Cold Dark Matter: Controversies on Small Scales David H

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Cold dark matter: controversies on small scales David H. Weinberg ∗, James S. Bullock †, Fabio Governato ‡, Rachel Kuzio de Naray §, and Annika H. G. Peter ∗ † ∗Ohio State University, Columbus, OH, USA,†University of California at Irvine, Irvine, CA, USA,‡University of Washington, Seattle, WA, USA, and §Georgia 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 | 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 simulations 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. 2002; Somerville 2002). Alternatively, super- the measured vc(r) at small radii. However, despite uncer- novae and stellar winds from the first generation of stars could tainties in individual cases, improvements in the observations, drive remaining gas out of the shallow potential wells of these sample sizes, and modeling have led to a clear overall picture: low mass halos. Complicating the situation, searches using a majority of galaxy rotation curves are better fit with cored the Sloan Digital Sky Survey have discovered another ∼ 15 3 5 dark matter profiles than with NFW-like dark matter profiles, “ultra-faint” satellites with luminosities of only 10 − 10 L and some well observed galaxies cannot be fit with NFW-like (e.g., Willman et al. 2005; Belokurov et al. 2007). The high- profiles, even when one allows halo concentrations at the low latitude SDSS imaging covered only ∼ 20% of the sky, and end of the theoretically predicted distribution and accounts for many of the newly discovered dwarfs are so faint that they uncertainties in modeling the baryon component (e.g., Kuzio could only be seen to 50-100 kpc (Koposov et al. 2008; Walsh de Naray et al. 2008). Resolving the cusp-core problem there- et al. 2009), so extrapolating to the full volume within the fore requires modifying the halo profiles of typical spiral galax- Milky Way virial radius suggests a population of several hun- ies away from the profiles that N-body simulations predict for dred faint dwarf satellites (Tollerud et al. 2008). Estimates collisionless CDM. from stellar dynamics imply that the mass of dark matter in 7 Figure 2 illustrates the “missing satellite” problem. The the central 0.3 kpc of the host subhalos is M0.3 ≈ 10 M 3 7 left panel shows the projected dark matter density distribu- across an enormous range of luminosities, L ∼ 10 − 10 L 12 tion of a 10 M CDM halo formed in a cosmological N-body (encompassing the “classical” dwarf spheroidals as well as the simulation. Because CDM preserves primordial fluctuations SDSS dwarfs), which suggests that the mapping between halo down to very small scales, halos today are filled with enormous mass and luminosity becomes highly stochastic near this mass numbers of subhalos that collapse at early times and preserve threshold (Strigari et al. 2008). The luminosity function of their identities after falling into larger systems. Prior to 2000, the faint and ultra-faint dwarfs can be explained by semi- there were only nine dwarf satellite galaxies known within the analytic models invoking photoionization and stellar feedback (e.g., Koposov et al. 2009; Macciòet al. 2009), though the effi-

