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Abstract Observations and theory suggest that core-collapse supernovae can span a range of explosion energies, and when sub-energetic the shockwave initiating the explosion can decelerate to speeds comparable to the escape speed of the progenitor. In these cases, gravity will complicate the explosion hydrodynamics and conceivably cause the shock to stall at large radii within the progenitor star. To understand these unique properties of weak explosions, we develop a perturbative approach for modeling the propagation of an initially strong shock into a time-steady, infalling medium in the gravitational field of a compact object. This method writes the shock position and the post-shock velocity, density, and pressure as series solutions in the (time-dependent) ratio of the freefall speed to the shock speed, and predicts that the shock stalls within the progenitor if the explosion energy is below a critical value. We show that our model agrees very well with hydrodynamic simulations, and accurately predicts (for example) the time-dependent shock position and velocity and the radius at which the shock stalls. Our results have implications for black hole formation and the newly detected class of fast X-ray transients (FXTs). In particular, we propose that a “phantom shock breakout”—where the outer edge of the star falls through a stalled shock—can yield a burst of X-rays without a subsequent optical/UV signature, similar to FXTs. This model predicts the rise time of the X-ray burst,t_d, and the mean photon energy,kT, are anticorrelated, approximately as $T\propto t_{\mathrm{d}}^{-5/8}$. 

Abstract A star completely destroyed in a tidal disruption event (TDE) ignites a luminous flare that is powered by the fallback of tidally stripped debris to a supermassive black hole (SMBH) of massM_•. We analyze two estimates for the peak fallback rate in a TDE, one being the “frozen-in” model, which predicts a strong dependence of the time to peak fallback rate,t_peak, on both stellar mass and age, with 15 days ≲t_peak≲ 10 yr for main sequence stars with masses 0.2 ≤M_⋆/M_⊙≤ 5 andM_•= 10⁶M_⊙. The second estimate, which postulates that the star is completely destroyed when tides dominate the maximum stellar self-gravity, predicts thatt_peakis very weakly dependent on stellar type, with $t_{\mathrm{peak}}=\left(23.2\pm 4.0\mathrm{days}\right){\left(M_{•}/{10}^6{M}_{\odot }\right)}^{1/2}$for 0.2 ≤M_⋆/M_⊙≤ 5, while $t_{\mathrm{peak}}=\left(29.8\pm 3.6\mathrm{days}\right){\left(M_{•}/{10}^6{M}_{\odot }\right)}^{1/2}$for a Kroupa initial mass function truncated at 1.5M_⊙. This second estimate also agrees closely with hydrodynamical simulations, while the frozen-in model is discrepant by orders of magnitude. We conclude that (1) the time to peak luminosity in complete TDEs is almost exclusively determined by SMBH mass, and (2) massive-star TDEs power the largest accretion luminosities. Consequently, (a) decades-long extra-galactic outbursts cannot be powered by complete TDEs, including massive-star disruptions, and (b) the most highly super-Eddington TDEs are powered by the complete disruption of massive stars, which—if responsible for producing jetted TDEs—would explain the rarity of jetted TDEs and their preference for young and star-forming host galaxies.