Density fluctuation effects on collective neutrino oscillations in O-Ne-Mg core-collapse supernovae

We investigate the effect of matter density fluctuations on supernova collective neutrino flavor oscillations. In particular, we use full multiangle, three-flavor, self-consistent simulations of the evolution of the neutrino flavor field in the envelope of an O-Ne-Mg core-collapse supernova at shock breakout (neutronization neutrino burst) to study the effect of the matter density “bump” left by the He-burning shell. We find a seemingly counterintuitive increase in the overall ${\nu }_{\mathrm{e}}$ survival probability created by this matter density feature. We discuss this behavior in terms of the interplay between the matter density profile and neutrino collective effects. While our results give new insights into this interplay, they also suggest an immediate consequence for supernova neutrino burst detection: it will be difficult to use a burst signal to extract information on fossil burning shells or other fluctuations of this scale in the matter density profile. Consistent with previous studies, our results also show that the interplay of neutrino self-coupling and matter fluctuation could cause a significant increase in the ${\nu }_{\mathrm{e}}$ survival probability at very low energy.

Figure 1

The electron number density for two matter profiles plotted as functions of radius in the resonance region for the $\Delta m_{\mathrm{atm}}^2$ mass state splitting. The solid line indicates the original matter density profile of Refs. 25, 26, called Bump. The dash-dotted line indicates the artificial density profile with the bump artificially removed, called No Bump.

Figure 2

The scale height of the neutrino-electron forward scattering potential evaluated at the MSW resonance location for each neutrino energy. The solid line indicates the first MSW resonance scale height of neutrinos moving through the original matter density profile of Refs. 25, 26, while the dashed line indicates the scale heights of the multiple resonances. The dash-dotted line indicates the MSW resonance scale heights of neutrinos moving through the No Bump density profile.

Figure 3

Bump. Left panel: Electron neutrino survival probability $P_{\nu \nu }$ (color/shading key at top left) for the normal mass hierarchy is shown as a function of cosine of emission angle, $\cos {\vartheta }_{\mathrm{R}}$, and neutrino energy, $E$ in MeV, plotted at a radius of $r=5000\mathrm{km}$. Right: Mass basis (key top right, inset) emission angle-averaged neutrino energy distribution functions versus neutrino energy, $E$. The dashed curve gives the initial ${\nu }_{\mathrm{e}}$ emission angle-averaged energy spectrum. A kink in the density profile used, taken from Refs. 25, 26, leads to multiple MSW resonances for low energy neutrinos.

Figure 4

No Bump. Left panel: Electron neutrino survival probability $P_{\nu \nu }$ (color/shading key at top left) for the normal mass hierarchy is shown as a function of cosine of emission angle, $\cos {\vartheta }_{\mathrm{R}}$, and neutrino energy, $E$ in MeV, plotted at a radius of $r=5000\mathrm{km}$. Right: Mass basis (key top right, inset) emission angle-averaged neutrino energy distribution functions versus neutrino energy, $E$. The dashed curve gives the initial ${\nu }_{\mathrm{e}}$ emission angle-averaged energy spectrum. The kink in the density profile taken from Refs. 25, 26 has been artificially removed from the density profile used in this simulation.

Figure 5

The electron neutrino survival probability as a function of neutrino energy shown at the final radius $r=5000\mathrm{km}$. The solid line indicates the survival probability for neutrinos after moving through the Bump profile, while the dashed line indicates the survival probability for neutrinos after moving through the No Bump profile.

Figure 6

Left panel: The combined matter and neutrino self-coupling forward scattering potentials experienced by radially emitted neutrinos as a function of radius. Right: The combined matter and neutrino self-coupling forward scattering potentials experienced by tangentially emitted neutrinos as a function of radius. The dotted and dash-dotted lines indicate the upper and lower neutrino energies, respectively, to experience multiple neutrino-background enhanced MSW resonances in the desynchronized limit.

