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Sum of the masses of the Milky Way and M31: A likelihood-free inference approach

Pablo Lemos1,*, Niall Jeffrey2,1, Lorne Whiteway1, Ofer Lahav1, Noam Libeskind, I3,4, and Yehuda Hoffman5

  • 1Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
  • 2Laboratoire de Physique de l’Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, Paris, France
  • 3Leibniz-Institut fr Astrophysik Potsdam (AIP), An der Sternwarte 16, 14482 Potsdam, Germany
  • 4University of Lyon, UCB Lyon-1/CNRS/IN2P3, IPN Lyon, France
  • 5Racah Institute of Physics, Hebrew University, Jerusalem, 91904 Israel

  • *pablo.lemos.18@ucl.ac.uk
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Phys. Rev. D 103, 023009 – Published 11 January, 2021

DOI: https://doi.org/10.1103/PhysRevD.103.023009

Abstract

We use density estimation likelihood-free inference, Λ cold dark matter simulations of ∼2M galaxy pairs, and data from Gaia and the Hubble Space Telescope to infer the sum of the masses of the Milky Way and Andromeda (M31) galaxies, the two main components of the local group. This method overcomes most of the approximations of the traditional timing argument, makes the writing of a theoretical likelihood unnecessary, and allows the nonlinear modeling of observational errors that take into account correlations in the data and non-Gaussian distributions. We obtain an M200 mass estimate MMW+M31=4.6−1.8+2.3×1012  M⊙ (68% C.L.), in agreement with previous estimates both for the sum of the two masses and for the individual masses. This result is not only one of the most reliable estimates of the sum of the two masses to date, but is also an illustration of likelihood-free inference in a problem with only one parameter and only three data points.

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References (83)

