A parametric model for externally irradiated protoplanetary disks with photoevaporative winds

Protoplanetary disks in massive star-forming regions may be exposed to ultraviolet radiation fields orders of magnitude stronger than the interstellar background. This intense radiation drives photoevaporative winds that fundamentally shape disk evolution and chemistry. However, full radiation hydrodynamic simulations of these systems remain computationally expensive, preventing systematic exploration of the parameter space. We present a parametric framework for efficiently generating density structures of externally irradiated protoplanetary disks with photoevaporative winds. Our approach implements a spherically diverging wind configuration with smooth transitions between the disk interior, the FUV-heated surface layer, and the wind itself. We validate this framework extensively against the FRIED grid of hydrodynamical simulations, demonstrating accurate reproduction of density structures across stellar masses from 0.3 to 3.0 M_sun, disk radii from 20 to 150 au, and external FUV fields from 100 to 100,000 G0. The complete framework is available as ‘PUFFIN’, a Python package that generates full 1D or 2D density structures in seconds to minutes, compared to weeks or months for equivalent hydrodynamical calculations. We demonstrate the scientific utility of this approach by modelling CO chemistry across a comprehensive parameter grid, using our density structures as inputs to thermochemical calculations. Our results show that external FUV irradiation significantly enhances CO gas-phase abundances through indirect heating mechanisms, which raise midplane temperatures and enhance thermal desorption of CO ice. This effect is strongest in the outer disk and scales with both external field strength and disk mass, with important implications for volatile budgets available to forming planets in clustered environments.

💡 Research Summary

The paper introduces a fast, physically motivated parametric framework—implemented in the publicly available Python package PUFFIN—for generating the density structure of protoplanetary disks that are externally irradiated by strong far‑ultraviolet (FUV) fields and that launch photoevaporative winds. Full radiation‑hydrodynamic (RHD) simulations of such systems are computationally prohibitive, limiting systematic studies of how stellar mass, disk size, disk mass, and external FUV intensity affect disk evolution and chemistry. PUFFIN circumvents this bottleneck by constructing a three‑component model: (i) an inner disk described by a standard power‑law surface density Σ(r)∝r⁻¹ with an exponential taper, (ii) a transition “plateau” region that smoothly bridges the disk edge to the wind, and (iii) an outer, spherically diverging wind with density ρ_wind=Ṁ/(4πr²v_R).

Key to the model is the parametrisation of the taper steepness γ as a function of stellar mass (M★), disk outer radius (r_d), and external FUV flux (F_FUV): γ = A·M★^α·r_d^β·F_FUV^ε. The constants A, α, β, ε, together with the transition‑width parameters p and q (which control the λ parameter governing the smoothness of the plateau‑to‑wind transition), are calibrated against the FRIED grid of 2‑D RHD simulations. Using an MCMC approach, the authors obtain well‑converged posterior distributions for all six free parameters, achieving density reproductions within ~10 % of the FRIED results across a wide parameter space (M★ = 0.3–3 M⊙, r_d = 20–150 au, F_FUV = 10²–10⁵ G₀).

The wind velocity is set equal to the local sound speed at the wind base, with the PDR temperature scaling as T_PDR = 200 K·(F_FUV/1000 G₀)^0.2, bounded between 10 K and 3000 K. This captures the sub‑linear increase of heating efficiency with FUV due to grain charging effects. The model selects, at each radius, the maximum of the disk, plateau, and wind densities, ensuring a physically consistent profile that transitions from a dense, Keplerian disk to a low‑density, radially expanding outflow.

To demonstrate scientific utility, the authors couple PUFFIN‑generated density and temperature fields to a thermochemical code and compute CO abundances over a comprehensive grid. They find that external FUV irradiation indirectly raises midplane temperatures via infrared re‑processing in the wind, which in turn enhances thermal desorption of CO ice. The CO gas‑phase abundance is most strongly boosted in the outer disk (>100 au), with the effect scaling positively with both FUV strength and disk mass. This mechanism can raise CO column densities to near‑interstellar values even in environments where isolated disks would show severe CO depletion, implying that external irradiation can replenish volatile reservoirs available for planet formation in clustered regions.

PUFFIN produces full 1‑D or 2‑D density structures in seconds to minutes, a dramatic speed‑up compared with weeks‑long RHD runs. The authors make the code openly available, discuss potential extensions (e.g., inclusion of non‑spherical winds, dust evolution, additional chemical networks), and argue that PUFFIN will enable systematic, high‑dimensional studies of disk evolution, chemistry, and observable signatures in massive star‑forming regions.