On the theory of disc photoevaporation

We discuss a hydrodynamical model for the dispersal of protoplanetary discs around young, low-mass (<1.5 M?) stars by photoevaporation from the central objects energetic radiation, which considers the far-ultraviolet (FUV) as well as the X-ray component of the radiation field. We present analytical scaling relations and derive estimates for the total mass-loss rates, as well as discussing the existence of similarity solutions for flows from primordial discs and discs with inner holes. Furthermore, we perform numerical calculations which span a wide range of parameter space and allow us to provide accurate scalings of the mass-loss rates with the physical parameters of the systems (X-ray and FUV luminosity, stellar mass, disc mass, disc temperature and inner hole radius). The model suggests that the X-ray component dominates the photoevaporative mass-loss rates from the inner disc. The mass-loss rates have values in the range from 10-11 to 10-7 M? yr-1 and scale linearly with X-ray luminosity, with only a weak dependence on the other parameters explored. However, in the case of high FUV-to-X-ray luminosity ratios (LFUV/LX > 100), the FUV constricts the X-ray flow and may dominate the mass loss. Simulations of low-mass discs with inner holes demonstrate a further stage of disc clearing, which we call thermal sweeping. This process occurs when the mid-plane pressure drops to sufficiently low values. At this stage, a bound, warm, X-ray heated region becomes sufficiently large and unstable, such that the remaining disc material is cleared on approximately dynamical time-scales. This process significantly reduces the time taken to clear the outer regions of the disc, resulting in an expected transition disc population that will be dominated by accreting objects, as indicated by recent observations.