Investigating the Chemically Homogeneous Evolution Channel and its Role in the Formation of the Enigmatic Binary Black Hole Progenitor Candidate HD 5980

Chemically homogeneous evolution (CHE) is a promising channel for forming massive binary black holes. The enigmatic, massive Wolf-Rayet (WR) binary HD 5980 A&B has been proposed to have formed through this channel. We investigate this claim by comparing its observed parameters with CHE models. Using MESA, we simulate grids of close massive binaries then use a Bayesian approach to compare them with the stars' observed orbital period, masses, luminosities, and hydrogen surface abundances. The most probable models, given the observational data, have initial periods ~3 days, widening to the present-day ~20 day orbit as a result of mass loss -- correspondingly, they have very high initial stellar masses ($\gtrsim$150 M$_\odot$). We explore variations in stellar wind-mass loss and internal mixing efficiency, and find that models assuming enhanced mass-loss are greatly favored to explain HD 5980, while enhanced mixing is only slightly favoured over our fiducial assumptions. Our most probable models slightly underpredict the hydrogen surface abundances. Regardless of its prior history, this system is a likely binary black hole progenitor. We model its further evolution under our fiducial and enhanced wind assumptions, finding that both stars produce black holes with masses ~19-37 M$_\odot$. The projected final orbit is too wide to merge within a Hubble time through gravitational waves alone. However, the system is thought to be part of a 2+2 hierarchical multiple. We speculate that secular effects with the (possible) third and fourth companions may drive the system to promptly become a gravitational-wave source.