The possibility of emersion of the outer layers in a massive star simultaneously with iron-core collapse: A hydrodynamic model

Abstract

Abstract-We analyze the behavior of the outer envelope in a massive star during and after the collapse of its iron core into a protoneutron star (PNS) in terms of the equations of one-dimensional spherically symmetric ideal hydrodynamics. The profiles obtained in the studies of the evolution of massive stars up to the final stages of their existence, immediately before a supernova explosion (Boyes et al. 1999), are used as the initial data for the distribution of thermodynamic quantities in the envelope. We use a complex equation of state for matter with allowances made for arbitrary electron degeneracy and relativity, the appearance of electron-positron pairs, the presence of radiation, and the possibility of iron nuclei dissociating into free nucleons and helium nuclei. We performed calculations with the help of a numerical scheme based on Godunov's method. These calculations allowed us to ascertain whether the emersion of the outer envelope in a massive star is possible through the following two mechanisms: first, the decrease in the gravitational mass of the central PNS through neutrino-signal emission and, second, the effect of hot nucleon bubbles, which are most likely formed in the PNS corona, on the envelope emersion. We show that the second mechanism is highly efficient in the range of acceptable masses of the nucleon bubbles (≤0.01M ⊙ ) simulated in our hydrodynamic calculations in a rough, spherically symmetric approximation.

The toroidal iron atmosphere of a protoneutron star: Numerical solution

“…In this paper, as in our previous paper (Imshennik et al 2002), we use the equation of state for the matter treated as a mixture of a perfect Boltzmann gas of nuclei with a perfect Fermi-Dirac electron-positron gas and blackbody radiation. In a wide temperature range, the matter is assumed to be a mixture of a baryonic component that includes free nucleons (n, p) and helium ( 4 2 He) and iron ( 56 26 Fe) nuclides, and a Fermi-Dirac electron-positron gas with blackbody radiation.…”

“…This is especially true for the * E-mail: imshennik@vxitep.itep.ru outer layers of a high-mass star. Imshennik et al (2002) reduced the question about the hydrodynamic behavior of the outer part of the iron core (the second stage of its collapse) and other outer layers of a collapsing star to the problem of their accretion from a hydrostatic equilibrium onto the embryo of a protoneutron star (PNS) with a mass of about 1M ⊙ . The end of the first stage of iron core collapse was taken as the initial time of hydrodynamic post-shock accretion; the corresponding problem was formulated by Brown et al (1992).…”

“…Application of this solution to the physical conditions near PNSs (with masses (1.4-1.8)M ⊙ ) showed that the accretion rate was very high, (20-30)M ⊙ s −1 at the above typical densities ρ eFe and a neutron star mass of 1.8M ⊙ . On the other hand, the 1 Imshennik et al (2002) showed that the previously assumed influence of the decrease in the gravitational mass of a PNS due to intense neutrino energy losses during collapse was negligible: it does not lead to the emersion of the outer stellar layers in a wide range of total masses, (12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)M⊙. Unfortunately, another effect, the imitation of nucleon bubbles embedded in an initial spherically symmetric configuration under equilibrium conditions, was considered with the erroneous overestimation of their total energy attributable to the unacceptably abrupt changes in initial specific internal energy at the outer boundary of the nucleon bubbles.…”

“…A natural continuation of the above studies of analytical solutions seems to be the application of our numerical method of solution (Imshennik et al 2002) to the problem of postshock accretion near neutron stars, using a complete equation of state with temperature effects (arbitrary electron degeneracy, the appearance of positrons, the presence of a nuclide gas and blackbody radiation), and a consistent allowance for the gravitational interaction, including the twodimensional self-gravitation of the accreted matter. As was done previously (Imshennik et al 2002), the hydrostatic equilibrium solutions obtained in evolutionary calculations (Boyes et al 1999) and modified to incorporate the quasi-one-dimensional rotation effects can also be used as the initial time and the initial conditions that describe the statement of the postshock accretion problem (see above). Note that the accuracy of the hydrostatic equilibrium of these outer layers, including the action of centrifugal forces is not of such fundamental importance as it was in Imshennik et al (2002), because it essentially does not matter precisely what time is taken as the initial one in the unsteady-state hydrodynamic simulation of the outer layers of a high-mass star under consideration.…”

“…As was done previously (Imshennik et al 2002), the hydrostatic equilibrium solutions obtained in evolutionary calculations (Boyes et al 1999) and modified to incorporate the quasi-one-dimensional rotation effects can also be used as the initial time and the initial conditions that describe the statement of the postshock accretion problem (see above). Note that the accuracy of the hydrostatic equilibrium of these outer layers, including the action of centrifugal forces is not of such fundamental importance as it was in Imshennik et al (2002), because it essentially does not matter precisely what time is taken as the initial one in the unsteady-state hydrodynamic simulation of the outer layers of a high-mass star under consideration.…”