- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Letters

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Dark Matter Velocity Distributions for Direct Detection: Astrophysical Uncertainties Are Smaller Than They Appear

Dylan Folsom1,*, Carlos Blanco2,1,3,†, Mariangela Lisanti1,4, Lina Necib5, Mark Vogelsberger5, and Lars Hernquist6

  • *Contact author: dfolsom@princeton.edu
  • †NASA Einstein Fellow.
PDF

Phys. Rev. Lett. 135, 211004 – Published 20 November, 2025

DOI: https://doi.org/10.1103/wmpq-mw4h

Abstract

The sensitivity of direct detection experiments depends on the phase-space distribution of dark matter near the Sun, which can be modeled theoretically using cosmological hydrodynamical simulations of Milky Way–like galaxies. However, capturing the halo-to-halo variation in the local dark matter speeds—a necessary step for quantifying the astrophysical uncertainties that feed into experimental results—requires a sufficiently large sample of simulated galaxies, which has been a challenge. In this Letter, we quantify this variation with nearly 100 Milky Way–like galaxies from the tng50 simulation, the largest sample to date at this resolution. Moreover, we introduce a novel phase-space scaling procedure that endows every system with a reference frame that accurately reproduces the local standard-of-rest speed of our Galaxy, providing a principled way of extrapolating the simulation results to real-world data. The ensemble of predicted speed distributions is well characterized by the standard halo model, a Maxwell-Boltzmann distribution truncated at the escape speed, though the individual distributions can deviate from it, especially at high speeds. The dark matter–nucleon cross section limits placed by these speed distributions vary by ∼60% about the median. This places the 1σ astrophysical uncertainty at or below the level of the systematic uncertainty of current ton-scale detectors, even down to the energy threshold. The predicted uncertainty remains unchanged when subselecting on those tng50 galaxies with merger histories similar to the Milky Way. Tabulated speed distributions, as well as Maxwell-Boltzmann fits, are provided for use in computing direct detection bounds or projecting sensitivities.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (92)

