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The dynamical mass of the Coma cluster from deep learning


In 1933, Fritz Zwicky's famous investigations of the mass of the Coma cluster led him to infer the existence of dark matter1. His fundamental discoveries have proven to be foundational to modern cosmology; as we now know, such dark matter makes up 85% of the matter and 25% of the mass–energy content in the universe. Galaxy clusters like Coma are massive, complex systems of dark matter, hot ionized gas and thousands of galaxies, and serve as excellent probes of the dark matter distribution. However, empirical studies show that the total mass of such systems remains elusive and difficult to precisely constrain. Here we present new estimates for the dynamical mass of the Coma cluster based on Bayesian deep learning methodologies developed in recent years. Using our novel data-driven approach, we predict Coma's M200c mass to be 1015.10±0.15h−1M within a radius of 1.78 ± 0.03 h−1 Mpc of its centre. We show that our predictions are rigorous across multiple training datasets and statistically consistent with historical estimates of Coma's mass. This measurement reinforces our understanding of the dynamical state of the Coma cluster and advances rigorous analyses and verification methods for empirical applications of machine learning in astronomy.

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Fig. 1: Machine learning workflow for dynamical cluster-mass inference.
Fig. 2: Observational sample of Coma cluster galaxies.
Fig. 3: M200c mass estimates of the Coma cluster.

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Data availability

The MDPL2 ROCKSTAR catalogue is made publicly available through the CosmoSim database at The UniverseMachine catalogues of the MDPL2 simulation that support the findings of this study are available from P. Behroozi ( and A. Hearin (, but restrictions apply to the availability of these data, which were used under license for the current study and so are not publicly available. Data are, however, available from the corresponding author upon reasonable request and with permission of P. Behroozi and A. Hearin. The Uchuu DR1 ROCKSTAR halo catalogue is available via the Skies and Universes website ( The Uchuu UniverseMachine (Uchuu-UM) galaxy catalogues will be soon available via the Skies and Universes website ( The sky positions, spectroscopic redshifts and stellar masses are made available from SDSS DR12 ( All mock cluster observation catalogues, trained machine learning models and processed Coma observation catalogues generated during the current study are available from the corresponding author upon reasonable request.

Code availability

All machine learning models are built in Python using the Tensorflow framework ( Code for generating the mock cluster observations, training the machine learning models and running our inference pipeline is made available at Jupyter notebooks detailing specific training and data analysis procedures are available from the corresponding author upon reasonable request.


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We greatly appreciate the helpful insight, comments and paper notes from A. Farahi during the development of this research. This work is supported by NSF AI Institute: Physics of the Future, NSF PHY-2020295 and the McWilliams–PSC Seed Grant Program. The computing resources necessary to complete this analysis were provided by the Pittsburgh Supercomputing Center. The CosmoSim database used in this paper is a service by the Leibniz Institute for Astrophysics Potsdam (AIP). The MultiDark database was developed in cooperation with the Spanish MultiDark Consolider Project CSD2009-00064. We thank Instituto de Astrofísica de Andalucía CSIC, New Mexico State University and the Spanish research and academic network (RedIRIS) for hosting the Skies and Universes site for cosmological simulation products as well as T. Ishiyama, F. Prada, A. Klypin and M. Sinha for contributing the Uchuu DR1 dataset.

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Authors and Affiliations



M.H. coordinated the research, wrote the data analysis code and prepared the manuscript. M.H., M.N., M.M.R and H.T. designed the experiment and interpreted the results. M.N., M.M.R. and H.T. helped present the main findings and gave feedback on the manuscript. M.C., A.L. and F.R. gathered, parsed and analysed observational measurements of the Coma system.

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Correspondence to Matthew Ho.

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Nature Astronomy thanks Shubhendu Trivedi and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Ho, M., Ntampaka, M., Rau, M.M. et al. The dynamical mass of the Coma cluster from deep learning. Nat Astron 6, 936–941 (2022).

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