{H}}_{\mathrm{MSW}}$, plotted as a function of $|{\mathbf{H}}_{\mathrm{MSW}}|/|{\mathbf{H}}_{\mathrm{v}}|$ as the system moves through resonance. The idealized NFIS (solid line) shows the evolution of ${\mathbf{S}}^{(0)}$ in the ideal, strong neutrino self-coupling case. The dashed line, dotted-dashed line, and dotted line show the evolution of $\mathbf{S}$ as calculated for neutrino luminosities $0.4L_0$, ${10}^{-1/2}{L}_0$, and ${10}^{-1}{L}_0$, respectively.

Figure 6

The expected signal from the neutronization burst of Ref. 31, in the normal neutrino mass hierarchy, created by integrating the final emission angle averaged neutrino spectral energy distribution and fluxes over the first 30 ms of the neutrino burst signal. Left panel: Scaled neutrino number flux, summed over all neutrino flavors, shown in the vacuum mass basis. Right panel: Scaled antineutrino number flux, summed over all neutrino flavors, shown in the vacuum mass basis.

Figure 7

The expected signal from the neutronization burst of Ref. 32, in the normal neutrino mass hierarchy, created by integrating the final emission angle averaged neutrino spectral energy distribution and fluxes over the first 30 ms of the neutrino burst signal. Left panel: Scaled neutrino number flux, summed over all neutrino flavors, shown in the vacuum mass basis. Right panel: Scaled antineutrino number flux, summed over all neutrino flavors, shown in the vacuum mass basis.

Figure 8

The expected signal from the neutronization burst of Ref. 31, in the inverted neutrino mass hierarchy, created by integrating the final emission angle averaged neutrino spectral energy distribution and fluxes over the first 30 ms of the neutrino burst signal. Left panel: Scaled neutrino number flux, summed over all neutrino flavors, shown in the vacuum mass basis. Right panel: Scaled antineutrino number flux, summed over all neutrino flavors, shown in the vacuum mass basis.

Figure 9

The expected signal from the neutronization burst of Ref. 32, in the inverted neutrino mass hierarchy, created by integrating the final emission angle averaged neutrino spectral energy distribution and fluxes over the first 30 ms of the neutrino burst signal. Left panel: Scaled neutrino number flux, summed over all neutrino flavors, shown in the vacuum mass basis. Right panel: Scaled antineutrino number flux, summed over all neutrino flavors, shown in the vacuum mass basis.

Figure 10

The expected signal from the neutronization burst of Ref. 31, in the normal neutrino mass hierarchy, created by integrating the final emission angle averaged neutrino spectral energy distribution and fluxes over the first 30 ms of the neutrino burst signal. Left panel: Scaled neutrino number flux, summed over all neutrino flavors, shown in the neutrino flavor basis. Right panel: Scaled antineutrino number flux, summed over all neutrino flavors, shown in the neutrino flavor basis.

Figure 11

The expected signal from the neutronization burst of Ref. 32, in the normal neutrino mass hierarchy, created by integrating the final emission angle averaged neutrino spectral energy distribution and fluxes over the first 30 ms of the neutrino burst signal. Left panel: Scaled neutrino number flux, summed over all neutrino flavors, shown in the neutrino flavor basis. Right panel: Scaled antineutrino number flux, summed over all neutrino flavors, shown in the neutrino flavor basis.

Figure 12

The expected signal from the neutronization burst of Ref. 31, in the inverted neutrino mass hierarchy, created by integrating the final emission angle averaged neutrino spectral energy distribution and fluxes over the first 30 ms of the neutrino burst signal. Left panel: Scaled neutrino number flux, summed over all neutrino flavors, shown in the neutrino flavor basis. Right panel: Scaled antineutrino number flux, summed over all neutrino flavors, shown in the neutrino flavor basis.

Figure 13

The expected signal from the neutronization burst of Ref. 32, in the inverted neutrino mass hierarchy, created by integrating the final emission angle averaged neutrino spectral energy distribution and fluxes over the first 30 ms of the neutrino burst signal. Left panel: Scaled neutrino number flux, summed over all neutrino flavors, shown in the neutrino flavor basis. Right panel: Scaled antineutrino number flux, summed over all neutrino flavors, shown in the neutrino flavor basis.