Disentangling the protoplanetary disk gas mass and carbon depletion through combined atomic and molecular tracers^★

¹ Leiden Observatory, Leiden University, PO Box 9513, 2300 RA Leiden, The Netherlands
e-mail: sturm@strw.leidenuniv.nl
² European Southern Observatory, Karl-Schwarzschild-Strasse 2, 85748 Garching bei München, Germany

Received: 9 June 2022
Accepted: 16 September 2022

Abstract

Context. The total disk gas mass and elemental C, N, and O composition of protoplanetary disks are crucial ingredients for improving our understanding of planetary formation. Measuring the gas mass is complicated, since H₂ cannot be detected in the cold bulk of the disk and the elemental abundances with respect to hydrogen are degenerate with gas mass in all disk models.

Aims. We aim to determine the gas mass and elemental abundances ratios C/H and O/H in the transition disk around LkCa 15, one of the few disks for which HD data are available, in combination with as many chemical tracers as possible.

Methods. We present new NOrthern Extended Millimeter Array observations of CO, ¹³CO, C¹⁸O, and optically thin C¹⁷O J = 2−1 lines, along with high angular-resolution Atacama Large Millimeter Array millimeter continuum and CO data to construct a representative model of LkCa 15. Using a grid of 60 azimuthally symmetric thermo-chemical DALI disk models, we translated the observed fluxes to elemental abundances and constrained the best-fitting parameter space of the disk gas mass.

Results. The transitions that constrain the gas mass and carbon abundance the most are C¹⁷O J = 2−1, N₂H⁺ J = 3−2 and HD J = 1−0. Using these three molecules, we find that the gas mass in the LkCa 15 disk is M_g = 0.01_−0.004^+0.01 M_⊙, which is a factor of 6 lower than previous estimations. This value is consistent with cosmic ray ionization rates between 10⁻¹⁶−10⁻¹⁸ s⁻¹, where 10⁻¹⁸ s⁻¹ is a lower limit based on the HD upper limit. The carbon abundance is C/H = (3 ± 1.5) × 10⁻⁵, implying a moderate depletion of elemental carbon by a factor of 3–9. All other analyzed transitions also agree with these numbers, within a modeling uncertainty of a factor of 2. Using the resolved C₂H image we find a C/O ratio of ~1, which is consistent with literature values of H₂O depletion in this disk. The absence of severe carbon depletion in the LkCa 15 disk is consistent with the young age of the disk, but stands in contrast to the higher levels of depletion seen in older cold transition disks.

Conclusions. Combining optically thin CO isotopologue lines with N₂H⁺ is promising with regard to breaking the degeneracy between gas mass and CO abundance. The moderate level of depletion for this source with a cold, but young disk, suggests that long carbon transformation timescales contribute to the evolutionary trend seen in the level of carbon depletion among disk populations, rather than evolving temperature effects and presence of dust traps alone. HD observations remain important for determining the disk’s gas mass.