Is there tension between observed small scale structure and cold dark matter?

Louis Strigari Stanford University Cosmic Frontier 2013 March 8, 2013 Predictions of the standard Cold Dark Matter model

26 3 1 1. Density profiles rise towards the centersannv 3of 10galaxies cm s (1) h i' ⇥ ⇢ Universal for all halo masses ⇢(r)= s (2) (r/r )(1 + r/r )2 Navarro-Frenk-White (NFW) model s s

2. Abundance of ‘sub-structure’ (sub-halos) in galaxies

Sub-halos comprise few percent of total halo mass Most of mass contained in highest- mass sub-halos Subhalo Mass Function Subhalo

Mass[Solar mass]

1 Problems with the standard Cold Dark Matter model

1. Density of dark matter halos: Faint, dark matter-dominated galaxies appear less dense that predicted in simulations

General arguments: Kleyna et al. MNRAS 2003, 2004;Goerdt et al. APJ2006; de Blok et al. AJ 2008 Dwarf spheroidals: Gilmore et al. APJ 2007; Walker & Penarrubia et al. APJ 2011; Angello & Evans APJ 2012

2. ‘Missing satellites problem’: Simulations have more dark matter subhalos than there are observed dwarf satellite galaxies

Earilest papers: Kauffmann et al. 1993; Klypin et al. 1999; Moore et al. 1999 Solutions to the issues in Cold Dark Matter

1. The theory is wrong i) Not enough physics in theory/simulations (Talks yesterday by M. Boylan-Kolchin, M. Kuhlen) [Wadepuhl & Springel MNRAS 2011; Parry et al. MRNAS 2011; Pontzen & Governato MRNAS 2012; Brooks et al. ApJ 2012] ii) Cosmology/dark matter is wrong (Talk yesterday by A. Peter)

2. The data is wrong i) Kinematics of dwarf spheroidals (dSphs) are more difficult than assumed ii) Counting satellites a) Many more faint satellites around the Milky Way b) Milky Way is an oddball [Liu et al. 2010, Tollerud et al. 2011, Guo et al. 2011, Strigari & Wechsler ApJ 2012]

Dark matter solutions

1. Self-interacting dark matter Scattering cross section much larger than standard WIMP cross section

2. Warm dark matter Dark matter has larger velocity in the early Universe than standard WIMPs Self-interacting dark matter

✦ Canonical WIMP model Interaction rate in Milky Way 1013 times greater than age of Universe!

✦ Bounds from halo shapes [Miralda-escude 2002] and galaxy cluster collisions [Markevitch et al. 2004, Randall et al. 2008, Rocha et al. 2013, Peter et al. 2013]

✦ Upper bound 20 orders of magnitude greater than corresponding WIMP cross section Self-interacting dark6 M. Vogelsberger matter et al. simulations

✦ Halos, subhalos less dense than cold dark matter

✦ Halos, subhalos more spherical than cold dark matter

Vogelsberger et al 2012

Figure 3. Density projections of the Aq-A halo for the different DM models of Table 1 (RefP0-3). The projection cube has a side length of 270 kpc. Clearly, the disfavoured RefP1 model with a large constant cross section produces a very different density distribution with a spherical core in the centre, contrary to the elliptical and cuspy CDM halo. Also, substructures are less dense and more spherical in this simulation. The vdSIDM models RefP2 and RefP3 on the other hand can hardly be distinguished from the CDM case (RefP0).

for the different models. whereas the right panel shows the mean works at full strength irrespective of (sub)halo mass. Although this 1 free path =(⇢ T /m ) as a function of radius for the SIDM case is ruled out by current astrophysical constraints (see Section h i models. The dotted, dashed and solid lines show different levels 2.1), it serves as a reference for the effect of a large scattering cross of resolution, characterised by a particle mass mp and a Plummer section at the scales of MW-like haloes in a full cosmological sim- equivalent gravitational softening length ✏: Aq-A-5 (mp =3.143 ulation. On the contrary, RefP2 and RefP3 result in a main halo 6 5 ⇥ 10 M , ✏ =684.9 pc), Aq-A-4 (mp =3.929 10 M , ✏ = whose density profile follows very closely the one from the CDM 4 ⇥ 342.5 pc) and Aq-A-3 (mp =4.911 10 M , ✏ =120.5 pc). The prediction of RefP0 down to 1 kpc from the centre. At smaller radii, ⇥ runs show good convergence for radii larger than 2.8✏ indicated by where the typical particle velocities are smaller, self-interaction is the vertical lines. large enough to produce a core. The mean free path radial profile In the figure we see that RefP1 develops a large core reach- clearly illustrates the radius where collisions are more important ing the solar circle ( 7 kpc). This is because the cross section for the different SIDM models, which is around the core radius. It ⇠ has no velocity dependence in this case and the particle scattering also highlights the difference between the RefP2 and RefP3 mod-

© 2012 RAS, MNRAS 000, 1–14 138 A. Boyarsky et al. / Dark Universe 1 (2012) 136–154 ments) (see e.g. [10] and references therein). Searches for the annihilation products of these particles (indirect detection) are performed by PAMELA, Fermi and other high-energy cosmic missions (see e.g. reviews [11,12]). No convincing signals has been observed so far in either ‘‘direct’’ or ‘‘indirect’’ searches. Additionally, no hints of new physics at electroweak had turned up at the LHC or in any other experiments. This makes alternative approaches to the DM problem ever more viable.

2. Sterile neutrino dark matter

Another viable generalization of the neutrino DM idea is given by sterile neutrino dark matter sce- nario [13–20], see [14,15] for review. Sterile neutrino is a right-chiral counterpart of the left-chiral neutrinos of the SM (called ‘active ’ neutrinos in this context). Adding these particles to the SM Lagrangian makes neutrinos massive and is therefore their existence provides a simple and natural explanation of the observed neutrino flavor oscillations. These particles are singlet leptons because they carry no charges with respect to the Standard Model gauge groups (hence the name), and there- fore along with their Yukawa interaction with the active neutrinos (=‘Dirac mass’) they can have a Majorana mass term (see e.g. [16] for details). They interact with the matter via creation of virtual active neutrino (quadratic mixing) and in this way they effectively participate in weak reactions (see e.g. Fig. 1(a)). At energies much below the masses of the W and Z-bosons, their interaction can be described by the analog of the Fermi theory with the Fermi coupling constant GF suppressed by the active-sterile neutrino mixing angleh – the ratio of their Dirac to Majorana masses (Fig. 1(b)) : m 2 h2 Dirac; a 1 a ¼ M ð Þ sterile N Majorana X

(this mixing can be different for different flavors a). It was observed long ago that such particles can be produced in the Early Universe through mixing with active neutrinos [13] and have a correct relic density for any mass [13,17-27]. The existence of sterile neutrinos is motivated by the observational phenomena beyond the Standard Model (unlike WIMPs that are motivated first of all by the theoretical considerations of stability of the Higgs mass against quantum corrections that could require a fine-tuning of parameters of the model). Namely, sterile neutrinos would provide a simple and natural explanations of the neutrino flavor oscil- lations [20-23]. However, a single sterile neutrino would be unable to explain the two observed mass splittings between Standard Model neutrinos – at least two sterile neutrinos are needed for that. Moreover, should sterile neutrino play the role of DM, its mixing with active neutrinos would be too small to contribute significantly to the flavor oscillations – its life time should be very large and, therefore, interaction strength should be too feeble [24,25]. Therefore, in order to explain dark matter and neutrino mass (one for each SM flavor), the minimal model should contain 3 right-handed Warm dark matter

✦ Particle falls out of equilibrium with large velocities `Sterile’ neutrinos with mass ~ 1-10 keV [Dodelson & Widrow 1994; Shi & Fuller 1999; Abazajian et al. 2012]

✦ Particles not absolutely stable Lifetimes longer than age of Universe DM

✦ Photons from decays be detectable in modern and forthcoming x-ray detectors

Fig. 1. Example of interactions of sterile neutrino: decay N mem m (panel (a)) and its effective Fermi-like description (panel ! a a (b)) and loop-mediated decay N ? c + ma (panel (c)). Warm dark matter simulations

Cold dark matter WarmSatelliteSatellite dark Galaxies Galaxies matter in WDM in WDM5 5

FigureFigure 3. Images 3. Images of the of CDM the CDM (left) (left) and WDM and WDM (right) (right) level 2level haloes 2 haloes at z =0.Intensityindicatestheline-of-sightprojectedsquar at z =0.Intensityindicatestheline-of-sightprojectedsquarLovell et al 2011e e of theof density, the density, and hueand the hue projected the projected density-weighted density-weighted velocity velo dispersion,city dispersion, ranging ranging from blue from (low blue velocity (low velocity dispersio dispersion) to yellown) to yellow (high (high velocityvelocity dispersion). dispersion). Each Each box is box 1.5 is Mpc 1.5 Mpc on a onside. a side.Note Note the sharp the s causticsharp caustics visible visible at large at radii large in radii the in WDM the WDM image, image, severalofwhich severalofwhich are alsoare also present, present, although although less well less defined, well defined, in the in CDM the CDM case. case.

