A Map of Required Envelope Ejection Efficiency Across Donor Mass from One to Twenty Solar Masses

This paper examines a grid of donors from one to twenty solar masses with companions of 0.8 solar masses, core fractions and radii following stated scaling relations, each required to emerge at eight solar radii, with the required efficiency recorded for structure parameters of 0.3, 0.5 and 1.0. 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: alpha_required_max_lambda0.5 = 1.23; alpha_required_min_lambda0.5 = 0.773; fraction_above_unity_lambda0.5 = 0.375. The method, inputs and limitations are stated in full so that any reader can reproduce or rescale every number from the deposited calculation script. This calculation holds the conventions fixed and varies only the donor, which is the comparison the literature rarely makes cleanly because each published system arrives with its own adopted structure parameter and its own target separation. 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.