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Distribution of Phantom Dark Matter in Dwarf Spheroidals Alistair O

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Distribution of Phantom Dark Matter in Dwarf Spheroidals Alistair O A&A 640, A26 (2020) Astronomy https://doi.org/10.1051/0004-6361/202037634 & c ESO 2020 Astrophysics Distribution of phantom dark matter in dwarf spheroidals Alistair O. Hodson1,2, Antonaldo Diaferio1,2, and Luisa Ostorero1,2 1 Dipartimento di Fisica, Università di Torino, Via P. Giuria 1, 10125 Torino, Italy 2 Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Torino, Via P. Giuria 1, 10125 Torino, Italy e-mail: [email protected],[email protected] Received 31 January 2020 / Accepted 25 May 2020 ABSTRACT We derive the distribution of the phantom dark matter in the eight classical dwarf galaxies surrounding the Milky Way, under the assumption that modified Newtonian dynamics (MOND) is the correct theory of gravity. According to their observed shape, we model the dwarfs as axisymmetric systems, rather than spherical systems, as usually assumed. In addition, as required by the assumption of the MOND framework, we realistically include the external gravitational field of the Milky Way and of the large-scale structure beyond the Local Group. For the dwarfs where the external field dominates over the internal gravitational field, the phantom dark matter has, from the star distribution, an offset of ∼0:1−0:2 kpc, depending on the mass-to-light ratio adopted. This offset is a substantial fraction of the dwarf half-mass radius. For Sculptor and Fornax, where the internal and external gravitational fields are comparable, the phantom dark matter distribution appears disturbed with spikes at the locations where the two fields cancel each other; these features have little connection with the distribution of the stars within the dwarfs. Finally, we find that the external field due to the large-scale structure beyond the Local Group has a very minor effect. The features of the phantom dark matter we find represent a genuine prediction of MOND, and could thus falsify this theory of gravity in the version we adopt here if they are not observationally confirmed. Key words. galaxies: dwarf – galaxies: kinematics and dynamics – gravitation – dark matter 1. Introduction the presence of a non-baryonic dark matter component (see e.g. Clifton et al. 2012 or Joyce et al. 2015 for reviews). There are If we assume that Newtonian dynamics is applicable on scales fewer modified gravity theories that attempt to remove the neces- of galaxies and beyond, there must be an additional gravitational sity of dark matter on galactic scales. We focus here on Modified source, other than baryons, to explain the observed dynamics. Newtonian Dynamics (MOND; Milgrom 1983a; Bekenstein & This source is most commonly attributed to cold dark mat- Milgrom 1984), which is the most investigated of these theories ter (CDM; e.g. Del Popolo 2014). Combining a CDM com- (Famaey & McGaugh 2012). ponent with a cosmological constant Λ is the essence of the In this work we investigate the dynamics of dwarf ΛCDM model, which has been widely adopted (e.g. Ostriker & spheroidals in MOND. Revealing the nature of dwarf spheroidals Steinhardt 1995; Peebles 2015). is particularly relevant because, in the standard framework, their The ΛCDM model is most successful in explaining the dynamical properties depend both on the cosmic properties of observed properties of our Universe on cosmic scales (see for dark matter and on the nature of the dark matter particle itself example Planck Collaboration I 2020 and references therein). (e.g. Broadhurst et al. 2020); more importantly, the current unde- However, in addition to the lack of a direct detection of a dark tection of gamma-ray signals from dark matter particle annihila- matter particle and because the nature of the cosmological con- tion (e.g. Strigari 2018) intriguingly vitalises the exploration of stant is still unknown, there are some issues on the galactic scale, theories of gravity with no dark matter. for example the missing satellite problem, the cusp-core prob- The luminosity of the classical dwarf spheroidals is in the 5 7 lem, or the satellite alignments, that make the acceptance of range ∼10 −10 L (e.g. Irwin & Hatzidimitriou 1995; Mateo the ΛCDM model without reservation somewhat difficult (e.g. 1998) with velocity dispersion approximately in the range Famaey & McGaugh 2013; Bullock & Boylan-Kolchin 2017; ∼6−10 km s−1 (e.g. Walker et al. 2007). In the context of ΛCDM, De Martino et al. 2020). Until these issues can be understood by assuming that the dwarf spheroidals are in equilibrium, the in the context of ΛCDM (e.g. Del Popolo & Le Delliou 2017), Jeans analysis shows that these systems require extended dark investigating alternative scenarios is certainly legitimate. matter halos to explain the velocity dispersion profiles (e.g. One possibility is that dark matter has different properties to Walker et al. 2009). Łokas(2009) also suggested that some CDM: it could be slightly warmer, self-interacting (e.g. Spergel dwarf spheroidals may be explained by a mass-follows-light & Steinhardt 2000), very light and fuzzy (e.g. Hu et al. 2000; model, but they still are dark matter dominated. The main dif- Nhan Luu et al. 2018), or it could be a superfluid (Berezhiani & ference between the studies of Walker et al.