51ÁÔÆæÈë¿Ú

Abstract:

Motivated by the eruptive mass loss inferred from Luminous Blue Variable (LBV) stars, we present 1D hydrodynamical simulations of the response from sudden energy injection into the interior of a very massive ($100 \, M_\odot$) star. For a fiducial case with total energy addition set to a factor $f=0.5$ of the net stellar binding energy, and applied within the stellar envelope, we detail the dynamical response that leads to ejection of the outermost $7.2 \, M_\odot$. We find that the ejecta's variations in time $t$ and radius $r$ for the velocity $v$, density $\rho$, and temperature $T$ are quite well fit by similarity forms in the variable $r/t \approx v$. Specifically the scaled density follows a simple exponential decline $\rho t^{3} \sim \exp (-r/v_{\rm o} t)$. This `exponential similarity' leads to analytic scaling relations for total ejecta mass $\Delta M$ and kinetic energy $\Delta K$ that agree well with the hydrodynamical simulations, with the specific-energy-averaged speed related to the exponential scale speed $v_{\rm o}$ through ${\bar v} \equiv \sqrt{2 \Delta K/\Delta M} = \sqrt{12} \, v_{\rm o}$, and a value comparable to the star's surface escape speed, $v_{\rm esc}$. Models with energy added in the core develop a surface shock breakout that propels an initial, higher-speed ejecta ($>$5000km s$^{-1}$), but the bulk of the ejected material still follows the same exponential similarity scalings with ${\bar v} \approx v_{\rm esc}$. A broader parameter study examines how the ejected mass and energy depends on the energy-addition factor $f$, for three distinct model series that locate the added energy in either the core, envelope, or near-surface. We conclude by discussing the relevance of these results for understanding LBV outbursts and other eruptive phenomena, such as failed supernovae and pulsational pair instability events.