Computations of the collapse of a stellar iron core allowing for the absorption, emission, and scattering of electron neutrinos and anti-neutrinos

Abstract

The collapse of the iron core of a star with mass 1.4M is computed. The initial model was chosen to be polytropic, P ∝ ρ 1+1/n , with n = 3. The equation of state takes into account the equilibrium radiation of photons, a mixture of Fermi gases comprised of free nucleons and ideal gases comprised of nuclei (Fe, He) in equilibrium with respect to nuclear reactions, and electron-positron gas. The transport equation for electron neutrinos and anti-neutrinos is also included. The absorption and emission of neutrinos and anti-neutrinos with the participation of free nucleons and nuclei is taken into account, as well as scattering on electrons. The main goal of this study is to develop a numerical method for the joint solution of the gas-dynamical equations for matter and the Boltzmann kinetic equations for the distribution functions of various types of neutrinos in both optically thin and optically thick regions. The spherically symmetrical case is considered, but the dependences of the distribution functions on all the phase-space variables-the mass coordinate, particle energy, cosine of the angle between the radius vector and the particle momentum, and time, (m, , μ, t)-are retained in the description of the neutrino transport. When computing reaction rates, the exact quantum-mechanical expressions for the probabilities of processes are used, with integration over the entire momentum phase space. The gas-dynamical variables depend on the mass coordinate and time, (m, t). The solution yields neutrino light curves, which have narrow maximum with characteristic widths ≈10 ms. This makes it possible to place constraints on the mass of the electron neutrino based on the detection of short bursts of radiation, 4 eV. Part of the neutrino energy is absorbed in the envelope of the stellar core (∼10 50 erg). This is associated with the higher mean neutrino energies in this model, which is more exact than models with neutrino thermal conductivity. This approach is of interest for the application of multi-dimensional models taking into account large-scale convection.

Supernova explosion mechanism taking into account large-scale convection and neutrino transport

“…Typically, the neutrino emission lasts for >10 s. The narrow width of the neutrino light curve at the emission maximum (10 ms) is related to the neutronization of matter during the passage of the accretion shock; however, only a few percent of the energy is released during this time. The neutron density increases sharply and the Y e value decreases behind the shock; the maximum of the neutrino light curve lags the kinetic-energy maximum by 30 ms, corresponding to the time for the propagation of the neutrinos from the neutrinosphere to the boundary at 2 × 10 8 cm [84]. A narrow maximum observed in the light curve would enable placing a limit of 4 eV on the neutrino mass, if the neutrinos were detected from a Galactic source at a distance of 10 kpc.…”

“…One specific feature of the solution [84] was the large kinetic energy of the ejected envelope in the spherically symmetric case: 3 × 10 50 erg (Fig. 2).…”

“…Figure 1 displays the luminosity of the neutrinos (circles) and antineutrinos (squares), the mean energy of the neutrinos (filled circles) and antineutrinos (filled squares), and the total energy of the star (dashed line) at different moments in time during the collapse of the iron core of a star with a mass of 1.4 M [84]. A special feature of this solution is the high mean neutrino energy ( 10 MeV) that is obtained from the solution of the Boltzmann equations, compared to the neutrino heat-conduction energy (∼5 MeV).…”

“…We estimated l sh to be l sh = R star,min = R star (t = 4.3648 s) = 5 × 10 7 cm, and estimated the concentration using the mean density of the mass that has been shed, 0.047 M , as calculated in [84]. The estimated number of electrons in the envelope is then N sh = 2.8 × 10 55 , the electron concentration is n e = 5.3 × 10 31 cm −3 , and E F /m e c 2 = 4.5.…”

A Multidimensional Multicomponent Gas Dynamic with the Neutrino Transfer in Gravitational Collapse

“…The main expected effects from large-scale convection are not only the increasing of the neutrino energy flux, but also the increasing of the average energy for outgoing neutrinos, because large-scale convection facilitates the neutrino transport from a "hot" central region. The average neutrino energy 30 MeV, even with the same neutrino luminosity such as a 1D model of collapse, provides the kinetic energy of the envelope ∼10 51 erg [24], because the cross section of neutrino scattering on electron with the small Fermi energy is proportional to the average neutrino energy [27][28][29]. To understand the possibility of such important effect due to convection, we calculated 2D collapse with neutrino spectrum [30,31].…”