  1. D. G. Cerdeno and A. M. Green, Direct detection of WIMPs, in Particle Dark Matter Observations, Models and Searches (Cambridge University Press, Cambridge, England, 2010), 10.1017/CBO9780511770739.018.
  2. T. Lin, Sub-GeV dark matter models and direct detection, SciPost Phys. Lect. Notes 43 (2022).10.21468/SciPostPhysLectNotes.43
  3. T.-T. Yu, 2024 TASI lectures: A dark matter primer, in The Frontiers of Particle Theory (2025), 10.48550/arXiv.2506.05234.
  4. C. McCabe, Astrophysical uncertainties of dark matter direct detection experiments, Phys. Rev. D 82, 023530 (2010).
  5. D. Baxter et al., Recommended conventions for reporting results from direct dark matter searches, Eur. Phys. J. C 81, 907 (2021).
  6. J. Aalbers et al., A next-generation liquid xenon observatory for dark matter and neutrino physics, J. Phys. G 50, 013001 (2023).
  7. I. Wasserman, Possibility of detecting heavy neutral fermions in the Galaxy, Phys. Rev. D 33, 2071 (1986).
  8. A. K. Drukier, K. Freese, and D. N. Spergel, Detecting cold dark-matter candidates, Phys. Rev. D 33, 3495 (1986).
  9. K. Freese, J. Frieman, and A. Gould, Signal modulation in cold-dark-matter detection, Phys. Rev. D 37, 3388 (1988).
  10. R. Wojtak, E. L. Łokas, S. Gottlöber, and G. A. Mamon, Radial velocity moments of dark matter haloes, Mon. Not. R. Astron. Soc. 361, L1 (2005).
  11. S. H. Hansen, B. Moore, M. Zemp, and J. Stadel, A universal velocity distribution of relaxed collisionless structures, J. Cosmol. Astropart. Phys. 01 (2006) 014.
  12. M. Vogelsberger, S. D. M. White, A. Helmi, and V. Springel, The fine-grained phase-space structure of cold dark matter haloes, Mon. Not. R. Astron. Soc. 385, 236 (2008).
  13. M. Vogelsberger, A. Helmi, V. Springel, S. D. M. White, J. Wang, C. S. Frenk, A. Jenkins, A. Ludlow, and J. F. Navarro, Phase-space structure in the local dark matter distribution and its signature in direct detection experiments, Mon. Not. R. Astron. Soc. 395, 797 (2009).
  14. M. Kuhlen, N. Weiner, J. Diemand, P. Madau, B. Moore, D. Potter, J. Stadel, and M. Zemp, Dark matter direct detection with non-Maxwellian velocity structure, J. Cosmol. Astropart. Phys. 02 (2010) 030.
  15. A. M. Green, Dependence of direct detection signals on the WIMP velocity distribution, J. Cosmol. Astropart. Phys. 10 (2010) 034.
  16. M. Vogelsberger and J. Zavala, Direct detection of self-interacting dark matter, Mon. Not. R. Astron. Soc. 430, 1722 (2013).
  17. N. Bozorgnia and G. Bertone, Implications of hydrodynamical simulations for the interpretation of direct dark matter searches, Int. J. Mod. Phys. A 32, 1730016 (2017).
  18. F. S. Ling, E. Nezri, E. Athanassoula, and R. Teyssier, Dark matter direct detection signals inferred from a cosmological N-body simulation with baryons, J. Cosmol. Astropart. Phys. 02 (2010) 012.
  19. P. B. Tissera, S. D. M. White, S. Pedrosa, and C. Scannapieco, Dark matter response to galaxy formation, Mon. Not. R. Astron. Soc. 406, 922 (2010).
  20. A. Pillepich, M. Kuhlen, J. Guedes, and P. Madau, The distribution of dark matter in the Milky Way’s disk, Astrophys. J. 784, 161 (2014).
  21. I. Butsky, A. V. Macciò, A. A. Dutton, L. Wang, A. Obreja, G. S. Stinson, C. Penzo, X. Kang, B. W. Keller, and J. Wadsley, NIHAO project II: Halo shape, phase-space density and velocity distribution of dark matter in galaxy formation simulations, Mon. Not. R. Astron. Soc. 462, 663 (2016).
  22. C. Kelso, C. Savage, M. Valluri, K. Freese, G. S. Stinson, and J. Bailin, The impact of baryons on the direct detection of dark matter, J. Cosmol. Astropart. Phys. 08 (2016) 071.
