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Stellar dynamics and dark matter in Local Group dwarf galaxies

Abstract

When interpreted within the standard framework of Newtonian gravity and dynamics, the kinematics of stars and gas in dwarf galaxies reveals that most of these systems are completely dominated by their dark matter halos. These dwarf galaxies are thus among the best astrophysical laboratories to study the structure of dark halos and the nature of dark matter. We review the properties of the dwarf galaxies of the Local Group from the point of view of stellar dynamics. After describing the observed kinematics of their stellar components and providing an overview of the dynamical modelling techniques, we look into the dark matter content and distribution of these galaxies, as inferred from the combination of observed data and dynamical models. We also briefly touch upon the prospects of using nearby dwarf galaxies as targets for indirect detection of dark matter via annihilation or decay emission.

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Fig. 1: Global properties of the stellar component of Local Group DGs.
Fig. 2: Dynamical mass of LG DGs.
Fig. 3: Mass and density profiles of the Draco dSph.
Fig. 4: Mass and density profiles of the Fornax dSph.
Fig. 5: Mass and density profiles of the Sculptor dSph.

References

  1. Cimatti, A., Fraternali, F. & Nipoti, C. Introduction to Galaxy Formation and Evolution: From Primordial Gas to Present-Day Galaxies (Cambridge Univ. Press, 2019).

    Google Scholar 

  2. Bertone, G. & Tait, T. M. P. A new era in the search for dark matter. Nature 562, 51–56 (2018).

    ADS  Article  Google Scholar 

  3. Bullock, J. S. & Boylan-Kolchin, M. Small-scale challenges to the Λ CDM paradigm. Annu. Rev. Astron. Astrophys. 55, 343–387 (2017).

    ADS  Article  Google Scholar 

  4. Dekel, A. & Silk, J. The origin of dwarf galaxies, cold dark matter, and biased galaxy formation. Astrophys. J. 303, 39–55 (1986).

    ADS  Article  Google Scholar 

  5. Arora, N. et al. NIHAO-LG: The uniqueness of Local Group dwarf galaxies. Preprint at https://arxiv.org/abs/2109.07487 (2021).

  6. Read, J. I., Iorio, G., Agertz, O. & Fraternali, F. The stellar mass-halo mass relation of isolated field dwarfs: a critical test of Λ CDM at the edge of galaxy formation. Mon. Not. R. Astron. Soc. 467, 2019–2038 (2017).

    ADS  Google Scholar 

  7. Leung, G. Y. C. et al. Joint gas and stellar dynamical models of WLM: an isolated dwarf galaxy within a cored, prolate DM halo. Mon. Not. R. Astron. Soc. 500, 410–429 (2021).

    ADS  Article  Google Scholar 

  8. Lelli, F. Gas dynamics in dwarf galaxies as testbeds for dark matter and galaxy evolution. Nat. Astron. 6, 35–47 (2022). .

  9. Simon, J. D. The faintest dwarf galaxies. Annu. Rev. Astron. Astrophys. 57, 375–415 (2019).

    ADS  Article  Google Scholar 

  10. van den Bergh, S. The Local Group of galaxies. Astron. Astrophys. Rev. 9, 273–318 (1999).

    ADS  Article  Google Scholar 

  11. Putman, M. E. et al. The gas content and stripping of Local Group dwarf galaxies. Astrophys. J. 913, 53 (2021).

    ADS  Article  Google Scholar 

  12. Milgrom, M. A modification of the Newtonian dynamics as a possible alternative to the hidden mass hypothesis. Astrophys. J. 270, 365–370 (1983).

    ADS  Article  Google Scholar 

  13. Angus, G. W. Dwarf spheroidals in MOND. Mon. Not. R. Astron. Soc. 387, 1481–1488 (2008).

    ADS  Article  Google Scholar 

  14. Hernandez, X., Mendoza, S., Suarez, T. & Bernal, T. Understanding local dwarf spheroidals and their scaling relations under modified Newtonian dynamics. Astron. Astrophys. 514, A101 (2010).

    ADS  MATH  Article  Google Scholar 

  15. Serra, A. L., Angus, G. W. & Diaferio, A. Implications for dwarf spheroidal mass content from interloper removal. Astron. Astrophys. 524, A16 (2010).

    ADS  MATH  Article  Google Scholar 

  16. Safarzadeh, M. & Loeb, A. The challenge to MOND from ultra-faint dwarf galaxies. Astrophys. J. Lett. 914, L37 (2021).

    ADS  Article  Google Scholar 

  17. McGaugh, S. S. MOND prediction for the velocity dispersion of the “Feeble Giant” Crater II. Astrophys. J. Lett. 832, L37 (2016).

    Article  Google Scholar 

  18. Caldwell, N. et al. Crater 2: an extremely cold dark matter halo. Astrophys. J. 839, 20 (2017).

    ADS  Article  Google Scholar 

  19. Mateo, M. L. Dwarf galaxies of the Local Group. Annu. Rev. Astron. Astrophys. 36, 435–506 (1998).

    ADS  Article  Google Scholar 

  20. Tolstoy, E., Hill, V. & Tosi, M. Star-formation histories, abundances, and kinematics of dwarf galaxies in the Local Group. Annu. Rev. Astron. Astrophys. 47, 371–425 (2009).

    ADS  Article  Google Scholar 

  21. Battaglia, G., Helmi, A. & Breddels, M. Internal kinematics and dynamical models of dwarf spheroidal galaxies around the Milky Way. N. Astron. Rev. 57, 52–79 (2013).

    ADS  Article  Google Scholar 

  22. Walker, M. in Planets, Stars and Stellar Systems Vol. 5 (eds Oswalt, T. D. & Gilmore, G.) 1039–1089 (Springer, 2013).

  23. Strigari, L. E. Dark matter in dwarf spheroidal galaxies and indirect detection: a review. Rep. Prog. Phys. 81, 056901 (2018).

    ADS  Article  Google Scholar 

  24. Muraveva, T., Clementini, G., Garofalo, A. & Cusano, F. A fresh look at the RR Lyrae population in the Draco dwarf spheroidal galaxy with Gaia. Mon. Not. R. Astron. Soc. 499, 4040–4053 (2020).

