A parametric model for externally irradiated protoplanetary disks with photoevaporative winds

TL;DR

This work tackles how external ultraviolet irradiation from nearby massive stars alters the chemical evolution of protoplanetary disks. It introduces PUFFIN, a parametric framework that efficiently generates physically motivated 1D and 2D density structures including photoevaporative winds, calibrated against the FRIED grid and validated against select 2D hydrodynamic simulations. By coupling these density structures to thermochemical modelling (via DALI), the study shows that external FUV irradiation can strongly enhance midplane gas-phase CO through indirect heating, an effect that grows with decreasing stellar mass and with disk radius. The framework enables rapid, large-parameter surveys of disk-wind chemistry and provides a practical tool for interpreting observations and guiding planet-formation in clustered environments. Overall, external irradiation is a first-order control on disk chemistry and volatile budgets, not a mere perturbation, with PUFFIN offering a scalable means to explore these effects across diverse stellar and disk properties.

Abstract

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.

Figures (16)

• Figure 1: Schematic illustration of the 1D parametric model density profile. The model comprises three distinct regions: (i) the disk interior with a power-law profile ($r=0$ to $r=r_\text{d}$), (ii) a smooth transition region where the exponential taper and 'plateau' prescriptions bridge the disk and wind densities ($r=r_\text{d}$ to $r=r_\text{d} + \delta r$), and (iii) the outer photoevaporative wind following a spherically diverging profile ($r=r_\text{d} + \delta r$ to $r=r_\text{out}$). The vertical dashed lines mark the disk edge radius $r_\text{d}$, and the end of the transition region $\delta r$. The blue shaded area highlights the transition zone where disk and wind profiles are smoothly connected.
• Figure 2: Posterior distributions for the parameters governing the exponential taper that links the disk outer edge to the spherically expanding wind in our 1D model. The parameter $A$ sets the overall normalisation, while $\alpha$, $\beta$, and $\varepsilon$ describe the dependence of the taper on stellar mass, disk radius, and external FUV field strength, respectively. The MCMC was run for 40,000 iterations and yields well-converged constraints on all four parameters.
• Figure 3: Density profiles comparing our 1D parametric model (solid lines) with fried models (dotted lines) across different stellar masses and external FUV field strengths. Columns show increasing FUV field strength (100, 1000, 10,000, and 100,000 G$_0$). Rows represent different stellar masses (0.3, 0.6, 1.0, 1.5, 3.0 $M_\odot$). Each subplot displays four different disk sizes ($r_\text{d} = 20, 40, 80, 150$ au) represented by different colours. All models use a fixed surface density scaling parameter of $\Sigma_\text{1au} = 1000$ g cm$^{-3}$.
• Figure 4: Streamlines from a representative photoevaporation model with disk radius $r_\text{d} = 100$ au and external FUV field $F_\text{FUV} = 5000 \; G_0$. Streamlines are traced backward from a spherical surface in the outer wind region to their origins at the disk surface. The convergence of these streamlines identifies a focal point on the midplane located at approximately $r_\text{focal}=0.5 r_\text{d}$.
• Figure 5: Schematic illustration of the three main components that constitute our 2D parametric model. First panel: The disk component, following hydrostatic equilibrium with a vertical density profile modified by external FUV heating. Second panel: The disk-wind transition region, or 'halo', which provides a smooth bridge between the disk surface and the wind through an exponential taper extending outward from the disk surface. Third panel: The spherically diverging photoevaporative wind, emanating from a focal point located at approximately $0.5\;r_{\rm d}$ on the midplane. Fourth panel: The final density structure at any location in the full 2D model is determined by taking the maximum density among these three components.