Can photoevaporation open gaps in protoplanetary discs?

Problem Statement
The dispersal of protoplanetary discs is a critical factor in determining the timing and conditions of planet formation. While photoevaporation—the removal of gas via thermally driven winds launched by high-energy stellar radiation—is widely recognized as a key dispersal mechanism, the theoretical basis for how it opens and sustains gaps remains uncertain. Standard models typically rely on one-dimensional (1D) viscous evolution calculations where the photoevaporative mass-loss rate, $\dot{\Sigma}(r)$, is treated as a fixed sink term derived from static two-dimensional (2D) simulations. This approach implicitly assumes that the mass-loss profile remains constant even as the disc structure evolves. The authors argue that this neglects a crucial feedback loop: as a gap begins to form, the local disc structure changes, potentially altering the wind launch conditions, reducing local mass-loss rates, and allowing viscous inflow to refill the depleted region. If photoevaporation is self-limiting in this manner, it may be less efficient at clearing gas at the radii where giant planets form than previously assumed, with significant implications for core accretion and migration models.

Methodology
To investigate whether photoevaporation alone can open and sustain gaps when the flow dynamically responds to disc structure, the authors employed a two-phased computational approach:

1. Phase I (1D Evolution): They used the viscous evolution code spock to simulate a disc undergoing X-ray photoevaporation until the onset of gap formation. The simulation evolved a gas surface density profile ($\Sigma$) over 2.1 Myr, incorporating a mass-loss profile from Picogna et al. (2019). This phase established the initial conditions for the 2D simulations, specifically a state where a partial depletion in surface density had developed.
2. Phase II (2D Radiation-Hydrodynamics): The surface density profile from the 1D simulation at 2.1 Myr was mapped into an axisymmetric 2D ($r-\theta$) spherical coordinate system using the pluto code. These simulations modeled the photoevaporative outflow and its interaction with the disc.
   • Model p-g: Utilized the evolved surface density from Phase I, which included a pre-existing density depletion.
   • Model p-ng: Utilized a modified initial surface density profile where the depletion was suppressed (replaced by a power law) to assess the impact of initial morphology on gap opening.
   • The simulations employed a line-of-sight heating approximation and assumed radiative equilibrium, decoupling radiative transfer from hydrodynamics to reduce computational cost.

Key Results

• Self-Limiting Gap Formation: In the 2D simulations, once a density depression formed, the local mass-loss rate decreased sharply within the gap region. This occurred because the depleted region remained in the shadow of the inner disc, reducing exposure to stellar irradiation. Consequently, the gap did not deepen into a fully evacuated cavity.
• Partial Refilling: Viscous inflow and radial mass transport along the disc surface (and through the wind) acted to partially refill the depleted region. The system evolved toward a persistent, partially depleted zone rather than a clean inner hole.
• Insensitivity to Initial Conditions: Comparing models with (p-g) and without (p-ng) an initial depletion showed that the long-term evolutionary outcome was largely independent of the initial disc morphology. In both cases, the system self-regulated to a state of partial depletion.
• Limitations of 1D Prescriptions: The authors tested a first-order prescription to approximate the 2D behavior in 1D models by scaling the primordial mass-loss profile based on the local surface density depletion. While this improved agreement over static prescriptions, the 1D models still evolved too rapidly and produced deeper gaps than the 2D simulations. This discrepancy highlights the inability of 1D models to capture radial mass transport along the disc surface and the complex interplay of shadowing.
• Observational Signatures: Although the gas gap remains partially filled, the pressure maximum at the outer edge of the depression may still act as an efficient trap for dust grains. This could produce observational signatures resembling transition discs (inner cavities in continuum emission) even without complete gas clearing.

Significance and Claims
The paper challenges the standard paradigm that photoevaporation efficiently carves clean inner cavities and directly produces transition discs. Instead, the authors propose that photoevaporation may lead to a quasi-steady state characterized by a persistent, partially depleted zone. This suggests that discs exhibiting moderate depletion without complete inner clearing may represent systems influenced by photoevaporation but not fully dispersed.

The authors provide a modest, first-order prescription to approximate this self-regulated behavior in 1D disc evolution models, which is suitable for use in planet formation and population synthesis studies. However, they explicitly state that this prescription remains approximate and cannot fully capture the multidimensional nature of the flow, particularly radial mass redistribution. The paper concludes that further multidimensional simulations and parameter-space exploration are necessary to derive robust recipes for global disc and planet population models. The work underscores the need to move beyond static mass-loss treatments to understand the interplay between internal winds and planet formation pathways.