    ADS  Article  Google Scholar 

  25. Fritz, T. K. et al. Gaia DR2 proper motions of dwarf galaxies within 420 kpc. Orbits, Milky Way mass, tidal influences, planar alignments, and group infall. Astron. Astrophys. 619, A103 (2018).

    Article  Google Scholar 

  26. McConnachie, A. W. & Venn, K. A. Revised and new proper motions for confirmed and candidate Milky Way dwarf galaxies. Astron. J. 160, 124 (2020).

    ADS  Article  Google Scholar 

  27. Battaglia, G., Taibi, S., Thomas, G. F. & Fritz, T. K. Gaia early DR3 systemic motions of Local Group dwarf galaxies and orbital properties with a massive Large Magellanic Cloud. Astron. Astrophys. 657, A54 (2022).

    ADS  Article  Google Scholar 

  28. Walker, M. G., Olszewski, E. W. & Mateo, M. Bayesian analysis of resolved stellar spectra: application to MMT/Hectochelle observations of the Draco dwarf spheroidal. Mon. Not. R. Astron. Soc. 448, 2717–2732 (2015).

    ADS  Article  Google Scholar 

  29. Gaia Collaboration. Gaia Data Release 2. Kinematics of globular clusters and dwarf galaxies around the Milky Way. Astron. Astrophys. 616, A12 (2018).

  30. Simon, J. D. Gaia proper motions and orbits of the ultra-faint Milky Way satellites. Astrophys. J. 863, 89 (2018).

    ADS  Article  Google Scholar 

  31. Li, H. et al. Gaia EDR3 proper motions of Milky Way dwarfs. I. 3D motions and orbits. Astrophys. J. 916, 8 (2021).

    ADS  Article  Google Scholar 

  32. Patel, E. et al. The orbital histories of Magellanic satellites using Gaia DR2 proper motions. Astrophys. J. 893, 121 (2020).

  33. Geha, M., Guhathakurta, P., Rich, R. M. & Cooper, M. C. Local Group dwarf elliptical galaxies. I. Mapping the dynamics of NGC 205 beyond the tidal radius. Astron. J. 131, 332–342 (2006).

    ADS  Article  Google Scholar 

  34. Li, T. S. et al. The first tidally disrupted ultra-faint dwarf galaxy? A spectroscopic analysis of the Tucana III stream. Astrophys. J. 866, 22 (2018).

    ADS  Article  Google Scholar 

  35. Ji, A. P. et al. Kinematics of Antlia 2 and Crater 2 from the Southern Stellar Stream Spectroscopic Survey (S5). Astrophys. J. 921, 32 (2021).

    ADS  Article  Google Scholar 

  36. Peñarrubia, J., Navarro, J. F., McConnachie, A. W. & Martin, N. F. The signature of galactic tides in Local Group dwarf spheroidals. Astrophys. J. 698, 222–232 (2009).

    ADS  Article  Google Scholar 

  37. van der Marel, R. P. Magellanic Cloud structure from near-infrared surveys. II. Star count maps and the intrinsic elongation of the Large Magellanic Cloud. Astron. J. 122, 1827–1843 (2001).

    ADS  Article  Google Scholar 

  38. Lewis, G. F. et al. Inside the whale: the structure and dynamics of the isolated Cetus dwarf spheroidal. Mon. Not. R. Astron. Soc. 375, 1364–1370 (2007).

    ADS  Article  Google Scholar 

  39. Battaglia, G. et al. The kinematic status and mass content of the Sculptor dwarf spheroidal galaxy. Astrophys. J. Lett. 681, L13 (2008).

    ADS  Article  Google Scholar 

  40. Walker, M. G., Mateo, M. & Olszewski, E. W. Systemic proper motions of Milky Way satellites from stellar redshifts: the Carina, Fornax, Sculptor, and Sextans dwarf spheroidals. Astrophys. J. Lett. 688, L75 (2008).

    ADS  Article  Google Scholar 

  41. Fraternali, F., Tolstoy, E., Irwin, M. J. & Cole, A. A. Life at the periphery of the Local Group: the kinematics of the Tucana dwarf galaxy. Astron. Astrophys. 499, 121–128 (2009).

    ADS  Article  Google Scholar 

  42. Kirby, E. N., Bullock, J. S., Boylan-Kolchin, M., Kaplinghat, M. & Cohen, J. G. The dynamics of isolated Local Group galaxies. Mon. Not. R. Astron. Soc. 439, 1015–1027 (2014).

    ADS  Article  Google Scholar 

  43. Wheeler, C. et al. The no-spin zone: rotation versus dispersion support in observed and simulated dwarf galaxies. Mon. Not. R. Astron. Soc. 465, 2420–2431 (2017).

    ADS  Article  Google Scholar 

  44. Collins, M. L. M. et al. Dynamical evidence for a strong tidal interaction between the Milky Way and its satellite Leo V. Mon. Not. R. Astron. Soc. 467, 573–585 (2017).

    ADS  Google Scholar 

  45. Kirby, E. N. et al. Chemistry and kinematics of the late-forming dwarf irregular galaxies Leo A, Aquarius, and Sagittarius DIG. Astrophys. J. 834, 9 (2017).

    ADS  Article  Google Scholar 

  46. Kacharov, N. et al. Prolate rotation and metallicity gradient in the transforming dwarf galaxy Phoenix. Mon. Not. R. Astron. Soc. 466, 2006–2023 (2017).

    ADS  Article  Google Scholar 

  47. Spencer, M. E. et al. The binary fraction of stars in dwarf galaxies: the case of Leo II. Astron. J. 153, 257 (2017).

    ADS  Article  Google Scholar 

  48. Taibi, S. et al. Stellar chemo-kinematics of the Cetus dwarf spheroidal galaxy. Astron. Astrophys. 618, A122 (2018).

    Article  Google Scholar 

  49. Collins, M. L. M. et al. A detailed study of Andromeda XIX, an extreme local analogue of ultradiffuse galaxies. Mon. Not. R. Astron. Soc. 491, 3496–3514 (2020).

    ADS  Article  Google Scholar 

  50. Hermosa Muñoz, L. et al. Kinematic and metallicity properties of the Aquarius dwarf galaxy from FORS2 MXU spectroscopy. Astron. Astrophys. 634, A10 (2020).

