Partial Stellar Explosions -- Ejected Mass and Minimal Energy

TL;DR

This study investigates how the ejected mass from stellar explosions depends on the explosion energy, revealing a minimal energy threshold below which no mass is ejected, with implications for pre-supernova outbursts.

Contribution

The paper introduces a combined analytical and numerical approach to quantify the relationship between explosion energy and ejecta mass across different stellar types, highlighting a minimal explosion energy threshold.

Findings

Ejected mass scales as E^{2.4-3.0} for energies below stellar binding energy.

A minimal explosion energy of 10^{46}-10^{47} erg exists, independent of stellar radius.

Minimal ejecta mass varies from 10^{-8} to 10^{-2} solar masses across stellar types.

Abstract

Many massive stars appear to undergo enhanced mass loss during late stages of their evolution. In some cases, the ejected mass likely originates from non-terminal explosive outbursts, rather than continuous winds. Here we study the dependence of the ejecta mass, $m_{\rm ej}$, on the energy budget $E$ of an explosion deep within the star, using both analytical arguments and numerical hydrodynamics simulations. Focusing on polytropic stellar models, we find that for explosion energies smaller than the stellar binding energy, the ejected mass scales as $m_{\rm ej} \propto E^{\varepsilon_{m}}$, where $\varepsilon_m = 2.4-3.0$ depending on the polytropic index. The loss of energy due to shock breakout emission near the stellar edge leads to the existence of a minimal mass-shedding explosion energy, corresponding to a minimal ejecta mass. For a wide range of progenitors, from Wolf-Rayet stars to red supergiants, we find a similar limiting energy of $E_{\rm min} \approx 10^{46}-10^{47} \rm \, erg$, almost independent of the stellar radius. The corresponding minimal ejecta mass varies considerably across different progenitors, ranging from $\sim \! 10^{-8} \, \rm M_\odot$ in compact stars, up to $\sim \! 10^{-2} \, \rm M_\odot$ in red supergiants. We discuss implications of our results for pre-supernova outbursts driven by wave heating, and complications caused by the non-constant opacity and adiabatic index of realistic stars.