2 www.pnas.org/cgi/doi/10.1073/pnas.0709640104 Footline Author 12 Fig. 2. The missing satellite and “too big to fail” problems. (Left) Projected dark matter distribution (600 kpc on a side) of a simulated, 10 M CDM halo (Garrison-Kimmel, Boylan-Kolchin, & Bullock, in preparation). As in Figure 1, the numerous small subhalos far exceed the number of known Milky Way satellites. Circles mark the nine most massive subhalos. (Right) Spatial distribution of the “classical” satellites of the Milky Way. The central densities of the subhalos in the left panel are too high to host the dwarf satellites in the right panel, predicting stellar velocity dispersions higher than observed. The diameter of the outer sphere in the right panel is 300 kpc; relative to the simulation prediction (and to the Andromeda galaxy) the Milky Way’s satellite system is unusually centrally concentrated (Yniguez et al. 2013). ciency of converting baryons to stars remains surprisingly low Solutions in Baryonic Physics? (∼ 0.1% − 1%) well above the photoionization threshold, and When the cusp-core problem was first identified, the conven- it is unclear which if any of the ultra-faint dwarfs are “fossils” tional lore was that including baryonic physics would only from before the epoch of reionization (Bovill & Ricotti 2009). exacerbate the problem by adiabatically contracting the dark Despite the gaps in understanding, it seems reasonable for now matter density distribution (Blumenthal et al. 1986; Flores to regard the relation between low mass subhalos and ultra- & Primack 1994). Navarro, Eke, & Frenk (1996) proposed faint dwarfs as a puzzle of galaxy formation physics rather a scenario, which seemed extreme at the time, for producing than a contradiction of CDM. a cored dark matter distribution: dissipative baryons draw Instead, attention has focused recently on the most lumi- in the dark matter orbits adiabatically by slowly deepening nous satellites. Circles in Figure 2 mark the nine most mas- the gravitational potential, then release them suddenly when sive subhalos in the simulation, which one would expect to the supernova feedback of a vigorous starburst blows out a host galaxies like the Milky Way’s “classical” dwarf satellites. substantial fraction of the baryonic material, leaving the dark However, the mass in the central regions of these subhalos matter halo less concentrated than the one that would have exceeds the mass inferred from stellar dynamics of observed formed in the absence of baryons. Since then, hydrodynamic dwarfs, by a factor ∼ 5 (Boylan-Kolchin et al. 2011, 2012; simulations have greatly improved in numerical resolution and Springel et al. 2008; Parry et al. 2012). While it is pos- in the sophistication with which they model star formation sible in principle that these massive subhalos are dark and and supernova feedback. With the combination of a high gas that the observed dwarfs reside in less massive hosts, this density threshold for star formation and efficient feedback, outcome seems physically unlikely; in the spirit of the times, simulations successfully reproduce the observed stellar and Boylan-Kolchin et al. (2011) titled this conflict “too big to cold gas fractions of field galaxies. The ejection of low angular fail.” The degree of discrepancy varies with the particular re- momentum gas by feedback plays a critical role in suppressing alization of halo substructure and with the mass of the main the formation of stellar bulges in dwarf galaxies (Governato et halo, but even for a halo mass at the low end of estimates al. 2010), another long-standing problem in early simulations for the Milky Way the discrepancy appears too large to be a of galaxy formation. The episodic gas outflows also produce statistical fluke, and a similar conflict is found in the satellite rapid fluctuations of the gravitational potential, in contrast to system of the Andromeda galaxy (Tollerud et al. 2012). While the steady growth assumed in adiabatic contraction models. “missing satellites” in low mass subhalos may be explained by Figure 3, based on Governato et al. (2012), illustrates the baryonic effects, the “too big to fail” problem arises in more impact of this episodic feedback on the dark matter density massive systems whose gravitational potential is dominated profile. In the left panel, the upper dot-dashed curve shows by dark matter. In its present form, therefore, the satellite the final halo profile of an N-body simulation run with grav- puzzle looks much like the cusp-core problem: numerical sim- ity and dark matter only. Other curves show the evolution of ulations of CDM structure formation predict too much mass the dark matter density profile in a hydrodynamic simulation in the central regions of halos and subhalos. Indeed, Walker with star formation and feedback, from the same initial con- & Peñarrubia(2011), Amorisco et al. (2013), and others have ditions. Over time, the central dark matter density drops, reported evidence that the Milky Way satellites Fornax and and the cuspy profile is transformed to one with a nearly Sculptor have cored density profiles. constant density core (lower solid curve). Pontzen & Gov- ernato (2012) present an analytic model that accurately de- scribes this transformation (and its dependence on simulation assumptions); essentially, the rapid fluctuations in the central potential pump energy into the dark matter particle orbits, so