  1. F. Leclercq, Bayesian optimization for likelihood-free cosmological inference, Phys. Rev. D 98, 063511 (2018).
  2. J. Alsing, T. Charnock, S. Feeney, and B. Wandelt, Fast likelihood-free cosmology with neural density estimators and active learning, Mon. Not. R. Astron. Soc. 488, 5093 (2019).
  3. M. Betoule, R. Kessler, J. Guy, J. Mosher, D. Hardin et al. Improved cosmological constraints from a joint analysis of the SDSS-II and SNLS supernova samples, Astron. Astrophys. 568, A22 (2014).
  4. Y.-C. Wang, Y.-B. Xie, T.-J. Zhang, H.-C. Huang, T. Zhang, and K. Liu, Likelihood-free cosmological constraints with artificial neural networks: An application on hubble parameters and SN Ia, arXiv:2005.10628.
  5. N. Jeffrey, J. Alsing, and F. Lanusse, Likelihood-free inference with neural compression of DES SV weak lensing map statistics, arXiv:2009.08459 [MNRAS (to be published)], 10.1093/mnras/staa3594.
  6. J. Brehmer, S. Mishra-Sharma, J. Hermans, G. Louppe, and K. Cranmer, Mining for dark matter substructure: Inferring subhalo population properties from strong lenses with machine learning, Astrophys. J. 886, 49 (2019).
  7. D. K. Ramanah, R. Wojtak, and N. Arendse, Simulation-based inference of dynamical galaxy cluster masses with 3D convolutional neural networks, arXiv:2009.03340 [MNRAS (to be published)], 10.1093/mnras/staa3922.
  8. L. Tortorelli, M. Fagioli, J. Herbel, A. Amara, T. Kacprzak, and A. Refregier, Measurement of the B-band galaxy luminosity function with approximate Bayesian computation, J. Cosmol. Astropart. Phys. 09 (2020) 048.
  9. F. D. Kahn and L. Woltjer, Intergalactic matter and the Galaxy, Astrophys. J. 130, 705 (1959).
  10. www.cosmosim.org
  11. F. Prada, A. A. Klypin, A. J. Cuesta, J. E. Betancort-Rijo, and J. Primack, Halo concentrations in the standard Λ cold dark matter cosmology, Mon. Not. R. Astron. Soc. 423, 3018 (2012).
  12. K. Riebe, A. M. Partl, H. Enke, J. Forero-Romero, S. Gottlöber, A. Klypin, G. Lemson, F. Prada, J. R. Primack, M. Steinmetz, and V. Turchaninov, The MultiDark database: Release of the Bolshoi and MultiDark cosmological simulations, Astron. Nachr. 334, 691 (2013).
  13. G. Meylan, J. P. Madrid, and D. Macchetto, Hubble space telescope science metrics, Publ. Astron. Soc. Pac. 116, 790 (2004).
  14. Gaia Collaboration, The Gaia mission, Astron. Astrophys. 595, A1 (2016).
  15. M. McLeod, N. Libeskind, O. Lahav, and Y. Hoffman, Estimating the mass of the local group using machine learning applied to numerical simulations, J. Cosmol. Astropart. Phys. 12 (2017) 034.
  16. F. V. Bonassi, L. You, and M. West, Bayesian Learning from marginal data in bionetwork models, Stat. Appl. Genetics Mol. Biol. 10, 49 (2011).
  17. Y. Fan, D. J. Nott, and S. A. Sisson, Approximate Bayesian computation via regression density estimation, arXiv:1212.1479.
  18. G. Papamakarios and I. Murray, Fast ε-free inference of simulation models with Bayesian conditional density estimation, arXiv:1605.06376.
  19. https://github.com/justinalsing/pydelfi
  20. D. Lynden-Bell, The dynamical age of the local group of galaxies, Observatory 101, 111 (1981), https://ui.adsabs.harvard.edu/abs/1981Obs...101..111L/abstract.
  21. J. Binney and S. Tremaine, Galactic Dynamics (Princeton University Press, 1987).
  22. C. Partridge, O. Lahav, and Y. Hoffman, Weighing the local group in the presence of dark energy, Mon. Not. R. Astron. Soc. 436, L45 (2013).
  23. M. McLeod and O. Lahav, The two body problem in the presence of dark energy and modified gravity: Application to the local group, J. Cosmol. Astropart. Phys. 09 (2020) 056.
  24. D. Benisty, E. I. Guendelman, and O. Lahav, Milky Way and Andromeda past-encounters in different gravity models: The impact on the estimated local group mass, arXiv:1904.03153 [Phys. Rev. D (to be published)].
  25. P. J. E. Peebles, Orbits of the nearby Galaxies, Astrophys. J. 429, 43 (1994).
  26. S. Phelps, A. Nusser, and V. Desjacques, The mass of the Milky Way and M31 using the method of least action, Astrophys. J. 775, 102 (2013).
  27. Y.-S. Li and S. D. M. White, Masses for the local group and the Milky Way, Mon. Not. R. Astron. Soc. 384, 1459 (2008).
  28. R. E. Gonzalez, A. V. Kravtsov, and N. Y. Gnedin, On the mass of the local group, Astrophys. J. 793, 91 (2014).
  29. D. B. Rubin, Bayesianly justifiable and relevant frequency calculations for the applied statistician, Ann. Stat. 12, 1151 (1984).
  30. M. Rosenblatt, Remarks on some nonparametric estimates of a density function, Ann. Math. Stat. 27, 832 (1956).
  31. E. Parzen, On estimation of a probability density function and mode, Ann. Math. Stat. 33, 1065 (1962).
