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Cold Dark Matter: Controversies on Small Scales David H Cold dark matter: controversies on small scales David H. Weinberg ∗, James S. Bullock y, Fabio Governato z, Rachel Kuzio de Naray x, and Annika H. G. Peter ∗ y ∗Ohio State University, Columbus, OH, USA,yUniversity of California at Irvine, Irvine, CA, USA,zUniversity of Washington, Seattle, WA, USA, and xGeorgia State University, Atlanta, GA, USA Submitted to Proceedings of the National Academy of Sciences of the United States of America The cold dark matter (CDM) cosmological model has been remark- tensions with observations that have remained thorns in the ably successful in explaining cosmic structure over an enormous span side of the CDM hypothesis. First, simulations show that of redshift, but it has faced persistent challenges from observations CDM collapse leads to cuspy dark matter halos whose cen- that probe the innermost regions of dark matter halos and the prop- tral density profiles rise as r−β with β ∼ 1 − 1:5, while ob- erties of the Milky Way's dwarf galaxy satellites. We review the served galaxy rotation curves favor constant density cores in current observational and theoretical status of these \small scale controversies." Cosmological simulations that incorporate only grav- the dark matter distribution (Flores & Primack 1994; Moore ity and collisionless CDM predict halos with abundant substructure 1994; Navarro, Frenk, & White 1997, hereafter NFW; Moore and central densities that are too high to match constraints from et al. 1999a). Second, simulated halos retain a large amount galaxy dynamics. The solution could lie in baryonic physics: recent of substructure formed by earlier collapses on smaller scales, numerical simulations and analytic models suggest that gravitational predicting hundreds or thousands of subhalos in contrast to potential fluctuations tied to efficient supernova feedback can flat- the ∼ 10 \classical" satellites of the Milky Way (Klypin et ten the central cusps of halos in massive galaxies, and a combination al. 1999; Moore et al. 1999b). These two conflicts are often of feedback and low star-formation efficiency could explain why most referred to as the \cusp-core problem" and the \missing satel- of the dark matter subhalos orbiting the Milky Way do not host vis- lites problem." We will argue below that these two problems ible galaxies. However, it is not clear that this solution can work in the lowest mass galaxies where discrepancies are observed. Alterna- have largely merged into one, and that the most puzzling as- tively, the small-scale conflicts could be evidence of more complex pect of the Milky Way's satellite galaxies is not their number physics in the dark sector itself. For example, elastic scattering but their low central matter densities, which again imply mass from strong dark matter self-interactions can alter predicted halo profiles shallower than the naive CDM prediction. mass profiles, leading to good agreement with observations across In this brief article, based on our panel discussion at the a wide range of galaxy mass. Gravitational lensing and dynamical 2012 Sackler Symposium on Dark Matter, we attempt to sum- perturbations of tidal streams in the stellar halo provide evidence for marize the current state of the CDM controversies at a level an abundant population of low mass subhalos in accord with CDM that will be useful to those not immersed in the field. The key predictions. These observational approaches will get more powerful question is whether the conflicts between N-body predictions over the next few years. and observed galaxy properties can be resolved by \baryonic physics" | gas cooling, star formation, and associated feed- cosmology j dark matter back | or whether they require different properties of the dark matter itself. Introduction The cold dark matter (CDM) hypothesis | that dark matter Cores, Cusps, and Satellites consists of a weakly interacting particle whose velocity disper- sion in the early universe was too small to erase structure on Figure 1 illustrates the \cusp-core" problem. To set the galactic or sub-galactic scales | emerged in the early 1980s scene, the left panel superposes an optical image of the low and quickly became a central element of the theory of cosmic surface brightness galaxy F568-3 onto a numerical simulation structure formation. Influential early papers include Peebles' of a cold dark matter halo. The inner mass profile of a dark (1982) calculation of cosmic microwave background (CMB) matter halo can be probed by rotation curve measurements; for circular motions in a spherical matter distribution, the ro- anisotropies and the matter power spectrum, Blumenthal et p al.'s (1984) investigation of galaxy formation in CDM, and tation speed is simply vc(r) = GM(r)=r, where M(r) is the Davis et al.'s (1985) numerical simulations of galaxy cluster- mass interior to radius r. Points with error bars show the ing. By the mid-1990s, the simplest