Document MESA log density and atmosphere analogy

experiments/LOG_DENSITY_ASSESSMENT_2026-09-19.md

@@ -311,6 +311,19 @@ convergence result, speedup, or virial improvement is claimed.
 
 ## Primary-source context
 
+The analogy to 1D stellar codes is supported by MESA's current
+[`star_utils.f90`](https://github.com/MESAHub/mesa/blob/main/star/private/star_utils.f90):
+`get_rho_and_lnd_from_xh` reconstructs a zone's density with `exp(lnd)`, while
+`store_rho_in_xh` stores `log(rho)`. Its documented
+[`T(tau)` atmosphere treatment](https://docs.mesastar.org/en/latest/atm/t-tau.html)
+sets surface pressure and temperature at a selected optical depth. An ordinary
+atmosphere match with positive gas pressure therefore avoids requiring
+`log(0)` at an exact vacuum interface; this is the relevant inference for our
+boundary choice, not a claim about every MESA mode. These zonewise logarithmic
+variables support investigating independent log density, but do not establish
+positivity between nodes of our high-order FEM reconstruction or resolve its
+exact zero-density free surface.
+
 Vijaywargiya and Fu, *Two Finite Element Approaches for the Porous Medium
 Equation That Are Positivity Preserving and Energy Stable* (2024), formulate a
 pointwise exponential log-density method and explicitly discuss the infinite