Radiation-hydrodynamic models of X-ray and EUV photoevaporating protoplanetary discs

We present the first radiation-hydrodynamic model of a protoplanetary disc irradiated with an X-ray extreme ultraviolet (X-EUV) spectrum. In a model where the total ionizing luminosity is divided equally between X-ray and EUV luminosity, we find a photoevaporation rate of 1.4 × 10−8 M⊙ yr−1, which is two orders of magnitude greater than the case of EUV photoevaporation alone. Thus, it is clear that the X-rays are the dominant driving mechanism for photoevaporation. This can be understood inasmuch as X-rays are capable of penetrating much larger columns (∼1022 cm−2) and can thus effect heating in denser regions and at larger radius than the EUV. The radial extent of the launching region of the X-ray-heated wind is 1–70 au compared with the pure EUV case where the launch region is concentrated around a few au. When we couple our wind mass-loss rates with models for the disc's viscous evolution, we find that, as in the pure EUV case, there is a photoevaporative switch, such that an inner hole develops at ∼1 au at the point when the accretion rate in the disc drops below the wind mass-loss rate. At this point, the remaining disc material is quickly removed in the final 15–20 per cent of the disc's lifetime. This is consistent with the 105 yr transitional time-scale estimated from observations of T Tauri stars. We however note several key differences to previous EUV-driven photoevaporation models. The two orders of magnitude higher photoevaporation rate is now consistent with the average accretion rate observed in young stars and will cut the disc off in its prime. Moreover, the extended mass-loss profile subjects the disc to a significant period (∼20 per cent of the disc's lifetime) of ‘photoevaporation-starved accretion’. We also caution that although our mass-loss rates are high compared to some accretion rates observed in young stars, our model has a rather large X-ray luminosity of 2 × 1030 erg s−1; further modelling is required in order to investigate the evolutionary implications of the large observed spread of X-ray luminosities in T Tauri stars.