Constraining the gas mass of Herbig disks using CO isotopologues
Authors: Stapper L. M. , Hogerheijde M. R. , van Dishoeck E. F. , Lin L. , Ahmadi A. , Booth A. S. , Grant S. L. , Immer K. , Leemker M. , Pérez-Sánchez A. F. 
Published: December 2023

Context. The total disk mass sets the formation potential for exoplanets. Obtaining the disk mass is however not an easy feat, as one needs to consider the optical thickness, temperature, photodissociation, and freeze-out of potential mass tracers. Carbon-monoxide (CO) has been used as a gas mass tracer in T Tauri disks, but was found to be less abundant than expected due to the freeze-out and chemical conversion of CO on the surfaces of cold dust grains. The disks around more massive intermediate mass pre-main sequence stars called Herbig disks are likely to be warmer, allowing for the possibility of using CO as a more effective total gas mass tracer.
Aims. This work aims to obtain the gas mass and size of Herbig disks observed with ALMA and compare these to previous works on T Tauri disks and debris disks.
Methods. Using ALMA archival data and new NOEMA data of 12CO, 13CO, and C 18O transitions of 35 Herbig disks within 450 pc, the masses were determined using the thermo-chemical code Dust And Lines (DALI). A grid of models was run spanning five orders of magnitude in disk mass, for which the model CO line luminosities could be linked to the observed luminosities. Survival analysis was used to obtain cumulative distributions of the resulting disk masses. These were compared with dust masses from previous work to obtain gas-to-dust ratios for each disk. In addition, radii for all three isotopologues were obtained.
Results. The majority of Herbig disks for which 13CO and C18O were detected are optically thick in both. For these disks, the line flux essentially only traces the disk size and only lower limits to the mass can be obtained. Computing the gas mass using a simple optically thin relation between line flux and column density results in an underestimate of the gas mass of at least an order of magnitude compared to the masses obtained with DALI. The inferred gas masses with DALI are consistent with a gas-to-dust ratio of at least 100. These gas-to-dust ratios are two orders of magnitude higher compared to those found for T Tauri disks using similar techniques, even over multiple orders of magnitude in dust mass, illustrating the importance of the chemical conversion of CO in colder T Tauri disks. Similar high gas-to-dust ratios are found for Herbig group I and II disks. Since group II disks have dust masses comparable to T Tauri disks, their higher CO gas masses illustrate the determining role of temperature. Compared to debris disks, Herbig disks have gas masses higher by four orders of magnitude. At least one Herbig disk, HD 163296, has a detected molecular disk wind, but our investigation has not turned up other detections of the CO disk wind in spite of similar sensitivities.
Conclusions. Herbig disks are consistent with a gas-to-dust ratio of at least 100 over multiple orders of magnitude in dust mass. This indicates a fundamental difference between CO emission from Herbig disks and T Tauri disks, which is likely linked to the warmer temperature of the Herbig disks.