    Article  Google Scholar 

  51. Taibi, S. et al. The Tucana dwarf spheroidal galaxy: not such a massive failure after all. Astron. Astrophys. 635, A152 (2020).

    Article  Google Scholar 

  52. Belland, B., Kirby, E., Boylan-Kolchin, M. & Wheeler, C. NGC 6822 as a probe of dwarf galactic evolution. Astrophys. J. 903, 10 (2020).

    ADS  Article  Google Scholar 

  53. Gregory, A. L. et al. Uncovering the orbit of the hercules dwarf galaxy. Mon. Not. R. Astron. Soc. 496, 1092–1104 (2020).

    ADS  Article  Google Scholar 

  54. Kirby, E. N. et al. Elemental abundances in M31: the kinematics and chemical evolution of dwarf spheroidal satellite galaxies. Astron. J. 159, 10 (2020).

    Article  Google Scholar 

  55. Leaman, R. et al. The resolved structure and dynamics of an isolated dwarf galaxy: a VLT and Keck spectroscopic survey of WLM. Astrophys. J. 750, 33 (2012).

    ADS  Article  Google Scholar 

  56. Geha, M. et al. Local Group dwarf elliptical galaxies. II. Stellar kinematics to large radii in NGC 147 and NGC 185. Astrophys. J. 711, 361–373 (2010).

    ADS  Article  Google Scholar 

  57. Martínez-García, A. M., del Pino, A., Aparicio, A., van der Marel, R. P. & Watkins, L. L. Internal rotation of Milky Way dwarf spheroidal satellites with Gaia Early Data Release 3. Mon. Not. R. Astron. Soc. 505, 5884–5895 (2021).

    ADS  Article  Google Scholar 

  58. Tollerud, E. J. et al. The SPLASH survey: spectroscopy of 15 M31 dwarf spheroidal satellite galaxies. Astrophys. J. 752, 45 (2012).

    ADS  Article  Google Scholar 

  59. Higgs, C. R. & McConnachie, A. W. Solo dwarfs IV: comparing and contrasting satellite and isolated dwarf galaxies in the Local Group. Mon. Not. R. Astron. Soc. 506, 2766–2779 (2021).

    ADS  Article  Google Scholar 

  60. Collins, M. L. M. et al. Comparing the observable properties of dwarf galaxies on and off the Andromeda plane. Astrophys. J. Lett. 799, L13 (2015).

    ADS  Article  Google Scholar 

  61. Fu, S. W., Simon, J. D. & Alarcón Jara, A. G. Dynamical histories of the Crater II and Hercules dwarf galaxies. Astrophys. J. 883, 11 (2019).

    ADS  Article  Google Scholar 

  62. Gregory, A. L. et al. Kinematics of the Tucana dwarf galaxy: an unusually dense dwarf in the Local Group. Mon. Not. R. Astron. Soc. 485, 2010–2025 (2019).

    ADS  Article  Google Scholar 

  63. Zhu, L., van de Ven, G., Watkins, L. L. & Posti, L. A discrete chemo-dynamical model of the dwarf spheroidal galaxy Sculptor: mass profile, velocity anisotropy and internal rotation. Mon. Not. R. Astron. Soc. 463, 1117–1135 (2016).

    ADS  Article  Google Scholar 

  64. Hagen, J. H. J., Helmi, A. & Breddels, M. A. Axisymmetric Schwarzschild models of an isothermal axisymmetric mock dwarf spheroidal galaxy. Astron. Astrophys. 632, A99 (2019).

    ADS  Article  Google Scholar 

  65. Hayashi, K., Chiba, M. & Ishiyama, T. Diversity of dark matter density profiles in the galactic dwarf spheroidal satellites. Astrophys. J. 904, 45 (2020).

    ADS  Article  Google Scholar 

  66. Massari, D. et al. Three-dimensional motions in the Sculptor dwarf galaxy as a glimpse of a new era. Nat. Astron. 2, 156–161 (2018).

    ADS  Article  Google Scholar 

  67. Massari, D. et al. Stellar 3D kinematics in the Draco dwarf spheroidal galaxy. Astron. Astrophys. 633, (2020).

  68. Tolstoy, E. et al. Two distinct ancient components in the Sculptor dwarf spheroidal galaxy: first results from the Dwarf Abundances and Radial velocities Team. Astrophys. J. Lett. 617, L119–L122 (2004).

    ADS  Article  Google Scholar 

  69. Battaglia, G. et al. The DART imaging and CaT survey of the Fornax dwarf spheroidal galaxy. Astron. Astrophys. 459, 423–440 (2006).

    ADS  Article  Google Scholar 

  70. Battaglia, G. et al. Study of the Sextans dwarf spheroidal galaxy from the DART Ca II triplet survey. Mon. Not. R. Astron. Soc. 411, 1013–1034 (2011).

    ADS  Article  Google Scholar 

  71. Walker, M. G. & Peñarrubia, J. A method for measuring (slopes of) the mass profiles of dwarf spheroidal galaxies. Astrophys. J. 742, (2011).

  72. Amorisco, N. C. & Evans, N. W. Dark matter cores and cusps: the case of multiple stellar populations in dwarf spheroidals. Mon. Not. R. Astron. Soc. 419, 184–196 (2012).

    ADS  Article  Google Scholar 

  73. Fabrizio, M. et al. The Carina Project. X. On the kinematics of old and intermediate-age stellar populations. Astrophys. J. 830 (2016).

  74. Kordopatis, G., Amorisco, N. C., Evans, N. W., Gilmore, G. & Koposov, S. E. Chemodynamic subpopulations of the Carina dwarf galaxy. Mon. Not. R. Astron. Soc. 457, 1299–1307 (2016).

    ADS  Article  Google Scholar 

  75. Pace, A. B. et al. Multiple chemodynamic stellar populations of the Ursa Minor dwarf spheroidal galaxy. Mon. Not. R. Astron. Soc. 495, 3022–3040 (2020).

    ADS  Article  Google Scholar 

  76. Ibata, R., Chapman, S., Irwin, M., Lewis, G. & Martin, N. A near-zero velocity dispersion stellar component in the Canes Venatici dwarf spheroidal galaxy. Mon. Not. R. Astron. Soc. 373, L70–L74 (2006).

