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Probing Dark Matter Self-Interaction with Ultra-Faint Dwarf Galaxies

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Probing Dark Matter Self-Interaction with Ultra-Faint Dwarf Galaxies IPMU20-0085 Probing Dark Matter Self-interaction with Ultra-faint Dwarf Galaxies Kohei Hayashi,1 Masahiro Ibe,2, 3 Shin Kobayashi,2 Yuhei Nakayama,2 and Satoshi Shirai3 1Astronomical Institute, Tohoku University, Sendai, Miyagi, 980-8578, Japan 2ICRR, The University of Tokyo, Kashiwa, Chiba 277-8582, Japan 3Kavli IPMU (WPI), UTIAS, The University of Tokyo, Kashiwa, Chiba 277-8583, Japan (Dated: August 7, 2020) Self-interacting dark matter (SIDM) has gathered growing attention as a solution to the small scale problems of the collisionless cold dark matter (DM). We investigate the SIDM using stellar kinematics of 23 ultra-faint dwarf (UFD) galaxies with the phenomenological SIDM halo model. The UFDs are DM-dominated and have less active star formation history. Accordingly, they are the ideal objects to test the SIDM, as their halo profiles are least affected by the baryonic feedback processes. We found no UFDs favor non-zero self-interaction and some provide stringent constraints within the simple SIDM modeling. Our result challenges the simple modeling of the SIDM, which urges further investigation of the subhalo dynamical evolution of the SIDM. INTRODUCTION galaxies. The UFDs are considered to be more DM- dominated and have less active star formation history. Collisionless cold dark matter (CDM) has successfully Besides, the typical DM velocities of the UFDs, v = (10) km=s, are close to those of the dwarf galaxies which explained the large scale structures of the Universe, such O as the galaxy clusters (e.g. [1{4]). On smaller scales than seem to favor the SIDM. Therefore, the UFDs are ideal the galaxies, however, it has been pointed out that some environments to derive robust constraints on the velocity- dependent cross-section at the typical velocity of v 10 observed features seem to conflict with the CDM predic- ∼ tions (for reviews, see Refs. [5,6]). For example, observa- km/s. tions of the rotation curves of the gas-rich dwarf galaxies favor cored dark matter (DM) halo profiles, while the CDM predicts cuspy profiles [7{10]. MODELS Self-interacting dark matter (SIDM) [11] has gathered growing attention as a solution to those discrepancies (see The stellar motion in a DM dominated system such as also Ref. [5] for a review). The DM scattering thermal- a dwarf spheroidal galaxy (dSph) is governed by the DM izes the inner halo and makes the isothermal cores. The gravitational potential, ΦDM. Assuming that an UFD SIDM provides a consistent fit to the DM halo profile is a spherically symmetric and DM dominated steady- of the dwarf galaxies for a scattering cross sections per state system, the DM potential relates to the moments of unit mass σ=m of (1) cm2/g [12{17][18]. The required the stellar distribution function through the Jeans equa- O cross-section, however, has a tension with the upper lim- tion [36]: 2 its, σ=m . 0:1{1 cm /g, obtained from the studies of 2 2 merging and relaxed galaxy clusters [19{27]. Due to this @ν(r)σ (r) 2βani(r)σ (r) @ΦDM r + r = ν(r) ; (1) tension, more interests are put on the velocity-dependent @r r − @r self-interaction, which evade the cluster constraints. where r denotes the radius from the center of the UFD While the SIDM provides a consistent fit to the dwarf and ν(r) is the intrinsic stellar distribution. The velocity galaxies, however, it is still not conclusive whether the dispersions of the stars are defined by σr; σθ and σφ in a collisionless CDM cannot explain those features. The dis- spherical coordinate system. Here, from spherical sym- crepancies between the observations and the CDM pre- metry, we take σθ = σφ, and the stellar orbital anisotropy arXiv:2008.02529v1 [astro-ph.CO] 6 Aug 2020 dictions are based on the simulations without the bary- is defined by β (r) 1 σ2/σ2. In this work, we onic effects. The baryonic effects could alter the predic- ani θ r adopt a general and realistic≡ − anistropy modeling derived tions and make the collisionless CDM consistent with the by Ref. [37]: observations. For example, bursty star formation might η cause CDM to heat up at the center of the dwarf galax- β0 + β (r=rβ) 1 ies and form the cored DM profile [28{33]. To separate βani(r) = η ; (2) 1 + (r=rβ) those possibilities, it is ideal to investigate the DM