A core-collapse supernova is generated by the passage of a shockwave through the envelope of a massive star, where the shock wave is initially launched from the “bounce” of the neutron star formed during the collapse of the stellar core. Instead of successfully exploding the star, however, numerical investigations of core-collapse supernovae find that this shock tends to “stall” at small radii (≲ 10 neutron star radii), with stellar material accreting onto the central object through the standing shock. Here, we present time-steady, adiabatic solutions for the density, pressure, and velocity of the shocked fluid that accretes onto the compact object through the stalled shock, and we include the effects of general relativity in the Schwarzschild metric. Similar to previous works that were carried out in the Newtonian limit, we find that the gas “settles” interior to the stalled shock; in the relativistic regime analyzed here, the velocity asymptotically approaches zero near the Schwarzschild radius. These solutions can represent accretion onto a material surface if the radius of the compact object is outside of its event horizon, such as a neutron star; we also discuss the possibility that these solutions can approximately represent the accretion of gas onto a newly formed black hole following a core-collapse event. Our findings and solutions are particularly relevant in weak and failed supernovae, where the shock is pushed to small radii and relativistic effects are large.

A tidal disruption event (TDE) occurs when the gravitational field of a supermassive black hole (SMBH) destroys a star. For TDEs in which the star enters deep within the tidal radius, such that the ratio of the tidal radius to the pericenter distance β satisfies β ≫ 1, the star is tidally compressed and heated. It was predicted that the maximum density and temperature attained during deep TDEs scale as ∝ β 3 and ∝ β 2, respectively, and nuclear detonation is triggered by β ≳ 5, but these predictions have been debated over the last four decades. We perform Newtonian smoothed-particle hydrodynamics simulations of deep TDEs between a Sun-like star and a 106 M ⊙ SMBH for 2 ≤ β ≤ 10. We find that neither the maximum density nor temperature follow the ∝ β 3 and ∝ β 2 scalings or, for that matter, any power-law dependence, and that the maximum-achieved density and temperature are reduced by ∼1 order of magnitude compared to past predictions. We also perform simulations in the Schwarzschild metric and find that relativistic effects modestly increase the maximum density (by a factor of ≲1.5) and induce a time lag relative to the Newtonian simulations, which is induced by time dilation. We also confirm that the time the star spends at high density and temperature is a very small fraction of its dynamical time. We therefore predict that the amount of nuclear burning achieved by radiative stars during deep TDEs is minimal.

No abstract

The dissociation and ionization of hydrogen, during the formation of giant planets via core accretion, reduces 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 > 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.