Very Massive Stars and Pair-Instability Supernovae: Mass-loss Framework for low Metallicity

Very massive stars (VMS) up to 200-300 $M_\odot$ have been found in the Local Universe. If they would lose little mass they produce intermediate-mass black holes or pair-instability supernovae (PISNe). Until now, VMS modellers have extrapolated mass-loss vs. metallicity ($Z$) exponents from optically-thin winds, resulting in a range of PISN thresholds that might be unrealistically high in $Z$, as VMS develop optically-thick winds. We utilize the transition mass-loss rate of Vink and Gr\"afener (2012) that accurately predicts mass-loss rates of Of/WNh ("slash") stars that characterize the morphological transition from absorption-dominated O-type spectra to emission-dominated WNh spectra. We develop a wind efficiency framework, where optically thin winds transition to enhanced winds, enabling us to study VMS evolution at high redshift where individual stars cannot be resolved. We present a MESA grid covering $Z_\odot/2$ to $Z_\odot/100$. VMS above the transition evolve towards lower luminosity, skipping the cool supergiant phase but directly forming pure He stars at the end of hydrogen burning. Below the transition, VMS evolve as cooler luminous blue variables (LBVs) or yellow hypergiants (YHGs), naturally approaching the Eddington limit. Strong winds in this YHG/LBV regime -- combined with a degeneracy in luminosity -- result in a mass-loss runaway where a decrease in mass increases wind mass loss. Our models indicate an order-of-magnitude lower threshold than usually assumed, at $Z_\odot/20$ due to our mass-loss runaway. While future work on LBV mass loss could affect the PISN threshold, our framework will be critical for establishing definitive answers on the PISN threshold and galactic chemical evolution modelling.