  32. J. S. Simonoff, Smoothing Methods in Statistics, Springer Series in Statistics (Springer, New York, 1996).
  33. C. M. Bishop, Mixture density networks, Technical Report, 1994, https://research.aston.ac.uk/en/publications/mixture-density-networks.
  34. C. M. Bishop, Pattern Recognition and Machine Learning (Information Science and Statistics) (Springer-Verlag, Berlin, Heidelberg, 2006).
  35. G. Papamakarios, Theo Pavlakou, and Iain Murray. Masked autoregressive flow for density estimation, in NIPS’17: Proceedings of the 31st International Conference on Neural Information (2017), pp. 2338–2347.
  36. E. Cameron and A. N. Pettitt, Approximate Bayesian computation for astronomical model analysis: a case study in galaxy demographics and morphological transformation at high redshift, Mon. Not. R. Astron. Soc. 425, 44 (2012).
  37. A. Weyant, C. Schafer, and W. Michael Wood-Vasey, Likelihood-free cosmological inference with Type Ia Supernovae: Approximate Bayesian computation for a complete treatment of uncertainty, Astrophys. J. 764, 116 (2013).
  38. J. Akeret, A. Refregier, A. Amara, S. Seehars, and C. Hasner, Approximate Bayesian computation for forward modeling in cosmology, J. Cosmol. Astropart. Phys. 08 (2015) 043.
  39. C. H. Hahn, M. Vakili, K. Walsh, A. P. Hearin, D. W. Hogg, and D. Campbell, Approximate Bayesian computation in large-scale structure: constraining the galaxy–halo connection, Mon. Not. R. Astron. Soc. 469, 2791 (2017).
  40. A. Peel, C.-A. Lin, F. Lanusse, A. Leonard, J.-L. Starck, and M. Kilbinger, Cosmological constraints with weak lensing peak counts and second-order statistics in a large-field survey, Astron. Astrophys. 599, A79 (2017).
  41. T. Kacprzak, J. Herbel, A. Amara, and A. Rfrgier, Accelerating approximate Bayesian computation with quantile regression: Application to cosmological redshift distributions, J. Cosmol. Astropart. Phys. 02 (2018) 042.
  42. J. Alsing, B. Wandelt, and S. Feeney, Massive optimal data compression and density estimation for scalable, likelihood-free inference in cosmology, Mon. Not. R. Astron. Soc. 477, 2874 (2018).
  43. J. Alsing and B. Wandelt, Generalized massive optimal data compression, Mon. Not. R. Astron. Soc. 476, L60 (2018).
  44. A. F. Heavens, E. Sellentin, and A. H Jaffe, Extreme data compression while searching for new physics, Mon. Not. R. Astron. Soc. 498, 3440 (2020).
  45. G. Papamakarios, D. Sterratt, and I. Murray, Sequential neural likelihood: Fast likelihood-free inference with autoregressive flows, in The 22nd International Conference on Artificial Intelligence and Statistics (PMLR, 2019), pp. 837–848, http://proceedings.mlr.press/v89/papamakarios19a.html.
  46. J.-M. Lueckmann, G. Bassetto, T. Karaletsos, and J. H Macke, Likelihood-free inference with emulator networks, in Proceedings of The 1st Symposium on Advances in Approximate Bayesian Inference (PMLR, 2019), pp 32–53, http://proceedings.mlr.press/v96/lueckmann19a.html.
  47. A. Knebe, S. R. Knollmann, S. I. Muldrew, F. R. Pearce, and M. A. Aragon-Calvo et al. Haloes gone MAD: The halo-finder comparison project, Mon. Not. R. Astron. Soc. 415, 2293 (2011).
  48. S. Holland, The distance to the M31 globular cluster system, Astron. J. 115, 1916 (1998).
  49. Y. C. Joshi, A. K. Pandey, D. Narasimha, R. Sagar, and Y. Giraud-Hiraud, Identification of 13 cepheids and 333 other variables in M 31, Astron. Astrophys. 402, 113 (2003).
  50. I. Ribas, C. Jordi, F. Vilardell, E. L. Fitzpatrick, R. W. Hilditch, and E. F. Guinan, First determination of the distance and fundamental properties of an eclipsing binary in the andromeda galaxy, Astrophys. J. Lett. 635, L37 (2005).
  51. A. McConnachie and M. Irwin, Structural parameters for the m31 dwarf spheroidals, Mon. Not. R. Astron. Soc. 365, 1263 (2006).
  52. R. P. van der Marel, M. A. Fardal, S. T. Sohn, E. Patel, G. Besla, A. del Pino, J. Sahlmann, and L. L. Watkins, First Gaia dynamics of the Andromeda system: DR2 proper motions, orbits, and rotation of M31 and M33, Astrophys. J. 872, 24 (2019).
  53. R. P. van der Marel, G. Besla, T. J. Cox, S. T. Sohn, and J. Anderson, The M31 velocity vector. III. Future Milky Way M31-M33 orbital evolution, merging, and fate of the sun, Astrophys. J. 753, 9 (2012).
  54. R. P. van der Marel and P. Guhathakurta, M31 transverse velocity and local group mass from satellite kinematics, Astrophys. J. 678, 187 (2008).
  55. J. Skilling et al., Nested sampling for general Bayesian computation, Bayesian Anal. 1, 833 (2006), https://projecteuclid.org/euclid.ba/1340370944.
