Context. The analysis of spectral energy distributions (SEDs) of protoplanetary disks to determine their physical properties is known to be highly degenerate. Hence, a full Bayesian analysis is required to obtain parameter uncertainties and degeneracies. The main challenge here is computational speed, as one proper full radiative transfer model requires at least a couple of CPU minutes to compute.
Aims: We performed a full Bayesian analysis for 30 well-known protoplanetary disks to determine their physical disk properties, including uncertainties and degeneracies. To circumvent the computational cost problem, we created neural networks (NNs) to emulate the SED generation process.
Methods: We created two sets of MCFOST Monte Carlo radiative transfer disk models to train and test two NNs that predict SEDs for continuous and discontinuous disks, with 18 and 26 free model parameters, respectively. A Bayesian analysis was then performed on 30 protoplanetary disks with SED data collected by the FP7-Space DIANA project to determine the posterior distributions of all parameters. We ran this analysis twice, (i) with old distances and additional parameter constraints as used in a previous study, to compare results, and (ii) with updated distances and free choice of parameters to obtain homogeneous and unbiased model parameters. We evaluated the uncertainties in the determination of physical disk parameters from SED analysis, and detected and quantified the strongest degeneracies.
Results: The NNs are able to predict SEDs within ~1 ms with uncertainties of about 5% compared to the true SEDs obtained by the radiative transfer code. We find parameter values and uncertainties that are significantly different from previous values obtained by χ2 fitting. Comparing the global evidence for continuous and discontinuous disks, we find that 26 out of 30 objects are better described by disks that have two distinct radial zones. The analysed sample shows a significant trend for massive disks to have small scale heights, which is consistent with lower midplane temperatures in massive disks. We find that the frequently used analytic relationship between disk dust mass and millimetre-flux systematically underestimates the dust mass for high-mass disks (dust mass ≥10‒4 M☉). We determine how well the dust mass can be determined with our method for different numbers of flux measurements. As a byproduct, we created an interactive graphical tool that instantly returns the SED predicted by our NNs for any parameter combination.
