Gotta Go Fast: A Generalization of the Escape Speed to Fluid-dynamical Explosions and Implications for Astrophysical Transients
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909580441681920 |
|---|---|
| author | Paradiso, Daniel A. Coughlin, Eric R. |
| author_facet | Paradiso, Daniel A. Coughlin, Eric R. |
| contents | 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 $\sim 3M_{\odot}$ (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 $ρ(r) \propto r^{-2}$. Here we show that this condition -- the density profile being steeper than $ρ\propto r^{-2}$ -- 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 $ρ\propto r^{-n}$ at large radii. The speed of the shock diverges as $n\rightarrow 2$ 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 $\sim10^9$ cm, where the neutrino diffusion time equals the local dynamical time for most massive stars, which agrees with supernova simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_11527 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gotta Go Fast: A Generalization of the Escape Speed to Fluid-dynamical Explosions and Implications for Astrophysical Transients Paradiso, Daniel A. Coughlin, Eric R. High Energy Astrophysical Phenomena 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 $\sim 3M_{\odot}$ (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 $ρ(r) \propto r^{-2}$. Here we show that this condition -- the density profile being steeper than $ρ\propto r^{-2}$ -- 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 $ρ\propto r^{-n}$ at large radii. The speed of the shock diverges as $n\rightarrow 2$ 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 $\sim10^9$ cm, where the neutrino diffusion time equals the local dynamical time for most massive stars, which agrees with supernova simulations. |
| title | Gotta Go Fast: A Generalization of the Escape Speed to Fluid-dynamical Explosions and Implications for Astrophysical Transients |
| topic | High Energy Astrophysical Phenomena |
| url | https://arxiv.org/abs/2504.11527 |