Galaxy mass profiles with convolutional neural networks

TL;DR

This paper tackles the challenge of recovering dynamical mass profiles for dispersion-supported galaxies from line-of-sight stellar data, a problem hampered by projection effects and unknown velocity anisotropy. It introduces a two-branch convolutional neural network (CNN) that processes projected stellar distribution PDFs, combined with a normalising flow to yield a full posterior for the mass enclosed within ten radii. Trained on a diverse set of cosmological hydrodynamical simulations (NIHAO, AURIGA, FIRE), the model outperforms existing literature mass estimators in accuracy and provides mass estimates at radii lacking traditional estimators, with well-calibrated posteriors confirmed by TARP. However, the model’s generalisation across simulation domains is limited, showing biases when trained on one suite and tested on another; combining NIHAO and AURIGA improves transfer to FIRE but still exhibits residual biases, underscoring the need for domain adaptation and broader training sets for robust application to real galaxies.

Abstract

Determining the dynamical mass profiles of dispersion-supported galaxies is particularly challenging due to projection effects and the unknown shape of their velocity anisotropy profile. Our goal is to develop a machine learning algorithm capable of recovering dynamical mass profiles of dispersion-supported galaxies from line-of-sight stellar data. Traditionally, this task relies on time-consuming methods that require profile parameterization and assume dynamical equilibrium and spherical symmetry. We train a convolutional neural network model using various sets of cosmological hydrodynamical simulations of galaxies. By extracting projected stellar data from the simulated galaxies and feeding it into the model, we obtain the posterior distribution of the dynamical mass profile at ten different radii. Additionally, we evaluate the performance of existing literature mass estimators on our dataset. Our model achieves more accurate results than any literature mass estimator while also providing enclosed mass estimates at radii where no previous estimators exist. We confirm that the posterior distributions produced by the model are well-calibrated, ensuring they provide meaningful uncertainties. However, issues remain, as the method loses performance when trained on one set of simulations and applied to another, highlighting the importance of improving the generalization of ML methods trained on specific galaxy simulations.

Figures (14)

• Figure 1: Distribution of dynamical mass enclosed within the projected half-light radius ($R_{\rm h}$) of dispersion-supported galaxies for each suite of simulations. Blue and orange histograms show, respectively, the distributions of NIHAO and AURIGA galaxy projections with 100 bins, while the dashed black line histogram shows their distribution at 30 bins, which we made equal in the two suites by dropping excessive projections from each dataset. The dashed grey lines show the distribution of FIRE galaxy projections inside the mass range covered by NIHAO and AURIGA.
• Figure 2: Number density contours of projections of galaxies of NIHAO, AURIGA, and FIRE simulation suites in the space of the stellar mass--projected half light radius.
• Figure 3: Scheme of our CNN architecture. The CNN extracts the spatial and dynamical information of the galaxy from the projected stellar data and compresses it through a series of convolution and pooling operations. The CNN joins the information of the spatial and dynamical branches and further reduces the dimensionality for producing an N parameter output, representing the value estimated for the dynamical mass of the galaxy enclosed within N different radii. After training the CNN, the 32 neurons of penultimate layer are used as inputs to train a normalising flow model. The flow model learns a series of transformations to a N-dimensional Gaussian PDF, which are conditioned on the inputs, and outputs a posterior N-dimensional joint PDF for the N enclosed masses.
• Figure 4: Probability density function of the ratio between the enclosed mass calculated by the literature mass estimators and the true enclosed mass for all dispersion-supported simulated galaxies in our training dataset of mixed NIHAO and AURIGA simulations (solid histogram), and for galaxies from each simulation project separately (empty histograms with different line styles). In the case of the combined NIHAO and AURIGA dataset, the median ratio is represented by a vertical solid line, and percentiles 16th and 84th are depicted by dashed lines for the mixed dataset. The values of the median ratio and the 1$\sigma$ dispersion range are shown. Each row represents the results from a different mass estimator.
• Figure 5: CNN+MAF and mass estimator predictions for four random projections of four different galaxies in the validation set. Numerical profiles of cumulative mass calculated from the simulations are plotted as solid black lines, with CNN+MAF predictions shown as circles with their corresponding 1$\sigma$ uncertainties, and mass estimator calculations displayed as grey markers with black edges. The colour of the CNN+MAF circle markers varies depending on the dataset on which the model has been trained. Each panel is labelled with the identifier of the galaxy whose results are plotted in it, specifying the simulation suite, name, and number of the halo in our halo finder. We show full posterior distributions of the CNN+MAF predictions in Fig. \ref{['fig:CornerPlots']}.