Footline Author PNAS Issue Date Volume Issue Number 3 Fig. 3. Baryonic effects on CDM halo profiles in cosmological simulations, from Governato et al. (2012). (Left) The upper, dot-dash curve shows the cuspy dark matter density profile resulting from from a collisionless N-body simulation. Other curves show the evolution of the dark matter profile in a simulation from the same initial conditions that includes gas dynamics, star formation, and efficient feedback. By z = 0 (solid curve) the perturbations from the fluctuating baryonic potential have flattened the inner profile to a nearly constant density core. (Right) Logarithmic slope of the dark matter profile α measured at 0.5 kpc, as a function of galaxy stellar mass. Crosses show results from multiple hydrodynamic simulations. Squares show measurements from rotation curves of observed galaxies. The black curve shows the expectation for pure dark matter 7 simulations, computed from NFW profiles with the appropriate concentration. For M∗ > 10 M , baryonic effects reduce the halo profile slopes to agree with observations. that they no longer penetrate to the center of the halo. The “too big to fail.” Ram pressure in the Galactic halo could Governato et al. simulations use smoothed particle hydrody- then remove the gas from the dark subhalos. namics, and the same flattening of dark matter cusps is found These arguments point to isolated, low-mass galaxies with 6 7 in adaptive mesh refinement simulations that have similarly M∗ ∼ 10 − 10 M as ideal laboratories for testing the pre- episodic supernova feedback (Teyssier et al. 2012). dictions of CDM-based models. Dwarfs that are far separated The right panel of Figure 3 compares the density profile from a giant galaxy must rely on their own (modest) super- slopes of simulated galaxies to observational estimates from nova reservoirs for energy injection. Ferrero et al. (2012) 6 7 21cm measurements of nearby galaxies (Walter et al. 2008) have studied a population of ∼ 10 − 10 M field galaxies and to predictions for an NFW dark matter halo. The re- and argued that the central density problem persists even for duced central density slopes agree well with observations for relatively isolated dwarfs of this size. If this result holds up 7 galaxies with stellar mass M∗ > 10 M . Strong gas outflows in further investigations, it will become a particularly serious are observed in a wide variety of galaxies, including the likely challenge to CDM. 8 9 progenitors of M∗ ∼ 10 − 10 M dwarfs observed at z ∼ 2 (van der Wel et al. 2011). However, for galaxies with M∗ 7 below ∼ 10 M , analytic models suggest that with so few stars there is not enough energy in supernovae alone to cre- Solutions in Dark Matter Physics? ate dark matter cores of ∼ 1 kpc (Peñarrubiaet al. 2012). Instead of complex baryonic effects, the cusp-core and satel- More generally, Garrison-Kimmel et al. (2013) used idealized, lite problems could indicate a failure of the CDM hypothesis high resolution simulations to model potential fluctuations of itself. One potential solution is to make dark matter “warm,” the type expected in episodic feedback models and concluded so that its free-streaming velocities in the early universe are that the energy required for solving the “too big to fail” prob- large enough to erase primordial fluctuations on sub-galactic lem exceeds that available from supernovae in galaxies with scales. For a simple thermal relic, the ballpark particle mass 7 stellar masses below ∼ 10 M . The low mass galaxies in Fig- is m ≈ 1 keV, though details of the particle physics can al- ure 3 (from Governato et al. 2012) are consistent with this ter the relation between mass and the free-streaming scale, expectation, with density profile slopes that are negligibly af- which is the important quantity for determining the fluctua- fected by feedback at the 0.5 kpc scale. On the other hand, tion spectrum. Alternatively, the small scale fluctuations can high resolution simulations of luminous satellites in the halo be suppressed by an unusual feature in the inflationary poten- of Milky Way-like hosts do show reduced central dark matter tial (Kamionkowski & Liddle 2000). While collisionless col- densities, from a combination of early feedback effects with lapse of warm dark matter (WDM) still leads to a cuspy halo ram pressure stripping and tidal heating by the host halo and profile, the central concentration is lower than that of CDM disk, processes that can extract energy from the host galaxy’s halos when the mass scale is close to the spectral cutoff (e.g., gravitational potential (Arraki et al. 2012; Zolotov et al. 2012; Avila-Reese et al. 2001), thus allowing a better fit to observa- Brooks et al. 2013). Alternatively, Kuhlen et al. (2013) argue tions of galaxy rotation curves and dwarf satellite dynamics. that molecular cooling physics may make star formation ef- The mass function of halos and subhalos drops at low masses 10 ficiency highly stochastic at a halo mass as high as 10 M , because there are no small scale perturbations to produce col- so that even the Milky Way’s most massive subhalos are not lapsed objects, so the subhalo mass function can be brought into agreement with dwarf satellite counts. There have been numerous numerical simulations of structure formation with

4 www.pnas.org/cgi/doi/10.1073/pnas.0709640104 Footline Author 13 Mvir =4.2 10 M × ¯ 6 10 Collisionless CDM

105 m ρ

/ 104 ρ Self interacting DM − 103

102 101 102 r[kpc/h]

Fig. 4. Eﬀect of self-interacting dark matter (SIDM) on halo structure, from simulations by Rocha et al. (2013). The left panel shows a Milky Way mass CDM halo, and the middle panel shows the same halo from an SIDM simulation with cross-section of 1 cm2 g−1. The structure and substructure are similar, but the SIDM halo is rounder and less dense in the center. The right panel compares the density proﬁles of a CDM and SIDM halo, showing the core produced by elastic scattering. This halo has 13 M = 4.2 × 10 M , but similar behavior is found at other halo masses.

