Planetary evaporation by UV and X-ray radiation: basic hydrodynamics

We consider the evaporation of close-in planets by the star's intrinsic extreme-ultraviolet (EUV) and X-ray radiation. We calculate evaporation rates by solving the hydrodynamical problem for planetary evaporation including heating from both X-ray and EUV radiation. We show that most close-in planets (a < 0.1 au) are evaporating hydrodynamically, with the evaporation occurring in two distinct regimes: X-ray driven, in which the X-ray heated flow contains a sonic point, and EUV driven, in which the X-ray region is entirely sub-sonic. The mass-loss rates scale as L-X/a(2) for X-ray driven evaporation, and as Phi(1/2)(*)/a for EUV driven evaporation at early times, with mass-loss rates of the order of 10(10)-10(14) g s(-1). No exact scaling exists for the mass-loss rate with planet mass and planet radius; however, in general evaporation proceeds more rapidly for planets with lower densities and higher masses. Furthermore, we find that in general the transition from X-ray driven to EUV driven evaporation occurs at lower X-ray luminosities for planets closer to their parent stars and for planets with lower densities. Coupling our evaporation models to the evolution of the high-energy radiation - which falls with time - we are able to follow the evolution of evaporating planets. We find that most planets start off evaporating in the X-ray driven regime, but switch to EUV driven once the X-ray luminosity falls below a critical value. The evolution models suggest that while 'hot Jupiters' are evaporating, they are not evaporating at a rate sufficient to remove the entire gaseous envelope on Gyr time-scales. However, we do find that close in Neptune mass planets are more susceptible to complete evaporation of their envelopes. Thus we conclude that planetary evaporation is more important for lower mass planets, particularly those in the 'hot Neptune'/'super Earth' regime.