Density-path dependence of post-shock deposition

Quantify the influence of full density-path dependence on post-shock wave propagation, angular-momentum deposition, gap structure, and migration stalling in the structured disks modeled by the launch-dependent shock prescription.

Background

The adopted deposition tail depends on the launch density and shock location but does not update the nonlinear propagation coordinate using the density encountered along the entire post-shock path. The appendix contrasts this approximation with the density-weighted propagation coordinate in the weakly nonlinear theory of Rafikov.

The authors provide a concrete frozen-snapshot diagnostic comparing density-weighted and geometric post-shock increments, but they do not evaluate it or assign an error to the predicted stall radius or gap depth. The quantitative consequences of the omitted path dependence therefore remain unresolved.