Partial stellar explosions – ejected mass and minimal energy

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, mej, 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 $m_{\rm ej} \propto E^{\varepsilon _{\rm m}}$, where εm = 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 (RSGs), 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 RSGs. 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.

Wave-driven Mass Loss of Stripped Envelope Massive Stars: Progenitor-dependence, Mass Ejection, and Supernovae

“…The resultant mass loss ranges from ∼10 −3 -1 M e . For red supergiants losing mass via a shock, the actual mass loss sharply drops when the ratio of deposited energy to binding energy is less than roughly 0.5, as explained in Linial et al (2021). For compact stars with mass loss via super-Eddington winds, most of the deposited energy is used to lift mass out of the gravitational potential, so the total mass lost is closer to our estimate from Equation (4), as explained in Quataert et al (2016).…”

“…where R is the radius of the pre-explosion star. Equation (4) overestimates the ejecta mass in H-rich stars (Fuller 2017;Linial et al 2021), so our estimates for H-rich stars should be taken as upper limits. Similarly, if mass is ejected at the star's escape speed, the CSM radius R CSM would be…”

“…Due to their small binding energy, H-rich models are expected to eject as much as ∼0.5 M e , though the true ejected mass may be substantially smaller. If mass is ejected by an outgoing shock wave, Linial et al (2021) argued that the ejecta mass will likely be either nearly zero or a large fraction of the H envelope, so more detailed calculations should be performed for reliable estimates of the mass loss in H-rich models.…”

Pulsational pair-instability supernovae: gravitational collapse, black-hole formation, and beyond

“…The sonic pulses in Models R80Ar-NR, R80Ar, and C115 move on outward through the stars, carry energy, and can potentially trigger mass loss when reaching the loosely bound near-surface layers of the PPISN progenitors. Acoustic pulses and waves and the implications of associated weak energy release (much smaller than the binding energy of the entire star) for mass stripping from massive stars have recently been discussed by Coughlin et al (2018aCoughlin et al ( ,b, 2019; Linial et al (2021), and Matzner & Ro (2021). This possibility of shock/pulse triggered mass ejection will be analysed for our models later in Section 5.3.…”

“…Third, due to the mass loss in such PPISN episodes, the near-surface layers are not strictly in hydrostatic equilibrium. All these facts limit the possibility to analyse our models in close connection to the analytical considerations by Coughlin et al (2018a,b); Linial et al (2021), and Matzner & Ro (2021), where power-law and polytropic hydrostatic background structures were considered.…”