Envelope Ejection Budget for Forming a Low-Mass X-Ray Binary from a Neutron Star and a 1.8-Solar-Mass Giant

This paper examines a 1.8 solar-mass giant, core 0.50 and envelope 1.30 solar masses at 140 solar radii, engulfing a 1.40 solar-mass neutron star and emerging near five solar radii, after which the core evolves and the companion later fills its Roche lobe as the donor of a low-mass X-ray 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 = 1.268e+47; alpha_required = 0.540; af_alpha_0.5_Rsun = 4.67. The method, inputs and limitations are stated in full so that any reader can reproduce or rescale every number from the deposited calculation script. Here the mass ratio is favourable and the envelope is modest, so this calculation serves as the control case against the adverse supergiant systems: if ejection fails even here, the formalism is in trouble everywhere; if it succeeds comfortably, the failures elsewhere can be blamed on their ratios and binding energies with some confidence. 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.