Nuclear Adiabatic Effects of Electron-Positron Pairs on the Dynamical Instability of Very-Massive Stars

The adiabatic effects of electron-positron pair-production on the dynamical instability of very-massive stars is investigated from stellar progenitors of carbon-oxygen cores within the range of 64 M < MCO < 133 M both with and without rotation. At a very high temperature and relatively low density; the production of electron-positron pairs in the centres of massive stars leads the adiabatic index to below 4/3. The adiabatic quantities are evaluated by constructing a model into a thermodynamically consistent electron-positron equation of state (EoS) table. It is observed that the adiabatic indices in the instability regions of the rotating models are fundamentally positive with central temperature and density. Similarly, the mass of the oxygen core within the instability region has accelerated the adiabatic indices in order to compress the star, while the mass loss and adiabatic index in the non-rotating model exponentially decay. In the rotating models, a small amount of heat is required to increase the central temperature for the end fate of the massive stars. The dynamic of most of the adiabatic quantities show a similar pattern for all the rotating models. The non-rotating model may not be suitable for inducing the instability. Many adiabatic quantities have shown great effects on the dynamical instability of the massive stars due to electron-positron pair-production in their centres. The results of this work would be useful for better understanding of the end fate of very-massive stars.

Stationary Mach Configurations with Pulsed Energy Release on the Normal Shock

We obtained a theoretical analysis of stationary Mach configurations of shock waves with a pulsed energy release at the main (normal) shock and a corresponding change in gas thermodynamic properties. As formation of the stationary Mach configuration corresponds to one of two basic, well-known criteria of regular/Mach shock reflection transition, we studied here how the possibility of pulsed energy release at the normal Mach stem shifts the von Neumann criterion, and how it correlates then with another transition criterion (the detachment one). The influence of a decrease in the “equilibrium” gas adiabatic index at the main shock on a shift of the solution domain was also investigated analytically and numerically. Using a standard detonation model for a normal shock in stationary Mach configuration, and ordinary Hugoniot relations for other oblique shocks, we estimated influence of pulsed energy release and real gas effects (expressed by decrease of gas adiabatic index) on shift of von Neumann criterion, and derived some analytical relations that describe those dependencies.

Dynamical stability of giant planets: the critical adiabatic index in the presence of a solid core

ABSTRACT The dissociation and ionization of hydrogen, during the formation of giant planets via core accretion, reduce the effective adiabatic index γ of the gas and could trigger dynamical instability. We generalize the analysis of Chandrasekhar, who determined that the threshold for instability of a self-gravitating hydrostatic body lies at γ = 4/3, to account for the presence of a planetary core, which we model as an incompressible fluid. We show that the dominant effect of the core is to stabilize the envelope to radial perturbations, in some cases completely (i.e. for all γ &gt; 1). When instability is possible, unstable planetary configurations occupy a strip of γ values whose upper boundary falls below γ = 4/3. Fiducial evolutionary tracks of giant planets forming through core accretion appear unlikely to cross the dynamical instability strip that we define.

Modelling strains and stresses in continuously stratified rotating neutron stars

We introduce a Newtonian model for the deformations of a compressible, auto-gravitating and continuously stratified neutron star. The present framework can be applied to a number of astrophysical scenarios as it allows to account for a great variety of loading forces. In this first analysis, the model is used to study the impact of a frozen adiabatic index in the estimate of rotation-induced deformations: we assume a polytropic equation of state for the matter at equilibrium but, since chemical reactions may be slow, the perturbations with respect to the unstressed configuration are modeled by using a different adiabatic index. We quantify the impact of a departure of the adiabatic index from its equilibrium value on the stressed stellar configuration and we find that a small perturbation can cause large variations both in displacements and strains. As a first practical application, we estimate the strain developed between two large glitches in the Vela pulsar showing that, starting from an initial unstressed configuration, it is not possible to reach the breaking threshold of the crust, namely to trigger a starquake. In this sense, the hypothesis that starquakes could trigger the unpinning of superfluid vortices is challenged and, for the quake to be a possible trigger, the solid crust must never fully relax after a glitch, making the sequence of starquakes in a neutron star an history-dependent process.