Figure 7

Bump: The opening angle $\alpha$ between the collective NFIS and ${\mathbf{H}}_{\mathrm{MSW}}$ for the Bump profile, plotted as a function of $|{\mathbf{H}}_{\mathrm{MSW}}|/|{\mathbf{H}}_{\mathrm{V}}|$ as the system moves through resonance. The idealized NFIS (dot-dashed line) shows the evolution of ${\mathbf{S}}^{(0)}$ in the absence of any neutrino self-coupling. The solid line and dashed line show the evolution of $\mathbf{S}$ as calculated in multiangle and single-angle simulations, respectively, including the neutrino self-coupling potentials. The dotted line shows the evolution of $\mathbf{S}$ as calculated for a neutronization burst with $L_{\nu }\approx 0.1L_{{\nu }_{\mathrm{e}}}$ for all neutrino species other than ${\nu }_{\mathrm{e}}$. Note that the qualitative behavior of $\mathbf{S}$ for the multiangle, single-angle, and mixed flux treatments are quite similar.

Figure 8

No Bump: The opening angle $\alpha$ between the collective NFIS and ${\mathbf{H}}_{\mathrm{MSW}}$ for the No Bump profile, plotted as a function of $|{\mathbf{H}}_{\mathrm{MSW}}|/|{\mathbf{H}}_v|$ as the system moves through resonance. The idealized NFIS (dot-dashed line) shows the evolution of ${\mathbf{S}}^{(0)}$ in the absence of any neutrino self-coupling. The solid line and dashed line show the evolution of ${\mathbf{S}}^{(0)}$ as calculated in multiangle and single-angle simulations, respectively, including the neutrino self-coupling potentials. The dotted line shows the evolution of $\mathbf{S}$ as calculated for a neutronization burst with $L_{\nu }\approx 0.1L_{{\nu }_{\mathrm{e}}}$ for all neutrino species other than ${\nu }_{\mathrm{e}}$. Note that the qualitative behavior of $\mathbf{S}$ for the multiangle, single-angle, and mixed flux treatments are quite similar.

Figure 9

The average alignment of individual neutrino polarization vectors, ${\mathbf{s}}_{\omega }$, with the collective polarization vector, $\mathbf{S}$. The solid black line shows the Bump profile from Refs. 25, 26 and the dotted red line shows the modified No Bump profile. The shaded region indicates the physical position of the helium burning shell density feature present in the Bump profile.

Figure 10

No Bump: The precession of the collective polarization vector, $\mathbf{S}$, and the zeroth-order effective field ${\mathbf{S}}^{(0)}$, about the ${\widehat{\mathbf{e}}}_{\mathrm{z}}^{\mathrm{f}}$ axis as neutrinos move through resonance in the No Bump profile. The solid line shows the azimuthal angle, ${\varphi }_{\mathbf{S}}$, for the collective polarization vector $\mathbf{S}$. The dash-dotted line shows the azimuthal angle, ${\varphi }_{{\mathbf{S}}^{(0)}}$, for the zeroth-order effective field ${\mathbf{S}}^{(0)}$. The dotted line shows the value of ${\theta }_{\mathrm{m}}$ for $\mathbf{S}$ and ${\mathbf{S}}^{(0)}$ for reference, with a diamond symbol located at ${\theta }_{\mathrm{m}}=\pi /4$ where the system is at resonance.

Figure 11

Bump: The precession of the collective polarization vector, $\mathbf{S}$, and the zeroth-order effective field ${\mathbf{S}}^{(0)}$, about the ${\widehat{\mathbf{e}}}_{\mathrm{z}}^{\mathrm{f}}$ axis as neutrinos move through resonance in the Bump profile. The solid line shows the azimuthal angle, ${\varphi }_{\mathbf{S}}$, for the collective polarization vector $\mathbf{S}$. The dash-dotted line shows the azimuthal angle, ${\varphi }_{{\mathbf{S}}^{(0)}}$, for the zeroth-order effective field ${\mathbf{S}}^{(0)}$. The dotted line shows the value of ${\theta }_{\mathrm{m}}$ for $\mathbf{S}$ and ${\mathbf{S}}^{(0)}$ for reference, with a diamond symbol located at ${\theta }_{\mathrm{m}}=\pi /4$ where the system is at resonance. The shaded region indicates the physical position of the helium burning shell density feature present in the Bump profile.