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2022-07-02 06:59:54 By : Ms. Joanna Wang

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Nature Astronomy (2022 )Cite this article

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±0.15 h−1 M⊙ 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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The MDPL2 ROCKSTAR catalogue is made publicly available through the CosmoSim database at https://www.cosmosim.org/. The UniverseMachine catalogues of the MDPL2 simulation that support the findings of this study are available from P. Behroozi (pbehroozi@gmail.com) and A. Hearin (ahearin@anl.gov), 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 (http://skiesanduniverses.iaa.es/). The Uchuu UniverseMachine (Uchuu-UM) galaxy catalogues will be soon available via the Skies and Universes website (http://skiesanduniverses.iaa.es/). The sky positions, spectroscopic redshifts and stellar masses are made available from SDSS DR12 (https://www.sdss.org/dr12/spectro/galaxy_portsmouth/). 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.

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

Zwicky, F. Die rotverschiebung von extragalaktischen nebeln. Helv. Phys. Acta 6, 110–127 (1933).

Biviano, A. Our best friend, the Coma cluster (a historical review). In Untangling Coma Berenices: A New Vision of an Old Cluster, 1 (eds Mazure, A. et al.) (1998).

Kubo, J. M. et al. The mass of the Coma cluster from weak lensing in the Sloan Digital Sky Survey. Astrophys. J. 671, 1466–1470 (2007).

Gavazzi, R. et al. A weak lensing study of the Coma cluster. Astron. Astrophys. 498, L33–L36 (2009).

Hughes, J. P. The mass of the Coma cluster: combined X-ray and optical results. Astrophys. J. 337, 21–33 (1989).

The, L. S. & White, S. D. M. The mass of the Coma cluster. Astron. J. 92, 1248–1253 (1986).

Geller, M. J., Diaferio, A. & Kurtz, M. J. The mass profile of the Coma galaxy cluster. Astrophys. J. Lett. 517, L23–L26 (1999).

Falco, M. et al. A new method to measure the mass of galaxy clusters. Mon. Not. R. Astron. Soc. 442, 1887–1896 (2014).

Allen, S. W., Evrard, A. E. & Mantz, A. B. Cosmological parameters from observations of galaxy clusters. Annu. Rev. Astron. Astrophys. 49, 409–470 (2011).

Dodelson, S. et al. Cosmic visions dark energy: science. Preprint at https://doi.org/10.48550/arXiv.1604.07626 (2016).

Binney, J. & Tremaine, S. Galactic Dynamics Vol. 13 (Princeton Univ. Press, 2011).

Old, L. et al. Galaxy Cluster Mass Reconstruction Project. III. The impact of dynamical substructure on cluster mass estimates. Mon. Not. R. Astron. Soc. 475, 853–866 (2018).

Wojtak, R. et al. Galaxy Cluster Mass Reconstruction Project. IV. Understanding the effects of imperfect membership on cluster mass estimation. Mon. Not. R. Astron. Soc. 481, 324–340 (2018).

Ho, M. et al. A robust and efficient deep learning method for dynamical mass measurements of galaxy clusters. Astrophys. J. 887, 25 (2019).

Ho, M., Farahi, A., Rau, M. M. & Trac, H. Approximate Bayesian uncertainties on deep learning dynamical mass estimates of galaxy clusters. Astrophys. J. 908, 204 (2021).

Kodi Ramanah, D., Wojtak, R., Ansari, Z., Gall, C. & Hjorth, J. Dynamical mass inference of galaxy clusters with neural flows. Mon. Not. R. Astron. Soc. 499, 1985–1997 (2020).

Scott, D. W. Multivariate Density Estimation: Theory, Practice, and Visualization (Wiley, 2015).

Gal, Y. & Ghahramani, Z. Bayesian convolutional neural networks with Bernoulli approximate variational inference. Preprint at https://doi.org/10.48550/arXiv.1506.02158 (2015).

LeCun, Y., Bottou, L., Bengio, Y. & Haffner, P. Gradient-based learning applied to document recognition. Proc. IEEE 86, 2278–2324 (1998).

LeCun, Y., Bengio, Y. & Hinton, G. Deep learning. Nature 521, 436–444 (2015).

