Probing the neutrino mass hierarchy with the rise time of a supernova burst

The rise time of a Galactic supernova (SN) ${\overline{\nu }}_e$ light curve, observable at a high-statistics experiment such as the Icecube Cherenkov detector, can provide a diagnostic tool for the neutrino mass hierarchy at “large” 1–3 leptonic mixing angle ${\vartheta }_{13}$. Thanks to the combination of matter suppression of collective effects at early post-bounce times on one hand and the presence of the ordinary Mikheyev-Smirnov-Wolfenstein effect in the outer layers of the SN on the other hand, a sufficiently fast rise time on $\mathcal{O}(100)\mathrm{ms}$ scale is indicative of an inverted mass hierarchy. We investigate results from an extensive set of stellar core-collapse simulations, providing a first exploration of the astrophysical robustness of these features. We find that for all the models analyzed (sharing the same weak interaction microphysics) the rise times for the same hierarchy are similar not only qualitatively, but also quantitatively, with the signals for the two classes of hierarchies significantly separated. We show via Monte Carlo simulations that the two cases should be distinguishable at IceCube for SNe at a typical Galactic distance 99% of the time. Finally, a preliminary survey seems to show that the faster rise time for inverted hierarchy as compared to normal hierarchy is a qualitatively robust feature predicted by several simulation groups. Since the viability of this signature ultimately depends on the quantitative assessment of theoretical/numerical uncertainties, our results motivate an extensive campaign of comparison of different code predictions at early accretion times with implementation of microphysics of comparable sophistication, including effects such as nucleon recoils in weak interactions.

Figure 1

Early post-bounce evolution of luminosities (left-hand panels), and mean energies (right-hand panels) for a set of nine 1D simulation with progenitors of different masses (see text for details) as obtained by the Garching group [41]. Quantities for ${\nu }_e$, ${\overline{\nu }}_e$, and ${\nu }_x$ are shown in the top, middle, and bottom panels, respectively. The vertical line indicates the early timescale (100 ms) of particular interest in this article.

Figure 2

Early post-bounce evolution ($t_{\mathrm{p}.\mathrm{b}.}\le 0.2\mathrm{s}$) of luminosities (top panel), mean energies (middle panel) and $\alpha$-fit parameters (bottom panel) for the $15{\mathrm{M}}_{\odot }$ progenitor (see text for details), for ${\overline{\nu }}_e$ (solid lines) and ${\nu }_x$ (dashed lines) species.

Figure 3

Left-hand panel: average SN count rate signal in IceCube assuming a distance of 10 kpc, based on the simulations for a $15{\mathrm{M}}_{\odot }$ progenitor mass from the Garching group. Right-hand panel: illustrative example of the binned signal using 2 ms bins with typical Poisson error estimates accounting for the signal plus photomultiplier background noise, whose average value is shown as dot-dashed curve. A large ${\vartheta }_{13}$ is assumed here and in the following (see text for details).

Figure 4

Count rate functions $R_i(t)$ and the cumulative functions $K_i(x)$ for the Garching set of models; dashed (top) curves denote expectations for IH, solid (bottom) curves for NH. In these examples, $t_{\mathrm{end}}=100\mathrm{ms}$ is assumed.

Figure 5

Distribution of distances between the NH theoretical expectations for the $15{\mathrm{M}}_{\odot }$ model (1D) and 1000 simulations of the IH case. Dot-dashed line is the average, dashed line enclose the 1-sigma range (they enclose 68% of the simulation results).