20.0 20.0 associateassociate final satellite final satellite luminosity luminosity with the with maximum the maximum pro- pro- genitor mass for each surviving subhalo. This is essentially 10.0 genitor mass for each surviving subhalo. This is essentially 10.0 the mass of the object as it falls into the main halo. The 7.0 the mass of the object as it falls into the main halo. The 7.0 smallest subhalo in each of our samples has an infall mass smallest9 subhalo in each of our samples has9 an infall mass 5.0 of 3.2 × 10 M! 9in the WDM case, and 6.0 × 10 M! in9 the 5.0 of 3.2 × 10 M! in the WDM case, and 6.0 × 10 M! in the CDM case. 3.0 CDM case. 3.0 The LMC, SMC and the Sagittarius dwarf are all

[kpc] 2.0 The LMC, SMC and the Sagittarius dwarf are all

[kpc] 2.0 more luminous than the 9 dwarf spheroidals considered by max

r more luminous than the 9 dwarf spheroidals considered by max

r Boylan-Kolchin et al. (2011) and by us. As noted above, the Boylan-Kolchin et al. (2011) and by us. As noted above, the 1.0 Milky Way is exceptional in hosting galaxies as bright as 1.0 Milky Way is exceptional in hosting galaxies as bright as the Magellanic Clouds, while Sagittarius is in the process of Cold the Magellanic Clouds, while Sagittarius is in the process of 0.5 WarmCold being disrupted so its current mass is difficult to estimate. 0.5 Cold (TopWarm 12) being disrupted so its current mass is difficult to estimate. Cold (Top 12) Boylan-Kolchin et al. hypothesize that these three galaxies Warm (Top 12) Boylan-Kolchin et al. hypothesize−1 that these three galaxies Warm (Top 12) all have values of Vmax > 60kms at infall−1 and exclude sim- all have values of Vmax > 60kms at infall and exclude sim- 10 20 30 40 50 60 70 80 ulated subhaloes that have these values at infall as well as 10 20 −1 30 40 50 60 70 80 ulated subhaloes−1 that have these values at infall as well as Vmax [kms ] Vmax > 40kms at− the1 present day from their analysis. In V [kms−1] max whatV follows,max > 40kms we retainat all the subhaloes present but,day from where their appropri- analysis. In Figure 4. The correlation between subhalo maximum circular ate, wewhat highlight follows, those we retainthat might all subhaloes host large but, satellites where aki appropri-n Figure 4. The correlation between subhalo maximum circular velocity and the radius at which this maximum occurs. Sub- to theate, Magellanic we highlight Clouds those and that Sagittarius. might host large satellites akin haloesvelocity lying and within the 300kpc radius of at the which main this halo maximum centre occurs. are in- Sub- to the Magellanic Clouds and Sagittarius. haloes lying within 300kpc of the main halo centre are in- The circular velocity curves at z =0forthe12sub- cluded. The 12 CDM and WDM subhaloes with the most mas- The circular velocity curves at z =0forthe12sub- cluded. The 12 CDM and WDM subhaloes with the most mas- haloes which had the most massive progenitors at infall are sive progenitors are shown as blue and red filled circles respec- haloes which had the most massive progenitors at infall are tively;sive the progenitors remaining are subhaloes shown are as blue shown and as red empty filled circles. circlesThe respec- shown in Fig. 5 for both WDM and CDM. The circular shown in Fig. 5 for both WDM and CDM. The circular shadedtively; area the represents remaining the subhaloes 2σ confidence are region shown for as possible empty circles. hosts The velocities within the half-light radius of the 9 satellites mea- of theshaded 9 bright area represents Milky Way the dwarf 2σ confidence spheroidals region determined for possible by hosts suredvelocities by Wolf et within al. (2010) the half-light are also plotted radius asof thesymbols. 9 satellites Leo- mea- Boylan-Kolchinof the 9 bright et al. (2011).Milky Way dwarf spheroidals determined by II hassured the smallest by Wolf half-lightet al. (2010) radius, are also∼ 200pc. plotted To as compare symbols. Leo- Boylan-Kolchin et al. (2011). the satelliteII has the data smallest with the half-light simulations radius, we must∼ 200pc. first To check compare the convergencethe satellite of data the simulated with the simulations subhalo masses we must within first at check the same radii in the simulated subhaloes. To provide a fair least thisthe convergence radius. We find of the that simulated the median subhalo of the ratio masses of thewithin at comparisonthe same we radii must in the choose simulated the simulated subhaloes. subhaloes To provide that a fair massleast within this 200pc radius. in the We Aq-W2 find that and the Aq-W3 median simulations of the ratio is of the are mostcomparison likely to we correspond must choose to those the that simulated host the subhaloes 9 bright that W 2/Wmass3 ∼ within1.22, i.e., 200pc the in mass the Aq-W2within 200pc and Aq-W3 in the simulationsAq-W2 is dwarfare spheroidals most likely in to the correspond Milky Way. to those As stripping that host of the sub- 9 bright simulationW 2/W has3 ∼ converged1.22, i.e., to the better mass than within∼ 22%. 200pc in the Aq-W2 haloesdwarf preferentially spheroidals removes in the Milky dark matter Way. As relative stripping to the of sub- Assimulation can be inferred has converged from Fig. to better 5, the than WDM∼ 22%. subhaloes morehaloes centrally preferentially concentrated removes stellar component, dark matter we relative choose t too the have similarAs central can be masses inferred to from the observed Fig. 5, the satellite WDM galax subhaloes- more centrally concentrated stellar component, we choose to have similar central masses to the observed satellite galax- !c 2011 RAS, MNRAS 000, ??–8 !c 2011 RAS, MNRAS 000, ??–8 Theory and observations

✦ CDM, and non-CDM models now in better position to provide testable predictions

✦ Put aside theoretical aspects. Consider observational systematics

✦ Masses of dwarf spheroidals (dSphs) ✦ Count satellites Masses of dwarf spheroidals Dark matter in satellite galaxies (dwarf spheroidals)

✦ Velocity dispersion ~ 5-10 km/s

✦ Uncertainties ~ 1-2 km/s

✦Dark Common matter densities inover all observed satellites scales [Strigari et al. 2008]

Strigari et al, Nature 2008 Velocity dispersion [km/s]

Figure 1: The integrated mass of the Milky Way dwarf satellites, in units of solar masses, within Radius [parsecs] their inner 0.3 kpc as a function of their total luminosity, inunitsofsolarluminosities.Thecircle (red) points on the left refer to the newly-discovered SDSS satellites, while the square (blue) points refer to the classical dwarf satellites discovered pre-SDSS. The error bars reflect the points where the likelihood function falls off to 60.6% of its peak value.

4 Densities of dwarf spheroidals Density Velocity dispersion

15 15 fnx fnx fnx fnx 10 10

5 5 0 0 ✦ 15 15 Parameter space is very leo leo leo leo 10 10 degenerate. CDM-based ] ] -1 -1 5 NFW models fit all dwarf 5 0 0 spheroidals 15 15 car car car car 10 10

5 5

✦ Future measurements of 0 0 15 15 scu scu scu scu photometry and velocities will 10 10 Velocity dispersion [km s Velocity dispersion [km s

test these solutions Surface Density [Norm. arbitrary] 5 Surface Density [Norm. arbitrary] 5 0 0 15 15 sex sex sex sex 10 10 Strigari, Frenk, White 5 MNRAS 2010 5 0 0 0.1 0.1 1.0 1.0 10.0 10.0 100.0 100.0 0.0 0.0 0.5 0.5 1.0 1.0 1.5 1.5 RadiusRadius [arcmin] [arcmin] R [kpc]R [kpc]

FigureFigure 4 Photometric 4 Photometric profiles profiles (left ()left and) and velocity velocity dispersion dispersion profiles profiles (right (right) for) five for five classical classical dSphs, dSphs, usingusing LCDM-based LCDM-based models models for the for the dark dark matter matter potentials. potentials. From From Strigari Strigari et al. et [152]. al. [152].

