Weighing gas-rich starless halos: dark matter parameters inference from their gas distributions

Reionization-Limited $H_{I}$ Clouds (RELHICs) are starless dark matter halos retaining a significant neutral hydrogen($H_{I}$ ) reservoir. The gas resides in near hydrostatic equilibrium within the dark matter potential and in thermal equilibrium with the cosmic ultraviolet background. This simplicity allows analytic frameworks to link observable $H_{I}$ column densities directly to fundamental dark matter halo structural parameters. We systematically assess the accuracy of inferring host halo parameters from RELHIC gas distributions on an object-by-object basis, quantifying biases, intrinsic degeneracies, and the limits of parameter recovery. Using RELHICs from a redshift z = 0 high-resolution cosmological hydrodynamical simulation, we employ Bayesian nested sampling to infer dark matter halo mass and concentration. We evaluate this against 3D spherically averaged total gas and $H_{I}$ density profiles, alongside 2D $H_{I}$ column density profiles. We found that while the ensemble inference yields a robust, unbiased recovery of halo virial mass from 3D profiles, individual systems exhibit a mass-concentration degeneracy driven by local environmental density. Overdense environments yield slightly overestimated masses and underestimated concentrations; underdense regions show the inverse. We demonstrate that treating environmental density as a free parameter breaks this degeneracy and completely neutralizes the systematic mass bias. Although concentration recovery remains limited by simulation resolution, the virial mass is exceptionally well constrained, establishing a highly reliable framework for weighing starless halos in upcoming surveys.