Collision-induced mass loss and mass gain on an extremely massive star. An analytical approach and a static proto-globular cluster test-case

Abstract

The objective of this study is to analytically explore mass loss and gain induced by stellar collisions on a gas-accreting extremely massive star (aEMS, 10^3 <= M/M_sun <= 10^4). We also consider its contribution to the mass budget in the context of forming multiple stellar populations in a typical protoglobular cluster. We used MESA to build a series of aEMS models up to 2e4 M_sun for three [Fe/H] values, covering the metallicity range of Galactic GCs, with different treatments of super-adiabatic convection. We set analytical prescriptions to quantify collision-induced mass loss when a star spirals in and deposits energy into the envelope of the aEMS. We used a Monte Carlo approach to simulate the effects of multiple collisions on an aEMS of initial mass 10^3 M_sun in a static proto-GC, accounting for mass loss and gain from collisions, gas accretion, and stellar winds. We show that assumptions on super-adiabaticity in radiation-dominated layers significantly impact aEMS properties and their collision responses: extended stars tend to lose mass, while compact ones are more likely to gain it. Our MC simulations predict total mass lost and gained, along with timescales and contributions from winds and collisions. The results depend on both the aEMS structure and the gas accretion rate during the collision phase. Under certain conditions, the EMS shows a "conveyor belt" behavior, processing up to 10^5.5 M_sun of material in 5 Myr. This study provides theoretical predictions supporting aEMSs as contributors to the abundance anomalies observed in GCs. It emphasizes the need to include collision dynamics and mass transfer in aEMS formation and evolution models in dense stellar environments. We provide a grid of predictions for stellar M-R-[Fe/H]-structure relations and collision-induced mass loss and gain, suitable for hydro and N-body simulations.