Envelope Ejection at the Tip of the Red Giant Branch and the Birth Periods of Subdwarf B Binaries

This paper examines a one-solar-mass star at the tip of the red giant branch, helium core 0.47 and envelope 0.53 solar masses at 180 solar radii, with a 0.55 solar-mass companion emerging near 2.8 solar radii as a subdwarf B binary. 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: binding_energy_erg = 1.596e+46; alpha_required = 0.094; af_alpha_0.5_Rsun = 13.16. The method, inputs and limitations are stated in full so that any reader can reproduce or rescale every number from the deposited calculation script. Timing is the special feature here. 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.