Gas and dust mass in the disc around the Herbig Ae star HD 169142

Context. Spatially resolved observations of circumstellar discs at millimetre wavelengths allow detailed comparisons with theoretical models for the radial and vertical distribution of the material. Aims. We investigate the physical structure of the gas component of the disc around the pre-main-sequence star HD 169142 and test the disc model derived from the spectral energy distribution. Methods. The (CO)-C-13 and (CO)-O-18 J = 2-1 line emission was observed from the disc with 1.4 resolution using the Submillimeter Array. We adopted the disc physical structure derived from a model that fits the spectral energy distribution of HD 169142. We obtained the full three-dimensional information on the CO emission with the aid of a molecular excitation and radiative transfer code. This information was used for the analysis of our observations and previous (CO)-C-12 J = 2-1 and 1.3 mm continuum data. Results. The spatially resolved (CO)-C-13 and (CO)-O-18 emission shows a Keplerian velocity pattern. The disc is seen at an inclination close to 13 degrees from face-on. We conclude that the regions traced by different CO isotopologues are distinct in terms of their vertical location within the disc, their temperature, and their column densities. With the given disc structure, we find that freeze-out is not efficient enough to remove a significant amount of CO from the gas phase. Both observed lines match the model prediction both in flux and in the spatial structure of the emission. Therefore we use our data to derive the (CO)-C-13 and (CO)-O-18 mass and consequently the (CO)-C-12 mass with standard isotopic ratios. We constrain the total disc gas mass to (0.6-3.0) x 10(-2) M-circle dot. Adopting a maximum dust opacity of 2 cm(2) g(dust)(-1) we derive a minimum dust mass of 2.16 x 10(-4) M-circle dot from the fit to the 1.3 mm data. Comparison of the derived gas and dust mass shows that the gas-to-dust mass ratio of 100 is only possible under the assumption of a dust opacity of 2 cm(2) g(-1) and (CO)-C-12 abundance of 10(-4) with respect to H-2. However, our data are also compatible with a gas-to-dust ratio of 25, with a dust opacity of 1 cm(2) g(-1) and (CO)-C-12 abundance of 2 x 10(-4).