Fundamental properties of protoplanetary discs determined from simultaneous fits to thermal dust images and spectral energy distributions

Abstract

We present a novel machine learning method that is capable of rapidly and accurately producing dust-continuum model images and spectral energy distributions from training sets created using a detailed radiative transfer code. We create a training set that encompasses the parameter space for protoplanetary discs, and then couple the trained machine learning method with a Bayesian optimisation algorithm. We then simultaneously fitted 1.3 mm ALMA ODISEA survey images of protostellar discs in rho Oph, and their spectral energy distributions, in order to determine fundamental discs parameters such as dust masses and radii. We find that good simultaneous fits may be found for the Class II objects in the survey, although the spectral fits are poorer for the Class I and flat spectrum sources. We find that the dust mass distributions of discs is broader and shallower than that predicted from 1.3 mm flux dust mass estimates, substantially increasing the numbers of objects with high-mass and low-mass discs. We show that this is due to a combination of optical depth and dust temperature effects, which are strongly related to the disc size and inclination constraints provided by the imaging fits. We show that there is a significant decrease in disc scale height and disc flaring when moving from the the Class I objects, to the flat spectrum sources, and the Class II discs.

Figures (21)

• Figure 1: A schematic of the feed-forward, fully-connected neural network used to predict the model SEDs. The input layer (pink neurons) consists of the normalised model inputs $P_i$. The two dense (fully connected) hidden layers are shown in blue, with the final SED flux outputs ($F_i$) in green.
• Figure 2: A schematic of the autoencoder configuration. The original image (left hand panel) passes through three convolutional layers to reduce its size from $128 \times 128$ pixels to $16 \times 16$. The final convolutional layer is flattened and fully connected to a 100 neuron latent space ($L_1$ to $L_{100}$). Subsequently the reverse process is applied using convolutional transpose layers to recreate an approximation of the original image.
• Figure 3: A schematic of the decoder network. The inputs (pink symbols) are the normalised disc parameters $P_i$ (such as mass, inclination, radius etc), which are fully connected to two hidden layers (dark grey symbols) and then to the latent space ($L_i$, light grey symbols). The right-hand part of the schematic represents the decoder part of the (previously trained) autoencoder.
• Figure 4: The top panel shows the mean SED of the test dataset. The bottom panel shows the histogram of the mean absolute differences between the validation data and the output of the neutral network for each wavelength bin (colour scale). The mean (solid read line), 1-sigma and 2-sigma limits (dotted lines).
• Figure 5: The top panels are two-dimensional histograms comparing the normalised, scaled pixel values between the AE and the validation set (top left) and the latent space decoder model vs the validation set (top right). The bottom two panels show the distribution of the SSIM score of the two neural networks.