Ghostly galaxies as solitons of Bose-Einstein dark matter

Tom Broadhurst, Ivan De Martino, Hoang Nhan Luu, George F. Smoot, and S.-H. Henry Tye

Phys. Rev. D 101, 083012 – Published 8 April 2020

Abstract

The large dark cores of common dwarf galaxies are unexplained by the standard heavy particle interpretation of dark matter. This puzzle is exacerbated by the discovery of a very large but barely visible, dark matter dominated galaxy Antlia II orbiting the Milky Way, uncovered by tracking star motions with the Ĝaia satellite. Although Antlia II has a low mass, its visible radius is more than double any known dwarf galaxy, with an unprecedentedly low density core. We show that Antlia II favors dark matter as a Bose-Einstein condensate, for which the ground state is a stable soliton with a core radius given by the de Broglie wavelength. The lower the galaxy mass, the larger the de Broglie wavelength, so the least massive galaxies should have the widest soliton cores of lowest density. An ultralight boson of $m_{ψ} \sim 1.1 \times 10^{- 22} eV$ accounts well for the large size and slowly moving stars within Antlia II and agrees with boson mass estimates derived from the denser cores of more massive dwarf galaxies. For this very light boson, Antlia II is close to the lower limiting Jeans scale for galaxy formation permitted by the uncertainty principle, so other examples are expected but none significantly larger in size. This simple explanation for the puzzling dark cores of dwarf galaxies implies dark matter as an ultralight boson, such as an axion generic in string theory.

Received 20 August 2019
Accepted 25 March 2020

DOI:https://doi.org/10.1103/PhysRevD.101.083012

Physics Subject Headings (PhySH)

Dark matter Particle dark matter

Axions Galactic halos Galaxies

Gravitation, Cosmology & AstrophysicsParticles & Fields

Authors & Affiliations

Tom Broadhurst^1,2,3,*, Ivan De Martino ^2,†, Hoang Nhan Luu ^4,‡, George F. Smoot ^4,5,6,7,§, and S.-H. Henry Tye^4,8,¶

¹Department of Theoretical Physics, University of the Basque Country UPV/EHU, E-48080 Bilbao, Spain
²Donostia International Physics Center (DIPC), 20018 Donostia-San Sebastian (Gipuzkoa) Spain
³Ikerbasque, Basque Foundation for Science, E-48011 Bilbao, Spain
⁴Institute for Advanced Study and Department of Physics, Hong Kong University of Science and Technology, Hong Kong
⁵WF Chao Foundation Professor, IAS, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon 999077, Hong Kong
⁶Paris Centre for Cosmological Physics, APC, AstroParticule et Cosmologie, Université Paris Diderot, CNRS/IN2P3, CEA/lrfu, Paris, France
⁷Université Sorbonne Paris Cité, 10, rue Alice Domon et Leonie Duquet, 75205 Paris CEDEX 13, France
⁸Department of Physics, Cornell University, Ithaca, New York 14853, USA

^*tom.j.broadhurst@gmail.com
^†ivan.demartino@dipc.org
^‡hnhanxiii@gmail.com
^§gfsmoot@lbl.gov
^¶iastye@ust.hk

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Vol. 101, Iss. 8 — 15 April 2020

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Images

Figure 1
Here we show how the low mean density reported for Antlia II is readily reproduced by the wide solitonic core density profile of a low mass galaxy of $\sim 10^{9} M_{⊙}$ in the context of $ψ DM$ . For comparison, we compare the reported core mass densities of other well-studied dwarf spheroidal galaxies with the density profiles for $ψ DM$ , for the same boson mass, $m_{ψ} = 10^{- 22} eV$ , demonstrating the consistency with the family of predicted $ψ DM$ profiles, where soliton radius and mass are inversely related.
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Figure 2
The measured velocity dispersion (data points) [22], compared with the predictions of $ψ DM$ mass profiles for a range of light boson masses—see legend where $m_{ψ, 22} \equiv m_{ψ} / 10^{- 22}$ . The central decline in dispersion velocity for the lighter bosons matches well the data and reflects the low central mass density. This contrasts with the relatively more concentrated best fitting NFW profile (dashed curve) where an enhancement is expected, unlike the data.
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Figure 3
The plane of core radius versus $m_{ψ}$ as a function of galaxy mass (colour coded) predicted for $ψ DM$ that are limited to the hatched regions derived from the observations of Antlia II summarized in Table 1 (Appendix pp3). Specifically, we have used the observed core radius to obtain those regions. The Fornax, Sextans dwarf galaxies are included for comparison because their density profiles are understood not to have been modified significantly by tidal stripping. In this case, the hatched regions are derived using the constraints on the core radius and the boson mass listed in Table 1. The limiting Jeans mass is also indicated as a dashed black curve that places an upper limit on the radius of Antlia II at fixed $m_{ψ}$ . Despite the wide range of mass and radius, these three galaxies which span well over an order of magnitude in density are compatible with the same boson mass, $m_{ψ} \sim 10^{- 22} eV$ .
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Figure 4
2D marginalized contours of the model parameters $[m_{ψ}, M_{halo}]$ obtained from our MCMC analysis of Antlia II. The 68%, 95%, and 99% confidence levels are shown with the 1D marginalized likelihood distribution.
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Figure 5
Joint likelihood constraint on the boson mass from our Antlia II analysis (solid blue line), together with previous published work on Fornax (dotted red), Sextans (dashed cyan), Sculptor (dot dashed magenta), Draco (triple dotted dashed green). The final joint probability distribution for the boson mass is shown as the black solid curve.
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