    ADS  Article  Google Scholar 

  77. Koposov, S. E. et al. Accurate stellar kinematics at faint magnitudes: application to the Boötes I dwarf spheroidal galaxy. Astrophys. J. 736, (2011).

  78. Breddels, M. A. & Helmi, A. Complexity on dwarf galaxy scales: a bimodal distribution function in Sculptor. Astrophys. J. Lett. 791, (2014).

  79. McConnachie, A. W., Peñarrubia, J. & Navarro, J. F. Multiple dynamical components in Local Group dwarf spheroidals. Mon. Not. R. Astron. Soc. 380, L75–L79 (2007).

    ADS  Article  Google Scholar 

  80. Amorisco, N. C. & Evans, N. W. A troublesome past: chemodynamics of the Fornax dwarf spheroidal. Astrophys. J. Lett. 756, (2012).

  81. Cicuéndez, L. & Battaglia, G. Appearances can be deceiving: clear signs of accretion in the seemingly ordinary Sextans dSph. Mon. Not. R. Astron. Soc. 480, 251–260 (2018).

    ADS  Article  Google Scholar 

  82. Ho, N. et al. Stellar kinematics of the Andromeda II dwarf spheroidal galaxy. Astrophys. J. 758, (2012).

  83. Hidalgo, S. L., Aparicio, A., Martínez-Delgado, D. & Gallart, C. On the extended structure of the Phoenix dwarf galaxy. Astrophys. J. 705, 704–716 (2009).

    ADS  Article  Google Scholar 

  84. Battaglia, G., Rejkuba, M., Tolstoy, E., Irwin, M. J. & Beccari, G. A wide-area view of the Phoenix dwarf galaxy from Very Large Telescope/FORS imaging. Mon. Not. R. Astron. Soc. 424, 1113–1131 (2012).

    ADS  Article  Google Scholar 

  85. Thompson, G. P., Ryan, S. G. & Sibbons, L. F. The rotation of the halo of NGC 6822 from the radial velocities of carbon stars. Mon. Not. R. Astron. Soc. 462, 3376–3385 (2016).

    ADS  Article  Google Scholar 

  86. del Pino, A., Łokas, E. L., Hidalgo, S. L. & Fouquet, S. The structure of Andromeda II dwarf spheroidal galaxy. Mon. Not. R. Astron. Soc. 469, 4999–5015 (2017).

    ADS  Article  Google Scholar 

  87. del Pino, A., Aparicio, A., Hidalgo, S. L. & Łokas, E. L. Rotating stellar populations in the Fornax dSph galaxy. Mon. Not. R. Astron. Soc. 465, 3708–3723 (2017).

    ADS  Article  Google Scholar 

  88. Kim, H.-S., Han, S.-I., Joo, S.-J., Jeong, H. & Yoon, S.-J. A possible relic star cluster in the Sextans dwarf galaxy. Astrophys. J. Lett. 870, (2019).

  89. Lokas, E. L., Ebrova, I., DelPino, A. & Semczuk, M. Andromeda II as a merger remnant. Mon. Not. R. Astron. Soc. 445, L6–L10 (2014).

    ADS  Article  Google Scholar 

  90. Cardona-Barrero, S., Battaglia, G., Di Cintio, A., Revaz, Y. & Jablonka, P. Origin of stellar prolate rotation in a cosmologically simulated faint dwarf galaxy. Mon. Not. R. Astron. Soc. 505, L100–L105 (2021).

    ADS  Article  Google Scholar 

  91. Amorisco, N. C., Evans, N. W. & van de Ven, G. The remnant of a merger between two dwarf galaxies in Andromeda II. Nature 507, 335–337 (2014).

    ADS  Article  Google Scholar 

  92. Annibali, F. et al. DDO 68: a flea with smaller fleas that on him prey. Astrophys. J. Lett. 826, (2016).

  93. Bullock, J. S. & Johnston, K. V. Tracing galaxy formation with stellar halos. I. Methods. Astrophys. J. 635, 931–949 (2005).

    ADS  Article  Google Scholar 

  94. Peñarrubia, J., Navarro, J. F. & McConnachie, A. W. The tidal evolution of Local Group dwarf spheroidals. Astrophys. J. 673, 226–240 (2008).

    ADS  Article  Google Scholar 

  95. Errani, R., Penarrubia, J. & Tormen, G. Constraining the distribution of dark matter in dwarf spheroidal galaxies with stellar tidal streams. Mon. Not. R. Astron. Soc. 449, L46–L50 (2015).

    ADS  Article  Google Scholar 

  96. Errani, R. & Peñarrubia, J. Can tides disrupt cold dark matter subhaloes? Mon. Not. R. Astron. Soc. 491, 4591–4601 (2020).

    ADS  Article  Google Scholar 

  97. Nipoti, C., Cherchi, G., Iorio, G. & Calura, F. Effective N-body models of composite collisionless stellar systems. Mon. Not. R. Astron. Soc. 503, 4221–4230 (2021).

    ADS  Article  Google Scholar 

  98. Battaglia, G., Sollima, A. & Nipoti, C. The effect of tides on the Fornax dwarf spheroidal galaxy. Mon. Not. R. Astron. Soc. 454, 2401–2415 (2015).

    ADS  Article  Google Scholar 

  99. Iorio, G., Nipoti, C., Battaglia, G. & Sollima, A. The effect of tides on the Sculptor dwarf spheroidal galaxy. Mon. Not. R. Astron. Soc. 487, 5692–5710 (2019).

    ADS  Article  Google Scholar 

  100. Genina, A., Read, J. I., Fattahi, A. & Frenk, C. S. Can tides explain the low dark matter density in Fornax? Mon. Not. R. Astron. Soc. 510, 2186–2205 (2022).

    ADS  Article  Google Scholar 

  101. Borukhovetskaya, A., Errani, R., Navarro, J. F., Fattahi, A. & Santos-Santos, I. The tidal evolution of the Fornax dwarf spheroidal and its globular clusters. Mon. Not. R. Astron. Soc. 509, 5330–5339 (2022).