  23. J. D. Sloane, M. R. Buckley, A. M. Brooks, and F. Governato, Assessing astrophysical uncertainties in direct detection with Galaxy simulations, Astrophys. J. 831, 93 (2016).
  24. N. Bozorgnia, F. Calore, M. Schaller, M. Lovell, G. Bertone, C. S. Frenk, R. A. Crain, J. F. Navarro, J. Schaye, and T. Theuns, Simulated Milky Way analogues: Implications for dark matter direct searches, J. Cosmol. Astropart. Phys. 05 (2016) 024.
  25. R. Poole-McKenzie, A. S. Font, B. Boxer, I. G. McCarthy, S. Burdin, S. G. Stafford, and S. T. Brown, Informing dark matter direct detection limits with the ARTEMIS simulations, J. Cosmol. Astropart. Phys. 11 (2020) 016.
  26. N. Bozorgnia, A. Fattahi, C. S. Frenk, A. Cheek, D. G. Cerdeño, F. A. Gómez, R. J. J. Grand, and F. Marinacci, The dark matter component of the Gaia radially anisotropic substructure, J. Cosmol. Astropart. Phys. 07 (2020) 036.
  27. A. Hryczuk, E. Karukes, L. Roszkowski, and M. Talia, Impact of uncertainties in the halo velocity profile on direct detection of sub-GeV dark matter, J. High Energy Phys. 07 (2020) 081.
  28. A. Nuñez-Castiñeyra, E. Nezri, P. Mollitor, J. Devriendt, and R. Teyssier, Cosmological simulations of the same spiral galaxy: Connecting the dark matter distribution of the host halo with the subgrid baryonic physics, J. Cosmol. Astropart. Phys. 05 (2023) 012.
  29. G. E. Lawrence, A. R. Duffy, C. A. Blake, and P. F. Hopkins, Gusts in the headwind: Uncertainties in direct dark matter detection, Mon. Not. R. Astron. Soc. 524, 2606 (2023).
  30. P. G. Staudt, J. S. Bullock, M. Boylan-Kolchin, D. Kirkby, A. Wetzel, and X. Ou, Sliding into DM: Determining the local dark matter density and speed distribution using only the local circular speed of the galaxy, J. Cosmol. Astropart. Phys. 08 (2024) 022.
  31. F. Hammer, M. Puech, L. Chemin, H. Flores, and M. D. Lehnert, The Milky Way, an Exceptionally quiet galaxy: Implications for the formation of spiral galaxies, Astrophys. J. 662, 322 (2007).
  32. T. C. Licquia, J. A. Newman, and M. A. Bershady, Does the Milky Way obey spiral galaxy scaling relations?, Astrophys. J. 833, 220 (2016).
  33. N. Boardman, G. Zasowski, J. A. Newman, B. Andrews, C. Fielder, M. Bershady, J. Brinkmann, N. Drory, D. Krishnarao, R. R. Lane, T. Mackereth, K. Masters, and G. S. Stringfellow, Are the Milky Way and Andromeda unusual? A comparison with Milky Way and Andromeda analogues, Mon. Not. R. Astron. Soc. 498, 4943 (2020).
  34. T. Tsukui, E. Wisnioski, J. Bland-Hawthorn, and K. Freeman, The emergence of galactic thin and thick discs across cosmic history, Mon. Not. R. Astron. Soc. 540, 3493 (2025).
  35. D. Nelson, A. Pillepich, V. Springel, R. Pakmor, R. Weinberger, S. Genel, P. Torrey, M. Vogelsberger, F. Marinacci, and L. Hernquist, First results from the tng50 simulation: Galactic outflows driven by supernovae and black hole feedback, Mon. Not. R. Astron. Soc. 490, 3234 (2019).
  36. A. Pillepich, D. Nelson, V. Springel, R. Pakmor, P. Torrey, R. Weinberger, M. Vogelsberger, F. Marinacci, S. Genel, A. van der Wel, and L. Hernquist, First results from the tng50 simulation: The evolution of stellar and gaseous discs across cosmic time, Mon. Not. R. Astron. Soc. 490, 3196 (2019).
  37. A. Helmi, C. Babusiaux, H. H. Koppelman, D. Massari, J. Veljanoski, and A. G. A. Brown, The merger that led to the formation of the Milky Way’s inner stellar halo and thick disk, Nature (London) 563, 85 (2018).
