Kendall G. Shepherd, Guglielmo Costa, Cristiano Ugolini, Guglielmo Volpato, Diego Bossini, Cecilia Sgalletta, Francesco Addari, Alessandro Bressan, Leo Girardi, Mario Spera

Very massive stars (VMS) play a fundamental role in astrophysics due to their winds and supernovae (SN), and their role as massive black hole (BH) progenitors. However, their origin and evolution remain a significant challenge. Recent theoretical work and observations suggest that VMS approaching the Eddington limit may experience mass loss above the standard wind predictions. This study investigates how enhanced winds influence single and binary VMS evolution, observable properties, and resulting BH populations. New stellar wind prescriptions, sensitive to the Eddington parameter ($\Gamma_e$) and the luminosity-to-mass ratio, were implemented into the stellar evolution code PARSEC v2.0. These updated single-star tracks (100 - 600 M$_{\odot}$ at Z=0.006) were used to model the VMS population in the Tarantula Nebula and integrated into the SEVN binary evolution code. The $\Gamma_e$-enhanced single-star tracks match observed VMS properties better than standard models. Explaining the most massive star, R136a1, through a single-star origin suggests a zero-age main sequence (ZAMS) mass limit of $<$ 400 M$_{\odot}$ regardless of the wind recipe used. However, binary stellar mergers also offer a suitable origin for R136a1 and other observed VMS, potentially lowering the upper ZAMS mass limit by ~100 M$_{\odot}$. In binaries, enhanced winds inhibit main-sequence stellar mergers and limit BH production above the pair-instability mass gap's lower edge (~50 M$_{\odot}$). Binary BHs merging in a Hubble time with enhanced winds yield more primary BHs above 30 M$_{\odot}$ and enable secondary BHs between 30-40 solar masses, a range not found with standard stellar winds at LMC metallicity. This study highlights the crucial role that stellar winds and binary interactions play in VMS evolution and offers predictions relevant for interpreting VMS observations and gravitational wave source origins.