WDM; recent examples include Polisensky & Ricotti (2011), 2000), but recent numerical studies show that these concerns Anderhalden et al. (2012), Lovell et al. (2012), Macciòet al. are not borne out in fully cosmological simulations. Instead, (2012), Schneider et al. (2012), and Angulo et al. (2013). simulations show that there is a viable window of mass and Warm dark matter is a “just-so” solution to CDM’s prob- cross-section where self-interacting dark matter (SIDM) can lems, requiring a particle mass (or free-streaming velocity) produce cored dark matter profiles and remain consistent with that is tuned to the particular scale of dwarf galaxy halos. observational constraints (Rocha et al. 2013; Peter et al. However, the more serious challenge to WDM is observational, 2013). for two reasons. First, WDM does too good a job in elim- Figure 4, based on Rocha et al. (2013), compares the struc- inating power on small scales; for a thermal relic of mass ture and density profiles of halos formed from the same initial m = 2 keV, there are too few subhalos in the Milky Way to conditions with collisionless CDM and SIDM. Elastic scatter- host the known satellite galaxies (Polisensky & Ricotti 2011). ing in the central regions, where an average particle expe- It also appears in conflict with observations of strong-lens sys- riences a few collisions per Hubble time, flattens the density tems, which show evidence for a significant subhalo fraction cusp and reduces triaxiality. The scattering mechanism would 8 as well as the existence of small (10 M ) subhalos (Dalal & operate across a wide range of halo masses, allowing SIDM to Kochanek 2002; Dobler & Keeton 2006; Vegetti et al. 2010a,b, address both the rotation curves of Milky Way-like galaxies 2012; Fadely & Keeton 2011, 2012). Second, suppressing pri- and the central densities of dwarf satellites. Because they are mordial fluctuations on small scales alters the predicted struc- more weakly bound, SIDM subhalos are more easily subject ture of Lyman-α forest absorption towards quasars at high to tidal disruption than CDM subhalos. However, the sup- redshift, where these scales are still in the quasi-linear regime pression of the low-mass subhalo count is not significant for (Narayanan et al. 2000). Recent studies of the Lyman-α forest allowed cross sections except in the innermost region of the set a lower limit on the dark matter particle mass of several host halo (Vogelsberger et al. 2012; Rocha et al 2013). Thus, keV, high enough that the dark matter is effectively “cold” SIDM can solve the cusp-core problem while leaving enough from the point of view of the cusp-core problem (Seljak et subhalos to host Milky Way satellites, unlike WDM. al. 2006; Viel et al. 2008; but see Abazajian 2006 for a coun- The prospects for SIDM appear much more hopeful than terclaim of a lower minimum particle mass). Even setting for WDM (though for a summary of pro-WDM views see Bier- these problems aside, it appears that WDM on its own does mann et al. 2013). Velocity-independent cross sections in the not fix the shape of rotation curves across the full range of range ∼ 0.1 − 0.5 cm2 g−1 create cores that are approximately galaxy masses where conflict with CDM is observed (Kuzio the right size for Milky Way dwarf galaxies, spiral galaxies, de Naray et al. 2010). While some uncertainties in the nu- and galaxy clusters (Newman et al. 2013a,b; Rocha et al. merical simulations and observational data remain, it appears 2013) while leaving halos triaxial enough to match observa- that WDM cannot solve the cusp-core and missing satellite tions (Peter et al. 2013). Cross sections in this range are also problems while remaining consistent with Lyman-α forest and consistent with observations of merging galaxy clusters (Clowe substructure observations. et al. 2006; Randall et al. 2008; Dawson et al. 2012). More- An alternative idea, made popular by Spergel & Stein- over, particle model builders have recently focused attention hardt (2000), is that cold dark matter has weak interactions on new classes of “hidden sector” models that generically pro- with baryons but strong self-interactions. The required scat- duce SIDM particle candidates, although in general the elas- tering cross-section is roughly (m/g)−1 cm2 where m is the tic scattering cross section has a strong velocity dependence particle mass; note that 1 cm2 g−1 ≈ 1 barn GeV−1 is approx- (Ackerman et al. 2009; Buckley 2010; Feng et al. 2010; Tulin imately a nuclear-scale cross section. In this case, elastic scat- et al. 2013a,b). For these models, strong self-interactions may tering in the dense central regions of halos is frequent enough only be present in a narrow range of halo mass, leaving halos to redistribute energy and angular momentum among par- on other scales effectively collisionless. Observationally, the ticles, creating an isothermal, round core of approximately goal is to either rule out or find evidence for SIDM cross sec- constant density (Burkert 2000). Some early studies suggested tions σ > 0.1 cm2 g−1, as for smaller cross-sections the halo that this idea was ruled out by gravitational lensing (Miralda- phenomenology is likely to be indistinguishable from CDM. Escudé2002) or by catastrophic gravitational core collapse There are alternative dark matter physics mechanisms found in a simulation of an isolated halo (Kochanek & White that could reduce the central densities of halos, including par-