  38. V. Belokurov, D. Erkal, N. W. Evans, S. E. Koposov, and A. J. Deason, Co-formation of the disc and the stellar halo, Mon. Not. R. Astron. Soc. 478, 611 (2018).
  39. A. J. Deason and V. Belokurov, Galactic archaeology with Gaia, New Astron. Rev. 99, 101706 (2024).
  40. E. Aprile et al. (XENON Collaboration), Dark matter search results from a one ton-year exposure of XENON1T, Phys. Rev. Lett. 121, 111302 (2018).
  41. E. Aprile et al. (XENON Collaboration), First dark matter search with nuclear recoils from the XENONnT experiment, Phys. Rev. Lett. 131, 041003 (2023).
  42. J. Aalbers et al. (LZ Collaboration), Dark matter search results from 4.2  tonne−years of exposure of the LUX-ZEPLIN (LZ) experiment, Phys. Rev. Lett. 135, 011802 (2025).
  43. V. Springel, S. D. M. White, G. Tormen, and G. Kauffmann, Populating a cluster of galaxies—I. Results at z=0, Mon. Not. R. Astron. Soc. 328, 726 (2001).
  44. K. Dolag, S. Borgani, G. Murante, and V. Springel, Substructures in hydrodynamical cluster simulations, Mon. Not. R. Astron. Soc. 399, 497 (2009).
  45. D. Folsom, M. Lisanti, L. Necib, D. Horta, M. Vogelsberger, and L. Hernquist, Cosmological simulations of stellar halos with Gaia Sausage–Enceladus analogs: Two sausages, one bun?, Astrophys. J. 983, 119 (2025).
  46. D. Sotillo-Ramos, A. Pillepich, M. Donnari, D. Nelson, L. Eisert, V. Rodriguez-Gomez, G. Joshi, M. Vogelsberger, and L. Hernquist, The merger and assembly histories of Milky Way- and M31-like galaxies with tng50: Disc survival through mergers, Mon. Not. R. Astron. Soc. 516, 5404 (2022).
  47. A. Pillepich, D. Sotillo-Ramos, R. Ramesh, D. Nelson, C. Engler, V. Rodriguez-Gomez, M. Fournier, M. Donnari, V. Springel, and L. Hernquist, Milky Way and Andromeda analogues from the tng50 simulation, Mon. Not. R. Astron. Soc. 535, 1721 (2024).
  48. D. A. Gadotti, Structural properties of pseudo-bulges, classical bulges and elliptical galaxies: A sloan digital sky survey perspective, Mon. Not. R. Astron. Soc. 393, 1531 (2009).
  49. J. Bovy and H.-W. Rix, A direct dynamical measurement of the Milky Way’s disk surface density profile, disk scale length, and dark matter profile at 4  kpc<R<9  kpc, Astrophys. J. 779, 115 (2013).
  50. J. Lian, G. Zasowski, B. Chen, J. Imig, T. Wang, N. Boardman, and X. Liu, The broken-exponential radial structure and larger size of the Milky Way galaxy, Nat. Astron. 8, 1302 (2024).
  51. M. Jurić et al., The Milky Way tomography with SDSS. I. Stellar number density distribution, Astrophys. J. 673, 864 (2008).
  52. H.-W. Rix and J. Bovy, The Milky Way’s stellar disk. Mapping and modeling the Galactic disk, Astron. Astrophys. Rev. 21, 61 (2013).
  53. J. Bland-Hawthorn and O. Gerhard, The galaxy in context: Structural, kinematic, and integrated properties, Annu. Rev. Astron. Astrophys. 54, 529 (2016).
  54. S. Varma, M. Huertas-Company, A. Pillepich, D. Nelson, V. Rodriguez-Gomez, A. Dekel, S. M. Faber, P. Iglesias-Navarro, D. C. Koo, and J. Primack, The building up of observed stellar scaling relations of massive galaxies and the connection to black hole growth in the tng50 simulation, Mon. Not. R. Astron. Soc. 509, 2654 (2022).
  55. Y. Rosas-Guevara, S. Bonoli, M. Dotti, D. Izquierdo-Villalba, A. Lupi, T. Zana, M. Bonetti, D. Nelson, V. Springel, L. Hernquist, and M. Vogelsberger, The evolution of the barred galaxy population in the tng50 simulation, Mon. Not. R. Astron. Soc. 512, 5339 (2022).
  56. M. J. Reid and A. Brunthaler, The proper motion of Sagittarius A*. II. The mass of Sagittarius A*, Astrophys. J. 616, 872 (2004).
