Interacting binaries on the Main Sequence as in-situ tracers of mass transfer efficiency and stability

Understanding the transfer of mass and angular momentum in binary interactions is crucial for modelling the evolution of any interacting binary after the first mass transfer phase. We constrain the efficiency and stability of thermal timescale mass transfer in massive binary evolution using the observed population of massive interacting binaries on the Main Sequence (`Algols') in the Milky Way, Large and Small Magellanic Clouds. Assuming the present-day mass of the donor star represents its initial convective core mass at Zero-Age Main Sequence, we estimate its initial mass using detailed stellar evolution models. From the initial donor mass, we calculate the range of initial accretor masses (for different mass transfer efficiencies). By imposing physical constraints on the above initial parameter ranges, we derive the mass transfer efficiency, stability and angular momentum loss that can reproduce the current properties of each Algol binary. We find that purely conservative or non-conservative mass transfer cannot explain the current mass ratio and orbital period of all massive Algols. Angular momentum conservation rules out conservative mass transfer in $\sim$28\,\% of massive Algols in the SMC. About three-quarters of all massive Algols are consistent with having undergone inefficient mass transfer ($\lesssim$\,50\,\%), while the remaining systems, mostly residing in the LMC and Milky Way, require mass transfer to have been more efficient than 25\%. The current sample of massive Algols does not require mass transfer to be efficient at the shortest orbital periods (2\,d) at any metallicity. We find evidence that mass transfer on the Main Sequence needs to be stable for initial accretor-to-donor mass ratios as unequal as $\sim 0.6$. The massive Algols in the SMC seem to have undergone less efficient mass transfer than those in the LMC and Milky Way. (Abridged)