Supernova deleptonization asymmetry: Impact on self-induced flavor conversion

Sovan Chakraborty, Georg Raffelt, Hans-Thomas Janka, and Bernhard Müller

Phys. Rev. D 92, 105002 – Published 2 November 2015

Abstract

During the accretion phase of a core-collapse supernova (SN), the deleptonization flux has recently been found to develop a global dipole pattern [lepton emission self-sustained asymmetry (LESA)]. The $ν_{e}$ number flux $F_{ν_{e}}$ is much larger than $F_{{\bar{ν}}_{e}}$ in one direction, whereas they are approximately equal, or even $F_{ν_{e}} ≲ F_{{\bar{ν}}_{e}}$ , in the opposite direction. We use a linearized stability analysis in a simplified SN model to study the impact of the $ν_{e} - {\bar{ν}}_{e}$ flux asymmetry on self-induced neutrino flavor conversion. While a small lepton-number flux facilitates self-induced flavor conversion, “multiangle matter suppression” is more effective. Overall, we find that for large matter densities which are relevant below the shock wave, self-induced flavor conversion remains suppressed in the LESA context and, thus, irrelevant for neutrino-driven explosion dynamics.

Received 4 December 2014

DOI:https://doi.org/10.1103/PhysRevD.92.105002

Authors & Affiliations

Sovan Chakraborty¹, Georg Raffelt¹, Hans-Thomas Janka², and Bernhard Müller³

¹Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), Föhringer Ring 6, 80805 München, Germany
²Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Strasse 1, 85748 Garching, Germany
³Monash Centre for Astrophysics, School of Physics and Astronomy, Building 79P, Monash University, Victoria 3800, Australia

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Vol. 92, Iss. 10 — 15 November 2015

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Images

Figure 1
Physical characteristics of our benchmark SN model in the minimum (blue lines) and maximum (red lines) lepton-flux directions. The data have been smoothed (running averages) over approximately 20 ms. Top: Number fluxes of the species $ν_{e}$ , ${\bar{ν}}_{e}$ and $ν_{x}$ . The $ν_{x}$ flux (representing any of $ν_{μ}$ , ${\bar{ν}}_{μ}$ , $ν_{τ}$ and ${\bar{ν}}_{τ}$ ) is similar in both directions. The ${\bar{ν}}_{e}$ flux develops a large asymmetry at around 150 ms p.b. In the direction of minimal lepton number flux, the ${\bar{ν}}_{e}$ flux is as large as the $ν_{e}$ flux, in the opposite direction it is as small as the $ν_{x}$ flux. Middle: Asymmetry parameter $ε$ of the lepton-number flux as defined in Eq. (7). Bottom: Effective neutrino-neutrino interaction strength $μ_{R}$ at the reference radius $R = 15 km$ ; see Eq. (10).
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Figure 2
Contour plot of the instability growth rate $κ$ for the simplified SN model described in the text. The effective neutrino-neutrino interaction strength $μ$ and the matter effect $λ$ were defined in Eq. (9). Notice that $κ$ , $λ$ and $μ$ are given in units of the vacuum oscillation frequency $ω_{0}$ . The upper right quadrant ( $μ, λ > 0$ ) of the right panel corresponds to inverted mass ordering (IO) and the asymmetry parameter $ε = + \frac{2}{3}$ , shows the traditional bimodal instability. The lower left quadrant ( $μ, λ < 0$ ), corresponding to normal mass ordering (NO) and $ε = + \frac{2}{3}$ , shows only the MAA instability. The upper left and lower right quadrants, corresponding to opposite signs of $μ$ and $λ$ , represent the $ε = - \frac{2}{3}$ cases. The right panel (bimodal and MZA instabilities) arises from the the first block in the eigenvalue equation (11). The left panel arises from the second block, deriving from solutions which break axial symmetry (MAA instability).
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Figure 3
Same as Fig. 2 for $ε = 0$ . Notice the expanded scale of $κ$ values. In both figures, the lowest contour is for $κ = 0.25 ω_{0}$ .
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Figure 4
Instability footprints corresponding to the contour plots of Fig. 2 (red for $ε = 2 / 3$ ) and of Fig. 3 (blue for $ε = 0$ ), where both $μ$ and $λ$ are measured in units of the vacuum oscillation frequency $ω_{0}$ . The limiting growth rate to construct the footprints is $κ = 0.01 ω_{0}$ . For inverted mass ordering, the bimodal instability applies (upper right panel). For normal mass ordering, the lower MZA and MAA panels apply, but in practice only the lower left panel (MAA) is relevant because the MAA footprint is closer to the SN density profile than the MZA footprint.
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Figure 5
Bimodal instability regions for the indicated $ε$ values. The $ε = 2 / 3$ and 0 footprints are the same as those shown in the upper right panel of Fig. 4. We here also show the equivalent radius coordinate on the horizontal axis as well as a representative SN density profile inspired by our LESA models. The steep drop in density at around 200 km is the shock front.
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Figure 6
Same as Fig. 5, now for the MAA instability region, corresponding to the lower left panel of Fig. 4.
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