Final Separation and Gravitational-Wave Merger Time for a Black Hole Engulfed by a 25-Solar-Mass Supergiant

This paper examines a 25 solar-mass supergiant, core 8.0 and envelope 17.0 solar masses at 1100 solar radii, engulfing a 10 solar-mass black hole and emerging, if ejection succeeds, near 15 solar radii before the core collapses to a second black hole of about 7 solar masses. Using published input values and the standard energy comparison between envelope binding and orbital release, the calculation addresses the specific budget that decides the outcome for this pairing. The headline results are: gw_merger_time_Gyr = 6.338; alpha_required = 0.502; period_at_af_days = 1.586. The method, inputs and limitations are stated in full so that any reader can reproduce or rescale every number from the deposited calculation script. The black hole plus supergiant interaction is where envelope physics meets gravitational-wave astronomy most directly. Agreement and disagreement with published values for this class are reported at their actual size, and the conclusions are limited to what the budget arithmetic supports.