Optically-thick accretion discs with advection

The structures of optically-thick accretion discs with radial advection have been investigated by the iteration and integration algorithms. The advective cooling term changes mostly the inner part of disc solution, and even results in an optically-thick advection-dominated accretion flow (ADAF). Three distinct branches－the outer Shakura－Sunyaev disc (SSD), the inner ADAF and the middle transition layer－are found for a super-Eddington disc. The SSD－ADAF transition radius can be estimated as 18$(\dot{M}/\dot{M}_E)R_G$ where R_G is the Schwarzschild radius, $\dot{M}$ is the mass accretion rate and $\dot{M}_E$ is the Eddington accretion rate. SSD solutions calculated with the iteration and integration methods are identical, while ADAF solutions obtained by these two methods differ greatly. Detailed algorithms and their differences have been analysed. The iteration algorithm is not self-consistent, since it implies that the dimensionless advection factor $\xi$ is invariant, but in the inner ADAF region the variation of $\xi$ is not negligible. The integration algorithm is always effective for the whole region of an optically-thick disc if the accretion rate is no smaller than 10^-4$\dot{M}_E$. For optically-thin discs, the validity of these two algorithms is different. We suggest that the integration method be employed to calculate the global solution of a disc model without assuming $\xi$ to be a constant. We also discuss its application to the emergent continuum spectrum in order to explain observational facts.