SchwarszchildSchwarszchild mass mass estimates estimates have have now now been been published published for three for three dSphs, dSphs, Fornax, Fornax, Sculptor, Sculptor, and and Draco.Draco. Using Using a cored a cored model model for thefor the stellar stellar light light profile, profile, Jardel Jardel and and Gebhardt Gebhardt [154] [154] find find a mass a mass withinwithin the the half-light half-light radius radius that that is consistent is consistent with with those those deduced deduced from from moment moment and and distribution distribution function-basedfunction-based methods. methods. Breddels Breddels et al. et [155] al. [155] determine determine that that the the mass mass of Sculptor of Sculptor within within 1 kpc 1 kpc is is 108 10M8 ,M which, which is again is again in agreement in agreement with with the the above above methods. methods. Jardel Jardel et al. et [156] al. [156] determine determine a a ⇠ ⇠ lowerlower bound bound to the to the mass mass of Draco of Draco of a of few a few times times 108 10M8 Mwithinwithin a physical a physical radius radius of about of about 500 500 pc pc wherewhere kinematics kinematics of stars of stars are aremeasured. measured.

4.3.4.3. Ultra-faint Ultra-faint satellites satellites MeasuringMeasuring the the velocity velocity dispersion, dispersion, and and thus thus the the mass, mass, of ultra-faint of ultra-faint satellites satellites poses poses di↵erent di↵erent setssets of challenges of challenges in comparison in comparison to measuring to measuring the the velocity velocity dispersions dispersions of classical of classical satellites. satellites. First, First, by theirby their very very nature, nature, the theconstituent constituent stars stars are arefainter, fainter, with with typical typical target target stars stars having having a magnitude a magnitude of rof=r 20= 2021.21. For For a realistic a realistic exposure exposure level, level, the the Keck/DEIMOS Keck/DEIMOS spectrograph spectrograph provides provides a signal- a signal- to-noiseto-noise on a on star a star of this of this magnitude magnitude of approximately of approximately 15 [157]. 15 [157]. Second, Second, the the measured measured uncertainties uncertainties derivedderived from from the the stellar stellar spectra spectra are areapproximately approximately 2 23 km/s,3 km/s, which, which, because because it is it within is within about about a a factorfactor of two of two of the of the intrinsic intrinsic velocity velocity dispersions dispersions of the of the systems, systems, complicates complicates the the extraction extraction of the of the intrinsicintrinsic velocity velocity dispersion dispersion that that arises arises from from the the distribution distribution function function (Low (Low velocity velocity dispersions dispersions at at thisthis level level have have been been measured measured in globular in globular clusters clusters [158]). [158]). Third, Third, the themeasured measured line-of-sight line-of-sight velocities velocities maymay contain contain a component a component that that is due is due to the to the motion motion of the of the star star around around a binary a binary companion. companion. Early Early studiesstudies of classical of classical dSphs dSphs indicated indicated that that this this binary binary contamination contamination was was1 12 km/s,2 km/s, so it so is it a is a ⇠ ⇠ smallsmall systematic systematic to classical to classical satellite satellite mass mass measurements measurements [159]. [159]. However, However, as measurements as measurements of low of low velocityvelocity dispersion dispersion globular globular clusters clusters clearly clearly indicate indicate that that binaries binaries do significantly do significantly contaminate contaminate the the velocityvelocity dispersion dispersion of bound of bound stellar stellar systems systems [160], [160], detailed detailed understanding understanding of this of this e↵ect e↵ect is required is required in ultra-faintin ultra-faint satellites. satellites. 38 38 Multiple populationsKinematicstatusandmasscontentoftheSculptordSph in Sculptor dwarf spheroidal 3

Metal Rich (MR) and Metal Poor (MP) population (Battaglia et al 2008) KinematicstatusandmasscontentoftheSculptordSph 3

FIG.2.—NumbersurfacedensityprofileofRGBstarsinSclfrom FIG.3.—l.o.s.velocitydispersionprofile(squareswitherrorbars), from FIG.2.—NumbersurfacedensityprofileofRGBstarsinSclfromESO/WFI photometry (squares with error-bars) overlaid to the best-fitting rotation-subtractedFIG.3.—l.o.s.velocitydispersionprofile(squareswitherror GSR velocities, for the MR (a), MP (b) and all (c) RGB bars), from ESO/WFI photometrytwo (squares component with model (soliderror-bars) line) given overlaid by the sum to of athe Sersic best-fitting (dotted line) starsrotation-subtracted in Scl. The lines show the GSR best-fitting velocities, pseudo-isother for themal MR sphere (a), (solid) MP (b) and all (c) RGB and Plummer (dashed line) profiles. These are obtained from the rescaled and NFW model (dashed) in the hypothesis of β = βOM.Panelc)shows two component modelprofiles (solid that line) best fit, given respectively, by the the sum distribution of a Sersic of RHB (dottedand BHB line) stars thatstars the best-fitting in Scl. Thepseudo-isothermal lines show sphere the with best-fittingβ = βOM (solid) pseudo-isother and the mal sphere (solid) and Plummer (dashed(diamonds line) profiles. and asterisks These with error-bars, are obtained respectively) from in Scl. the The rescaled Galactic NFWand model NFW with modelβ =const (dashed) (dashed) are in statistically the hypothesis indistinguishable. of β = βOM.Panelc)shows profiles that best fit,stellar respectively, contamination the has distribution been subtracted from of RHB each point.and BHB stars that the best-fitting pseudo-isothermal sphere with β = βOM (solid) and the (diamonds and asterisks with error-bars, respectively) in Scl. The Galactic NFW model with β =const (dashed) are statistically indistinguishable. tions8 is (Binney & Mamon 1982): stellar contaminationdefining has been an subtracted elliptical annulus from each (distance point. bin), is: ∞ 2 ρ∗(r)σ r 2 v −v 2 2 2 r,∗ R − ( i ) σ (R)= (1 β )dr (2) σ2 σ2 los 2 2( + i ) 8 # 2 2 NMW N e tions is (BinneyΣ∗(R) R &√ Mamonr R 1982):− r P (vi v, σ)= fMW + . (1) − defining an elliptical annulus| (distanceNT bin),NT is:2π(σ2 + σ2) where R is the projected radius (on the sky), r is the 3D i ∞ 2 2 ! radius. The l.o.s. velocity2 dispersion dependsρ∗(r) on:σr, the∗ r mass R NMW and N are the expected number(vi of−v MW)2 and Scl RGB 2 − surfaceσ densitylos(RΣ)=∗(R) and mass density ρ∗(r) of the tracer,(1 β )dr (2) stars in a distance bin (NT = NMW +2(Nσ).2+fσMW2) is the velocity 2 2 2 N N e i which in our case areΣ the∗( MRR) and#R the MP√r RGBR stars; the− r distributionMW of MW stars, which we assume does not change 2 2 P (vi v, σ)= fMW + . (1) tracer velocity anisotropy β,definedasβ =1 σ−θ /σr ,which | acrossN theT face of Scl, andN isT derived2π from(σ2 the+ Besanc¸onσ2) model we allow to be different for MR and MP stars;− the radial ve- (Robin et al. 2003) selecting stars along the l.o.s.i and with where R is the projected radius (on the sky), r is the 3D locity dispersion σ ∗ for the specific component, which de- magnitudes and colors similar! to the Scl RGB stars. We as- radius. Ther, l.o.s. velocity dispersion depends on: the mass NMW and N are the expected number of MW and Scl RGB pends on the total mass distribution (for the general solution sume that the Scl velocity distribution is a Gaussian whose seesurface Battaglia density et al. 2005).Σ∗(R) and mass density ρ∗(r) of the tracer, stars in a distancepeak bin velocity (NT =v andN dispersionMW +Nσ).(thefMW quantitiesis the we velocity want to de- We consider two DM mass models: a pseudo-isothermal rive) are allowed to vary with projected radius. We derive the which in our case are the MR and the MP RGB stars; the distribution of MW stars, which we assume does not change sphere, typically cored, (see Battaglia et al. 2005), and an 2 2 normalization factors, NMW/NT and N/NT directly from the tracer velocity anisotropy β,definedasβ =1 σ /σ ,which across the face of Scl, and is derived from the Besanc¸on model NFW profile, cusped (Navarro, Frenk & White 1996). Since θ r observed RGB surface density profile and relative foreground thewe contribution allow to of be the different stars to the for total MR mass and of the MP sys- stars;− the radial ve- (Robin et al. 2003)density. selecting To estimate stars the fraction along of theMW interlopers l.o.s. and in the with MR temlocity is negligible dispersion for reasonableσr,∗ for stellar the M/L specific ratios, component,we do which de- magnitudes and colorsand MP sub-samples similar to we the simply Scl count RGB how stars. many Westars withas- not consider it further. As β is unknown we explore two velocities

• Walker & Penarrubia (ApJ 2011) state that multiple populations are inconsistent with an NFW profile AVirialCoreinSculptor 3

• Agnello & Evans (ApJ 2012) use virial theorem to Metal poor rule out NFW profile

[Scale density] Metal rich 10 Log Log10 [Scale radius (kpc)] Figure 1. Left: Virial stripes for the two stellar populations in Sculptor in a cusped NFW potential, including the self-gravity ofthestellar populations (Υ! = 8). Purple shows the metal-rich population, blue the metal-poor population. In each stripe, the central line is the mean value of log10(ρ0), whilst the median and outer lines follow the 1σ and 2σ deviations. Center and Right: Virial stripes for the two stellar populations in a NFW potential with small core, without (Υ! = 0) and with (Υ! = 8) self-gravity.

