Herschel survey and modelling of externally-illuminated photoevaporating protoplanetary disks

Context. Protoplanetary disks undergo substantial mass-loss by photoevaporation, a mechanism that is crucial to their dynamical evolution. However, the processes regulating the gas energetics have not so far been well constrained by observations. Aims. We aim to study the processes involved in disk photoevaporation when it is driven by far-UV photons (i.e. 6 < E < 13 : 6 eV). Methods. We present a unique Herschel survey and new ALMA observations of four externally-illuminated photoevaporating disks (a. k. a. proplyds). To analyse these data, we developed a 1D model of the photodissociation region (PDR) of a proplyd, based on the Meudon PDR code. Using this model, we computed the far infrared line emission. Results. With this model, we successfully reproduce most of the observations and derive key physical parameters, that is, the densities at the disk surface of about 106 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 di ff er from those dominating in classical PDRs, meaning the grain photo-electric e ff ect and cooling by [OI] and [CII] FIR lines. This specific energetic regime is associated to an equilibrium dynamical point of the photoevaporation flow: the mass-loss rate is self-regulated to keep the envelope column density at a value that maintains the temperature at the disk surface around 1000 K. From the physical parameters derived from our best-fit models, we estimate mass-loss rates -of the order of 10 7 M fi /yr -that are in agreement with earlier spectroscopic observation of ionised gas tracers. This holds only if we assume photoevaporation in the supercritical regime where the evaporation flow is launched from the disk surface at sound speed. Conclusions. 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.