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Register a new userKompaneets equation for neutrinos: Application to neutrino heating in supernova explosions
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Yudai Suwa
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We derive a `Kompaneets equation for neutrinos, which describes how the distribution function of neutrinos interacting with matter deviates from a Fermi-Dirac distribution with zero chemical potential. To this end, we expand the collision integral in the Boltzmann equation of neutrinos up to the second order in energy transfer between matter and neutrinos. The distortion of the neutrino distribution function changes the rate at which neutrinos heat matter, as the rate is proportional to the mean square energy of neutrinos, $E_ u^2$. For electron-type neutrinos the enhancement in $E_ u^2$ over its thermal value is given approximately by $E_ u^2/E_{ u,rm thermal}^2=1+0.086(V/0.1)^2$ where $V$ is the bulk velocity of nucleons, while for the other neutrino species the enhancement is $(1+delta_v)^3$, where $delta_v=mV^2/3k_BT$ is the kinetic energy of nucleons divided by the thermal energy. This enhancement has a significant implication for supernova explosions, as it would aid neutrino-driven explosions.
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Active galactic nuclei (AGN) are prominent environments for stellar capture, growth and formation. These environments may catalyze stellar mergers and explosive transients, such as thermonuclear and core-collapse supernovae (SNe). SN explosions in AGN discs generate strong shocks, leading to unique observable signatures. We develop an analytical model which follows the evolution of the shock propagating in the disc until it eventually breaks out. We derive the peak luminosity, bolometric lightcurve, and breakout time. The peak luminosities may exceed $10^{45}$ erg s$^{-1}$ and last from hours to days. The brightest explosions occur in regions of reduced density; either off-plane, or in discs around low-mass central black holes ($sim 10^6 M_odot$), or in starved subluminous AGNs. Explosions in the latter two sites are easier to observe due to a reduced AGN background luminosity. We perform suites of 1D Lagrangian radiative hydrodynamics SNEC code simulations to validate our results and obtain the luminosity in different bands, and 2D axisymmetric Eulerian hydrodynamics code HORMONE simulations to study the morphology of the ejecta and its deviation from spherical symmetry. The observed signature is expected to be a bright blue, UV, or X-ray flare on top of the AGN luminosity from the initial shock breakout, while the subsequent red part of the lightcurve will largely be unobservable. We estimate the upper limit for the total event rate to be $mathcal{R}lesssim 100 rm yr^{-1} Gpc^{-3}$ for optimal conditions and discuss the large uncertainties in this estimate. Future high-cadence transient searches may reveal these events. Some existing tidal disruption event candidates may originate from AGN supernovae.
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Aims: We present neutrino light curves and energy spectra for two representative type Ia supernova explosion models: a pure deflagration and a delayed detonation. Methods: We calculate the neutrino flux from $beta$ processes using nuclear statistical equilibrium abundances convoluted with approximate neutrino spectra of the individual nuclei and the thermal neutrino spectrum (pair+plasma). Results: Although the two considered thermonuclear supernova explosion scenarios are expected to produce almost identical electromagnetic output, their neutrino signatures appear vastly different, which allow an unambiguous identification of the explosion mechanism: a pure deflagration produces a single peak in the neutrino light curve, while the addition of the second maximum characterizes a delayed-detonation. We identified the following main contributors to the neutrino signal: (1) weak electron neutrino emission from electron captures (in particular on the protons Co55 and Ni56) and numerous beta-active nuclei produced by the thermonuclear flame and/or detonation front, (2) electron antineutrinos from positron captures on neutrons, and (3) the thermal emission from pair annihilation. We estimate that a pure deflagration supernova explosion at a distance of 1 kpc would trigger about 14 events in the future 50 kt liquid scintillator detector and some 19 events in a 0.5 Mt water Cherenkov-type detector. Conclusions: While in contrast to core-collapse supernovae neutrinos carry only a very small fraction of the energy produced in the thermonuclear supernova explosion, the SN Ia neutrino signal provides information that allows us to unambiguously distinguish between different possible explosion scenarios. These studies will become feasible with the next generation of proposed neutrino observatories.
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