Gal, Y. & Ghahramani, Z. Dropout as a Bayesian approximation: representing model uncertainty in deep learning. In Proc. 33rd International Conference on Machine Learning (eds Balcan, M. F. & Weinberger, K. Q.) 1050-1059 (PMLR, 2016); https://proceedings.mlr.press/v48/gal16.html

Srivastava, N., Hinton, G., Krizhevsky, A., Sutskever, I. & Salakhutdinov, R. Dropout: a simple way to prevent neural networks from overfitting. J. Mach. Learn. Res. 15, 1929–1958 (2014).

Kodi Ramanah, D., Wojtak, R. & Arendse, N. Simulation-based inference of dynamical galaxy cluster masses with 3D convolutional neural networks. Mon. Not. R. Astron. Soc. 501, 4080–4091 (2021).

Ishiyama, T. et al. The Uchuu simulations: Data Release 1 and dark matter halo concentrations. Mon. Not. R. Astron. Soc. 506, 4210–4231 (2021).

Klypin, A., Yepes, G., Gottlöber, S., Prada, F. & Heß, S. MultiDark simulations: the story of dark matter halo concentrations and density profiles. Mon. Not. R. Astron. Soc. 457, 4340–4359 (2016).

Behroozi, P., Wechsler, R. H., Hearin, A. P. & Conroy, C. UNIVERSEMACHINE: the correlation between galaxy growth and dark matter halo assembly from z = 0–10. Mon. Not. R. Astron. Soc. 488, 3143–3194 (2019).

van Dokkum, P. G. & van der Marel, R. P. The star formation epoch of the most massive early-type galaxies. Astrophys. J. 655, 30–50 (2007).

Alam, S. et al. The eleventh and twelfth data releases of the Sloan Digital Sky Survey: final data from SDSS-III. Astrophys. J. Suppl. Ser. 219, 12 (2015).

Abell, G. O., Corwin, J., Harold, G. & Olowin, R. P. A catalog of rich clusters of galaxies. Astrophys. J. Suppl. Ser. 70, 1–138 (1989).

Maraston, C. Evolutionary population synthesis: models, analysis of the ingredients and application to high-z galaxies. Mon. Not. R. Astron. Soc. 362, 799–825 (2005).

Łokas, E. L. & Mamon, G. A. Dark matter distribution in the Coma cluster from galaxy kinematics: breaking the mass-anisotropy degeneracy. Mon. Not. R. Astron. Soc. 343, 401–412 (2003).

Planck Collaboration et al. Planck 2013 results. XVI. Cosmological parameters. Astron. Astrophys. 571, A16 (2014).

Villaescusa-Navarro, F. et al. Robust marginalization of baryonic effects for cosmological inference at the field level. Preprint at https://doi.org/10.48550/arXiv.2109.10360 (2021).

Bishop, M. A. Mixture Density Networks Technical Report NCRG/94/004 (Aston Univ., 1994); https://publications.aston.ac.uk/id/eprint/373/1/NCRG_94_004.pdf

Planck Collaboration et al. Planck 2015 results. XXIV. Cosmology from Sunyaev–Zeldovich cluster counts. Astron. Astrophys. 594, A24 (2016).

Behroozi, P. S., Wechsler, R. H. & Wu, H.-Y. The ROCKSTAR phase-space temporal halo finder and the velocity offsets of cluster cores. Astrophys. J. 762, 109 (2013).

Navarro, J. F., Frenk, C. S. & White, S. D. M. A universal density profile from hierarchical clustering. Astrophys. J. 490, 493–508 (1997).

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.

McWilliams Center for Cosmology, Department of Physics, Carnegie Mellon University, Pittsburgh, PA, USA

Matthew Ho, Markus Michael Rau, Alexa Lansberry, Faith Ruehle & Hy Trac

NSF AI Planning Institute for Physics of the Future, Carnegie Mellon University, Pittsburgh, PA, USA

Matthew Ho, Markus Michael Rau & Hy Trac

Space Telescope Science Institute, Baltimore, MD, USA

Department of Physics & Astronomy, Johns Hopkins University, Baltimore, MD, USA

Department of Physics, University of California, Santa Barbara, Santa Barbara, CA, USA

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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.

The authors declare no competing interests.

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

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Ho, M., Ntampaka, M., Rau, M.M. et al. The dynamical mass of the Coma cluster from deep learning. Nat Astron (2022). https://doi.org/10.1038/s41550-022-01711-1

DOI: https://doi.org/10.1038/s41550-022-01711-1

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