Mass constraints for 15 protoplanetary disks from HD 1-0

Hydrogen deuteride (HD) rotational line emission can provide reliable protoplanetary disk gas mass measurements, but it is difficult to observe and detections have been limited to three T-Tauri disks. No new data have been available since the \emph{Herschel} Space Observatory mission ended in 2013. We set out to obtain new disk gas mass constraints by analysing upper limits on HD 1-0 emission in \emph{Herschel}/PACS archival data from the DIGIT key programme. With a focus on the Herbig Ae/Be disks, whose stars are more luminous than T Tauris, we determine upper limits for HD in data previosly analysed for its line detections. Their significance is studied with a grid of models run with the DALI physical-chemical code, customised to include deuterium chemistry. Nearly all the disks are constrained to $M_{\rm gas}\leq0.1\,$M$_{\odot}$, ruling out global gravitational instability. A strong constraint is obtained for the HD 163296 disk mass, $M_{\rm gas} \leq 0.067\,$M$_{\odot}$, implying $Δ_{\rm g/d}\leq100$. This HD-based mass limit is towards the low end of CO-based mass estimates for the disk, highlighting the large uncertainty in using only CO and suggesting that gas-phase CO depletion in HD 163296 is at most a factor of a few. The $M_{\rm gas}$ limits for HD 163296 and HD 100546, both bright disks with massive candidate protoplanetary systems, suggest disk-to-planet mass conversion efficiencies of $M_{\rm p}/(M_{\rm gas} + M_{\rm p})\approx10$ to $40\,$% for present-day values. Near-future observations with SOFIA/HIRMES will be able to detect HD in the brightest Herbig~Ae/Be disks within $150\,$pc with $\approx10\,$h integration time.

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