  Protoplanetary disks around young stars are the sites of planet formation.
While the dust mass can be estimated using standard methods, determining the
gas mass - and thus the amount of material available to form giant planets -
has proven to be very difficult. Hydrogen deuteride (HD) is a promising
alternative to the commonly-used gas mass tracer, CO. We aim to examine the
robustness of HD as tracer of the disk gas mass, specifically the effect of gas
mass on the HD FIR emission and its sensitivity to the vertical structure.
Deuterium chemistry reactions relevant for HD were implemented in the
thermochemical code DALI and models were run for a range of disk masses and
vertical structures. The HD J=1-0 line intensity depends directly on the gas
mass through a sublinear power law relation with a slope of ~0.8. Assuming no
prior knowledge about the vertical structure of a disk and using only the HD
1-0 flux, gas masses can be estimated to within a factor of 2 for low mass
disks (M$_{\rm disk} < 10^{-3}$ M$_\odot$). For more massive disks, this
uncertainty increases to more than an order of magnitude. Adding the HD 2-1
line or independent information about the vertical structure can reduce this
uncertainty to a factor of ~3 for all disk masses. For TW Hya, using the radial
and vertical structure from Kama et al. 2016b the observations constrain the
gas mass to $6\cdot10^{-3}$ M$_\odot$ < M$_{\rm disk} < 9\cdot10^{-3}$
M$_\odot$. Future observations require a 5$\sigma$ sensitivity of
$1.8\cdot10^{-20}$ W m$^{-2}$ ($2.5\cdot10^{-20}$ W m$^{-2}$) and a spectral
resolving power R > 300 (1000) to detect HD 1-0 (HD 2-1) for all disk masses
above $10^{-5}$ M$_\odot$ with a line-to-continuum ratio > 0.01. These results
show that HD can be used as an independent gas mass tracer with a relatively
low uncertainty and should be considered as an important science goal for
future FIR missions.