    ADS  Article  Google Scholar 

  102. Binney, J. & Tremaine, S. Galactic Dynamics 2nd edn (Princeton Univ. Press, 2008).

  103. Ciotti, L. Introduction to Stellar Dynamics (Cambridge Univ. Press, 2021).

    MATH  Book  Google Scholar 

  104. Łokas, E. L., Mamon, G. A. & Prada, F. Dark matter distribution in the Draco dwarf from velocity moments. Mon. Not. R. Astron. Soc. 363, 918–928 (2005).

    ADS  Article  Google Scholar 

  105. Łokas, E. L. The mass and velocity anisotropy of the Carina, Fornax, Sculptor and Sextans dwarf spheroidal galaxies. Mon. Not. R. Astron. Soc. 394, L102–L106 (2009).

    ADS  Article  Google Scholar 

  106. Strigari, L. E., Frenk, C. S. & White, S. D. M. Kinematics of Milky Way satellites in a Lambda cold dark matter universe. Mon. Not. R. Astron. Soc. 408, 2364–2372 (2010).

    ADS  Article  Google Scholar 

  107. Breddels, M. A. & Helmi, A. Model comparison of the dark matter profiles of Fornax, Sculptor, Carina and Sextans. Astron. Astrophys. 558, (2013).

  108. Richardson, T. & Fairbairn, M. Analytical solutions to the mass-anisotropy degeneracy with higher order Jeans analysis: a general method. Mon. Not. R. Astron. Soc. 432, 3361–3380 (2013).

    ADS  Article  Google Scholar 

  109. Strigari, L. E., Frenk, C. S. & White, S. D. M. Dynamical constraints on the dark matter distribution of the Sculptor dwarf spheroidal from stellar proper motions. Astrophys. J. 860, (2018).

  110. Pascale, R., Posti, L., Nipoti, C. & Binney, J. Action-based dynamical models of dwarf spheroidal galaxies: application to Fornax. Mon. Not. R. Astron. Soc. 480, 927–946 (2018).

    ADS  Article  Google Scholar 

  111. Read, J. I. et al. Breaking beta: a comparison of mass modelling methods for spherical systems. Mon. Not. R. Astron. Soc. 501, 978–993 (2021).

    ADS  Article  Google Scholar 

  112. Agnello, A. & Evans, N. W. A virial core in the Sculptor dwarf spheroidal galaxy. Astrophys. J. Lett. 754, (2012).

  113. Strigari, L. E., Frenk, C. S. & White, S. D. M. Dynamical models for the Sculptor dwarf spheroidal in a Λ CDM Universe. Astrophys. J. 838, (2017).

  114. Pascale, R., Binney, J., Nipoti, C. & Posti, L. Action-based models for dwarf spheroidal galaxies and globular clusters. Mon. Not. R. Astron. Soc. 488, 2423–2439 (2019).

    ADS  Article  Google Scholar 

  115. Binney, J. & Mamon, G. A. M/L and velocity anisotropy from observations of spherical galaxies, or must M87 have a massive black hole ? Mon. Not. R. Astron. Soc. 200, 361–375 (1982).

    ADS  Article  Google Scholar 

  116. Woo, J., Courteau, S. & Dekel, A. Scaling relations and the fundamental line of the local group dwarf galaxies. Mon. Not. R. Astron. Soc. 390, 1453–1469 (2008).

    ADS  Google Scholar 

  117. Wolf, J. et al. Accurate masses for dispersion-supported galaxies. Mon. Not. R. Astron. Soc. 406, 1220–1237 (2010).

    ADS  Google Scholar 

  118. Sanders, J. L. & Evans, N. W. Mass estimators for flattened dispersion-supported galaxies. Astrophys. J. Lett. 830, (2016).

  119. Errani, R., Peñarrubia, J. & Walker, M. G. Systematics in virial mass estimators for pressure-supported systems. Mon. Not. R. Astron. Soc. 481, 5073–5090 (2018).

    ADS  Article  Google Scholar 

  120. McGaugh, S. S., Lelli, F. & Schombert, J. M. Radial acceleration relation in rotationally supported galaxies. Phys. Rev. Lett. 117, (2016).

  121. Lelli, F., McGaugh, S. S., Schombert, J. M. & Pawlowski, M. S. One law to rule them all: the radial acceleration relation of galaxies. Astrophys. J. 836, (2017).

  122. Strigari, L. E. et al. A common mass scale for satellite galaxies of the Milky Way. Nature 454, 1096–1097 (2008).

    ADS  Article  Google Scholar 

  123. Read, J. I., Walker, M. G. & Steger, P. Dark matter heats up in dwarf galaxies. Mon. Not. R. Astron. Soc. 484, 1401–1420 (2019).

    ADS  Article  Google Scholar 

  124. Navarro, J. F., Frenk, C. S. & White, S. D. M. The structure of cold dark matter halos. Astrophys. J. 462, 563 (1996).

    ADS  Article  Google Scholar 

  125. Navarro, J. F., Eke, V. R. & Frenk, C. S. The cores of dwarf galaxy haloes. Mon. Not. R. Astron. Soc. 283, L72–L78 (1996).

    ADS  Article  Google Scholar 

  126. Read, J. I. & Gilmore, G. Mass loss from dwarf spheroidal galaxies: the origins of shallow dark matter cores and exponential surface brightness profiles. Mon. Not. R. Astron. Soc. 356, 107–124 (2005).

    ADS  Article  Google Scholar 

  127. Mashchenko, S., Wadsley, J. & Couchman, H. M. P. Stellar feedback in dwarf galaxy formation. Science 319, 174 (2008).

    ADS  Article  Google Scholar 

  128. Di Cintio, A. et al. The dependence of dark matter profiles on the stellar-to-halo mass ratio: a prediction for cusps versus cores. Mon. Not. R. Astron. Soc. 437, 415–423 (2014).

    ADS  Article  Google Scholar 

  129. Madau, P., Shen, S. & Governato, F. Dark matter heating and early core formation in dwarf galaxies. Astrophys. J. Lett. 789, (2014).

  130. Nipoti, C. & Binney, J. Early flattening of dark matter cusps in dwarf spheroidal galaxies. Mon. Not. R. Astron. Soc. 446, 1820–1828 (2015).

    ADS  Article  Google Scholar 

  131. Sawala, T. et al. The APOSTLE simulations: solutions to the Local Groupas cosmic puzzles. Mon. Not. R. Astron. Soc. 457, 1931–1943 (2016).