$ = r /r r [in kpc] r [in kpc] r [in kpc] c s s s s the stellar mass-to-light ratio Υ!,whichmaybedifferent for (Υ! 0) (Υ! = 4) (Υ! = 8) the two populations. The projected potential energy W has 1 0.72→ 1.06 1.23 los 0.5 0.94 1.40 1.54 acontributionWdm from the dark component and a correction 0.25 1.2 1.92 2.20 Wsel f from the two luminous ones. For Plummer profiles, we 0.125 1.6 2.88 3.28 have for the i th population: 0.0625 2.4 4.48 4.96 − 2 2 Wsel f,i = π Gµ0,iRh,i Υ!, jµ0, jR w Rh,i/Rh, j , (16) Table 1 h, j #j Minimum rs for two-sigma overlapping of the virial stripes. $ % with x3 (5x2 + 3)K(1 x2) (x2 + 7)E(1 x2) Hence, a necessary condition for a NFW halo to support two w(x) = & − − − ' , (17) stellar populations with Plummer profiles is 3(1 x2)3 − 2 where K, EarecompleteellipticintegralsandΥ!, j is the lu- σ0,r Rh,r > 2 . (14) minous mass-to-light ratio of the j th population. As the µ0, j !σ0,p " !Rh,p " are given by number counts and not− directly by luminosities, This is identical to eq (22) of Amorisco & Evans (2012a), acommonrescalingisappliedtobothpopulationssuchthat derived under different assumptions. If, instead of Plummer the total luminosity is fixed at the observed value (taken from profiles, exponential laws are used to fit the surface brightness table 6 in Irwin & Hatzidimitriou 1995). profiles, then the numerical factor becomes 1.9insteadof2in The leftmost panel of Figure 1 shows the virial stripes for eqn (11). The analogue of eqn (13) is unchanged, so that the the two populations in Sculptor, excluding and including the necessary condition for an NFW halo to support two stellar effects of the self-gravity for the luminous component. The populations with exponential surface brightness profiles is two stripes never overlap at the 2σ level. This confirms the result deduced from our simple argument in the previous sec- 2 σ0,r Rh,r tion: there is no NFW halo compatible with the kinetic ener- > 1.9 . (15) gies of the two stellar components in Sculptor. The center and !σ " !R " 0,p h,p rightmost panels of Figure 1 show the virial stripes when the Using the best-fitting values provided above for Sculptor, itis dark halo density is the simplest cored analogue of the NFW immediate to check that the NFW potential is ruled out. Note halo, namely that the constraints are simply the requirement that there isa ρ0 NFW model with r < .Thisisamuchlooserconstraint cNFW = . (18) s $2 + 2/ 2 1/2 + 2/ 2 than requiring consistency∞ with an NFW model with a con- ( r rs ) (1 r rs ) centration c 20, as predicted by cold dark matter theories. In this case, the stripes do overlap at the 2σ level provided the ≈ core radius rc rs$ is at least 150 pc, if the self-gravity of 3.2. The Virial Stripes the stellar populations≡ is neglected. Incorporating self-gravity The simple results already suggest that the energetics of the causes the core radius to increase somewhat, as we see in two populations are inconsistent with an NFW profile. How- Table 1. This shows how the minimum rs for 2σ overlap ever, it is prudent to confirm this result numerically, discard- varies with changing Υ! for different models. The first col- umn (Υ! 0) stands for models in which the self-gravity of ing some of the simplifying assumptions made above. → Since the measured profiles come with errors, we operate the stars is omitted. Since both half-light radii are smalleror in the following manner. For each value of rs,wecomputeρ0 equal to rs in the dark matter only case, adding self-gravity is separately for the two populations for many different photo- expected to yield larger cores, as in fact is confirmed by the metric (8) and kinematic (9) profiles. We weight each result results in the Table. with the likelihood of the fit. Then, varying rs produces a 4. DISCUSSION AND CONCLUSIONS virial stripe for each population in the (ρ0, rs)-plane. If the two stripes overlap at 2σ at a particular rs,thenthemodelfor The arguments in this Letter show that the kinematics of the potential is plausible at the 2σ level. Nothing prevents us multiple populations in dSphs provide a substantial challenge from including the contribution of the luminous tracers to the to the predictions of cold dark matter cosmogonies. In the potential as well. The virial equations then depend also on case of one of the best studied dSphs, Sculptor, there is no Do the multiple stellar populations in the Sculptor dwarf spheroidal rule out cold dark matter? 3

40 1.0

35

0.5 30 (kpc)] s

0.0 (km/s) 25 [r 10 max

V 0.68 Log 20

−0.5 0.9 0.68 0.9 15

−1.0 10 7.0 7.5 8.0 8.5 9.0 789 −3 Log10 [ρs (Mo kpc )] Log10 [M200 (Mo)]

Figure 1. 68% c.l. and 90% c.l. contours for (ρs,rs)(left)and(M200 − Vmax)(right)fromananalysisthatfitstoboththephotometry and the kinematics of the different populations. For both the MR and MP population, we use the velocity anisotropy profile oftheform Equation 3.

10.000 10.000 20 mp mr β=0 β = 0 β = 0 1.000Multiple populations1.000 in Sculptor dwarf15 spheroidal

0.100 0.100 10 • WP11 and AE12 modeling turn out to be not general enough 0.010 0.010 5 Velocity dispersion [km/s]

•Surface Density [norm arbitrary] Construct generalized modelSurface Density [norm arbitrary] of photometry and kinematics of dSphs

0.001 0.001 0 1 10 100 1 10 100 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 • MaximumRadius [arcmin]likelihood analysis (Strigari,Radius Frenk, [arcmin] White 2013 in prep) Radius [kpc]

10.000 10.000 20 mp mr β variable Metalβ variablepoor β variable Metal poor 1.000 1.000 Metal rich 15

0.100 0.100 10

0.010 0.010 5 Metal rich Velocity dispersion [km/s] Surface Density [norm arbitrary] Surface Density [norm arbitrary]

0.001 0.001 0 1 10 100 1 10 100 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Radius [arcmin] Radius [arcmin] Radius [kpc]

Figure• 3.NFWUpper panels:profilesFrom left are to right, consistent the photometry of with the MP, MRthe populations, multipleand the populations velocity dispersions of the populations for the set of parameters that maximize the likelihood. In the velocity dispersion figure, the upper data and curve is for the MPpopulation, and the bottom data and curve is for the MR population. The parameters for these curves are given above the horizontal line in Table 1. Lower panels:Sameasupperthreepanels,exceptnowassumethevariableβ(r)modelinEquation3.Theparametersofthecurvesare given below the horizontal line in Table 1. The data is from (Battaglia et al. 2008) Multiple populations in Sculptor dwarf spheroidal

Testable predictions

• Orbits of the inner, metal rich population are radial

• Cusp in the stellar density profile

• Forthcoming HST observations provide astrometry < 10 km/s (almost the the projected SIM sensitivity) Counting satellites Hundreds of Milky Way Satellites? 5

TABLE 1 PROPERTIES OF KNOWN MILKY WAY SATELLITE GALAXIES.DATA ARE FROM BOTHUN &THOMPSON (1988); MATEO (1998); GREBEL ET AL.(2003);SIMON &GEHA (2007); MARTIN ET AL.(2008);DE JONG ET AL.(2008).

a b Satellite MV LV [L!] dsun[kpc] Rhalf [pc] !

