Abstract
Recent theoretical work indicates that the neutrino radiation in core-collapse supernovae may be susceptible to flavor instabilities that set in far behind the shock, grow extremely rapidly, and have the potential to profoundly affect supernova dynamics and composition. Here we analyze the nonlinear collective oscillations that are prefigured by these instabilities. We demonstrate that a zero-crossing in $n_{\nu_e} - n_{\bar{\nu}_e}$ as a function of propagation angle is not sufficient to generate instability. Our analysis accounts for this fact and allows us to formulate complementary criteria. Using Fornax simulation data, we show that fast collective oscillations qualitatively depend on how forward-peaked the neutrino angular distributions are.
Highlights
In this paper we address a key aspect of neutrino physics in core-collapse supernovae
It has been realized that the neutrino flavor field in core-collapse supernovae is prone to a host of instabilities [1,2,3,4,5,6,7,8,9,10,11] that were artificially concealed by the symmetries adopted in older studies [12,13,14,15,16,17,18]
Of particular urgency is the subclass known as fast instabilities, so named because they exhibit gropwffiffith rates proportional to the self-coupling potential μ 1⁄4 2GFnν and are not suppressed by the typically much smaller vacuum oscillation frequency ω 1⁄4 δm2=2E [19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34]. They are commonly, if not always, associated with zero crossings of the electron lepton number carried by neutrinos as a function of propagation angle
Summary
In terms of the difference vectors and their counterpart sum vectors Sl 1⁄4 Pl þ Pl, the multipole equations of motion are [62]. The possibility for collective pendulum motion is built into the structure of Eq (2). Raffelt and Sigl [62] showed that the dipole term is the driving force behind kinematic decoherence. This remains true on short timescales, and it is clear from Eq (1) that D1 causes dephasing of neutrinos with different values of v. The higher conservation laws, which encode the fact that all angular moments are dynamically linked, may have utility for closing the moment hierarchy in a sensible way. We can be more specific about the connection to kinematic decoherence by recalling that S0 obeys a pendulum equation as well [13,62,68,69], with energy
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