Radiation thermo-chemical models of protoplanetary disks I. Hydrostatic disk structure and inner rim

This paper introduces a new disk code, called ProDiMo, to calculate the thermo-chemical structure of protoplanetary disks and to interpret gas emission lines from UV to sub-mm. We combine frequency-dependent 2D dust continuum radiative transfer, kinetic gas-phase and UV photo-chemistry, ice formation, and detailed non-LTE heating & cooling balance with the consistent calculation of the hydrostatic disk structure. We include FeII and CO ro-vibrational line heating/cooling relevant for the high-density gas close to the star, and apply a modified escape probability treatment. The models are characterized by a high degree of consistency between the various physical, chemical and radiative processes, where the mutual feedbacks are solved iteratively. In application to a T Tauri disk extending from 0.5AU to 500AU, the models are featured by a puffed-up inner rim and show that the dense, shielded and cold midplane (z/r<0.1, TgTd) is surrounded by a layer of hot (5000K) and thin (10^7 to 10^8 cm^-3) atomic gas which extends radially to about 10AU, and vertically up to z/r0.5. This layer is predominantly heated by the stellar UV (e.g. PAH-heating) and cools via FeII semi-forbidden and OI 630nm optical line emission. The dust grains in this “halo” scatter the star light back onto the disk which impacts the photo-chemistry. The more distant regions are characterized by a cooler flaring structure. Beyond 100AU, Tgas decouples from Tdust even in the midplane and reaches values of about Tg~2Td. Our models show that the gas energy balance is the key to understand the vertical disk structure. Models calculated with the assumption Tg=Td show a much flatter disk structure.

💡 Research Summary

The paper presents ProDiMo (PROtoplanetary DIsk MOdel), a comprehensive numerical framework designed to compute the thermo‑chemical structure of protoplanetary disks in a fully self‑consistent manner. Traditional disk models typically treat dust radiative transfer, gas chemistry, and vertical hydrostatic balance separately, often assuming that the gas temperature (Tg) equals the dust temperature (Td). ProDiMo removes this simplification by coupling four major modules: (1) frequency‑dependent two‑dimensional dust continuum radiative transfer, which determines the local radiation field and dust temperature; (2) a kinetic gas‑phase and UV‑driven photochemistry network that includes hundreds of species and reactions, with explicit treatment of PAH charging and X‑ray ionisation; (3) a detailed non‑LTE heating and cooling balance that, beyond the usual CO, H₂O, and O I cooling, incorporates Fe II and CO rovibrational line processes and uses a modified escape‑probability formalism to handle line trapping in high‑density regions; and (4) a hydrostatic equilibrium solver that uses the computed gas pressure (derived from Tg) to update the vertical density structure.

All modules are iterated until convergence, ensuring that changes in one component (e.g., a rise in Tg) feed back into the radiation field, chemistry, and pressure support, thereby achieving a mutually consistent solution. The authors apply the code to a representative T Tauri system with a disk extending from 0.5 AU to 500 AU and a total gas mass of 0.01 M⊙.

Key physical findings are:

• Puffed‑up inner rim – The innermost dust wall at ~0.5 AU is heated directly by stellar irradiation, causing it to expand vertically. This “puffed‑up” rim reduces the shadowing of the outer disk and allows stellar UV photons to reach larger radii.

• Hot atomic halo – Between 0.5 AU and ~10 AU, at heights 0.1 ≲ z/r ≲ 0.5, a thin layer of low‑density (10⁷–10⁸ cm⁻³) gas attains temperatures of ~5 000 K. The dominant heating mechanisms are PAH photo‑electric heating, UV absorption by small grains, and direct stellar UV. Cooling is governed primarily by semi‑forbidden Fe II lines and the O I 630 nm transition; Fe II becomes especially important because its upper levels are collisionally de‑excited in the high‑density regime, providing an efficient non‑LTE cooling channel.

• Flared outer disk – Beyond a few tens of AU the disk flares outward, with surface temperatures of a few hundred Kelvin. In the outermost regions (>100 AU) the gas thermally decouples from the dust: Tg can reach roughly twice Td because the gas continues to absorb stellar UV and X‑rays while the dust is shielded and cools efficiently. The increased gas pressure inflates the vertical scale height, reinforcing the flaring geometry.

• Impact of assuming Tg = Td – When the model is forced to keep Tg equal to Td, the vertical structure collapses into a much flatter configuration. The inner rim loses its puffed‑up shape, the hot atomic halo disappears, and the overall disk surface area exposed to stellar radiation is dramatically reduced. Consequently, synthetic line fluxes and continuum SEDs derived from such a simplified model would be inconsistent with observations.

The authors conclude that the gas energy balance is the primary driver of the vertical disk structure. Accurate treatment of heating (especially UV and PAH processes) and cooling (including Fe II and O I lines) is essential for realistic disk models. ProDiMo’s ability to capture the feedback between radiation, chemistry, temperature, and hydrostatic support makes it a powerful tool for interpreting current and upcoming observations from facilities such as ALMA, JWST, and ELT‑class spectrographs. The model also sets a foundation for future studies of planet‑forming environments, where the distribution of temperature, ionisation, and molecular abundances directly influences dust evolution, pebble formation, and the early stages of planetesimal growth.