Formation of black holes in the pair-instability mass gap: evolution of a post-collision star

The detection of GW190521 by the LIGO-Virgo collaboration has revealed the existence of black holes (BHs) in the pair-instability (PI) mass gap. Here, we investigate the formation of BHs in the PI mass gap via star -- star collisions in young stellar clusters. To avoid PI, the stellar-collision product must have a relatively small core and a massive envelope. We generate our initial conditions from the outputs of a hydro-dynamical simulation of the collision between a core helium burning star ($\sim 58$ M$_\odot$) and a main-sequence star ($\sim 42$ M$_\odot$). The hydro-dynamical simulation allows us to take into account the mass lost during the collision ($\sim 12$ M$_\odot$) and to build the chemical composition profile of the post-collision star. We then evolve the collision product with the stellar evolution codes PARSEC and MESA. We find that the post-collision star evolves through all the stellar burning phases until core collapse, avoiding PI. At the onset of core collapse, the post-collision product is a blue super-giant star. We estimate a total mass loss of about 1 M$_\odot$ during the post-collision evolution, due to stellar winds and shocks induced by neutrino emission in a failed supernova. The final BH mass is $\approx{87}$ M$_\odot$. Therefore, we confirm that the collision scenario is a suitable formation channel to populate the PI mass gap.