    ADS  Article  Google Scholar 

  132. Benítez-Llambay, A., Frenk, C. S., Ludlow, A. D. & Navarro, J. F. Baryon-induced dark matter cores in the EAGLE simulations. Mon. Not. R. Astron. Soc. 488, 2387–2404 (2019).

    ADS  Article  Google Scholar 

  133. Hui, L., Ostriker, J. P., Tremaine, S. & Witten, E. Ultralight scalars as cosmological dark matter. Phys. Rev. D 95, (2017).

  134. Fitts, A. et al. Dwarf galaxies in CDM, WDM, and SIDM: disentangling baryons and dark matter physics. Mon. Not. R. Astron. Soc. 490, 962–977 (2019).

    ADS  Article  Google Scholar 

  135. Burger, J. D. et al. Degeneracies between self-interacting dark matter and supernova feedback as cusp-core transformation mechanisms. Preprint at https://arxiv.org/abs/2108.07358 (2021).

  136. Jardel, J. R., Gebhardt, K., Fabricius, M. H., Drory, N. & Williams, M. J. Measuring dark matter profiles non-parametrically in dwarf spheroidals: an application to Draco. Astrophys. J. 763, (2013).

  137. Read, J. I., Walker, M. G. & Steger, P. The case for a cold dark matter cusp in Draco. Mon. Not. R. Astron. Soc. 481, 860–877 (2018).

    ADS  Article  Google Scholar 

  138. Jardel, J. R. & Gebhardt, K. The dark matter density profile of the Fornax dwarf. Astrophys. J. 746, (2012).

  139. Kaplinghat, M., Valli, M. & Yu, H.-B. Too big to fail in light of Gaia. Mon. Not. R. Astron. Soc. 490, 231–242 (2019).

    ADS  Article  Google Scholar 

  140. Breddels, M. A., Helmi, A., van den Bosch, R. C. E., van de Ven, G. & Battaglia, G. Orbit-based dynamical models of the Sculptor dSph galaxy. Mon. Not. R. Astron. Soc. 433, 3173–3189 (2013).

    ADS  Article  Google Scholar 

  141. Pascale, R. Dynamical Models of Dwarf Spheroidal Galaxies Based on Distribution Functions Depending on Actions PhD thesis, Univ. Bologna (2020).

  142. Pontzen, A. & Governato, F. Cold dark matter heats up. Nature 506, 171–178 (2014).

    ADS  Article  Google Scholar 

  143. Tollet, E. et al. NIHAO - IV: core creation and destruction in dark matter density profiles across cosmic time. Mon. Not. R. Astron. Soc. 456, 3542–3552 (2016).

    ADS  Article  Google Scholar 

  144. Lazar, A. et al. A dark matter profile to model diverse feedback-induced core sizes of Λ CDM haloes. Mon. Not. R. Astron. Soc. 497, 2393–2417 (2020).

    ADS  Article  Google Scholar 

  145. Robles, V. H. & Bullock, J. S. Orbital pericentres and the inferred dark matter halo structure of satellite galaxies. Mon. Not. R. Astron. Soc. 503, 5232–5237 (2021).

    ADS  Article  Google Scholar 

  146. Torrealba, G., Koposov, S. E., Belokurov, V. & Irwin, M. The feeble giant. Discovery of a large and diffuse Milky Way dwarf galaxy in the constellation of Crater. Mon. Not. R. Astron. Soc. 459, 2370–2378 (2016).

    ADS  Article  Google Scholar 

  147. Borukhovetskaya, A., Navarro, J. F., Errani, R. & Fattahi, A. Galactic tides and the Crater II dwarf spheroidal: a challenge to LCDM? Preprint at https://arxiv.org/abs/2112.01540 (2021).

  148. Evans, N. W., Sanders, J. L. & Geringer-Sameth, A. Simple J-factors and D-factors for indirect dark matter detection. Phys. Rev. D 93, (2016).

  149. Pace, A. B. & Strigari, L. E. Scaling relations for dark matter annihilation and decay profiles in dwarf spheroidal galaxies. Mon. Not. R. Astron. Soc. 482, 3480–3496 (2019).

    ADS  Article  Google Scholar 

  150. Bergström, S. et al. J-factors for self-interacting dark matter in 20 dwarf spheroidal galaxies. Phys. Rev. D 98, (2018).

  151. Ackermann, M. et al. Searching for dark matter annihilation from Milky Way dwarf spheroidal galaxies with six years of Fermi Large Area Telescope data. Phys. Rev. Lett. 115, (2015).

  152. Bonnivard, V. et al. Dark matter annihilation and decay in dwarf spheroidal galaxies: the classical and ultrafaint dSphs. Mon. Not. R. Astron. Soc. 453, 849–867 (2015).

    ADS  Article  Google Scholar 

  153. Geringer-Sameth, A., Koushiappas, S. M. & Walker, M. Dwarf galaxy annihilation and decay emission profiles for dark matter experiments. Astrophys. J. 801, (2015).

  154. Sanders, J. L., Evans, N. W., Geringer-Sameth, A. & Dehnen, W. Indirect dark matter detection for flattened dwarf galaxies. Phys. Rev. D 94, (2016).

  155. Hayashi, K. et al. Dark matter annihilation and decay from non-spherical dark halos in galactic dwarf satellites. Mon. Not. R. Astron. Soc. 461, 2914–2928 (2016).

    ADS  Article  Google Scholar 

  156. Klop, N., Zandanel, F., Hayashi, K. & Ando, S. Impact of axisymmetric mass models for dwarf spheroidal galaxies on indirect dark matter searches. Phys. Rev. D 95, (2017).

  157. Chiappo, A., Cohen-Tanugi, J., Conrad, J. & Strigari, L. E. Dwarf spheroidal J-factor likelihoods for generalized NFW profiles. Mon. Not. R. Astron. Soc. 488, 2616–2628 (2019).

    ADS  Article  Google Scholar 

  158. Horigome, S. et al. J-factor estimation of Draco, Sculptor, and Ursa Minor dwarf spheroidal galaxies with the member/foreground mixture model. Mon. Not. R. Astron. Soc. 499, 3320–3337 (2020).

    ADS  Article  Google Scholar 

  159. Simon, J. et al. Testing the nature of dark matter with extremely large telescopes. Bull. Am. Astron. Soc. 51, (2019).

