A Deep Learning Approach to Galaxy Cluster X-Ray Masses

We present a machine-learning approach for estimating galaxy cluster masses from Chandra mock images. We utilize a Convolutional Neural Network (CNN), a deep machine learning tool commonly used in image recognition tasks. The CNN is trained and tested on our sample of 7,896 Chandra X-ray mock observations, which are based on 329 massive clusters from the IllustrisTNG simulation. Our CNN learns from a low resolution spatial distribution of photon counts and does not use spectral information. Despite our simplifying assumption to neglect spectral information, the resulting mass values estimated by the CNN exhibit small bias in comparison to the true masses of the simulated clusters (-0.02 dex) and reproduce the cluster masses with low intrinsic scatter, 8% in our best fold and 12% averaging over all. In contrast, a more standard core-excised luminosity method achieves 15-18% scatter. We interpret the results with an approach inspired by Google DeepDream and find that the CNN ignores the central regions of clusters, which are known to have high scatter with mass.

[1]  Annalisa Pillepich,et al.  The X-ray cluster survey with eRosita: forecasts for cosmology, cluster physics and primordial non-Gaussianity , 2011, 1111.6587.

[2]  David A. Forsyth,et al.  Shape, Contour and Grouping in Computer Vision , 1999, Lecture Notes in Computer Science.

[3]  R. Teyssier,et al.  nIFTy galaxy cluster simulations – II. Radiative models , 2015, Monthly Notices of the Royal Astronomical Society.

[4]  Joop Schaye,et al.  The scatter and evolution of the global hot gas properties of simulated galaxy cluster populations , 2016, 1606.04545.

[5]  M. Bersanelli,et al.  Measuring the dynamical state of Planck SZ-selected clusters: X-ray peak – BCG offset , 2015, 1512.00410.

[6]  H. D. S'anchez,et al.  Improving galaxy morphologies for SDSS with Deep Learning , 2017, 1711.05744.

[7]  Annalisa Pillepich,et al.  First results from the IllustrisTNG simulations: the stellar mass content of groups and clusters of galaxies , 2017, 1707.03406.

[8]  Jürgen Schmidhuber,et al.  Deep learning in neural networks: An overview , 2014, Neural Networks.

[9]  Germany,et al.  The structural and scaling properties of nearby galaxy clusters. II. The M-T relation , 2005, astro-ph/0502210.

[10]  A. Merloni,et al.  Forecasts on dark energy from the X-ray cluster survey with eROSITA: constraints from counts and clustering , 2018, Monthly Notices of the Royal Astronomical Society.

[11]  V. Springel,et al.  Introducing the Illustris Project: simulating the coevolution of dark and visible matter in the Universe , 2014, 1405.2921.

[12]  S. Allen,et al.  Centre-excised X-ray luminosity as an efficient mass proxy for future galaxy cluster surveys , 2017, 1705.09329.

[13]  Danica J. Sutherland,et al.  A MACHINE LEARNING APPROACH FOR DYNAMICAL MASS MEASUREMENTS OF GALAXY CLUSTERS , 2014, 1410.0686.

[14]  Gregory F. Snyder,et al.  The illustris simulation: Public data release , 2015, Astron. Comput..

[15]  Emmanuel Bertin,et al.  Photometric redshifts from SDSS images using a convolutional neural network , 2018, Astronomy & Astrophysics.

[16]  A model for cosmological simulations of galaxy formation physics: multi-epoch validation , 2013, 1305.4931.

[17]  L. Waerbeke,et al.  The BAHAMAS project : the CMB-large-scale structure tension and the roles of massive neutrinos and galaxy formation , 2017, 1712.02411.

[18]  Yuan Yu,et al.  TensorFlow: A system for large-scale machine learning , 2016, OSDI.

[19]  M. Markevitch,et al.  Chandra Temperature Profiles for a Sample of Nearby Relaxed Galaxy Clusters , 2004, astro-ph/0412306.

[20]  B. Póczos,et al.  CMU DeepLens: deep learning for automatic image-based galaxy–galaxy strong lens finding , 2017, Monthly Notices of the Royal Astronomical Society.

[21]  V. Springel,et al.  Properties of galaxies reproduced by a hydrodynamic simulation , 2014, Nature.

[22]  Klaus Dolag,et al.  Observing simulated galaxy clusters with phox: a novel X‐ray photon simulator , 2011, 1112.0314.

[23]  Andrew Zisserman,et al.  Very Deep Convolutional Networks for Large-Scale Image Recognition , 2014, ICLR.

[24]  V. Springel,et al.  First results from the IllustrisTNG simulations: radio haloes and magnetic fields , 2017, Monthly Notices of the Royal Astronomical Society.

[25]  G. Kauffmann,et al.  First results from the IllustrisTNG simulations: the galaxy colour bimodality , 2017, 1707.03395.

[26]  T. Poggio,et al.  Hierarchical models of object recognition in cortex , 1999, Nature Neuroscience.

[27]  G. Lewis,et al.  Galaxy formation efficiency and the multiverse explanation of the cosmological constant with EAGLE simulations , 2018, 1801.08781.

[28]  Cca,et al.  First results from the IllustrisTNG simulations: matter and galaxy clustering , 2017, 1707.03397.

[29]  Danica J. Sutherland,et al.  DYNAMICAL MASS MEASUREMENTS OF CONTAMINATED GALAXY CLUSTERS USING MACHINE LEARNING , 2015, 1509.05409.

[30]  Vikhlinin Kravtsov The Astrophysical Journal, submitted Preprint typeset using L ATEX style emulateapj v. 11/27/05 A NEW ROBUST LOW-SCATTER X-RAY MASS INDICATOR FOR CLUSTERS OF GALAXIES , 2006 .