Footline Author PNAS Issue Date Volume Issue Number 5 4 ticle decay and particle-antiparticle annihilation (Kaplinghat ∼ 2, 000, 000 above 10 M ) are orbiting within the virial ra- et al. 2000; Peter et al. 2010) or the recently suggested possi- dius of the Milky Way and similar galaxies. Flux anomalies bility of escape from flavor-mixed quantum states (Medvedev in gravitational lenses have already provided important evi- 2013). dence for subhalos that collectively contain a few percent of the mass within their parent halos, a level roughly consistent with CDM predictions and an order of magnitude above that Conclusions expected from luminous satellites alone (Dalal & Kochanek Are the tensions between CDM predictions and observations 2002; Metcalf & Amara 2012). These anomalies do not di- on the scales of galactic cores and satellite halos telling us rectly probe the mass spectrum of the subhalos, though at 8 something about the fundamental properties of dark matter, masses M ∼ 10 M they produce detectable astrometric or are they telling us something interesting about the com- deviations in addition to flux anomalies (e.g., Vegetti et al. plexities of galaxy formation? After two decades of debate, 2012). Current constraints are derived from a small sample of the current state of the field is an unsatisfying stalemate (or, lensed radio-loud quasars, as optical flux anomalies could be perhaps, a draw by repetition). However, there are several produced by stellar microlensing. Statistics should improve directions for future progress that could resolve the question. dramatically after the launch of the James Webb Space Tele- Developments of the last several years have focused the scope, which can resolve lenses at mid-IR wavelengths that “small scale controversies” down to one fairly specific issue, are not affected by stellar microlensing because the quasar the influence of baryons on the dark matter halo profile in dust emission regions are too large. An alternative route is systems where the baryons are today greatly sub-dominant. to study cold tidal streams in the Milky Way, which would A variety of studies have shown that baryonic effects can be perturbed by the multitude of passing subhalos. Carl- plausibly account for cores in halos occupied by high surface- berg & Grillmair (2013, and references therein) argue that brightness galaxies and can plausibly suppress star formation observed tidal streams already show evidence of these pertur- in very low mass halos. Improved simulations may show that bations, and a combination of better numerical simulations, baryonic effects can soften cusps even in galaxies that are now more streams, and more detailed density and dynamical mea- dark matter dominated, or they may show that the energetics surements could yield definitive evidence for or against CDM’s arguments summarized above do indeed point to a genuine predicted subhalo population. Further theoretical work is problem for CDM that cannot be resolved by supernova feed- needed to determine whether lensing or stream perturbations back or galactic tides. Improved simulations of models with can distinguish CDM from SIDM. interacting dark matter may show that they can readily solve As emphasized throughout the Sackler Symposium, there the small scale problems, or they may show that cross-section are great hopes that underground detection experiments, γ- parameters chosen to match one set of observations ultimately ray observations, or collider experiments will identify the dark fail when confronted with another set. SIDM models might matter particle within the next decade. Such detections might also be ruled out if they predict halo shapes that can be ex- definitively demonstrate whether dark matter is cold and cluded by observations of stellar or gas dynamics. Improved weakly interacting, or they might unmask the particle while measurements of stellar velocities in satellite galaxies, and dis- yielding ambiguous answers to this question. In the mean- covery of new satellites from imaging surveys such as Pan- time, astronomers will continue their decades-long practice of STARRS and the Dark Energy Survey, may better delineate studying the dark sector by observing the visible. the satellite problem itself. These developments will affect the credibility of baryonic ACKNOWLEDGMENTS. We gratefully acknowledge our many collaborators whose and dark matter solutions to the CDM controversies, but they work we have summarized here. We thank Chris Kochanek for helpful comments on may not yield a definitive conclusion. More satisfactory would lensing constraints. Our work on these topics is supported by NASA and the NSF, be a direct test of the CDM prediction that vast numbers of including grants NNX10AJ95G, NNX 08AG84G, AST-1009505, AST-1009973, and 6 AST-0607819. low mass subhalos (∼ 20, 000 with masses > 10 M , and

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