SDSS-discovered Satellites Canes Venatici I -8.6 2.36 × 105 224 565 0.99 Leo T -8.0 5.92 × 104 417 170 0.76 Hercules -6.6 3.73 × 104 138 330 0.72 Bo¨otes I -6.3 2.83 × 104 60 242 1.0 Ursa Major IHundreds -5.5 of1. Milky36 × 104 Way Satellites?106 318 0.56 5 Leo IV -5.0 8.55 × 103 158 116 0.79 Canes Venatici II -4.9 7.80 × 103 151 74 0.47 Ursa Major II -4.2 4.TABLE09 × 103 1 32 140 0.78 TestingComaHow -4.1the rare3.7 × 10oddball3 is 44the Milky 77 hypothesis 0.97 Way Galaxy? PROPERTIES OF KNOWN MILKY WAY SATELLITE GALAXIES.DATA ARE FROM 3 BOTHUNBo¨otes&THOMPSON II(1988); -2.7 M1.ATEO03 × 10(1998); G43REBEL ET AL 72.(2003);S 0.2 IMON 3 &GWillmanEHA (2007); 1 M -2.7ARTIN1 ET.03 AL×.(2008);10 DE38JONG ET AL25.(2008). 0.99 ListSegue of 1 Milky -1.5 Way3.40 × 10satellites2 23 29 1.0 a b 5 SatelliteClassical MV (Pre-SDSS)LV [L!] Satellitesdsun[kpc] Rhalf [pc] ! Hundreds of Milky Way Satellites? 5 • theLarge area Magellanic of a group Cloud of -18.5 pixels2.15 of× S109contiguously49 2591 - 8 Small Magellanic∗ Cloud -17.1 5.92 × 10 63 1088 - above Sth(n ) (white line,SDSS-discovered Fig 2) is7 greater Satellites than 60.0 squareSagittarius arcminutes -15.0 8.55 × 10 28 125 - CanesFornax Venatici I -13.1 -8.6 1TABLE.249.36××10 1107 5 138224 460• 565Search - 0.99 MW-analogs in SDSS PROPERTIES OF KNOWN MILKY WAY SATELLITE GALAXIES.DATA ARE FROM or LeoLeo T I -11.9 -8.0 4.592.92××10106 4 270417 215 170 1.0 0.76 BOTHUN &THOMPSON (1988); MATEO (1998); GREBEL ET AL.(2003);Sfor satelliteIMON galaxies HerculesLeo II -10.1 -6.6 9.338.73××10105 4 205138 160 330 1.0 0.72 • &GEHA (2007); MARTIN ET AL.(2008);5 ×DE JONG∗ ET AL.(2008). any singleBo¨otesSculptor pixel I value is greater -9.8 -6.3 7.211 than.83××10 110.754 S88th60(n ). 110 242 - 1.0 5 UrsaSextans Major I -9.5 -5.5 5.140.36××10104 86106 335 318 - 0.56 We implement these adaptive density thresholds5 as a a b SatelliteLeoCarina IV M -9.4 -5.0V 4.8L92.V55[×L×!10]103 dsun94[kpc]158Rhalf 210•[pc] 116Probabilistic -! 0.79 model using Draco -9.4∗ 4.92 × 105 79 180 1.0 function ofCanes local Venatici stellar II density -4.9n , so7. that80 × 10 the3 algorithm151 74 0.47 Ursa Minor -8.9 1.49 × 105 69 200background - subtraction may be runUrsa over Major large II fieldsSDSS-discovered -4.2 with varying4.09 × 10 Satellites density3 32 and 140 0.78 3 allow direct comparisonComa between -4.1 fields3. of7 × greatly105 different44 77 0.97 aSatelliteCanes Venaticiprojected I half light -8.6 radius.2.36 × 10 3 224 565 0.99 densities. TheBo¨otes stellar II density -2.7n∗ is1 calculated.03 × 104 for43 each 72 0.2 bDetectionLeo efficiency T from Koposov -8.0 5 et.92 al.× (2007).10 417 170 0.76 pixel of the! smoothed, normalized, spatial× 4 array3 S,as Rely on spectroscopic and ◦ GalaxyWillmanHercules◦ sits within 1 the SDSS -6.6 -2.7 DR5 footprint.3.173.03× 1010 13838 330• 25 0.72 0.99 the 0.9 × 0.9 running average of the original4 2 spatial †SatelliteBo¨otesSegue is not 1 I used in fiducial -6.3 -1.5 LF correction.2.383.40××1010 6023 242photometric 29 1.0 1.0 redshifts density arrayUrsaE. Major I -5.5 1.36 × 104 106 318 0.56 from data for the SDSS-IITo summarize SEGUELeo survey our IV algorithm: (BelokurovClassical -5.0 et al.8. (Pre-SDSS)55 × 10comparison3 Satellites158 that includes 116 the 0.79 DR5 dwarf Leo T; this exten- 2007). All of the objects we listCanes in this Venatici table have II large -4.9 mass7.-80 × 10sion3 9 is151 useful because 74 the known 0.47 dwarf satellite count is so Large Magellanic Cloud -18.5 2.15 × 103 49 2591 - to-light ratios (Martin et• al.Apply 2007;Ursa CMD Simon Major cuts, & II Geha bin 2007;spatial -4.2 Stri- positions4.09 × 10low of8 thatremaining32 even adding 140 one satellite 0.78 to the distribution increases Small Magellanic Cloud -17.1 5.92 × 103 63 1088 - gari et al. 2008). stars intoComaE -4.1 3.7 × 10the7 statistics44 significantly. 77 0.97 Sagittarius -15.0 8.55 × 103 28 125 - Bo¨otes II -2.7 1.03 × 10 7 43 72 0.2 For our fiducial corrections, followingFornax the convention -13.1 of1.49 × 103 The radial138 distribution 460 of all 23 - known Milky Way satel- Koposov et al. (2007), we• Smooth have notWillmanE includedwith 1 Plummer Segue -2.7 1, profile as1 it.03 to× 10 getlites6A is shown38 by the 25 magenta 0.99 dashed line in Figure 5. The SegueLeo I 1 -1.5 -11.9 3.440.92××10102 23270 29 215Fig. 1.0 4.— 1.0Aitoff projection of the DR6 footprint in Galactic does not lie inside the DR5 footprintLeo and II hence◦ the published◦ -10.1 9.38 ×four105 solid205 lines showcoordinates, 160 radial distributions 1.0 centered foron the four Galactic choices center.of Previously known • Calculate the 0.9 × 0.9 running mean5A¯ and run- DR5 detection limits are not applicable.Sculptor We do includeClassical -9.8 Segue (Pre-SDSS)7.11 ×subhalo10 Satellites populations:88dwarfs the 110 65 arelargest marked - vpeak with(upper) open subhalos blue circles, (65 satellites discovered in ning standard deviation Aσ 5 SDSS are marked with filled red circles. 1 in an alternative correction scenarioSextans below (see Table -9.5 3).5.40 ×LBA)109 as discussed86 in 335 Madau et - al. (2008), vpeak > 10 km Large Magellanic Cloud -18.5 2.15 × 10−15 49 2591 - −1 We do not correct the classical dwarfCarina satellite galaxies -9.4 for lu-4.92 ×s108 (upper-middle),94v 210peak > 5 km - s (lower-middle), and • DefineSmallS Magellanicas S =( CloudA − A¯ -17.1)/Aσ 5.92 × 10 5 63 1088 - minosity bias or sky coverage, becauseDraco appropriate detecti -9.4 on4.92 × 107 79−1 lines 180 of Figure 1.0 5. The positions of each of these detec- Sagittarius -15.0 8.55 × 10vmax5 >287 km s (lower). 125 We - note that the all-observed pro- limits for these classical dwarf satellitesUrsa Minor are unclear giv -8.9en that1.49 × 107 69tions 200 are cross-referenced - against the SIMBAD database • CalculateFornax array of threshold -13.1 values1.49 × S10fileth as is clearly function138 more 460centrally concentrated - than any of the the- ◦ ◦ 6 4 they are not part of a homogeneousLeo survey I like∗ SDSS. -11.9 We4.92 × 10oretical270 subhalo distributions. 215as well 1.0 However, as visually as shown inspected in Figur viae the SDSS Finding of stellar density n (from 0.9 ×0.9 running mean 5 assume that all satellites withinaSatellite thoseLeo projected magnitude II half lightbins -10.1 radius. woul9d.38 × 101,5 our limited205 ability 160Chart to detect Tool 1.0 faint. Ofsatellite our 100 galaxies detections, almost 19 are MW/Local of E) 5 have been discovered anywherebDetection in theSculptor efficiency sky, with from the Koposov-9.8 possible7.11 et al.× 10 (2007).certainly88 biases the 110 observedGroup dwarfs - satellite (counting population Bo¨otes to be moII,re Willman 1 and Segue exception of objects at low! GalacticGalaxySextans sits latitudes, within the where SDSS -9.5 DR5Milky5 footprint..40 × 105 86 335 - • Detections are where contiguous regionscentrally5 of pixels concentrated1), than 17 the are full Galactic population. globular clusters (including Koposov †SatelliteCarina is not used in fiducial -9.4 LF4 correction..92 × 10 94 210 - Way extinction and contaminationwith S>S becometh is significantgreater than (Will- 60.0 sq arcmin5 If weor includeany only1 the and 11 2), satellites 2 are known (excluding open SMC clusters, and 28 are clustering of man et al. 2004a). This assumptionDraco is conservative -9.4 in the4.92 × 10 79 180point sources 1.0 associated with background galaxies such from data for the SDSS-II SEGUEsingle pixelUrsa survey Minor is greater (Belokurov than -8.9 1 et.751 al..49××S10thLMC)5.comparison that69 are brightthat 200 includes enough - to the be DR5 detected dwarf within Leo417 T; thiskpc exten- sense that it will bias our total numerical estimate low, but (MV ! −7), we obtainas unresolved the thick blue distant dashed globular line. This clusters, dis- and four are Abell 2007). All of the objects we list in this table have large mass§ - sion is useful because the known dwarf satellite count is so it is only a minor effect, as3.5. oura correctionIdentifying described and Evaluating in 3 is Detectionstribution is significantlygalaxy closer clusters. to all of The the remaining theoretical 30 sub- do not correspond to to-lightdominated ratios (Martinby low luminosity et al. 2007; satellites.Satellite Simon projected & Geha half light 2007; radius. Stri- low that even addingany one catalogued satellite objects, to the distribution but color-magnitude increases diagrams of For eachbDetection of our efficiency DR6 datafrom Koposov strips et defined al. (2007).halo in distributions,§3.1, the and matches quite well within r ∼ 50 kpc, gari etBefore al. 2008). we use the radial distribution! of Via Lactea subha- the statistics significantly.only a handful of these are consistent enough with a faint steps outlinedGalaxy sits in within the previous the SDSS DR5 sections footprint. arewhere repeated the incompleteness in correction to the luminosity func- Forlos our to correct fiducial the corrections, observed luminosity† following function, the convention it is impor of- The radial distributionMW satellite of all to 23 warrant known follow-up. Milky Way The satel- remainder may 0.5 magnitudeSatellite distance is not used in modulus fiducial LF intervals, correction.tion and will these matter 16 most. It is still more centrally concentrated Koposovtant to et investigate al. (2007), whether we have this assumption not included is even Segue self con 1,sis- as it thenlites the is distribution shown bybe theof galaxy all magenta subhalos, clusters dashed however, whose line asdetected in has Figure been center 5. The differs from its frames are layered to form a 3-dimensional array. This ◦ doesfromtent not data with lie forinside the the data the SDSS-II we DR5 have footprint SEGUE on the radial survey and distribution hence (Belokurov the ofpublished known et al. comparisonfour solid that lines includes showcataloged radial the DR5 centre distributions dwarf by more Leo for than T; four this∼ exten-choices0.25 , orof perhaps tidal 3D approach eliminates complications withnoted multiple in the de-past (at least for the classical satellites – e.g. Will- 2007).satellites. All of The the relevant objects comparison we list in this is showntable have in Figure large 5.mass We- sion is useful becausedebris. the known If the dwarf MW stellar satellite halo count is the is so result of accretion DR5 detection limits aretections not applicable. of a single We object do include using selectionSegue criteriamansubhalo et al. for 2004b; populations: dif- Diemand the et 65 al. largest 2004; Kravtsovvpeak(upper) et al. 2004). subhalos (65 to-lighthave normalized ratios (Martin to an et outer al. 2007; radius SimonRouter &=417 Gehakpc 2007; (slightly Stri- low that even addingof one dSph satellite then to evidence the distribution of this incre accretionases is expected. It 1 in an alternative correctionferent distance scenario moduli, below and (see selects Table out 3). theIn strongestLBA) order toas morede- discussed rigorously in Madau determine et al. whether (2008), thevpeak theoreti-> 10 km garilarger et al. than 2008). the Via Lactea virial radius) in order to allow a the− statistics1 significantly.should be noted that−1 objects with relatively large angu- We do not correct the classicaltection. dwarf The coordinates satellite galaxies of stars for withinlu- eachcals distribution detection(upper-middle), is consistentv with> that5 km of s the 11(lower-middle), “complete” and For our fiducial corrections, following the convention of The radial distributionlar size,peak of such all 23 as known Draco and Milky Sextans, Way satel- substantially increase minosity bias or sky coverage,and the CMD because within appropriate the detection’s detection area are plotted for −1 Koposov et al. (2007), we have not included Segue 1, as it litesvmax is shown> 7 km by s thethe(lower). magenta average We dashed stellar note line that density in the Figure ofall-observed the 5. area The they pro- occupy which limits for these classicallater dwarf visual satellites inspection. are unclear Galaxy giv clustersen that and point sources does not lie inside the DR5 footprint and hence the published fourfile solid is clearly lines more showincreases centrally radial distributions the concentrated threshold for density, thanfour choicesany meaning of theof th theye- are not as they are not part of aaround homogeneous partially survey resolved like background SDSS. We galaxies (such as DR5 detection limits are not applicable. We do include Segue subhalooretical populations: subhalo distributions.high the 65 above largest the However,vpeak density(upper) as threshold subhalosshown in as (65 Figur one mighte expect. their associated globular clusters) will contaminate the assume1 in an that alternative all satellites correction within scenario those magnitude below (see bins Table woul 3).d LBA)1, our as limited discussed abilityDue in Madau to to detect the et area al. faint (2008), threshold satellitevpeak however,galaxies> 10 km al theymost are still very detections, but these can be identifiable based on their haveWe been do not discovered correct the anywhere classical dwarf in the satellite sky, with galaxies the possible for lu- −certainly1 biases theprominent observed detections. satellite−1 population to be more CMDs (see Figure 9 in §4), leaving a list ofs potential(upper-middle), new vpeak > 5 km s (lower-middle), and exceptionminosity of bias objects or sky at coverage, low Galactic because latitudes, appropriate where detecti Milkyon −1 We recover all of the newly discovered objects that are Milky Way satellite galaxies and globularvmax clusters.centrally> 7 km concentrated At s (lower). than We the note full that population. the all-observed pro- Waylimits extinction for these and classical contamination dwarf satellites become are unclear significant given (Will- that within DR6 and the “classically” known Draco, Leo, Leo this point follow up observations are typicallyfile isIf necessary clearly we include more centrally only the concentrated 11 satellites than (excluding any of the SMC the- and manthey et are al. not 2004a). part of This a homogeneous assumption survey is conservative like SDSS. in We the II, Leo A, Sextans, and Pegasus DIG dwarfs. Our detec- to confirm the existence and nature of theseoreticalLMC) candidates. subhalo that are distributions. bright enough However, to be detected as shown within in Figur417e kpc assume that all satellites within those magnitude bins would tions of the new dwarfs are presented in Figures 6, 7, and sense that it will bias our total numerical estimate low, but 1,(M ourV limited! −7), ability we obtain to detect the thickfaint satellite blue dashed galaxies line. almost This dis- ithave is only been a minor discovered effect, anywhere as our4. APPLICATION correction in the sky, described with TO the SDSS possible in DATA§3 is RELEASEcertainlytribution 6 biases is significantly the8. observed These closer figures satellite to are all population identical of the theoretical to bethose mo outputre sub- by the auto- exception of objects at low Galactic latitudes, where Milky mated algorithm for each detection, aside from the addi- dominated by low luminosityWe apply satellites. our search algorithm (as describedcentrallyhalo in distributions,§3) concentrated to and than matches the full quite population. well within r ∼ 50 kpc, Way extinction and contamination become significant (Will- tion of figure titles (MV and distances from Martin et al. Before we use the radial21,439,777 distribution sources of withVia Lactear<22.subha-0 and g − r

