We study the efficiency and dynamics of supermassive black hole binary mergers driven by angular momentum loss to small‐scale gas discs. Such binaries form after major galaxy mergers, but their fate is unclear since hardening through stellar scattering becomes very inefficient at subparsec distances. Gas discs may dominate binary dynamics on these scales, and promote mergers. Using numerical simulations, we investigate the evolution of the semimajor axis and eccentricity of binaries embedded within geometrically thin gas discs. Our simulations directly resolve angular momentum transport within the disc, which at the radii of interest is likely dominated by disc self‐gravity. We show that the binary decays at a rate which is in good agreement with analytical estimates, while the eccentricity grows. Saturation of eccentricity growth is not observed up to values e≳ 0.35. Accretion on to the black holes is variable, and is roughly modulated by the binary orbital frequency. Scaling our results, we analytically estimate the maximum rate of binary decay that is possible without fragmentation occurring within the surrounding gas disc, and compare that rate to an estimate of the stellar dynamical hardening rate. For binary masses in the range 105≲M≲ 108 M⊙ we find that decay due to gas discs may dominate for separations below a∼ 0.01–0.1 pc, in the regime where the disc is optically thick. The minimum merger time‐scale is shorter than the Hubble time for M≲ 107 M⊙. This implies that gas discs could commonly attend relatively low‐mass black hole mergers, and that a significant population of binaries might exist at separations of a few hundredths of a parsec, where the combined decay rate is slowest. For more massive binaries, where this mechanism fails to act quickly enough, we suggest that scattering of stars formed within a fragmenting gas disc could act as a significant additional sink of binary angular momentum.

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.

We present a new model for protoplanetary disc evolution. This model combines viscous evolution with photoevaporation of the disc. However, in a companion paper we have shown that at late times such models must consider the effect of stellar radiation directly incident on the inner disc edge, and here we model the observational implications of this process. We find that the entire disc is dispersed on a time‐scale of the order of 105 yr after a disc lifetime of a few Myr, consistent with observations of T Tauri (TT) stars. We use a simple prescription to model the spectral energy distribution of the evolving disc, and demonstrate that the model is consistent with observational data across a wide range of wavelengths. We also note that the model predicts a short ‘inner hole’ phase in the evolution of all TT discs, and make predictions for future observations at mid‐infrared and millimetre wavelengths.