  160. Hobbs, D. et al. All-sky visible and near infrared space astrometry. Exp. Astron. 51, 783–843 (2021).

    ADS  Article  Google Scholar 

  161. WFIRST Astrometry Working Group. Astrometry with the Wide-Field Infrared Space Telescope. J. Astron. Telesc. Instrum. Syst. 5, (2019).

  162. Anderson, J., Bedin, L. R., Piotto, G., Yadav, R. S. & Bellini, A. Ground-based CCD astrometry with wide field imagers. I. Observations just a few years apart allow decontamination of field objects from members in two globular clusters. Astron. Astrophys. 454, 1029–1045 (2006).

    ADS  Article  Google Scholar 

  163. Strigari, L. E., Bullock, J. S. & Kaplinghat, M. Determining the nature of dark matter with astrometry. Astrophys. J. Lett. 657, L1–L4 (2007).

    ADS  Article  Google Scholar 

  164. Richardson, T. D., Spolyar, D. & Lehnert, M. D. Plan β: core or cusp? Mon. Not. R. Astron. Soc. 440, 1680–1689 (2014).

    ADS  Article  Google Scholar 

  165. Read, J. I. & Steger, P. How to break the density-anisotropy degeneracy in spherical stellar systems. Mon. Not. R. Astron. Soc. 471, 4541–4558 (2017).

    ADS  Article  Google Scholar 

  166. Guerra, J., Geha, M. & Strigari, L. E. Forecasts on the dark matter density profiles of dwarf spheroidal galaxies with current and future kinematic observations. Preprint at https://arxiv.org/abs/2112.05166 (2021).

  167. Torrealba, G. et al. At the survey limits: discovery of the Aquarius 2 dwarf galaxy in the VST ATLAS and the SDSS data. Mon. Not. R. Astron. Soc. 463, 712–722 (2016).

    ADS  Article  Google Scholar 

  168. Muñ oz, R. R. et al. A MegaCam survey of outer halo satellites. III. Photometric and structural parameters. Astrophys. J. 860, (2018).

  169. Torrealba, G. et al. Discovery of two neighbouring satellites in the Carina constellation with MagLiteS. Mon. Not. R. Astron. Soc. 475, 5085–5097 (2018).

    ADS  Article  Google Scholar 

  170. Koposov, S. E. et al. Snake in the clouds: a new nearby dwarf galaxy in the Magellanic bridge. Mon. Not. R. Astron. Soc. 479, 5343–5361 (2018).

    ADS  Article  Google Scholar 

  171. Kim, D. et al. Portrait of a dark horse: a photometric and spectroscopic study of the ultra-faint Milky Way satellite Pegasus III. Astrophys. J. 833, (2016).

  172. Mutlu-Pakdil, B. et al. A deeper look at the new Milky Way satellites: Sagittarius II, Reticulum II, Phoenix II, and Tucana III. Astrophys. J. 863, (2018).

  173. Cicuéndez, L. et al. Tracing the stellar component of low surface brightness Milky Way dwarf galaxies to their outskirts. I. Sextans. Astron. Astrophys. 609, (2018).

  174. Koposov, S. E., Belokurov, V., Torrealba, G. & Evans, N. W. Beasts of the southern wild: discovery of nine ultra faint satellites in the vicinity of the Magellanic Clouds. Astrophys. J. 805, (2015).

  175. Simon, J. D. et al. Birds of a feather? Magellan/IMACS spectroscopy of the ultra-faint satellites Grus II, Tucana IV, and Tucana V. Astrophys. J. 892, (2020).

  176. Saviane, I., Held, E. V. & Piotto, G. CCD photometry of the Tucana dwarf galaxy. Astron. Astrophys. 315, 40–51 (1996).

    ADS  Google Scholar 

  177. Martin, N. F. et al. The PAndAS view of the Andromeda satellite system. II. Detailed properties of 23 M31 dwarf spheroidal galaxies. Astrophys. J. 833, (2016).

  178. Collins, M. L. M. et al. Andromeda XXI—a dwarf galaxy in a low-density dark matter halo. Mon. Not. R. Astron. Soc. 505, 5686–5701 (2021).

    ADS  Article  Google Scholar 

  179. Tollerud, E. J., Geha, M. C., Vargas, L. C. & Bullock, J. S. The outer limits of the M31 system: kinematics of the dwarf galaxy satellites And XXVIII & And XXIX. Astrophys. J. 768, (2013).

  180. Higgs, C. R. et al. Solo dwarfs II: the stellar structure of isolated Local Group dwarf galaxies. Mon. Not. R. Astron. Soc. 503, 176–199 (2021).

    ADS  Article  Google Scholar 

  181. Cook, K. H. et al. The systemic velocity and internal kinematics of the dwarf galaxy LGS 3: an optical foray beyond the Milky Way. Publ. Astron. Soc. Pac. 111, 306–312 (1999).

    ADS  Article  Google Scholar 

  182. McConnachie, A. W. The observed properties of dwarf galaxies in and around the Local Group. Astron. J. 144, (2012).

  183. Lee, M. G. Stellar populations of the dwarf galaxy LGS 3 in the Local Group. Astron. J. 110, 1129 (1995).

    ADS  Article  Google Scholar 

  184. Crnojević, D. et al. A PAndAS view of M31 dwarf elliptical satellites: NGC 147 and NGC 185. Mon. Not. R. Astron. Soc. 445, 3862–3877 (2014).

    ADS  Article  Google Scholar 

  185. Drlica-Wagner, A. et al. Eight ultra-faint galaxy candidates discovered in year two of the Dark Energy Survey. Astrophys. J. 813, (2015).

  186. Longeard, N. et al. Pristine dwarf galaxy survey—I. A detailed photometric and spectroscopic study of the very metal-poor Draco II satellite. Mon. Not. R. Astron. Soc. 480, 2609–2627 (2018).

    ADS  Article  Google Scholar 

  187. Carlin, J. L. et al. Deep Subaru Hyper Suprime-Cam observations of Milky Way satellites Columba I and Triangulum II. Astron. J. 154, (2017).

  188. Walker, M. G., Mateo, M., Olszewski, E. W., Sen, B. & Woodroofe, M. Clean kinematic samples in dwarf spheroidals: an algorithm for evaluating membership and estimating distribution parameters when contamination is present. Astron. J. 137, 3109–3138 (2009).