Brighter Inhomogeneous Reionization andLuminosity-mass Satellites Galaxies mapping 3 galaxies ✦ vast majority of the 2500 Cold potential dark satellite matter galaxies; predicts for dozens these low-mass halos,∼ all starof formation‘dark’ satellites must happen more before massive than the dwarf spheroidals Magellanic zreion. With this in mind, we can define a subhalo as being a −20 Clouds satellite galaxy using a two parameter(‘Too big model:to fail Aproblem subhalo’ mustBoylan-Kolchin grow to a threshold mass, Met t,al. above 2011) which HI cooling will allow star formation, before the host halo reionizes at zreion in order to host a satellite. −15 dwarf ✦ Not enough ‘bright’ Milky Way spheroidalsFornax While we demonstrate the effects of varying both param- eters in the next section, thesatellites work of Abel et al. (2002) uses Mag −10 high resolution AMR simulations to model the formation of Magnitude 25-75 Subhalos ✦ Theoretical solutions 6 the first stars and indicates that we anticipate Mt 10 − per simulation 7 −1 Baryons ≈ 10 h M!. It is important to note that this process of hy- Alternative dark matter drogen cooling simply defines a minimum mass of the pop- −5 ulation of the dark matter subhalos that could host satellite galaxies. However, this work✦ Observational predicts the stars systematics forming in Is the Milky Way an oddball? 10 100 these halos to be very massive and short–lived. As such Circular VelocityVmax [km/s] these very first star forming halos cannot be the direct pro- genitors of Milky Way satellites, which are observed to be FIG.1.—Therelationshipbetweenmagnitudeandvmax for the r−, g−,and V− bands using abundance matching (solid red, green and black lines). The metal-enriched objects with stars presumably of masses less dashed lines show power law fits to the low-luminosity end. than a solar mass. More relevant here are the calculations of Wise & Abel (2008), who followed the build up of halos up V−band, we get to the masses when they start cooling via Lyman-alpha from 7.1 neutral hydrogen. They included the radiative as well as the vmax M − 5log(h)=18.2 − 2.5log . (1) supernova feedback from the first generation of massive stars. V 1km/s The short-lived sources keep ionizing the baryonic material !" # $ in the halos they form in, as well as their surroundings. How- When selecting the appropriate vmax for assigning a luminos- ever, as they turn off, material can cool again and repopulate ity, we follow the method of Conroy et al. (2006) and choose the dark matter halos. So while the baryon fraction (Fig. 4 in the peak vmax over the trajectory of the subhalo for subhalos Wise & Abel 2008) fluctuates and decreases at times to as lit- that eventually cross the 105K post-reionization star forming tle as 10%, star formation can continue as long as no sustained threshold. For subhalos that never reach this threshold, we use external UV flux sterilizes the halo. The latter case severely the value of vmax at zreion. In both cases, this then corresponds limits star formation and has been discussed many time in the roughly to the mass the halo had at the redshift they stopped literature (e.g., Babul & Rees 1992; Thoul & Weinberg 1996; rapidly forming stars. Kepner et al. 1999; Dijkstra et al. 2004). It seems clear then The appeal of this method is that we are able to ignore from the limited guidance we have from numerical simula- much of the poorly understood (and poorly simulated) physics tions that most Milky Way satellite halo progenitors experi- of galaxy formation using a statistical method that has been enced most of their star formation before they are permanently shown to, on average, reproduce a wide variety of observ- ionized. able properties for more massive galaxies (Conroy et al. 2006; Once we have identified satellite galaxies in the simula- Conroy & Wechsler 2009), as well as some properties of tion, we must assign magnitudes to them in order to make dwarf galaxies down to vmax 50km/s (Blanton et al. 2008). direct comparisons with observations and to account for ob- It is still unclear how this method∼ will fare at lower masses; servational completeness effects. This is done using two it must break down for small halos once they no longer host methods. First, we use a halo abundance matching method one galaxy on average. If this transition is sharp, however, (Kravtsov et al. 2004a; Blanton et al. 2008). Here, luminosi- it may be a reasonable approximation for most of the mass ties are assigned to halos by assuming a one-to-one corre- range where halos host galaxies. spondence between n(< MV ), the observed number density As a second approach for assigning magnitudes, we use a of galaxies brighter than Mv, with n(> vmax), the number toy model to predict the star formation rate and stellar mass density of simulated halos with maximum circular veloci- of a satellite combined with the stellar population synthesis 3 ties larger than vmax. For the distribution of magnitudes, we (SPS) code of Bruzual & Charlot (2003) . Here, we again as- use the double-Schechter fit of Blanton et al. (2005) for low sume that star formation begins when the satellite first crosses luminosity SDSS galaxies in the g− and r−bands down to the mass threshold, Mt, and ends at the reionization time, Mr = −12.375. The vmax values are taken from the halo catalog zreion. During this period, the star formation rate is set by the of a 160 Mpc/h simulation complete down to vmax 90km/s. dark matter mass of the subhalo, In order to extrapolate this to lower circular velocities,≈ we α MDM calculate a power-law fit to the low end of the dn/dv func- ! fcoldgas if MDM > Mt, z > zreion max SFR = 1 M! (2) tion. The resulting correspondence is shown in Figure 1 for % 0" # otherwise the r−, g−,andV−bands (red, green, and black curves). The V band magnitudes are calculated using the transformation V = where fcoldgas is the fraction of cold gas in the halo, and g − 0.55(g − r) − 0.03 from Smith et al. (2002). This method α and ! are free parameters. This is similar to model 1B implicitly assumes that all galaxies have average color. Since of Koposov et al. (2009), with a couple of key differences. the data from Blanton et al. (2005) is not deep enough to map First, we impose a hard truncation of star formation at the onto the dwarf galaxy distribution, we use a power law to ex- epoch of reionization, something they only consider using trapolate the MV (vmax) relation to lower magnitudes. For the 3 http://www.cida.ve/ bruzual/bc2003 6 LIU ET AL.

