Envelope Structure Parameter from Integrated Density Profiles of Giant Envelopes

This paper examines giant envelopes of 1.4 solar masses on 0.6 solar-mass cores at 200 solar radii, represented by power-law density profiles with indices between 2.0 and 3.5, integrated directly to obtain the structure parameter for each index. 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: lambda_min = 0.227; lambda_max = 0.638; lambda_span_factor = 2.8. The method, inputs and limitations are stated in full so that any reader can reproduce or rescale every number from the deposited calculation script. Rather than adopting a tabulated structure parameter, this calculation builds one. 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.