  56. W. J. Handley, M. P. Hobson, and A. N. Lasenby, POLYCHORD: Nested sampling for cosmology, Mon. Not. R. Astron. Soc. 450, L61 (2015).
  57. W. J. Handley, M. P. Hobson, and A. N. Lasenby, POLYCHORD: Next-generation nested sampling, Mon. Not. R. Astron. Soc. 453, 4385 (2015).
  58. W. Handley, anesthetic: Nested sampling visualisation, J. Open Source Softw. 4, 1414 (2019).
  59. T. O’Brien, K. Kashinath, N. Cavanaugh, W. Collins, and J. O’Brien, A fast and objective multidimensional kernel density estimation method: Fastkde, Computational Statistics and Data Analysis 101, 148 (2016).
  60. T. O’Brien, W. Collins, S. Rauscher, and T. Ringler, Reducing the computational cost of the ecf using a nufft: A fast and objective probability density estimation method, Computational Statistics and Data Analysis 79, 222 (2014).
  61. W. H. Press and P. Schechter, Formation of Galaxies and clusters of Galaxies by self-similar gravitational condensation, Astrophys. J. 187, 425 (1974).
  62. B. Diemer, COLOSSUS: A python toolkit for cosmology, large-scale structure, and dark matter halos, Astrophys. J. Suppl. Ser. 239, 35 (2018).
  63. https://bdiemer.bitbucket.io/colossus/index.html
  64. J. L. Tinker, A. V. Kravtsov, A. Klypin, K. Abazajian, M. S. Warren, G. Yepes, S. Gottlober, and D. E. Holz, Toward a halo mass function for precision cosmology: The limits of universality, Astrophys. J. 688, 709 (2008).
  65. Planck Collaboration, Planck 2018 results—VI. Cosmological parameters, Astron. Astrophys. 641, A6 (2020).
  66. N. I. Libeskind et al., The HESTIA project: Simulations of the local group, Mon. Not. R. Astron. Soc. 498, 2968 (2020).
  67. J. D. Diaz, S. E. Koposov, M. Irwin, V. Belokurov, and N. W. Evans, Balancing mass and momentum in the local group, Mon. Not. R. Astron. Soc. 443, 1688 (2014).
  68. D. Zaritsky and H. Courtois, A dynamics-free lower bound on the mass of our Galaxy, Mon. Not. R. Astron. Soc. 465, 3724 (2017).
  69. K. Hattori, M. Valluri, E. F. Bell, and I. U. Roederer, Old, metal-poor extreme velocity stars in the solar neighborhood, Astrophys. J. 866, 121 (2018).
  70. L. Posti and A. Helmi, Mass and shape of the Milky Way’s dark matter halo with globular clusters from Gaia and hubble, Astron. Astrophys. 621, A56 (2019).
  71. L. L. Watkins, R. P. van der Marel, S. T. Sohn, and N. W. Evans, Evidence for an intermediate-mass Milky Way from Gaia DR2 halo globular cluster motions, Astrophys. J. 873, 118 (2019).
  72. E. V. Karukes, M. Benito, F. Iocco, R. Trotta, and A. Geringer-Sameth, A robust estimate of the Milky Way mass from rotation curve data, J. Cosmol. Astropart. Phys. 05 (2020) 033.
  73. E. Corbelli, S. Lorenzoni, R. Walterbos, R. Braun, and D. Thilker, A wide-field H I mosaic of messier 31. II. The disk warp, rotation, and the dark matter halo, Astron. Astrophys. 511, A89 (2010).
  74. A. Tamm, E. Tempel, P. Tenjes, O. Tihhonova, and T. Tuvikene, Stellar mass map and dark matter distribution in M 31, Astron. Astrophys. 546, A4 (2012).
  75. P. R. Kafle, S. Sharma, G. F. Lewis, A. S. G. Robotham, and S. P. Driver, The need for speed: escape velocity and dynamical mass measurements of the Andromeda galaxy, Mon. Not. R. Astron. Soc. 475, 4043 (2018).
  76. J. Peñarrubia, F. A. Gómez, G. Besla, D. Erkal, and Y.-Z. Ma, A timing constraint on the (total) mass of the large magellanic cloud, Mon. Not. R. Astron. Soc. 456, L54 (2016).
  77. L. Theis and M. Bethge, Generative image modeling using spatial lstms, in NIPS’15: Proceedings of the 28th International Conference on Neural Information Processing Systems (2015), pp. 1927–1935.
  78. T. Salimans, A. Karpathy, X. Chen, and D. P. Kingma, PixelCNN++: Improving the PixelCNN with discretized logistic mixture likelihood and other modifications, arXiv:1701.05517.
  79. A. Lewis, getdist: A python package for analysing Monte Carlo samples, 2019, https://getdist.readthedocs.io.
  80. S. R. Hinton, ChainConsumer, J. Open Source Softw. 1, 00045 (2016).
  81. A. P. Dempster, N. M. Laird, and D. B. Rubin, Maximum likelihood from incomplete data via the em algorithm, J. R. Stat. Soc. Ser. B 39, 1 (1977).
  82. M. Germain, K. Gregor, I. Murray, and H. Larochelle, Made: Masked autoencoder for distribution estimation, in International Conference on Machine Learning (PMLR, 2015), pp. 881–889, http://proceedings.mlr.press/v37/germain15.html.
  83. L. Rayleigh, The problem of the random walk, Nature (London) 72, 318 (1905).

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Phys. Rev. D 103, 023009– Published 11 January, 2021
  • Received 29 October 2020
  • Accepted 18 December 2020
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