Helium-Star Envelope Ejection, Final Separation and Merger Time in the Second Interaction of a Double Neutron Star Progenitor

This paper examines a 3.0 solar-mass helium star, core 1.45 and helium envelope 1.55 solar masses at 12 solar radii, engulfing a 1.35 solar-mass neutron star and emerging near 1.0 solar radii before the core collapses to the second neutron star. 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 = 0.027; alpha_required = 0.746; period_at_af_days = 0.069. 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 second envelope phase in a double neutron star progenitor involves a helium star rather than a hydrogen giant: the envelope is compact, tightly bound per unit mass, and removed from a star only a few times larger than its own core. 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.