self- interaction in the environments with fewer baryons. where the four parameters are the inner anisotropy β0, In this letter, we discuss the constraints on the DM self- the outer anisotropy β , the sharpness of the transition 1 interaction cross-section by comparing the phenomeno- η, and the transition radius rβ. logical modeling of the SIDM halo profile [34, 35] and Solving Eq. (1), we obtain the intrinsic velocity disper- the stellar kinematics of the 23 ultra-faint dwarf (UFD) sion profiles, σr(r). However, such intrinsic dispersions 2 are not directly observed, and only the line-of-sight ve- there is a unique solution for Eqs. (6) and (7). However, locity distribution and the stellar surface density profile there can be multiple solutions for relatively large values are measurable. Therefore, we integrate σr(r) along the of (ρs; rs; σ=m t ). In that case, we choose the solution × age line-of-sight [36], which has the minimum value of r1 among the multiple solutions. This is because we assume that the SIDM halo Z 2 2 2 2 1 R ν(r)σr (r) profile gradually evolves from the NFW profile and the σ (R) = dr 1 βani(r) ; l:o:s: 2 p 2 2 Σ(R) R − r 1 R =r isothermal core, i.e., r1, is smaller in the past. Note that − (3) for parameters satisfying 3 3=2 where R is a projected radius, and Σ(R) is the surface σ 2 0:1M =pc 1 kpc 10 Gyr & 9 cm =g ; (8) density profile derived from the intrinsic stellar density m ρs rs tage ν(r) through an Abel transform. For the stellar density profile, we adopt the Plummer profile [38]. there is no solution consistent with continuity conditions (6) and (7). For such a large cross-section, the description In order to determine the gravitational potential of the with the isothermal core + NFW outskirt is no more SIDM halo, we adopt the halo model in Refs. [34, 35]. In valid, and hence, we discard such a large cross-section in the vicinity of the center of the DM halo, we assume this analysis. that the halo profile can be described by isothermal halo model, In Ref. [35], the 8 classical dSphs are used to investi- gate the DM self-interacting cross-section. There, it is h0(x) h(x) required that the parameters of the NFW profiles fall in h00(x) + 2 = e ; lim h(x) = lim h0(x) = 0: x 0 x 0 the region which encompasses those of the most-massive x − ! ! (4) 15 subhalos from the CDM-only simulation of Ref. [41]. This requirement is motivated to study how the SIDM Here, we define a normalized halo density, h ln(ρ/ρ ) ≡ 0 ameliorates the too-big-to-fail problem of the underlying and a normalized radius x = r=rc (rc = σ0=p4πGρ0), CDM-only simulaiton [42, 43]. In our analysis, on the where ρ0 and σ0 denote the DM density and the velocity other hand, we do not employ this requirement since we dispersion at the center of the halo [39], respectively. On use the UFDs, which are not in conflict with this problem. the other hand, at a larger scale than some radius r > r1, Instead, we require that the NFW parameters satisfy the we assume that the halo is described by the Navarro- concentration-mass relation of the subhalos suggested by Frenk-White (NFW) profile [40], the simulations in Ref. [44] (see also Ref. [45]): ρs " # ρ = : (5) 3 i 2 0 X M200 r=rs(1 + r=rs) c (M ; x ) =c 1 + ai log 200 200 sub 0 10 108h 1M i=1 − At the halo transition radius r = r , we impose continuity 1 [1 + b log (x )] : (9) conditions of the density and the mass, × 10 sub ρ Here, c0 = 19:9, ai = 0:195; 0:089; 0:089 , and h(xc1) s {− g ρ0e = 2 ; iso(r1) = NFW(r1); (6) b = 0:54 which are the best-fit parameters for the xs1(1 + xs1) R R − concentration-mass relation. M200 is the enclosed mass where = M(r)=(4πr3ρ(r)) is the ratio of the mass and within r200 in which the spherical overdensity is 200 R R r 3 times the critical density of the Universe, ρ , that is the density, M(r) = d r0ρ(r0) is the total halo mass crit 0 3 M = 200 (4π=3)r ρ . x r =r ; is a within the radius r, xc1 r1=rc and xs1 r1=rs. As 200 × 200 crit sub ≡ sub 200 host the central isothermal region≡ is formed by≡ the DM self- subhalo distance from the center of a host halo divided by r of the host halo. This requirement is based on interaction, r1 is determined by the self-interaction cross 200 section via, the modeling of Refs. [34, 35] in which the NFW param- eters should be the ones not affected by the DM self- σv σ v pπ interaction. ρ(r1)h i ρ(r1) h i : (7) m ' m ' 4tage In order to obtain xsub, we need to estimate r200 of the Milky Way halo, r .
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