Magellanic Cloud-like Galaxies Magellanic Clouds around other ‘Milky Ways’

Large Magellanic Cloud

Small Magellanic Cloud •About 600 systems with spectra on MC-like satellites

From cosmological surveys: •About 10,000 systems with • About 5% of ‘Milky Ways’ have photometric redshifts on MC-like ‘Magellanic Clouds’ [Liu et al. 2010, Lares et al. 2011; James & Ivory 2011; Tollerud et al. 2011, Guo et satellites al. 2011]

From simulations: • 5-10% of ‘Milky Ways’ have ‘Magellanic Clouds’ [Boylan-Kolchin et al. Liu et al. 2010 2009; Busha et al. 2010]

Fig. 2.— Images of selected MW-like hosts with exactly two MC-like satellites in the SDSS spectroscopic catalog, identified as those 1 objects within a radius of 150 kpc and within 300 km s of the host. Each image is scaled to 300 physical kpc on a side, centered on the host galaxy. Satellites identified as MC-like companions are circled in yellow. The 1st, 2nd, 4th, and 11th images (counting from left to right, top to bottom) show at least one bright, close companion to the MW-sized host. Image 11 shows two such objects at the same redshift as the central galaxy. In each of these cases, the companion is recognized as a satellite of the host but is too luminous to meet our criteria for being an MC-like satellite. The 5th, 6th, 8th, 9th, and 11th images feature prominent background objects with spectra at dissimilar redshifts. Background objects without spectra are clearly visible in every panel. The 5th and 12th panels exhibit fiber collisions. The blue object next to the upper left MC-like satellite in panel 5, though bright enough, did not have its spectrum collected or analyzed, similarly, the object to the right of the bluer MC-like satellite in panel 12 has no redshift or absolute magnitude information due to fiber collisions. Faintest satellites in SDSS Dwarf spheroidals around other ‘Milky Ways’

✦ Going fainter difficult because unreliable distances to satellites •Very few systems with spectra for Fornax-like satellites

✦ However it is the most About 1,000 systems with important regime for the • satellite abundance issue! photometric redshifts for Fornax- like satellites

✦ Can only use bright, nearby ‘Milky Ways’ Cosmic Abundance of Classical Satellites Satellites of other ‘Milky Ways’ 6 Strigari and Wechsler Strigari & Wechsler ApJ 2012

Milky Way magnitude primaries M31 magnitude primaries 100.0 100.0 • Down to limits of modern m m surveys, Milky Way is Δ Δ ‘normal’ (Strigari & Wechsler ApJ 2012)

10.0 10.0 Fnx Leo I NGC 147 AND VII • Is the solution to satellites Sgr NGC 205 LMC SMC NGC 185 issue likely due to incomplete M32 M33 theory? 1.0 1.0 Mean satellite number < Mean satellite number <

• Significant improvement very 0.1 0.1 soon with new larger scale surveys Cosmic2 Abundance4 6 of8 Classical10 Satellites2 4 6 8 10 Magnitudes fainter than primary (Δ m) Magnitudes fainter than primary (Δ m)

