Gotta Go Fast: A Generalization of the Escape Speed to Fluid-dynamical Explosions and Implications for Astrophysical Transients

A star’s ability to explode in a core-collapse supernova is correlated with its density profile, ρ ( r ), such that compact stars with shallow density profiles preferentially “fail” and produce black holes. This correlation can be understood from a mass perspective, as shallower density profiles enc...

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Bibliographic Details
Main Authors: Daniel A. Paradiso, Eric R. Coughlin
Format: Article
Language:English
Published: IOP Publishing 2025-01-01
Series:The Astrophysical Journal
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Online Access:https://doi.org/10.3847/1538-4357/adce6f
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Summary:A star’s ability to explode in a core-collapse supernova is correlated with its density profile, ρ ( r ), such that compact stars with shallow density profiles preferentially “fail” and produce black holes. This correlation can be understood from a mass perspective, as shallower density profiles enclose ∼3 M _⊙ (i.e., the maximum neutron-star mass) at relatively small radii, but could also be due to the fact that a shockwave (driving the explosion) inevitably stalls if the density profile into which it propagates is shallower than ρ ( r ) ∝  r ^−2 . Here, we show that this condition—the density profile being steeper than ρ  ∝  r ^−2 —is necessary, but not sufficient, for generating a strong explosion. In particular, we find solutions to the fluid equations that describe a shockwave propagating at a fixed fraction of the local freefall speed into a temporally evolving, infalling medium, the density profile of which scales as ρ  ∝  r ^− ^n at large radii. The speed of the shock diverges as n  → 2 and declines (eventually to below the Keplerian escape speed) as n increases, while the total energy contained in the explosion approaches zero as the shock recedes to large distances. These solutions therefore represent fluid-dynamical analogs of marginally bound orbits, and yield the “shock escape speed” as a function of the density profile. We also suggest that stellar explodability is correlated with the power-law index of the density at ∼10 ^9 cm, where the neutrino diffusion time equals the local dynamical time for most massive stars, which agrees with supernova simulations.
ISSN:1538-4357