# Herschel survey and modelling of externally-illuminated photoevaporating protoplanetary disks

## TL;DR

This study combines Herschel and ALMA observations with a new PDR model to analyze externally-illuminated photoevaporating disks, revealing their energetic regimes, physical parameters, and self-regulated mass-loss rates, advancing understanding of disk evolution.

## Contribution

The paper introduces a 1D PDR model tailored for proplyds, linking observations with physical parameters and identifying a unique energetic regime affecting disk photoevaporation.

## Key findings

- Derived densities at disk surfaces (~10^6 cm^-3)
- Estimated mass-loss rates (~10^-7 M_sun/yr)
- Identified a self-regulated energetic regime

## Abstract

Protoplanetary disks undergo substantial mass-loss by photoevaporation, a mechanism which is crucial to their dynamical evolution. However, the processes regulating the gas energetics have not been well constrained by observations so far. We aim at studying the processes involved in disk photoevaporation when it is driven by far-UV photons. We present a unique Herschel survey and new ALMA observations of four externally-illuminated photoevaporating disks (a.k.a. proplyds). For the analysis of these data, we developed a 1D model of the photodissociation region (PDR) of a proplyd, based on the Meudon PDR code and computed the far infrared line emission. We successfully reproduce most of the observations and derive key physical parameters, i.e. densities at the disk surface of about $10^{6}$ cm$^{-3}$ and local gas temperatures of about 1000 K. Our modelling suggests that all studied disks are found in a transitional regime resulting from the interplay between several heating and cooling processes that we identify. These differ from those dominating in classical PDRs, i.e. grain photo-electric effect and cooling by [OI] and [CII] FIR lines. This energetic regime is associated to an equilibrium dynamical point of the photoevaporation flow: the mass-loss rate is self-regulated to set the envelope column density at a value that maintains the temperature at the disk surface around 1000 K. From our best-fit models, we estimate mass-loss rates - of the order of $10^{-7}$ $\mathrm{M}_\odot$/yr - that are in agreement with earlier spectroscopic observation of ionised gas tracers. This holds only if we assume an evaporation flow launched from the disk surface at sound speed (supercritical regime). We have identified the energetic regime regulating FUV-photoevaporation in proplyds. This regime could be implemented into models of the dynamical evolution of protoplanetary disks.