    ADS  Article  Google Scholar 

  189. McConnachie, A. W. & Côté, P. Revisiting the influence of unidentified binaries on velocity dispersion measurements in ultra-faint stellar systems. Astrophys. J. Lett. 722, L209–L214 (2010).

    ADS  Article  Google Scholar 

  190. Dabringhausen, J., Kroupa, P., Famaey, B. & Fellhauer, M. Understanding the internal dynamics of elliptical galaxies without non-baryonic dark matter. Mon. Not. R. Astron. Soc. 463, 1865–1880 (2016).

    ADS  Article  Google Scholar 

  191. Martinez, G. D. et al. A complete spectroscopic survey of the Milky Way satellite Segue 1: dark matter content, stellar membership, and binary properties from a Bayesian analysis. Astrophys. J. 738, (2011).

  192. Minor, Q. E., Pace, A. B., Marshall, J. L. & Strigari, L. E. Robust velocity dispersion and binary population modelling of the ultrafaint dwarf galaxy Reticulum II. Mon. Not. R. Astron. Soc. 487, 2961–2968 (2019).

    ADS  Article  Google Scholar 

  193. Minor, Q. E. Binary populations in Milky Way satellite galaxies: constraints from multi-epoch data in the Carina, Fornax, Sculptor, and Sextans dwarf spheroidal galaxies. Astrophys. J. 779, (2013).

  194. Spencer, M. E. et al. The binary fraction of stars in dwarf galaxies: the cases of Draco and Ursa Minor. Astron. J. 156, (2018).

  195. Amorisco, N. C. & Evans, N. W. Phase-space models of the dwarf spheroidals. Mon. Not. R. Astron. Soc. 411, 2118–2136 (2011).

    ADS  Article  Google Scholar 

  196. Wilkinson, M. I., Kleyna, J., Evans, N. W. & Gilmore, G. Dark matter in dwarf spheroidals—I. Models. Mon. Not. R. Astron. Soc. 330, 778–791 (2002).

    ADS  Article  Google Scholar 

  197. Williams, A. A. & Evans, N. W. Made-to-measure dark matter haloes, elliptical galaxies and dwarf galaxies in action coordinates. Mon. Not. R. Astron. Soc. 448, 1360–1371 (2015).

    ADS  Article  Google Scholar 

  198. Schwarzschild, M. A numerical model for a triaxial stellar system in dynamical equilibrium. Astrophys. J. 232, 236–247 (1979).

    ADS  Article  Google Scholar 

  199. Kowalczyk, K., Łokas, E. L. & Valluri, M. Recovering the mass profile and orbit anisotropy of mock dwarf galaxies with Schwarzschild modelling. Mon. Not. R. Astron. Soc. 470, 3959–3969 (2017).

    ADS  Article  Google Scholar 

  200. Kowalczyk, K., Łokas, E. L. & Valluri, M. The effect of non-sphericity on mass and anisotropy measurements in dSph galaxies with Schwarzschild method. Mon. Not. R. Astron. Soc. 476, 2918–2930 (2018).

    ADS  Article  Google Scholar 

  201. Kowalczyk, K., del Pino, A., Łokas, E. L. & Valluri, M. Schwarzschild dynamical model of the Fornax dwarf spheroidal galaxy. Mon. Not. R. Astron. Soc. 482, 5241–5249 (2019).

    ADS  Article  Google Scholar 

  202. Jardel, J. R. & Gebhardt, K. Variations in a universal dark matter profile for dwarf spheroidals. Astrophys. J. Lett. 775, (2013).

  203. Evans, N. W., An, J. & Walker, M. G. Cores and cusps in the dwarf spheroidals. Mon. Not. R. Astron. Soc. 393, L50–L54 (2009).

    ADS  Article  Google Scholar 

  204. Walker, M. G. et al. A universal mass profile for dwarf spheroidal galaxies? Astrophys. J. 704, 1274–1287 (2009).

    ADS  Article  Google Scholar 

  205. Diakogiannis, F. I. et al. A novel JEANS analysis of the Fornax dwarf using evolutionary algorithms: mass follows light with signs of an off-centre merger. Mon. Not. R. Astron. Soc. 470, 2034–2053 (2017).

    ADS  Article  Google Scholar 

  206. Hayashi, K. & Chiba, M. Probing non-spherical dark halos in the galactic dwarf galaxies. Astrophys. J. 755, (2012).

  207. Łokas, E. L. Dark matter distribution in dwarf spheroidal galaxies. Mon. Not. R. Astron. Soc. 333, 697–708 (2002).

    ADS  Article  Google Scholar 

  208. Richardson, T. & Fairbairn, M. On the dark matter profile in Sculptor: breaking the β degeneracy with Virial shape parameters. Mon. Not. R. Astron. Soc. 441, 1584–1600 (2014).

    ADS  Article  Google Scholar 

  209. Genina, A. et al. To β or not to β: can higher order Jeans analysis break the mass-anisotropy degeneracy in simulated dwarfs? Mon. Not. R. Astron. Soc. 498, 144–163 (2020).

    ADS  Article  Google Scholar 

  210. Lazar, A. & Bullock, J. S. Accurate mass estimates from the proper motions of dispersion-supported galaxies. Mon. Not. R. Astron. Soc. 493, 5825–5837 (2020).

    ADS  Article  Google Scholar 

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Acknowledgements

We are grateful to N. Amorisco, K. Hayashi, M. Kaplinghat, R. Pascale, J. Read, M. Valli and L. Zhu for sharing their data. G.B. acknowledges support from the Agencia Estatal de Investigación del Ministerio de Ciencia en Innovación (AEI-MICIN) and the European Regional Development Fund (ERDF) under grant number AYA2017-89076-P, the AEI under grant number CEX2019-000920-S and the AEI-MICIN under grant number PID2020-118778GB-I00/10.13039/501100011033.

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G.B. and C.N. contributed equally to the design and writing of this Review.

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Battaglia, G., Nipoti, C. Stellar dynamics and dark matter in Local Group dwarf galaxies. Nat Astron 6, 659–672 (2022). https://doi.org/10.1038/s41550-022-01638-7

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