Effect of extended neutrino production region on collective oscillations in supernovae

Abstract

In supernovae neutrinos are emitted from a region with a width $r_{\mathrm{eff}}$ of a few kilometers (rather than from a surface of infinitesimal width). We study the effect of integration (averaging) over such an extended emission region on collective oscillations. The averaging leads to additional suppression of the correlation (off-diagonal element of the density matrix) by a factor $\sim 1/r_{\mathrm{eff}}{V}_e\sim 10^{-10}$, where $V_e$ is the matter potential. This factor enters the initial condition for further collective oscillations and, consequently, leads to a delay of the strong flavour transitions. We justify and quantify this picture using a simple example of collective effects in two intersecting fluxes. We have derived the evolution equation for the density matrix elements integrated over the emission region and solved it both numerically and analytically. For the analytic solution we have used linearized equations. We show that the delay of the development of the instability and the collective oscillations depends on the suppression factor due to the averaging (integration) logarithmically. If the instability develops inside the production region, the integration leads not only to a delay but also to a modification of the exponential grow.

arXiv comment31 pages, 5 figures, a few details and clarifications added. Accepted for publication in JCAP

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• Fast Neutrino Flavor Conversion at Late Time
• Stability of three neutrino flavor conversion in supernovae
• Coherence of oscillations in matter and supernova neutrinos