(2009) and Łokas Khoury 2015). If a different type of dark matter is not a solution, (2009) is the different method used to identify which stars are the observed dynamics on galactic scale might suggest that our members of the dwarf galaxy. As mentioned in Łokas(2009), her gravitational model is incomplete. Most modified gravity the- method is much stricter than that of Walker et al.(2009). Inde- ories focus on the nature of the cosmic accelerated expansion pendently of the exact dataset assumed to construct the velocity rather than on the dynamics of galaxies, and thus still assume dispersion profile, both studies conclude that dark matter must Article published by EDP Sciences A26, page 1 of 14 A&A 640, A26 (2020) dominate the baryonic matter in these galaxies, although, if the In this work, we investigate these issues in detail. We deter- assumption of dynamical equilibrium is dropped, the estimated mine the phantom dark matter distributions of the eight classical amount of dark matter in dwarf spheroidals might actually be dwarf spheroidal systems by adopting the QUasi-linear MOND smaller than currently thought or even totally absent (Hammer (QUMOND) formulation (Milgrom 2010). We perform calcula- et al. 2018). tions assuming both a spherical and an axisymmetric baryonic Modified Newtonian dynamics assumes that Newtonian matter distribution. We also quantify by how much, if at all, the gravity breaks down in environments where the gravitational phantom dark matter peaks are displaced from the baryons. acceleration is less than ≈10−10 m s−2. Thus, the dynamics of the In Sect.2 we outline the MOND equations used to calcu- dwarf spheroidals are qualitatively understood as they have low late the phantom dark matter density. We briefly discuss some internal accelerations, and the deviation from Newtonian gravity theoretical implications of the MOND paradigm in Sect.3. In should be large. High mass-to-light ratios were indeed predicted Sect.4 we describe the baryonic model used to describe the by Milgrom(1983a) years before they were actually measured dwarf galaxy and the Milky Way. In Sect.5 we determine the (e.g. Mateo et al. 1991). By assuming dynamical equilibrium and phantom dark matter density profiles and investigate the rele- spherical symmetry and by adopting a membership identification vance of external fields, other than the Milky Way, on the far- based on kinematic information, Serra et al.(2010) improved on thest dwarf spheroidals. Finally, we discuss our results in Sect.6 the work of Angus(2008) to show that MOND is successful in and conclude in Sect.7. explaining the velocity dispersion profiles of dwarf spheroidals, except for Carina, where the stellar mass-to-light ratio required 2. Quasi-linear MOND to match the velocity dispersion data is quite high compared to what is expected for the stellar population. Detailed N-body sim- Throughout this work, we will be using the QUMOND formula- ulations in MOND do not seem to alleviate this tension (Angus tion (Milgrom 2010) rather than the original A QUadratic Lag- et al. 2014). rangian (AQUAL) formulation (Bekenstein & Milgrom 1984). For simplicity, spherical symmetry is often assumed for the The AQUAL and QUMOND fomulations are identical for spher- stellar distribution of dwarf spheroidals, even though these sys- ical systems, but can produce different dynamics for systems of tems tend to be slightly flattened, with observed minor-to-major less symmetry. Therefore, our analysis of the dwarf spheroidals is technically testing QUMOND, though the general results and axis ratios .0:7 (Irwin & Hatzidimitriou 1995). In Newtonian conclusions will also apply to AQUAL. gravity, dwarf spheroidals have been studied by Hayashi & The advantage of QUMOND is that the phantom dark matter Chiba(2015) under the assumption that both the stellar and density can be determined analytically, even for triaxial systems, dark matter density components are axisymmetric. This study if the Newtonian gravitational potential is known analytically. performed a best-fit Jeans analysis by fitting derived velocity The models of dwarf spheroidals we present have an analytic dispersion profiles along three axes, the major, minor, and inter- ◦ solution for the Newtonian gravitational potential, making the mediate axes, where the intermediate axis forms an angle of 45 calculation for the phantom dark matter density simple. from the observed major axis. Hayashi & Chiba(2015) find that In QUMOND, the total gravitational potential Φ is related to the profiles are best fit by a dark matter distribution that is also the Newtonian potential ΦN by the equation flattened. However, the flattening predicted for the dark matter is 2 not necessarily the same as that of the stellar component, simi- r Φ = r · ν(y)rΦN ; (1) larly to high-resolution simulations of dwarf galaxies from the FIRE project (González-Samaniego et al.
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