  57. R. Abuter et al. (GRAVITY Collaboration), Improved GRAVITY astrometric accuracy from modeling optical aberrations, Astron. Astrophys. 647, A59 (2021).
  58. K. Abd El Dayem et al. (GRAVITY Collaboration), Improving constraints on the extended mass distribution in the galactic center with stellar orbits, Astron. Astrophys. 692, A242 (2024).
  59. J. Binney and S. Tremaine, Jeans equations for axisymmetric systems in Galactic Dynamics, edited by D. N. Spergel (Princeton University Press, Princeton, NJ, 2008), Chap. 4.8.2.
  60. J. Bovy, The asymmetric drift and the Sun’s motion, in Dynamics and Astrophysics of Galaxies (to be published), Chap. 10.3.1.
  61. R. Schönrich, J. Binney, and W. Dehnen, Local kinematics and the local standard of rest, Mon. Not. R. Astron. Soc. 403, 1829 (2010).
  62. D. Kawata, J. Bovy, N. Matsunaga, and J. Baba, Galactic rotation from Cepheids with Gaia DR2 and effects of non-axisymmetry, Mon. Not. R. Astron. Soc. 482, 40 (2019).
  63. S. Põder, M. Benito, J. Pata, R. Kipper, H. Ramler, G. Hütsi, I. Kolka, and G. F. Thomas, A Bayesian estimation of the Milky Way’s circular velocity curve using Gaia DR3, Astron. Astrophys. 676, A134 (2023).
  64. X. Ou, L. Necib, A. Wetzel, A. Frebel, J. Bailin, and M. Oeur, Decoding the galactic twirl: The downfall of Milky Way-mass galaxies rotation curves in the fire simulations, arXiv:2503.05877.
  65. A. R. Wetzel, P. F. Hopkins, J.-h. Kim, C.-A. Faucher-Giguère, D. Kereš, and E. Quataert, Reconciling dwarf galaxies with ΛCDM cosmology: Simulating a realistic population of satellites around a Milky Way-mass galaxy, Astrophys. J. 827, L23 (2016).
  66. A. Wetzel et al., Public data release of the fire-2 cosmological zoom-in simulations of galaxy formation, Astrophys. J. Suppl. Ser. 265, 44 (2023).
  67. J. Schaye et al., The EAGLE project: Simulating the evolution and assembly of galaxies and their environments, Mon. Not. R. Astron. Soc. 446, 521 (2015).
  68. R. A. Crain, J. Schaye, R. G. Bower, M. Furlong, M. Schaller, T. Theuns, C. Dalla Vecchia, C. S. Frenk, I. G. McCarthy, J. C. Helly, A. Jenkins, Y. M. Rosas-Guevara, S. D. M. White, and J. W. Trayford, The EAGLE simulations of galaxy formation: Calibration of subgrid physics and model variations, Mon. Not. R. Astron. Soc. 450, 1937 (2015).
  69. T. Sawala, C. S. Frenk, A. Fattahi, J. F. Navarro, R. G. Bower, R. A. Crain, C. Dalla Vecchia, M. Furlong, John. C. Helly, A. Jenkins, K. A. Oman, M. Schaller, J. Schaye, T. Theuns, J. Trayford, and S. D. M. White, The APOSTLE simulations: Solutions to the local group’s cosmic puzzles, Mon. Not. R. Astron. Soc. 457, 1931 (2016).
  70. A. Fattahi, J. F. Navarro, T. Sawala, C. S. Frenk, K. A. Oman, R. A. Crain, M. Furlong, M. Schaller, J. Schaye, T. Theuns, and A. Jenkins, The APOSTLE project: Local group kinematic mass constraints and simulation candidate selection, Mon. Not. R. Astron. Soc. 457, 844 (2016).
  71. P. F. Hopkins et al., fire-2 simulations: Physics versus numerics in galaxy formation, Mon. Not. R. Astron. Soc. 480, 800 (2018).
  72. J. Aalbers, B. Pelssers, J. R. Angevaare, and K. D. Morå, jelleaalbers/wimprates: V0.5.0, Zenodo (2023), 10.5281/zenodo.7636982.
  73. C. McCabe, The Earth’s velocity for direct detection experiments, J. Cosmol. Astropart. Phys. 02 (2014) 027.
  74. C. A. J. O’Hare, N. W. Evans, C. McCabe, G. Myeong, and V. Belokurov, Velocity substructure from Gaia and direct searches for dark matter, Phys. Rev. D 101, 023006 (2020).
