Hot accretion discs with thermal Comptonisation and advection in luminous black hole sources

We solve for the structure of a hot accretion disc with unsaturated thermal Comptonisation of soft photons and with advection, generalizing the classical model of Shapiro et al. The upper limit on the accretion rate due to advection constrains the luminosity to $\simless 0.15 y^{3/5} \alpha^{7/5}$ of the Eddington limit, where $y$ and $\alpha$ are the Compton and viscosity parameters, respectively. The characteristic temperature and Thomson optical depth of the inner flow at accretion rates within an order of magnitude of that upper limit are $\sim 10^9$ K and $\sim 1$, respectively. The resulting spectra are then in close agreement with the X-ray and soft \g-ray spectra from black-hole binaries in the hard state and Seyferts. At low accretion rates, bremsstrahlung becomes the dominant radiative process.