6 Strigari and Wechsler Strigari & Wechsler ApJ 2012 Figure 2. Left:Meannumberofsatellitesbrighterthan∆m magnitudes fainter than the primary galaxy, assuming primaries within ±0.25 magnitudes of the Milky Way. Blue diamonds are determined from the spectroscopic sample of satellites (method 1), black squares from the photometricMilky Way sample magnitude (method primaries 3). The solid errors are theM31 magnitude uncertainty primaries on the mean, the thin, dashed errors are the intrinsic scatter σs Right ( from Eq.100.0 3). The arrows indicate 90% c.l. upper limits.100.0 The redtrianglesindicatetheMilkyWaysatellites. :Sameasleft,except m ± . m for primariesΔ within 0 25 magnitudes of M31. Δ MW-like primaries and ∆m = [4, 5], we find a mean in- verified that our results are consistent with these authors trinsic scatter10.0 of σs = [0.56 0.04, 0.89 0.19],10.0 where the over the radial range considered, and further that we do Fnx± Leo I ± NGC 147 AND VII errors represent one-sigmaSgr uncertainties as above. TheNGC 205 not incur a significant bias by including galaxies within LMC SMC NGC 185 best-fitting values for σs are shown as thin, dashed er-M32 projected radii < 100 kpc. Tollerud et al. (2011) utilize ror bars in Fig. 2 for ∆m 7. Via the methodM33 out- the DR7 volume-limited spectroscopic sample and find 1.0 ≤ 1.0 lined inMean satellite number < Liu et al. (2011), we are also ableMean satellite number < to estimate that 40% of MW-analogs have satellites brighter than the full probability distribution down to ∆m =5;here the LMC∼ within 250 kpc. James & Ivory (2011) use Hα we find that the probability to obtain [0, 1, 2, 3] satel- narrow band imaging to search for start forming galax- 0.1 0.1 lites with ∆2 m<4 5 is [06 .59, 08.25, 010.11, 0.03, 0.02].2 Down4 6 ies around8 10 143 spiral galaxies like the MW, and find that to fainter magnitudes,Magnitudes fainter the than primary spectroscopic (Δ m) sampleMagnitudes is too fainternearly than primary two-thirds (Δ m) do not have satellites that resemble the sparse to measure the full satellite probability distribu- Magellanic Clouds. These latter two results are consis- tion.Figure 2. TheseLeft:Meannumberofsatellitesbrighterthan results indicate that there∆m magnitudes is still substantial fainter than the primary galaxy,tent assuming with prima theries spectroscopic within results that we present for ±0.25 magnitudes of the Milky Way. Blue diamonds are determined from the spectroscopic sample of satellites (method 1), black squares intrinsicfrom the photometric scatter sample in (method the 3). satellite The solid errors population, are the uncertainty even on the atmean, the the thin, dashedbright errors are satellites. the intrinsic scatter (σs from Eq. 3). The arrows indicate 90% c.l. upper limits. The redtrianglesindicatetheMilkyWaysatellites. Right:Sameasleft,except brightestfor primaries within scales.±0.25 magnitudes of M31. 6. MW-like primaries and ∆m = [4, 5], we find a mean in- verified that our results are consistent with theseDISCUSSION authors AND CONCLUSION trinsic scatter5. ofCOMPARISONσs = [0.56 0.04, 0. TO89 0 PREVIOUS.19], where the RESULTSover the radial range considered, and further that we do errors represent one-sigma± uncertainties± as above. The not incur a significant bias byWe including have galaxies used within DR8 photometric redshift data to limit best-fittingThere values have for beenσs are several shown as thin,recent dashed analyses er- projected on the radii pop-< 100 kpc.the Tollerud mean et al. number (2011) utilize of satellites around MW-analog galax- ror bars in Fig. 2 for ∆m 7. Via the method out- the DR7 volume-limited spectroscopic sample and find ulationlined in Liu of etbright al. (2011), satellites we≤ are also ablearound to estimate MW-analogthat 40% galaxies of MW-analogsies have down satellites to brighter ten than magnitudes fainter than the MW. At alongthe full probability the lines distribution presented down in to this∆m =5;here paper. Itthe is LMC instructive∼ within 250 kpc. Jamesleast & down Ivory (2011) to the use Hα scale of Sagittarius, the results indi- towe findcompare that the the probability results to obtain presented [0, 1, 2, 3] here satel- to thesenarrow previousband imaging to searchcate for that start forming the MW galax- is not a significant statistical outlier lites with ∆m<5 is [0.59, 0.25, 0.11, 0.03, 0.02]. Down ies around 143 spiral galaxies like the MW, and find that analyses.to fainter magnitudes, the spectroscopic sample is too nearly two-thirds do not havein satellites its number that resemble of bright, the classical satellites. sparseGuo to measure et al. the(2011) full satellite used probability SDSS DR7 distribu- to constructMagellanic the Clouds. lu- These latterOur two 90% results c.l. are consis- upper bound of " 13 satellites brighter tion. These results indicate that there is still substantial tent with the spectroscopic results that we present for minosityintrinsic scatter function in the satellite of satellites population, even down at the to thebright magnitude satellites. than the Fornax dSph already places a strict bound on scalebrightest of scales. Fornax, correcting for the incompleteness of the efficiency of galaxy formation at the dSph luminos- 6. DISCUSSION AND CONCLUSION SDSS.5. These authors used best-fitting photometric red- ity scale. This is particularly true considering that there COMPARISON TO PREVIOUS RESULTS We have used DR8 photometric redshift data to limit shiftsThere from have been DR7 several to recent eliminate analyses obvious on the pop- backgroundthe mean number galax- of satellitesare around anywhere MW-analog from galax- 25 75 dark matter subhalos in ies.ulation Our of bright analysis satellites di aroundffers MW-analog from these galaxies authorsies down in that to ten we magnitudesthe fainter Aquarius than the simulations MW. At ∼ (Springel− et al. 2008) that have utilizealong the linesboth presented DR8 in imaging this paper. and It is instructive a maximumleast down likelihood to the scale ofpresent-day Sagittarius, the results circular indi- velocities greater than that of For- to compare the results presented here to these previous cate that the MW is not a significant statistical outlier methodanalyses. that incorporates full photometricin redshift its number prob- of bright, classicalnax. satellites. However, it is very interesting to note that the ob- abilityGuo et distributions. al. (2011) used SDSS We DR7 toalso construct directly the lu- quantifyOur 90% the c.l. bias upper boundservational of " 13 satellites result brighter we present is perfectly consistent with minosity function of satellites down to the magnitude than the Fornax dSph already places a strict bound on inscale abundance of Fornax, correcting counts for for the faint incompleteness satellites of thatthe e isfficiency incurred of galaxy formationabundance at the dSph matching luminos- extrapolations for the satellite lu- whenSDSS. These utilizing authors available used best-fitting photometric photometric red-redshifts.ity scale. Via This some- is particularlyminosity true considering function, that there which predict 1.2, 1.7 satellites for shifts from DR7 to eliminate obvious background galax- are anywhere from 25 75 dark matter subhalos in ∼ whaties. Our di analysisfferent diff methodsers from these for authors cutting in that background we the Aquarius galaxies, simulations∼ (Springel−magnitude et al. 2008) diff thaterences have ∆m =7, 10 (Busha et al. 2011). Laresutilize both et al. DR8 (2011) imaging use and DR7a maximum data likelihood to obtainpresent-day a mean num-circular velocitiesThis greater does than not that guarentee of For- that such models will have the method that incorporates full photometric redshift prob- nax. However, it is very interesting to note that the ob- berability of distributions. satellites We down also directly to the quantify magnitude the bias of Sagittariusservational result for we presentcorrect is perfectly velocity consistent function; with in fact it appears increasingly projectedin abundanceradii counts for! faint100 satellites kpc. As that we is incurred discuss above,abundance we matching have extrapolationsdifficult for to the simultaneously satellite lu- match both the luminosities when utilizing available photometric redshifts. Via some- minosity function, which predict 1.2, 1.7 satellites for what different methods for cutting background galaxies, magnitude differences ∆m =7, 10∼ (Busha et al. 2011). Lares et al. (2011) use DR7 data to obtain a mean num- This does not guarentee that such models will have the ber of satellites down to the magnitude of Sagittarius for correct velocity function; in fact it appears increasingly projected radii ! 100 kpc. As we discuss above, we have difficult to simultaneously match both the luminosities Conclusions

• Important to both improve theory and understand observational systematics to get a handle to classic CDM issues

• CDM-based, NFW dark matter profiles are consistent with dwarf spheroidal data (dSph)

• Down to about the luminosity of Fornax, hints that the Milky Way is ‘average’

•Picture should be much more clear next few years...