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We discuss statistical relationships between the mass of protoplanetary disksand the hydrogen deuteride (HD) line emission and the dust spectral energydistribution (SED) determined using 3000 ProDiMo disk models. The models have15 free parameters describing disk physical properties, the central star, andthe local radiation field. The sampling of physical parameters is done using aMonte Carlo approach to evaluate the probability density functions ofobservables as a function of physical parameters. We find that the HDfractional abundance is almost constant even though the UV flux varies byseveral orders of magnitude. Probing the statistical relation between thephysical quantities and the HD flux, we find that low-mass (optically thin)disks display a tight correlation between the average disk gas temperature andHD line flux, while massive disks show no such correlation. We demonstrate thatthe central star luminosity, disk size, dust size distribution, and HD flux maybe used to determine the disk gas mass to within a factor of three. We alsofind that the far-IR and sub-mm/mm SEDs and the HD flux may serve as strongconstraints for determining the disk gas mass to within a factor of two. If theHD lines are fully spectrally resolved ($R\gtrsim 1.5\times10^6, \Deltav=0.2~\rm km\,s^{-1}$), the 56 $\mu$m and 112 $\mu$m HD line profiles alone mayconstrain the disk gas mass to within a factor of two.

Retrievals of Protoplanetary Disk Parameters using Thermochemical Models: I. Disk Gas Mass from Hydrogen Deuteride Spectroscopy