Can thermodynamic equilibrium be established in planet-forming disks?

¹ Kapteyn Astronomical Institute, University of Groningen, PO Box 800, 9700 AV Groningen, The Netherlands
² Space Research Institute, Austrian Academy of Sciences, Schmiedlstr. 6, 8042 Graz, Austria
³ Institute for Theoretical Physics and Computational Physics, Graz University of Technology, Petersgasse 16, 8010 Graz, Austria
⁴ Cavendish Laboratory, University of Cambridge, JJ Thomson Ave, Cambridge CB3 0HE, UK

^★ Corresponding author.

Received: 14 September 2024
Accepted: 29 April 2025

Abstract

Context. The inner regions of planet-forming disks are warm and dense. The chemical networks used for disk modelling so far were developed for a cold and dilute medium and do not include a complete set of pressure-dependent reactions. The chemical networks developed for planetary atmospheres include such reactions along with the inverse reactions related to the Gibb’s free energies of the molecules. The chemical networks used for disk modelling are thus incomplete in this respect.

Aims. We want to study whether thermodynamic equilibrium can be established in a planet-forming disk. We identify the regions in the disk most likely to reach thermodynamic equilibrium and determine the timescale over which this occurs.

Methods. We employ the theoretical concepts used in exoplanet atmosphere chemistry for the disk modelling with PROtoplanetary DIsk MOdel (PRODIMO). We develop a chemical network called CHemistry Assembled from exoplanets and dIsks for Thermodynamic EquilibriA (CHAITEA) that is based on the UMIST 2022, STAND, and large DIscANAlysis (DIANA) chemical networks. It consists of 239 species. From the STAND network, we adopt the concept of reversing all gas-phase reactions based on thermodynamic data. We use single-point models for a range of gas densities and gas temperatures to verify that the implemented concepts work and thermodynamic equilibrium is achieved in the absence of cosmic rays and photoreactions including radiative associations and direct recombinations. We then study the impact of photoreactions and cosmic rays that lead to deviations from thermodynamic equilibrium. We explore the chemical relaxation timescales towards thermodynamic equilibrium. Lastly, we study the predicted 2D chemical structure of a typical T Tauri disk when using the new CHAITEA network instead of the large DIANA standard network, including photorates, cosmic rays, X-rays, and ice formation.

Results. We find that abundances calculated with PRODIMO using the CHAITEA network agree with those from the equilibrium chemistry code Gleich-Gewichts-Chemie (GGchem) down to 600 K when the photorates, cosmic rays, and X-rays (benchmark) are absent. To measure the deviation between thermodynamic equilibrium and chemical kinetics, a measure, σ, is introduced that evaluates the mean logarithmic deviation between the two abundance sets, which is <1% in the benchmark case. In the presence of photoreactions, based on a local Planck radiation field, σ increases to ∼0.1 across all densities and temperatures. When the cosmic-ray ionisation rate is increased from zero to about 10⁻²⁵ s⁻¹, σ begins to become large (>1), affecting in particular the ions, and when it reaches the standard value of 10⁻¹⁷ s⁻¹, σ becomes >10. Low-temperature and low-density regions are more affected than high-temperature and high-density regions, as expected. The chemical relaxation timescales show a wide range, with both slow and fast chemical processes. The 2D disk models show that thermodynamic equilibrium cannot be established anywhere in the disk. However, a tiny, warm, high-density region directly behind the inner rim which is shielded from the cosmic rays, approaches thermodynamic equilibrium to some extent. In the warm intermittent molecular layer, which is observable, σ ≥ 10, and σ is even higher in other regions.

Conclusions. We have developed a new chemical network, CHAITEA, that merges planetary chemistry with disk chemistry and have implemented it in the 2D thermochemical disk code PRODIMO. The inclusion of termolecular and reverse reactions changes the chemical structure in the inner disk that is probed by JWST.