Figure 1

The matter density profile taken from Ref. 10. The profile is quite centrally concentrated, so much so that the scattered halo is only populated with an appreciable number of neutrinos inside a radius of $\sim 1000\mathrm{km}$.Reuse & Permissions

Figure 2

The neutrinosphere radius, as defined by the surface of optical depth $\tau =1$, shown as a function of neutrino energy.Reuse & Permissions

Figure 3

Initially neutrinos are emitted isotropically from energy-determined neutrinosphere surfaces, $R_{\nu }^{E_{\nu }}$. After emission, some neutrinos are scattered at wide angles into the neutrino halo (e.g., ${\nu }_{{\mathrm{k}}^{\prime }}/{\nu }_{\mathrm{k}}$ scattered to location at radius $r$ and angle of incidence ${\theta }_{\mathrm{k}}$), while the remainder continue on unimpeded to the halosphere surface at radius $R_{\mathrm{H}}$. The trajectories of all neutrinos emerging from the halosphere surface are characterized by the angle ${\vartheta }_{\mathrm{k}}$ they make relative to the outward unit normal on this surface and their propagation distance $l_{\mathrm{k}}$ from the halosphere surface.Reuse & Permissions

Figure 4

The neutrino emission intensity as a function of impact parameter at the halosphere surface. Line style indicates different neutrino energies: 10 MeV (solid line), 30 MeV (dash-dotted line), 50 MeV (dashed line), 70 MeV (dotted line).Reuse & Permissions

Figure 5

A comparison of the emission angle averaged results of flavor transformation calculations with the halo neutrinos included and with halo scattering neglected. Left: the calculation including the halo, mass basis (key top right, inset) neutrino energy distribution functions versus neutrino energy. The dashed curve gives the initial $\nu$ energy spectrum. Right: the calculation neglecting halo scattering, mass basis (key top right, inset) neutrino energy distribution functions versus neutrino energy. The dashed curve gives the initial $\nu$ energy spectrum. Both panels show the final state of neutrino flavor transformation at a radius of $r=12000\mathrm{km}$.Reuse & Permissions

Figure 6

A comparison of the modeled event rate for detected ${\nu }_{\mathrm{e}}$ captures in a 17 kt liquid Argon detector between calculations with and without the scattered neutrino halo. The spectral distortions created by the halo produce a clear swap signature between $20–30\mathrm{MeV}$, which constitute $\sim 15$ additional ${\nu }_{\mathrm{e}}$ events in this 20 ms time slice of the supernova signal.Reuse & Permissions

Figure 7

Results of flavor transformation calculations with the halo neutrinos included. Initial emission spectra are taken from Ref. 10, 7 ms postcore bounce. Left panels: electron neutrino occupation probability $P_{{\nu }_{\mathrm{e}}{\nu }_{\mathrm{x}}}$ (color/shading key at top of panel), where $x=1$, 2, 3 is the neutrino mass eigenstate, shown as a function of impact parameter, $b$ in units of neutrinosphere radius $R_{\nu }=60\mathrm{km}$, and neutrino energy, $E$ in MeV, plotted at a radius of $r=12000\mathrm{km}$. Right panels: electron antineutrino occupation probability $P_{{\overline{\nu }}_{\mathrm{e}}{\overline{\nu }}_{\mathrm{x}}}$ (color/shading key at top of panel), where $x=1$, 2, 3 is the antineutrino mass eigenstate, shown as a function of impact parameter, $b=R_{\mathrm{H}}\sin {\vartheta }_{\mathrm{k}}$, and neutrino energy, $E$ in MeV, plotted at a radius of $r=12000\mathrm{km}$.Reuse & Permissions

Figure 8

Same as Fig. 7 for ${\overline{\nu }}_{\mathrm{e}}$’s.Reuse & Permissions

Figure 9

Same as Fig. 9 for ${\nu }_{\mathrm{e}}$’s during the 15 ms time snapshot.Reuse & Permissions

Figure 10

Same as Fig. 9 for ${\overline{\nu }}_{\mathrm{e}}$’s during the 15 ms time snapshot.Reuse & Permissions

Figure 11

Emission angle averaged results of flavor transformation calculations at 7 ms postcore bounce comparing calculations with and without halo neutrino scattering. Left panel: mass basis (key top right, inset) neutrino energy distribution functions versus neutrino energy when halo scattering is included in the calculation. The dashed curve gives the initial ${\nu }_{\mathrm{e}}$ energy spectrum. Right panel: mass basis (key top right, inset) neutrino energy distribution functions versus neutrino energy when halo scattering is excluded from the calculation. The dashed curve gives the initial ${\overline{\nu }}_{\mathrm{e}}$ energy spectrum. Both panels show the final state of neutrino flavor transformation at a radius of $r=12000\mathrm{km}$.Reuse & Permissions

Figure 12

Top panels: the structure of the mass state $3/2$ swap in the neutrino (left) and antineutrino (right) sectors, displayed in terms of the mass state 3 occupation probability for the 7 ms postbounce calculation (notation and axes as in Fig. 7). Bottom panels: shown in black is the contour that satisfies the emission trajectory-dependent swap criterion of Eq. (5) for neutrinos (left) and antineutrinos (right). The thicker, lighter color contour shows the locations where a ${\nu }_{\mathrm{e}}$ or ${\overline{\nu }}_{\mathrm{e}}$ has a 50% probability to occupy mass state 3. The contours displayed are selected at a radius where $|{\widehat{H}}_{\nu \nu }|\sim {\omega }_{\mathrm{pr}}$ is satisfied for a given impact parameter, $b$.Reuse & Permissions

Figure 13

Top panels: the structure of the mass state 2 occupation probability in the neutrino (left) and antineutrino (right) sectors for the 15 ms postbounce calculation (notation and axes as in Fig. 7). Bottom panels: shown in solid black is the contour that satisfies the emission trajectory-dependent swap criterion of Eq. (5) for the mass state $3/2$ swap for neutrinos (left) and antineutrinos (right). Shown by the dashed black line is the contour that satisfies the emission trajectory-dependent swap criterion of Eq. (5) for the mass state $2/1$ swap for antineutrinos (right). The thicker, lighter color contour shows the locations where a ${\nu }_{\mathrm{e}}/{\overline{\nu }}_{\mathrm{e}}$ has a 50% probability to occupy mass state 2. The mass state $3/2$ contour and the mass state $2/1$ contour are selected at differing radius so that for both contours the condition $|{\widehat{H}}_{\nu \nu }|\sim {\omega }_{\mathrm{pr}}$ is satisfied individually for each combination of precession frequency, ${\omega }_{\mathrm{pr}}$, and impact parameter, $b$.Reuse & Permissions