CDM model with scale- measured rotation curve of F568-3 (from Kuzio de Naray et invariant primordial fluctuations and a critical matter density al. 2008). The dotted curve shows the vc(r) expected from the gravity of the stellar and gas components of the galaxy, which (Ωm = 1) had run afoul of multiple lines of observational arXiv:1306.0913v1 [astro-ph.CO] 4 Jun 2013 evidence, including the shape of the galaxy power spectrum, are subdominant even in the central regions. The solid curve estimates of the mean matter density from galaxy clusters and shows the predicted rotation curve including the contribution galaxy motions, the age of the universe inferred from estimates of an isothermal dark matter halo with a constant density of the Hubble constant, and the amplitude of matter cluster- core, which fits the data well. The dashed curve instead in- ing extrapolated forward from the fluctuations measured in corporates a halo with an NFW profile and a concentration the CMB. Many variants on \canonical" CDM were proposed to address these challenges, and by the turn of the century the combination of supernova evidence for cosmic acceleration Reserved for Publication Footnotes and CMB evidence for a flat universe had selected a clear win- ner: ΛCDM, incorporating cold dark matter, a cosmological constant (Λ), and inflationary initial conditions. Today, the ΛCDM scenario has a wide range of observational successes, from the CMB to the Lyman-α forest to galaxy clustering to weak gravitational lensing, and it is generally considered the \standard model" of cosmology. However, as the resolution of cosmological N-body simu- lations improved in the mid-to-late 1990s, they revealed two www.pnas.org/cgi/doi/10.1073/pnas.0709640104 PNAS Issue Date Volume Issue Number 1{8 Fig. 1. The cusp-core problem. (Left) An optical image of the galaxy F568-3 (small inset, from the Sloan Digital Sky Survey) is superposed on the the dark matter distribution from the \Via Lactea" cosmological simulation of a Milky Way-mass cold dark matter halo (Diemand et al. 2007). In the simulation image, intensity encodes the square of the dark matter density, which is proportional to annihilation rate and highlights low mass substructure. (Right) The measured rotation curve of F568-3 (points) compared to model fits assuming a cored dark matter halo (blue solid curve) or a cuspy dark matter halo with an NFW profile (red dashed curve, concentration c = 9:2, −1 V200 = 110 km s ). The dotted green curve shows the contribution of baryons (stars+gas) to the rotation curve, which is included in both model fits. An NFW halo profile overpredicts the rotation speed in the inner few kpc. Note that the rotation curve is measured over roughly the scale of the 40 kpc inset in the left panel. typical for galaxy mass halos. When normalized to match the ∼ 250 kpc virial radius of the Milky Way halo (illustrated observed rotation at large radii, the NFW halo overpredicts in the right panel), with the smallest having stellar velocity the rotation speed in the inner few kpc, by a factor of two or dispersions ∼ 10 km s−1. Klypin et al. (1999) and Moore et more. al. (1999b) predicted a factor ∼ 5 − 20 more subhalos above Early theoretical discussions of the cusp-core problem de- a corresponding velocity threshold in their simulated Milky voted considerable attention to the predicted central slope of Way halos. Establishing the \correspondence" between satel- the density profiles and to the effects of finite numerical reso- lite stellar dynamics and subhalo properties is a key technical lution and cosmological parameter choices on the simulation point (Stoehr et al. 2002), which we will return to below, but predictions (see Ludlow et al. 2013 for a recent, state-of-the- a prima facie comparison suggests that the predicted satellite art discussion). However, the details of the profile shape are population far exceeds the observed one. not essential to the conflict; the basic problem is that CDM Fortunately (or perhaps unfortunately), the missing satel- predicts too much dark matter in the central few kpc of typical lite problem seems like it could be solved fairly easily by galaxies, and the tension is evident at scales where vc(r) has baryonic physics. In particular, the velocity threshold at risen to ∼ 1=2 of its asymptotic value (see, e.g., Alam, Bul- which subhalo and dwarf satellite counts diverge is close to lock, & Weinberg 2002; Kuzio de Naray & Spekkens 2011). the ∼ 30 km s−1 value at which heating of intergalactic gas On the observational side, the most severe discrepancies be- by the ultraviolet photoionizing background should suppress tween predicted and observed rotation curves arise for fairly gas accretion onto halos, which could plausibly cause these small galaxies, and early discussions focused on whether beam halos to remain dark (Bullock, Kravtsov, & Weinberg 2000; smearing or non-circular motions could artificially suppress Benson et al.
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