Required Common-Envelope Efficiency for a One-Solar-Mass Red Giant with a White-Dwarf Companion

This paper examines a one-solar-mass red giant branch star, core mass 0.45 solar masses and envelope mass 0.55 solar masses at a radius of 120 solar radii, engulfing a 0.60 solar-mass white dwarf. 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 = 3.477e+46; alpha_required = 0.292; af_alpha_0.5_Rsun = 6.54. 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 red giant plus white dwarf channel is the cleanest laboratory for envelope ejection because neither star is expected to add a large extra energy source during the plunge. 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.