The vertical structure of T Tauri accretion discs - III. Consistent interpretation of spectra and visibilities with a two-layer model

We present a two-layer accretion disc model developed to simultaneously fit optical long baseline visibilities and spectral energy distributions of T Tauri accretion discs. This model allows us to access easily the physical conditions in the disc as the mid-plane or the surface temperature. Our model includes viscous heating, absorption of stellar irradiation, and thermalisation with the surrounding medium. The disc is modelled with concentric cylinders for which the vertical radiation transfer is computed using two layers with vertically averaged temperatures: the outer layer is heated by the stellar irradiation and by the inner layer, and the inner layer by viscous dissipation and by the outer layer. We investigate three prescriptions for the geometrical thickness of the disc: it is either proportional the scale height (model 1), given ad hoc (model 2), or zero (model 3). We then derive the disc structure in the case of the a and,13 viscosity prescriptions, as well as for various optical thickness regimes of the disc. This analytical model allows us to disentangle regions where the mid-plane temperature and the effective temperature are dominated by accretion from regions dominated by reprocessing of stellar light. In the case of a-prescription, we find that the structure of model 2 gives predictions very close to those of numerical simulations from previous authors. From the disc structure, we derive the spectral energy distributions, images and interferometric visibilities. We analyse the influence of the disc parameters on the resulting structure and on the observable outputs. We apply our model to interpret consistently the spectral energy distributions and visibilities of SU Aur and FU Ori for which interferometric data are available, and that are not known to be part of a multiple system. We were not able to derive a consistent fit for T Tau North, which might come from caveats in the flux correction from its South component, but were able to separately derive fits for its spectrum and its visibilities. We find that even a single interferometric measurement at one infrared wavelength can bring a very strong constraint on disc models. We predict that future massive interferometric observations of accretion discs will provide a breakthrough in the understanding of accretion disc physics.