[31]  C. A. Oxborrow,et al.  Planck2015 results , 2015, Astronomy & Astrophysics.

[32]  P. Ricker,et al.  The Effect of Merger Boosts on the Luminosity, Temperature, and Inferred Mass Functions of Clusters of Galaxies , 2002, astro-ph/0206161.

[33]  Kunihiko Fukushima,et al.  Neocognitron: A Self-Organizing Neural Network Model for a Mechanism of Visual Pattern Recognition , 1982 .

[34]  Paul La Plante,et al.  Identifying Reionization Sources from 21cm Maps using Convolutional Neural Networks , 2018, Monthly Notices of the Royal Astronomical Society.

[35]  Michelle Ntampaka,et al.  Machine Learning Applied to the Reionization History of the Universe in the 21 cm Signal , 2018, The Astrophysical Journal.

[36]  M. Donahue,et al.  Substructure and Scatter in the Mass-Temperature Relations of Simulated Clusters , 2008, 0806.0850.

[37]  G. Efstathiou,et al.  The evolution of large-scale structure in a universe dominated by cold dark matter , 1985 .

[38]  Yoshua Bengio,et al.  Object Recognition with Gradient-Based Learning , 1999, Shape, Contour and Grouping in Computer Vision.

[39]  Cca,et al.  The uniformity and time-invariance of the intra-cluster metal distribution in galaxy clusters from the IllustrisTNG simulations , 2017, 1707.05318.

[40]  P. Rosati,et al.  Searching for cool core clusters at high redshift , 2008, 0802.1445.

[41]  B. Maughan The LX-YX Relation: Using Galaxy Cluster X-Ray Luminosity as a Robust, Low-Scatter Mass Proxy , 2007, astro-ph/0703504.

[42]  R. C. Wolf,et al.  AUTOMATED TRANSIENT IDENTIFICATION IN THE DARK ENERGY SURVEY , 2015, 1504.02936.

[43]  Qiang Chen,et al.  Network In Network , 2013, ICLR.

[44]  Tony Mroczkowski,et al.  The Physics of Galaxy Cluster Outskirts , 2018, Space Science Reviews.

[45]  Massimo Meneghetti,et al.  X-ray morphological estimators for galaxy clusters , 2012 .

[46]  Daisuke Nagai,et al.  RESIDUAL GAS MOTIONS IN THE INTRACLUSTER MEDIUM AND BIAS IN HYDROSTATIC MEASUREMENTS OF MASS PROFILES OF CLUSTERS , 2009, 0903.4895.

[47]  V. Springel,et al.  A model for cosmological simulations of galaxy formation physics: multi-epoch validation , 2013, 1305.4931.

[48]  R. K. Smith,et al.  UPDATED ATOMIC DATA AND CALCULATIONS FOR X-RAY SPECTROSCOPY , 2012, 1207.0576.

[49]  Sander Dieleman,et al.  Rotation-invariant convolutional neural networks for galaxy morphology prediction , 2015, ArXiv.

[50]  Oliver Hahn,et al.  An adaptively refined phase–space element method for cosmological simulations and collisionless dynamics , 2015, 1501.01959.

[51]  S. Borgani,et al.  TEMPERATURE STRUCTURE OF THE INTRA-CLUSTER MEDIUM FROM SPH AND AMR SIMULATIONS , 2014, 1406.4410.

[52]  D. Nagai,et al.  GAS CLUMPING IN THE OUTSKIRTS OF ΛCDM CLUSTERS , 2011, 1103.0280.

[53]  C. Lintott,et al.  Galaxy Zoo: reproducing galaxy morphologies via machine learning★ , 2009, 0908.2033.

[54]  Amber D. Miller,et al.  LoCuSS: THE SUNYAEV–ZEL'DOVICH EFFECT AND WEAK-LENSING MASS SCALING RELATION , 2011, 1107.5115.

[55]  V. Springel,et al.  Introducing the Illustris Project: the evolution of galaxy populations across cosmic time , 2014, 1405.3749.

[56]  S. Paltani,et al.  The cool-core bias in X-ray galaxy cluster samples - I. Method and application to HIFLUGCS , 2010, 1011.3302.

[57]  E. Ramirez-Ruiz,et al.  First results from the IllustrisTNG simulations: a tale of two elements - chemical evolution of magnesium and europium , 2017, 1707.03401.

[58]  Annalisa Pillepich,et al.  Simulating galaxy formation with the IllustrisTNG model , 2017, 1703.02970.

[59]  D. Nagai,et al.  Testing X-Ray Measurements of Galaxy Clusters with Cosmological Simulations , 2006, astro-ph/0609247.

[60]  G. Hasinger,et al.  eROSITA science book: mapping the structure of the energetic universe , 2012, 1209.3114.

[61]  V. Springel,et al.  Simulating galaxy formation with black hole driven thermal and kinetic feedback , 2016, 1607.03486.

[62]  Dan McCammon,et al.  Interstellar photoelectric absorption cross-sections, 0.03-10 keV , 1983 .

[63]  Klaus Dolag,et al.  Investigating the velocity structure and X-ray observable properties of simulated galaxy clusters with PHOX , 2012, 1210.4158.

[64]  Jimmy Ba,et al.  Adam: A Method for Stochastic Optimization , 2014, ICLR.

[65]  S. Kay,et al.  An application of machine learning techniques to galaxy cluster mass estimation using the MACSIS simulations , 2018, Monthly Notices of the Royal Astronomical Society.

[66]  G. W. Pratt,et al.  XXIV. Cosmology from Sunyaev-Zeldovich cluster counts , 2015, 1502.01597.

[67]  Pablo A. Estévez,et al.  Deep-HiTS: Rotation Invariant Convolutional Neural Network for Transient Detection , 2017, ArXiv.