Population III binary black holes: effects of convective overshooting on formation of GW190521

GW190521 is a merger of two black holes (BHs), wherein at least one BH lies within the pair-instability (PI) mass gap, and it is difficult to form because of the effects of PI supernovae and pulsational PI (PPI). In this study, we examined the formation of GW190521-like BH-BHs under Population (Pop) III environments by binary population synthesis calculations. We reveal that convective overshooting in stellar evolution strongly affects the formation of GW190521-like BH-BHs. A model with a small overshoot parameter (similar to GENEC) can form GW190521-like BH-BHs. The derived merger rate is 4 × 10^-2 yr^-1 Gpc^-3 at a redshift of ~0.82, which is comparable to the merger rate of GW190521-like BH-BHs inferred by gravitational wave (GW) observations. In this model, a ~90 M_⊙ star collapses to form a ~90 M_⊙ BH by avoiding PPI and PISN even if it is a member of a binary star. This is because it expands up to 10² R_⊙, and lose only little mass through binary evolution. However, a model with a large overshoot parameter (similar to Stern) cannot form GW190521-like BH-BHs at all. Thus, we cannot conclude that a Pop III binary system is the origin of GW190521 because determination of the overshoot parameter involves highly uncertain. If a Pop III binary system is the origin of GW190521, the merger rate of BH-BHs including a 100-135 M_⊙ BH is substantially smaller than that of GW190521-like BH-BHs. This will be assessed by GW observations in the near future.