DiskMINT: Self-Consistent Thermochemical Disk Models with Radially Varying Gas and Dust -- Application to the Massive, CO-Rich Disk of IM Lup

TL;DR

This work addresses the challenge of reliably constraining gas masses in protoplanetary disks, where traditional CO-based inferences often require ad hoc depletion. It introduces DiskMINT, a self-consistent thermochemical framework that allows radially varying gas and dust distributions and includes key CO-chemistry processes such as selective photodissociation and CO/CO2 ice conversion, all coupled to vertical hydrostatic equilibrium. Applied to the IM Lup disk, the authors derive M_gas ≈ 0.02–0.08 M_sun and M_dust ≈ (8–13)×10^{−4} M_sun, with outer-disk dust-to-gas ratios around 0.01–0.02, and show that C^{18}O emission can trace both the total gas mass and its radial distribution without requiring global CO depletion; the outer disk is consistent with gas-dust evolution driven by radial drift. The results support using C^{18}O as a reliable mass tracer in self-consistent models and demonstrate how decoupled gas-dust modeling can extend gas-mass estimates to fainter or more distant disks, with implications for disk evolution and planetesimal formation potential.

Abstract

Disks around young stars are the birthplaces of planets, and the spatial distribution of their gas and dust masses is critical for understanding where and what types of planets can form. We present self-consistent thermochemical disk models built with DiskMINT, which extends its initial framework to allow for spatially decoupled gas and dust distributions. DiskMINT calculates the gas temperature based on thermal equilibrium with dust grains, solves vertical gas hydrostatic equilibrium, and includes key processes for the CO chemistry, specifically selective photodissociation, and freeze-out with conversion CO/CO$_2$ ice. We apply DiskMINT to study the IM Lup disk, a large massive disk, yet with an inferred CO depletion of up to 100 based on earlier thermochemical models. By fitting the multi-wavelength SED along with the millimeter continuum, ${\rm C^{18}O}$ radial emission profiles, we find $0.02-0.08\,{\rm M_\odot}$ for the gas disk mass, which are consistent with the dynamical-based mass within the uncertainties. We further compare the derived surface densities for dust and gas and find that the outer disk is drift-dominated, with a dust-to-gas mass ratio of approximately 0.01-0.02, which is likely insufficient to meet the conditions for the streaming instability to occur. Our results suggest that when interpreted with self-consistent thermochemical models, ${\rm C^{18}O}$ alone can serve as a reliable tracer of both the total gas mass and its radial distribution. This approach enables gas mass estimates in lower-mass disks, where dynamical constraints are not available, and in fainter systems where rare species like ${\rm N_2H^+}$ are too weak to detect.

Figures (15)

• Figure 1: Observational data that is used in this work. Left panel: spectral energy distribution (SED). Photometry in colored markers and Spitzer/IRS spectrum evans_molecular_2003evans_spitzer_2009 in magenta. A combined BT-settl stellar photosphere spectrum Allard_2003IAUS..211..325AAllard_2011ASPC..448...91A with a 8,500 K blackbody radiation fitting the UV data-point, and another blackbody radiation with 1,500 K from the radius of $R_{\star}$ to 0.055 AU represents the accreting gas disk at the inner edge, is shown as a gray line. Right panels: ALMA Band 6 continuum (240 GHz) radial profile from DSHARP andrews_disk_2018, and $\mathrm{C^{18}O}$ (2-1) radial profile (lower right) and disk-integrated line profile (lower left) from MAPS oberg_molecules_2021. The disk-integrated line profile is compiled from GoFishteague_gofish_2019, and the radial profiles are measured at each radius with an elliptical annulus with the inclination and position angles in the continuum image and the $\rm C^{18}O$ moment-0 maps, respectively. SED references: UV photometry from Swiftcleeves_IMLup_coupled_2016; optical photometry from APASS henden_vizier_2016, Gaiagaia_collaboration_gaia_2023, padgett_spitzer_2006; infrared photometry from 2MASS skrutskie_two_2006, WISEwright_wide-field_2010, Spitzerpadgett_spitzer_2006, AKARIishihara_akariirc_2010; and (sub)millimeter data from pinte_probing_2008, andrews_disk_2018, oberg_disk_2011, cleeves_variable_2017, huang_alma_2017, DSHARP huang_disk_2018, cleeves_IMLup_coupled_2016, and lommen_sma_2008.
• Figure 2: Flow chart summarizing the two approaches to estimate disk masses. The main difference between them is the surface density distributions of gas and dust. We solve vertical hydrostatic equilibrium (VHSE) for all models and include dust settling for the structured model (see Sections \ref{['subsec:data_driven_model_B']} and \ref{['subsec:theoretical_model_C']}), and we use the reduced chemical network that considers the isotope-selective photodissociation and grain surface chemistry to get the CO abundances. This flow chart only shows the main steps in DiskMINT, and more details are described in Deng_2023_diskmint.
• Figure 3: The synthetic SED compared with observation (top) and the synthetic $L_{\rm C^{18}O(2-1)}$ for different $M_{\rm gas}$ compared with observation (bottom) for the well-mixed model. In the top panel, the observations are shown in black points with errors, the Spitzer/IRS spectrum is shown in the magenta line, and the input stellar spectra with the stellar photosphere, UV, as well as the inner gas disk are shown in the dashed gray line. The synthetic SED of the model is shown in orange line, with the inferred $M_{\rm dust}$ shown on the upper right corner. In the bottom panel, the black horizontal line shows the $\rm C^{18}O(2-1)$ observation from MAPS, with its uncertainties shown as the dark gray area. The blue points show the model points with different $\varepsilon$, and the best-fit model with $\varepsilon=6.41\times10^{-3}$ is circled in blue, with its corresponding $M_{\rm gas}$ shown on the upper right corner.
• Figure 4: The flow chart demonstrates the steps to calculate dust settling when solving the vertical density distribution. The details on the procedures of solving thermal equilibrium and the vertical hydrostatic equilibrium are presented in Deng_2023_diskmint Section 2.1 and Figure 1. For all models, the well-mixed case where dust is coupled with gas, and the structured model where they decouple due to settling, the same convergence criterion is used --- that $\rho_{\rm gas}$ and $\rho_{\rm dust}$ attain a 5% accuracy with iterations.
• Figure 5: Compare observations and the results from structured model, in SED (top), cont. and $\rm C^{18}O(2-1)$ radial profiles (middle two panels) and $\rm C^{18}O(2-1)$ line spectra (bottom). The captions in the SED follow the top panel of Figure \ref{['fig:Result_Model_A']}, with the synthetic SED from the structured model shown in blue. The continuum and $\rm C^{18}O(2-1)$ radial profiles are created by measuring the total flux per area at each radius inside an annulus that is tilted to match the observed geometry, with the best-fit $M_{\rm dust}$ and $M_{\rm gas}$ shown at the upper right corners. The line spectra are made with GoFish without de-projection. Observations are shown in black lines, along with their uncertainties, in the radial profile and the line spectra.