The global structure of thin, stratified alpha-discs and the reliability of the one layer approximation

We report the results of a systematic comparison between the vertically ave raged model and the vertically explicit model of steady state, Keplerian, o ptically thick alpha -discs. The simulations have concerned discs currently found in three different systems: dwarf novas, young stellar objects and a ctive galactic nuclei. In each case? we have explored four decades of accre tion rates and almost the whole disc area (except the narrow region where t he vertically averaged model has degenerate solutions). We find that the on e layer approach gives a remarkably good estimate of the main physical quan tities in the disc, and specially the temperature at the equatorial plane w hich is accurate to within 30% for cases considered. The major deviations ( by a factor less than or similar to 4) are observed on the disc half-thickn ess. The sensitivity of the results to the a-parameter value has been teste d for 0.001 less than or equal to alpha less than or equal to 0.1 and appea rs to be weak. This study suggests that the ''precision" of the vertically averaged model. which is easy to implement should be sufficient in practice for many astrophysical applications.