Recombination Energy as a Fraction of Binding Energy in a Twelve-Solar-Mass Red Supergiant Envelope

This paper examines the envelope of a twelve-solar-mass red supergiant, mass 8.8 solar masses, hydrogen mass fraction 0.65 and helium mass fraction 0.33, bound to a 3.2 solar-mass core at 800 solar radii. 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: recombination_fraction_of_binding = 0.180; recombination_energy_erg = 2.581e+47; binding_energy_erg = 1.431e+48. The method, inputs and limitations are stated in full so that any reader can reproduce or rescale every number from the deposited calculation script. Scaling the recombination argument from a red giant to a red supergiant is not straightforward. 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.