  75. E. Aprile et al. (XENON Collaboration), An approximate likelihood for nuclear recoil searches with XENON1T data, Eur. Phys. J. C 82, 989 (2022).
  76. P. F. de Salas and A. Widmark, Dark matter local density determination: Recent observations and future prospects, Rep. Prog. Phys. 84, 104901 (2021).
  77. S. K. Lee, M. Lisanti, A. H. G. Peter, and B. R. Safdi, Effect of gravitational focusing on annual modulation in dark-matter direct-detection experiments, Phys. Rev. Lett. 112, 011301 (2014).
  78. A. J. Deason, V. Belokurov, S. E. Koposov, and L. Lancaster, Apocenter pile-up: Origin of the stellar halo density break, Astrophys. J. 862, L1 (2018).
  79. G. C. Myeong, N. W. Evans, V. Belokurov, J. L. Sanders, and S. E. Koposov, The Milky Way halo in action space, Astrophys. J. 856, L26 (2018).
  80. L. Lancaster, S. E. Koposov, V. Belokurov, N. W. Evans, and A. J. Deason, The halo’s ancient metal-rich progenitor revealed with BHB stars, Mon. Not. R. Astron. Soc. 486, 378 (2019).
  81. L. Necib, M. Lisanti, and V. Belokurov, Inferred evidence for dark matter kinematic substructure with SDSS-Gaia, Astrophys. J. 874, 3 (2019).
  82. A. Fattahi, V. Belokurov, A. J. Deason, C. S. Frenk, F. A. Gómez, R. J. J. Grand, F. Marinacci, R. Pakmor, and V. Springel, The origin of galactic metal-rich stellar halo components with highly eccentric orbits, Mon. Not. R. Astron. Soc. 484, 4471 (2019).
  83. G. Iorio and V. Belokurov, Chemo-kinematics of the Gaia RR Lyrae: The halo and the disc, Mon. Not. R. Astron. Soc. 502, 5686 (2021).
  84. G. Besla, A. H. G. Peter, and N. Garavito-Camargo, The highest-speed local dark matter particles come from the Large Magellanic Cloud, J. Cosmol. Astropart. Phys. 11 (2019) 013.
  85. K. Donaldson, M. S. Petersen, and J. Peñarrubia, Effects on the local dark matter distribution due to the Large Magellanic Cloud, Mon. Not. R. Astron. Soc. 513, 46 (2022).
  86. A. Smith-Orlik, N. Ronaghi, N. Bozorgnia, M. Cautun, A. Fattahi, G. Besla, C. S. Frenk, N. Garavito-Camargo, F. A. Gómez, R. J. J. Grand, F. Marinacci, and A. H. G. Peter, The impact of the Large Magellanic Cloud on dark matter direct detection signals, J. Cosmol. Astropart. Phys. 10 (2023) 070.
  87. R. J. J. Grand, F. A. Gómez, F. Marinacci, R. Pakmor, V. Springel, D. J. R. Campbell, C. S. Frenk, A. Jenkins, and S. D. M. White, The Auriga project: The properties and formation mechanisms of disc galaxies across cosmic time, Mon. Not. R. Astron. Soc. 467, 179 (2017).
  88. N. W. Evans, C. A. J. O’Hare, and C. McCabe, Refinement of the standard halo model for dark matter searches in light of the Gaia Sausage, Phys. Rev. D 99, 023012 (2019).
  89. H. Zhu, R. Guo, J. Shen, J. Liu, C. Liu, X.-X. Xue, L. Zhang, and S. Mao, Deciphering the kinematic substructure of local dark matter with LAMOST K giants, Astrophys. J. 974, 167 (2024).
  90. D. Folsom, folsomde/dm_velocity_distributions: V1.1, Zenodo, 2025, 10.5281/zenodo.17086920.
  91. https://tng-project.org.
  92. S. Garrison-Kimmel, A. Wetzel, P. F. Hopkins, R. Sanderson, K. El-Badry, A. Graus, T. K. Chan, R. Feldmann, M. Boylan-Kolchin, C. C. Hayward, J. S. Bullock, A. Fitts, J. Samuel, C. Wheeler, D. Kereš, and C.-A. Faucher-Giguère, Star formation histories of dwarf galaxies in the fire simulations: Dependence on mass and local group environment, Mon. Not. R. Astron. Soc. 489, 4574 (2019).

Outline

Information

Phys. Rev. Lett. 135, 211004– Published 20 November, 2025
  • Received 28 May 2025
  • Accepted 27 October 2025
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation