Dark Matter Signals from Dwarf Galaxies
CVnII
LeoIV Louie Strigari UMaI Stanford University Sextans Ursa Minor BootesI/II Draco Coma W1 Herc Segue1 UMaII
Milky Way
Sag LMC Shedding Light on Dark Matter Carina University of Maryland SMC April 2, 2009 Sculptor
Fornax 100,000 light years
Based on work with: James Bullock, Rouven Essig, Marla Geha, Manoj Kaplinghat, Greg Martinez, Neelima Sehgal, Josh Simon, Erik Tollerud, Beth Willman, Joe Wolf Milky Way Circa 2009
Satellite Year Discovered
LMC 1519
SMC 1519
Sculptor 1937
Fornax 1938
Leo II 1950
Leo I 1950
Ursa Minor 1954
Draco 1954
Carina 1977 Image: Marla Geha
Sextans 1990
Sagittarius 1994
Ursa Major I 2005
Willman 1 2005
Ursa Major II 2006
Bootes I 2006
Canes Venatici I 2006
Canes Venatici II 2006
Coma Berenices 2006
Segue 1 2006
Leo IV 2006
Hercules 2006
Bootes II 2007
Leo V 2008 Segue 2 2009 What is the minimum mass dark matter halo? What is the minimum mass ``galaxy?” 10 Springel et al.
Our measured mass function for the ‘A’ halo is well
0 approximated by 10 Springel et al. 2008 dN M n = a0 , (4) Also Deimand, Kuhlen, Madau, dM m0 -2 ! " 10 Via Lactea 7 Star with n = 1.9, and an amplitude of a0 =8.21 10 /M50 = −5 −1 × −5 ] 3.26 10 M for a pivot point of m0 = 10 M50 = Galaxies? -1 "
? • O × 7 2.52 10 M". This means that the expected total mass in Clusters? 10-4
[ M × all subhalos less massive than our resolution limit mres is sub
M mres n+2 n+2 d dN a0 mres mlim
N / -6 Mtot( Luminosity Aq-A-3 → 10-8 and our nominal subhalo resolution limit of mres =3.24 Aq-A-4 4 × Aq-A-5 10 M" in the Aq-A-1 simulation, this gives Mtot =1.1 11 × 10 M", corresponding to about 4.5% of the mass of the -10 10 halo within r50. While non-negligible, this is considerably 104 105 106 107 108 109 1010 smaller than the total mass in the substructures that are al- M [ MO • ] Figure: Shane Walsh sub ready resolved 11 by the simulation. The latter is 13.2% of the ] 10 • O mass within r50 for the Aq-A-1 simulation. We hence con- clude that despite the very broad mass spectrum assumed in [ M Half-light radius sub this extrapolation, the total mass in subhalos is still domi- M d nated by the most massive substructures, and an upper limit N / 10 d 10 for the total mass fraction in subhalos is 18% within r50 Belokurov et al. 2006, 2 ∼ sub for the ‘Aq-A’ halo. Gilmore et al. 2007 M 4 5 6 7 8 9 10 We caution, however, that the extrapolation to the ther- 10 10 10 10 10 10 10 Msub [ MO • ] mal limit extends over 10 orders of magnitude! This is il- lustrated explicitly in Figure 7, where we show the mass Figure 6. Differential subhalo abundance by mass in the ‘A’ halo fraction in substructures above a given mass limit, com- within the radius r50. We show the count of subhalos per logarith- bining the direct simulation results with the extrapolation mic mass interval for different resolution simulations of the same above. We also include an alternative extrapolation in which halo. The bottom panel shows the same data but multiplied by a a steeper slope of 2 is assumed. In this case, the total factor M 2 to compress the vertical dynamic range. The dashed − sub mass fraction in substructures would approximately double lines in both panels show a power-law dN/dM ∝ M −1.9. For each if the thermal limit lies around one Earth mass. If it is much of the resolutions, the vertical dotted lines in the lower panel mark −12 smaller, say at mlim 10 M", the mass fraction in sub- the masses of subhalos that contain 100 particles. ∼ structure could grow to 50% within r50, still leaving room ∼ for a substantial smooth halo component. Notice, however, part of the differential mass function that it exhibits a true that within 100 kpc even this extreme extrapolation results power-law behaviour, and that the slope of this power law is in a substructure mass fraction of only about 5%. Most of shallower than 2, though not by much. Our results are best the mass of the inner halo is smoothly distributed. − −1.9 fit by a power law dN/dM M , the same slope found Within r50 the mass fraction in resolved substructures ∝ by Gao et al. (2004), but significantly steeper than Helmi varies around 11% for our 6 simulations at resolution level et al. (2002) found for their rich cluster halo. The exact value 2, each of which has at least 160 million particles in this obtained for the slope in a formal fit varies slightly between region. Table 2 lists these numbers, which are 12.2% (Aq-A- 1.87 and 1.93, depending on the mass range selected for 2 simulation), 10.5% (Aq-B-2), 7.2% (Aq-C-2), 13.1% (Aq- − − the fit; the steepest value of 1.93 is obtained when the fit D-2), 10.8% (Aq-E-2), and 13.4% (Aq-F-2). This gives an − 6 7 is restricted to the mass range 10 M" to 10 M" for the average of 11.2% within r50 down to the relevant subhalo 5 Aq-A-1 simulation. mass resolution limit, 2 10 M". This is similar to the ∼ × The small tilt of the slope n = 1.9 away from 2 substructure mass fractions found by earlier work on galaxy − − is quite important. For n = 2, the total predicted mass cluster halos (e.g. Ghigna et al., 1998; Springel et al., 2001a; − in substructures smaller than a given limit m0 would be De Lucia et al., 2004) and Galaxy-sized halos (Stoehr et al., logarithmically divergent when extrapolated to arbitrarily 2003) once the different limiting radius (r200 instead of r50) small masses. If realized, this might suggest that there is no is corrected for. However, it is larger than the 5.3% inside r50 smooth halo at all, and that ultimately all the mass is con- reported by Diemand et al. (2007a) for a Milky Way-sized tained in subhalos. However, even for the logarithmically di- halo. vergent case the total mass in substructures does not become In Figure 8, we compare the differential subhalo mass large enough for this to happen, because a sharp cut-off in functions of these six halos, counting the numbers of subha- the subhalo mass spectrum is expected at the thermal free- los as a function of their mass normalized to the M50 of their streaming limit of the dark matter. Depending on the spe- parent halo. Interestingly, this shows that at small subhalo cific particle physics model, this cut-off lies around an Earth masses the subhalo abundance per unit halo mass shows −6 −12 mass, at 10 M", but could be as low as 10 M" in very little halo-to-halo scatter. In fact, the mean differential ∼ certain scenarios (Hofmann et al., 2001; Green et al., 2004). abundance is well fit by equation (4) with the parameters "c 0000 RAS, MNRAS 000, 000–000 Mapping satellites onto CDM subhalos 8 Koposov et al. 2009 Luminosity function [e.g. Bullock et al. 2001, Benson et al. 2002, Somerville et al. 2002, Kravtsov et al. 2004, Koposov et al. 2008, Tollerud et al. 2008, Busha et al. 2009, Bovill & Ricotti 2009, 8 Koposov et al. 2009] Kravtsov et al. 2004 Magnitude Fig. 5.— Model predictions for the observed satellite population, Nobs(MV ), including radial selection effects for the SDSS dwarfs. Horizontal bars show the number of currently known satellites (Table 2) in 2-magnitude bins; empty bins are plotted with an arrow. The SDSS and classical dwarfs are separated by the vertical line at MV = −11; note that the y-axes for these two populations differ by a factor of five so that the model predictions (which incorporate a factor of 1/5 below MV = −11 to account for SDSS sky coverage) are −4 continuous across the boundary. Left Panel: Predictions of Model 1A, with M∗ ∝ MRadial/Velocity, for three values of F∗. For F∗ = 10 distribution, the green sat band shows the bin-by-bin ±1σ range of the predictions from multiple realizations; the logarithmic width of this band is similar for other models. Model curves have been slightly smoothed with a polynomial filter. Right[e.g. Panel: WillmanComparison et of al. Model 2004, 1A (red Kravtsov curve) to Modelet al. 2004] 10 ∝ α 1B, where the stellar mass fraction in halos with Msat < 10 M# is is F∗ Msat, with α = 1 (green band) or α = 2 (blue curve). of those systems above the 50% completeness limits suppression is approximately what is needed to explain of Koposov et al. (2008). We exclude two systems, BooII the observed shape of Nobs(MV ).Fig. Linear 7.— The suppression cumulative velocity function of the dark matter Fig. 8.— The fraction of satellites within a certain distance from satellites in the three galactic halos (solid lines compared to the the center of their host galaxy. The solid lines show distributions of and LeoV (Walsh et al. 2007; Belokurov et al. 2008), (α = 1, green band) is not sufficient,average predicting cumulative an velocity excess function of dwarf galaxies around the the ΛCDM satellites in the three galactic halos, while the connected which fall below this detection threshold, but their in- of faint dwarfs when normalized toMilky the Way bright and dwarfs. Andromeda All galaxies (stars). For the objects in stars show the distribution of dwarf galaxies around the Milky Way. clusion would not affect our analysis significantly. of our modelsKinematics fail to match the brightestsimulations [e.g. binVcirc Strigari (comprisedis the maximum et al. circular 2007, velocity, 2008, while Li for theet Lo-al. 2008,The Maccio figure shows et that al. radial 2008] distribution of observed satellites is cal Group galaxies it is either the circular velocity measured from more compact than that of the overall population of dark matter The left panel of Figure 5 compares our simplest model of the SMC and LMC); we deferrotation discussion curve or of from this the dis- line-of-sight velocity dispersion assum- satellites. The dashed lines show distributions for the luminous (M∗ ∝ M , Model 1A) to the observed satellite counts, crepancy to the end of this Section.ing isotropic velocities. Both observed and simulated objects are satellites in our model (§ 6). The population of luminous satellites sat 1 now including the satellite galaxy selection effects in the Figure 6 shows the expected Nselected(M within) distributions the radius of 200h− kpc from the center of their is the same in this and previous figures. host.obs TheV dashed lines show the velocity function for the luminous model. We randomly sample each of the six Monte Carlo for Model 2, which has a sharp satellitesVcrit threshold in our model for described the in § 6. The minimum stellar mass 5 of the luminous satellites for the three hosts ranges from ≈ 10 M" halo simulations five times (choosing 1/5 of the faint suppression of SF after reionization in6 small halos. As to ≈ 10 M", comparable to the observed range. lation. The median distance of observed satellites within satellites but always keeping the full set for MV < −11), in Figure 3, the predicted Nobs(MV ) is bimodal, with 200h−1 kpc is 60h−1 kpc and 85h−1 kpc for the MW and compute the mean model prediction as the mean of these a bright peak corresponding to halos that exceeded Vcrit M31, respectively. For the DM satellites the correspond- −1 −1 30 samplings, and compute the rms dispersion among before zsat and a faint peak correspondinglarger than to a stars given formed value, for the objects located within ing median distances are 116h kpc, 121h kpc, and −1 these 30 in each absolute magnitude bin. Despite the se- before reionization. Raising the stellar200h−1 fractionkpc of theirF∗ hostwith halo. The figure compares the 120h kpc. Although the median for M31 satellites is lection bias against low luminosity satellites, this model other parameters fixed (orange vs.CVFs blue) for shifts the DMboth satellites peaks and observed satellites of the smaller than that of the DM satellites, their radial distri- fails drastically for any choice of F∗, predicting a much horizontally to higher MV ; the faintMW peak and Andromeda also increases5 and highlights the “missing satel- butions are formally consistent. However, the comparison steeper luminosity function than observed. For example, in height because the brighter (thoughlite problem” still faint) (Kauffmann satel- et al. 1993; Klypin et al. 1999b; with the M31 satellites is difficult at present because typ- −4 the model with F∗ = 10 matches the observed counts lites can be seen over a larger fractionMoore ofet theal. 1999a): MW virial a large difference in the number of ical distance errors are 20 50 kpc (and ! 70 kpc for some galaxies), comparable∼ to− the distance to the host. near MV = −9 but predicts far too many satellites fainter volume. Lowering Vcrit with otherdwarf-size parameters DM fixedsatellites (red in simulations and the observed number of dwarfs in the Local Group. For the MW satellites the typical distance errors are an than MV = −6. Selection effects and newly discovered vs. blue) has no impact on the faint peak, but the bright satellites have not altered this basic discrepancy, first peak extends to fainter magnitudesFigure and grows 8 shows in the height normalized cumulative radial distri- order of magnitude smaller and the comparison is consid- bution of the DM satellites compared to the radial distri- erably more meaningful. The Kolmogorov-Smirnov (KS) emphasized by Klypin et al. (1999) and Moore et al. because lower mass halos can now be populated with test gives probability of (6 8) 10−4 that the MW satel- bution of satellites around the Milky Way within the same − × (1999). The green band shows the 1σ dispersion in pre- stars after reionization. Raising zradius.rei (green The vs. Local blue) Group with data is from the compilation of lites are drawn from the same radial distribution as the dicted counts, and it is clear that statistical fluctuations other parameters fixed has no impactGrebel on et the al. (2003).bright peak, The figure clearly shows that the spa- DM satellites. This has also been pointed out recently by will not resolve the discrepancy either. but it shifts the faint peak downwardstial distribution in amplitude of dwarf and galaxies around the Milky Way Taylor et al. (2003), who compared the spatial distribution In the right panel we apply our purely empirical mod- slightly downwards in location becauseis more compact halos have than ac-the distribution of the DM popu- of the MW satellites to results of their semi-analytic model α of galaxy formation. Thus, in addition to the vastly dif- ification, M∗/Msat ∝ M below a halo mass Msat = creted less mass by this higher redshift.orbits and the While development photo- of the tangentially-biased dispersion in 10 −3 ferent abundances of the observed and predicted satellites, M0 = 10 M# (Model 1B). With F∗ = 10 and α = 2, ionization suppression reduces thethe discrepancy outer parts. A similar with result the has been found by Kazantzidis et al. this model achieves reasonable agreement with the the number of faint satellites seen in(2004) Model and 1A, Moore these et al. sharp (2003). The solution of the Jeans equation there is a discrepancy in the radial distribution. Models for Vm is sensitive to the exact value of the anisotropy parameter that aim to reproduce the abundance of the LG satellites observed Nobs(MV ) over the full range 0 ≥ MV ≥−15. threshold models predict a gap(Zentner between & Bullock the faint 2003; Kazantzidisand et al. 2003). 5 should therefore be able to reproduce the radial distribu- The agreement can be further improved by adjusting F∗ bright satellites that is clearly at oddsWe use with the circular the data. velocities compiled by Klypin et al. (1999b) tion as well. with updated values of circular velocity for the Large and Small and M0, so it appears that this level of mass-dependent Figure 7 compares the Model 2 predictions with those −1 −1 Magellanic Clouds of Vm = 50 km s and 60 km s , respectively (van der Marel et al. 2002) 6. a model of star formation in dwarf halos Dwarf halo kinematics Classical satellites Ultra-faint satellites Walker et al. Simon & Geha 2007 ApJ Walker et al ApJL 2008 Satellite Masses Derived from spherical-symmetric analysis with variable velocity anisotropy Up to 8 parameters are free, though all not necessary for the faintest systems Agrees with results from Lokas 2009, given assumptions Strigari et al. 2008 Does not appear that the satellite distribution correlates with z=0 mass [Kazantzidis et al. 2003, Kravtsov et al 2004, Moore et al. 2005] Estimated total mass-to-light ratios: 10-1000+ Segue 1: Least luminous known galaxy (Geha et al. 2009) Tidal effects important, but not within stellar radius (Penarrubbia et al. 2008) Tidal Disruption and Rotation Rotation in this sense detected in M15 GC [Drukier et al. 1998] New results for ultra- faints in M. Geha talk, Friday 1 Error projections assuming 1 km/s 0.8 rotation/gradient w1 com uma II 0.6 Theoretical error modeling indicates that hundreds of stars needed for detection of 0.4 a gradient 0.2 0 0 2 4 6 8 0 2 4 6 8 0 2 4 6 8 A [km/s] A [km/s] A [km/s] Rotation Amplitude Central mass and luminosity of Milky Way satellites 3 LCDM and the M300/M600 relation Inhomogeneous Reionization and Satellites Galaxies 7 Inhomogeneous Reionization and Satellites Galaxies 3 Maccio’, Kang, Moore 2008 vast majority of the ∼ 2500 potential satellite galaxies; for ] these low-mass halos, all star formation must happen before • O 106 1000 z . With this in mind, we can define a subhalo as being a /L reion !20 • O satellite galaxy using a two parameter model: A subhalo must 105 grow to a threshold mass, Mt, above which HI cooling will allow star formation, before the host halo reionizes at zreion in !15 4 order to host a satellite. 10 ) 100 While we demonstrate the effects of varying both param- max eters in the next section, the work of Abel et al. (2002) uses Mag 103 N(>V high resolution AMR simulations to model the formation of Magnitude !10 Mass/Luminosity [M 6 102 the first stars and indicates that we anticipate Mt ≈ 10 ! FIG. 2.— Mass within 300 pc versus luminosity. Red dots show results from our FIG. 3.— Upper10 panel: distribution of the circular velocity at the time of accretion for 7 !1 numerical model, black points with error bars are the observational results from S08. visible satellites. Lower panel: the distribution of their accretion redshift 10 h M!. It is important to note that this process of hy- !5 Upper panel: no correction for the concentration related density evolution. Lower panel: drogen cooling simply defines a minimum mass of the pop- correction included (see text). zreion = 6.6 ulation of the dark matter subhalos that could host satellite Busha et al. 2009 zreion = 9.6 z = 11.6 galaxies. However, this work predicts the stars forming in 10 100 density profile of lowreion concentrated dark matter haloes, we man- ] V • O 7 1 these halos to be very massive and short–lived. As such Circular Velocitymax [km/s] Their values,10 and associated uncertainties, are obtained via a ually reduce the δc parameter by a factor 2 in all haloes with a these very first star forming halos cannot be the direct pro- 2 [M concentration less than 10 at10 the moment of infalling, results χ minimization0.3 procedure (see Macciò et al. 2008 for more V genitors of Milky Way satellites, which are observed to be FIG. 1.— The relationship between magnitude and vmax for the r!, g!, and max M are shown in lower panel of Figure 2. V! bands using abundance matching (solid red, green and black lines). The details). Under the assumption that the density profile within metal-enriched objects with stars presumably of masses less dashed lines Extrapolation show power law of fits toabundance the low-luminosity matching end. technique As expected this modification mainly applies to high lumi- than a solar mass. More relevant here are the calculations of 300 pc does not evolve from the time of accretion to z = 0 we FIG. 7.— The peak circular velocity functions for subhalos hosting [e.g. Kravtsov et al. 2004] implies the least luminous can compute the present value of M for each satellite using satellitenosity haloes, galaxies. since The they solid were line the shows most the massive velocity ones funct ation time for o allf via Wise & Abel (2008), who followed the build up of halos up V band, we get 0.3 ! 8 6 Lacteainfall,subhalos. and thus likelyThe red to dotted, be less green concentrated. dashed, and When blue dash-dotte a possibled lines to the masses when they start cooling via Lyman-alpha from galaxies live in halos of about 10 Msun eq 2. 10 7.1 showmodification the distribution of the density for subhalos profile hosting for low satellite concentration galaxies hal foroeszreion = v The upper2 panel in3 Figure4 2 show the5 results6 for the7 relation neutral hydrogen. They included the radiative as well as the max 10 10 10 10 10 10 × 8 MV ! 5log(h) = 18.2 ! 2.5log . (1) 6is.6 taken,9.6, and into 11.6 account with Tvir the(M upt) = turn 3 10 in theK, as numerical in Figure 5.M0 The.3/L longrela- dashed supernova feedback from the first generation of massive stars. 1km/s between mass within 300 pc andL [L luminosityO •] as obtained in our ! $ V blacktion at line high shows luminosities observed distribution almost vanishes for Milky and Way numerical satellites, rescorrectedults for The short-lived sources keep ionizing the baryonic material " # numerical model (red crosses) versus the observational results sky coverage and detection efficiency. The cyan bands show combined Monte When selecting the appropriate vmax for assigning a luminos- See also Li, Helmi, De Lucia, Stoehr 2008; are now in better agreement with the observational data. in the halos they form in, as well as their surroundings. How- FIG.(black 6.— Top dots Panel: withThe error ratio bars). of subhalo Here we mass plot at the results time onlyof accretion for sim- to Carlo and statistical errors. ity, we follow the method of Conroy et al. (2006) and choose Koposov et al. 2009 The presence of a baryonic component inside the dark matter ever, as they turn off, material can cool again and repopulate luminosityulated for satellites our abundance that satisfy matching the model detection (red circles)threshold with ofzreion the SDSS=9.6. the dark matter halos. So while the baryon fraction (Fig. 4 in the peak vmax over the trajectory of the subhalo. BecauseFilled circle represent halos that are within the SDSS completeness radius, halo can by itself modify the density profile of the halo, due to luminosities are set using the maximal v , changing z as determined by Koposov et al. 2008. This means that satellite 3 Wise & Abel 2008) fluctuates and decreases at times to as lit- max reionequationluminosity 3, while open and circles distance are haveoutside to this satisfy distance. theCy followingan stars represent relation massthe adiabatic of Tvir compression(Mt) = 8 × 10 processK as (e.g. in Figure Blumenthal 5. Here, et al. 1 the986, solid tle as 10%, star formation can continue as long as no sustained has no effect on the luminosity of an individual galaxy, al-Milky Way satellites. In order to make this comparison, we used the values blackGnedin line et al. shows 2004). the In distribution our case we for expect all via this Lactea effectsubhalos, to be though the population of subhalo hosting satellites may still log(R/kpc) < 1.04 ! 0.228 Mv. The mean and the scatter of external UV flux sterilizes the halo. The latter case severely for mass within 300 kpc at the present epoch, M0.3, published in Strigari et al. whilenegligible the givenred dotted, that the green baryon dashed, fraction and of blueour haloes dot-dashed is much show limits star formation and has been discussed many time in the change. The appeal of this method is that we are able to ig-(2008)observational and converted datathem are to subhalo both well masses reproduced using their by publ ourished numerica relationl 6 lower then the universal one and satellites have been observed literature (e.g., Babul & Rees 1992; Thoul & Weinberg 1996; nore much of the poorly understood (and poorly simulated)for theresults average upMDM to( aM luminosity0.3) calibrated of toL N-body=2× 10 simulations., after thisBottom point Panel: sim- the distributions from our model for three values of zreion = to be dark matter dominated even in their central regions (S08). Kepner et al. 1999; Dijkstra et al. 2004). It seems clear then physics of galaxy formation using a statistical method that hasThe relationulations between seemM to0.3 suggestand luminosity an increase for our with abundance luminosity matching of modelM0.3, 6.6, 9.6, and 11.6. Because the abundance matching method from the limited guidance we have from numerical simula- been shown to, on average, reproduce a wide variety of ob-and observations.which is not Here, present we have in the converted data (even the masses if only of 3 the satellitevia Lactea galasub-xies wasNow more we turn successful to understand than the the origin SPS model of the relation in reproducing between the halo to M0.3 values using the formula provided6 by Strigari et al. (2008). tions that objects at the hydrogen cooling limit and below will servable properties for more massive galaxies (Conroy et al. have a luminosity greater than 10 L!). observedM0.3 and L luminosityfound by S08. function In upper without panel the of Figure need to 3 we tune show any pa- experience most of their star formation before they are perma- 2006; Conroy & Wechsler 2008), as well as some proper- the distribution of Vcirc at the time of accretion for visible satel- !1 These results7 are obtained9 under0.35 the assumption of no evo- rameters, we only include satellites that pass the radial cut of nently ionized. ties of dwarf galaxies down to vmax ∼ 50kms (Blanton et al.tion M0.3 = 10 M!(Mvir/10 M!) , where Mvir is the virial lites. The distribution peaks around V = 20 and has then a lution for the parameters defining the density profile (rs and equation 3 using the abundance matchingcirc criteria. As can be Once we have identified satellite galaxies in the simula- 2008). It is still unclear how this method will fare at lowermassδ of). the This subhalo assumption at the is time well ofmotivated accretion. by the We detailed must caution numer- sharp decline towards higher values of the circular velocity. As tion, we must assign magnitudes to them in order to make masses; it must break down for small halos once they no c seen, an earlier zreion suppresses the distribution of subhalos that thisical studyrelation carried is expected out by Kazantzidis to be dependent et al. 2004 on cosmology (K04, here- discussed in section.3, the sharp cutoff below Vcirc ∼ 20 km/s direct comparisons with observations and to account for ob- longer host one galaxy on average. If this transition is sharp, with all values of vmax, although the effect is more pronounced and ignoresafter, see all also scatter. the recent The results observations by Peñarrubia are remarkably et al. 2008). we K04ll comes from the inefficient H2 cooling in haloes with virial tem- servational completeness effects. This is done using two however, it may be a reasonable approximation for most of forperature low belowmass halos. 104K. Combining Still, this this suppression narrow distribution is present of even cir- for the mass range where halos host galaxies. matchedhave by shown our that model the withinner excellent density profile agreement is extremely for all robust but > methods. First, we use a halo abundance matching method vcularmax ∼ velocity20km/s, (between where 20 most! 40 of km/s) the classical with the theoretical dwarfs live. ex- This (Kravtsov et al. 2004a; Blanton et al. 2008). Here, luminosi- As a second approach for assigning magnitudes, we usethe a mostand that most it luminousis unmodified galaxies. by tidal In forces the lower even after panel tidal of stri Fig-p- indicatespectations that shownzreion in Figurecan effect 1, and satellite assuming galaxies that M ofdoes all not masses ties are assigned to halos by assuming a one-to-one corre- toy model to predict the star formation rate and stellar massure 6ping we consider removes athis large data fraction in a different of the initial way bymass. plotting TheyM have0.3 0.3 andevolve luminosities. after accretion, it is not surprising that all Milky Way spondence between n(< MV ), the observed number density of a satellite combined with the stellar population synthesisas a functionalso shown of that luminosity. the degree Here,of modification we take (if the any) data of directly the den- 3 satellitesThe long-dashed (observed and black simulated) line with have data a inner points mass again within rep- of galaxies brighter than Mv, with n(> vmax), the number (SPS) code of Bruzual & Charlot (2003) . Here, we again as-fromsity Strigari profile et depends al. (2008) on the and initial convert (i.e. the beforevia Lacteainfall) concsubhaloentra- resents the observations.7 The v values for the satel- density of simulated halos with maximum circular veloci- sume that star formation begins when the satellite first crossesmassestion to ofM the satelliteusing the dark above matter formula. halo. While While highly the concent numbersrated 300 pc always around 10 M!. It is thenmax interesting to ask why the mass threshold, M , and ends at the reionization time, 0.3 lites,these satellites including span errors, a wide were range calculated of luminosity. using In the the method lower of ties larger than vmax. For the distribution of magnitudes, we t are inhaloes general (with agreement,c ∼> 20, condition the abundance satisfied matching by the majority model of (red our use the double-Schechter fit of Blanton et al. (2005) for low zreion. During this period, the star formation rate is set by the simulated haloes) are able to keep the profile unchanged0.17 even Strigaripanel of etFigure.3, al. (2007b,a) we show using the accretion kinematic redshift data as taken a functi fromon the dark matter mass of the subhalo, circles) shows a clear trend with luminosity, M ∝ L , as luminosity SDSS galaxies in the g! and r!bands down to after several orbital periods, less concentrated0 haloes.3 V (c ≈ 9) literaturethe satellite (Walker circular et velocity. al. 2007; At a Simon given circular & Geha veloci 2007).ty satel- The line Mr = !12.375. The vmax values are taken from the halo catalog α opposed to the observations (cyan stars) which indicate more lites have a wide range of accretion redshifts. As we pointed MDM slightly modify their profile mainly by reducing the overall nor- was calculated using the 22 observed satellites and correct- of a 160 Mpc/h simulation complete down to v ≈ 90km/s. ! fcoldgas if MDM > Mt, z > zreion max SFR = 1 M! (2)of a common mass scale. The trend in our model results di- in section 3, filtering-mass is a strong function of redshift, so In order to extrapolate this to lower circular velocities, we malization (δc) by approximately a factor 2. ing them for SDSS sky coverage and detection efficiency % 0" # otherwise rectly from the abundance matching method, which assigns for a given Vcirc, the baryonic mass fraction of a satellite is sup- calculate a power-law fit to the low end of the dn/dvmax func- In order to take into account this expected modification of (Koposovet al. 2008). The cyan region denotes errors on luminosities to subhalos satellite based on vmax at the time pressed to different extend depending on its accretion redshift, tion. The resulting correspondence is shown in Figure 1 for where fcoldgas is the fraction of cold gas in the halo, and α this curve and were calculated using a Monte Carlo approach. the r!, g!, and V!bands (red, green, and black curves). The V and ! are free parameters. This is similar to model 1B ofof accretion. The addition of scatter into either the LV (vmax) In this approach, published errors are used where possible; band magnitudes are calculated using the transformation V = Koposov (2009), with a couple of key differences. First, weor M0.3(Mvir) relations, which we expect at these low mass where no robust errors are published, the average error distri- g ! 0.55(g ! r) ! 0.03 from Smith et al. (2002). This method impose a hard truncation of star formation at the epoch ofscales, can help to flatten this trend slightly and bring it more bution is mapped onto the remaining SDSS dwarfs. While this implicitly assumes that all galaxies have average color. Since reionization, something they only consider using their modelin line with observations. The SPS model (green triangles) the data from Blanton et al. (2005) is not deep enough to map where stellar mass is a constant fraction of dark matter mass. process does not produce uncorrelated error bars, it should be αalso produces a similar trend with luminosity albeit with a sig- onto the dwarf galaxy distribution, we use a power law to ex- Second, they treat stellar mass as being proportional MDM significantly more robust than simply using statistical uncer- nificantly larger scatter, making the slope of the M0.3(LV ) rela- trapolate the MV (vmax) relation to lower magnitudes. For the tainties. We should also note that, because the reconstruction 3 http://www.cida.ve/ bruzual/bc2003 tion consistent with zero. Previous studies of simulations have of vmax from observations gives a very strong lower bound but observed a similar trend (e.g., Maccio’ et al. 2008; Li et al. only a weak upper bound, the errors on the lowest points are 2008; Koposov 2009) using semi-analytic modeling of galax- probably underestimated because very few satellites will scat- ies and/or subhalo distributions. ter into this bin as we create a Monte Carlo representation of the distribution. These systematic errors were combined with 4.4. Circular Velocity and Radial Distributions statistical errors assuming a Poisson distribution. We next consider the mass distribution of the satellite galax- Figure 8 further explores the impact of varying zreion on the ies hosting halos. Figure 7 shows the changes in the vmax properties of the satellites and the subhalo hosts by consider- distribution for satellites as zreion is varied, given a threshold ing the radial distribution within the halo. The lines represent Dark Matter annihilation radiation in the Milky Way Fermi VERITAS ContributionContribution frfromom substructursubstructuree componentscomponents smoothsmooth main main halohalo emissionemissionsmooth (MainSm)(MainSm) main halo emission (MainSm) emissionemission from from resolved resolvedemission subhalos subhalos from resolved(SubSm+SubSub) (SubSm+SubSub) subhalos (SubSm+SubSub) smoothsmooth main main halohalo emissionemissionsmooth (MainSm)(MainSm) main halo emission (MainSm) emissionemission from from resolved resolvedemission subhalos subhalos from resolved(SubSm+SubSub) (SubSm+SubSub) subhalos (SubSm+SubSub) smoothsmooth main main halo halo emission emission (MainSm) (MainSm) emissionemission from resolvedresolved subhalos subhalos (SubSm+SubSub) (SubSm+SubSub) -0.50 -0.50 2.0 2.0Log(Intensity) Log(Intensity) -3.0 2.0 2.0 Log(Intensity) Log(Intensity) -0.50 2.0 Log(Intensity) -3.0 Springel 2.0 et Log(Intensity) al. Nature 2008 -0.50 -0.50 2.0 Log(Intensity) 2.0 Log(Intensity) -3.0 -3.0 2.0 Log(Intensity) 2.0 Log(Intensity) -0.50 -0.50 -0.50 2.0 Log(Intensity)2.0 Log(Intensity) 2.0 Log(Intensity) -3.0-3.0 -3.0 2.0 2.0 Log(Intensity) Log(Intensity) 2.0 Log(Intensity) unresolvedunresolved subhalo subhalo emission emission (MainUn) (MainUn) totaltotal emission emission unresolvedunresolved subhalo subhalo emission emissionunresolved (MainUn) (MainUn) subhalo emission (MainUn) totaltotal emission total emission unresolvedunresolved subhalo subhalo emission emissionunresolved (MainUn) (MainUn) subhalo emission (MainUn) totaltotal emission total emission 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 -0.50 2.0 Log(Intensity) -0.50 2.0 Log(Intensity) -0.50-0.50 2.0 2.0 Log(Intensity) Log(Intensity) -0.50-0.50 2.0 2.0Log(Intensity) Log(Intensity) -0.50 -0.50 2.0 Log(Intensity) 2.0 Log(Intensity) -0.50 -0.50 2.0 Log(Intensity) 2.0 Log(Intensity) -0.50 -0.50 2.0 Log(Intensity)2.0 Log(Intensity) -0.50-0.50 2.0 2.0 Log(Intensity) Log(Intensity) -0.50F igure 8: Different emission c o2.0m Log(Intensity)ponents. The top left panel shows an all-sky map of -0.50the main halo’s diffuse emission ( a2.0ve Log(Intensity)raged for different observer positions FiguFarniegdu8or:veeD8r:iaffzDeimrieffunettrhe)en,mtwieshmsiliieosnstihocenotmocpopmorinpgeohnttepsn.atnsT.elhTsehoteowtpospltehlfetfeptmapnaisensleiolsnhshofworowsmsaannllaarlel-ls-sosklkyvyemdmasauppbohffaltohse, fmroamiin ahharaallono’d’ssodmdififpfuoussseieteioemnmisoissnisoitnohne(aS(vaoevlraearrgacegidrecdfloefr.odTrihfdfeieflrfueemnrteinotobsoiebtrisveeserravspesorisgpintoieosdintsitons Figure 8: DiffereFannitgdueaoemrnavedicesh8rso:iavsouzeDnibrmihacfafzuoelitmorhe)ipun,ottcwhnle)uhe,mdniwletieshts.ithilheoTeintrhhtoceeoptnmortpirpgiborhliunetgtfehpitnotaptnnpsa.eafnonleTresllhasolelhwuotoswnprtssehlsteahofneltvmepamdlailsn-is(sesiskoluiynbos-nhfm)orsfowuarombpsmstoarfanulllctlarthurelelsr-seosmo.lklvyFaveieodnmdr shasuipuambblohph’falsillctohdisteiy,fffmaurnosadmeinSpringelfeaoahmrrarabialsnoensdt’ditsoeomrndmigf(prfapaouvopsesihetriitacoeigaonmelnodirsoenspfni torohotrnetehddeSu(iacofSvftloieaeo lrrnaeacal.rngtihrcteciedorlyecbf. lhsoeeTar.2008rvhvdTeeeihfbrlfeueepmelrouneimsnritoetiipsnooirobtneisesieestrinavetsesrdaigspansosiesgpdinotiteiondntsto Figure 8: Different emission components. The top left panel shows an all-sky map of the main halo’s diffuse emission (averaged for different observer positions Figuraend8:ovDerifafzeirmenutthe)aem,nawdicshhsoesivasolouceunhbrrtchasceauezoslibmotthohaipuanlotochrnwli)iuge,nedhncrwetltushpst.dihmaleenToitetrhohletceehsiorhetndoctwoprwinbsritliutretghihtfbhitaeuotptnGepiaomafanonuieresflolsairslaolhannuollbwnfuerrsoansemsrteahosneloaovflelalv4mdler0le-di(assrs(koucsiylboumv-nbem)i-nsdf)u.arssoubpTumbshbtosrethfaurabulctllocthourtesutro,sremeo.f.rlFavolFeimonofdrtrashpssiuaimrmnblaoephnp’lladlsiiglocoidimvstiye,fsfpaurotnohssdmeitSpringelffeieoaoxmrrnprbaebioesncensttdtteiteodetrhmrnsgegur(pSraaafopovapshlceihaietrciracoabcgalnrielirrgoedcrhpenletrpfn ot.rhedorTetseudsdhcSufietcoifroftlieuanmo rmntehcaal.nitilenhrltyoceuolshynebiar.t hsveieTase2008sorvhbvleaevesebrlsduneipmgesroneuispenbridroheteipsastoilroetoneinsestesdndoatwseassdnigpatnoseitnpdhtoetiont and over azimuth), while the top right panel shows the emission from all resolved subhalos, from a random position on the Solar circle. The luminosities assigned to Faingduroevae8cr:hasDzuiibmfhfueatrlhoe)ni,tnwcelhmuesiaodliceushsrtscifhsoreueunseibrrttchocshecatopasrolmteontrawhitpmigraneoithibcrnwtelugueptesdnirlmaoeitnmnsoste.hoimfltoet,ThsoirarhoehsadotcselhuwolwemtnudsoitnitrpwtnhirhbgeilaeutsehaotGfeiltaosmvapnpGeuhiadsfaenosur(iiresaocslunanilbalsllbn-hfyue)rosboanswueymrbaemsmsoamotafrllonulev4ftcer0ra4tediuacl0slr(o-ahecsslru.amvcklbmFeoyi-nd.o)i.nmsrTsu.TsuhabTihibpmsshethrepioabuslfblociaoocttsutitvhot,reoymefrm.ryamolnFlesmedaomffitrtnfoapospoairhartmnahnabeneplecloldltoigt’ocmesiiimvrtpdyegoisprafnatfonehpusndehsitteifeiocxoxvaerpnplemeberroceceitntstheptesedrdtirohosdsgekunurySarfc(afptoatahcihvlcoeaaientcrbradbratcloihrgiimrereghecydihtplnetrhaenfo.atsoedevsTsrsuesfhcdrtbfhetoiremfolfeunmtenoamrtlterhlaienleunlpytnfloruruosehneixsbasrteoveis(nesleivtsorsebevladvieenserastdneuispgbsrpronehuaospeabtiiledrhntoediatstoloeflodnnuostxweddinoswatnosnetpahtroeliytnhte each subhalo include thfreeier sctorenatmribinugtiloimn ifto, rasaslulmuninrgesaolsvpehder(icsaulbly-)syumbsmtreutcritcurhea.loF.oTrhsiismisplaicvietyryasnmdofoothr bceotmteprognreanpthoivcearl trheepsrkoyduthcatitodnomthienyatheasvtheebteoetanlrfleupxre(sitesnitnetdegarsatpeodiflntux is nearly aenadcohvseourubrahczaeilsmotuhintahct)lwu, dewrehetsifshlormeeueirotrhc1osect.t9srohetnetotahidtmpraiwtiebrnwsiiugttehhirloteiamnpiGsniamftaon,eourgeaosrlsasatslhsitulaehmnduonwibflwnreusgeiaxtsmthaohfrlaseovpGmefhdm4aetu0rh(isseacsusraimcibalolmn-ayn)iisbnsnfueyr.hbamoaTmsmlmtohro)eue.aftcblrF4tliouic0rntrteaheosrl.amlcoylmFol,vl.otieehnrfTde.tshpTbisimaosuhntbepitesohlblmiaocglitvoirtvieoysgerm,hysaftntrlsphedomaefmtnfoeopeoxarltphnsbreheaecolntotwtgedmeidsorvptmesghosurenratpefhtpaonehctsaieiocltxibvaspoulreenirrgcfetahohepctndenreoetsbhdskursueiyrgfcfSahtrthcoitoneamlentabsdrarstoihlcgflmeirhuroyitcnmnlhraeeats.sevslolsTeflcrhvtbohemedelptunsoaoumltnrlabeiluhnpnflatorsrluesoexstisoteoi(gdnelievtossteewhdaiensrast.teusioAgbprnthlaholeateimldenodatstpofldsuosxwhoinswtnotehtaherely sources that were smoo1t.h9etdimweisththae iGntaeugsrsaitaend bfleuaxmfromf 4t0hearmcmaininh.aTloh)e. Fbiontatollmy, tlheeftbpoattnoeml grivghest pthaneeelxspheocwtsedthseutroftaaclesubrrfiagchetnberisgshftnroemss farlolmunarlelscoolmvepdonseunbthsatologsetdhoewr. nAtlol mthaeps show the esaocuhrcsfuersbeehthasaltortewianmecrilenugdsmeliomthf1orie.te9hi,ereatsicdsmtusorruwenefmastimrctithienhbingebaugrtiGaiingloitsahmenputgnhisfrteesoa,sirtrasiecsnadisanlulbfllumeyunaxniisnmtrysfgermsoaofmflst4vepht0ethrdeaimcrr(micacshmiauanliblilnohny-.a).hslTaoyul’hmobhsi)essmd.tirbiFefusfotiucrntaistcaouevlmrlheeyeram,.yllotieFhs.fsmeotiTorpbohnasoi,intstmtaheoinlspmcdgloaiuimrcvisigepthyrsotythntaphesenamensdntaeoemfoxlovpteshreehmrboctaeowehptmdtsepepitsrnhokugenyrreftaonthpctcaheoltivlbcsdoeuraorrirlgmsftrcahieactenplneaesret,bkoeserydsixgutfchcreoatepnitmtotedofnsoatsarmltflhtrihfleuoneynumarxmtheaas(lipvoltshelcoveoifbenmtdtetoheptesganourlrnaberfleteshenuopadtxlrslveofle(tssidoutesgxdnseoiutintewbshtdsentgrrea.urtasaocArttpleutlyohldreimflns,atupwxshisehrneoewtahretlhye free streaming limit, asssuurfmaciengbraigshptnhesrsicianlluynistysmofmtheetrimcahinalhoa.loT’hsidsififsuaseveemryissmiono,oathndcoumseptohneesnatmoevmerapthpeinsgktyo tchoaltordoscmalien,aetxescetphtefotorttahleflmuaxp(iotfstihnetergesroaltveeddflsuuxbsitsruncetuarelys, where the sofruereces1ts.r9ethatamimtiwensgetrlheiemsimint,toeaog1sstru.sh9aruetfetmadisdcmciweanflelgbisuetrxhteaihgxfaeshtrepotiGnnhmdetaeesurtgsihtscroseiaanictlameolundynansibflisnityedusaemhxormaafmlrbotoleh)ym.fterfF4imatc0ihinaehaatiarenmlclryohmas,.aiunitlrhTnofhea.’hsacTiblesdoohib)itfe.srtfoiuFgbamshioenvttnraeteioelrmglsymyhsi,.tstlsmpheiaeofontboe,potlahtstnohcdemoluwmgsrsiepvgtothehnsteeepttnhsaotanetmaeoellvexssepumhrreoaftcwhaptcespeditsnhbkgseryuitgrotfhtactacnoltelsdosubsorrrmfsfiargccoiahnemltaenbt,aereilsgxlshcthfetonrepmoettmspofsotafrnrleotlhnflmuetusnxmartleola(sgipctoeosoltmvhifnepttrdhoe.engsAerurnalebltshesomdaltvaoloflpegsduetxdsshhuoeiobswr.wsntAretuthlaolcretmlutyhraepss, swhhoewreththee 1.9 times the integratedscflaluexexfrtoenmdsthtoe cmonasinidehraalbol)y. fFaintaelrlys,utrhfaecebobtrtiogmhtnreisgsh.t panel shows the total surface brightness from all components together. All maps show the fr1e.e9 stitsmrueerafsmactihenegbirnliigtmehgtintr,aetasesssdsuciunraflfmlauecixnenixtgfbstreroaoinmgfdshspttthnhteoeesrmcsmiocainanisnlilniuydhnehaisratlyasolbmo’osl)yfm.dtfFiheafetifinruimastceelalrhyiesna,multhorhifas.easlcoTiboe’hsonbit,dsrtoiafginmfshudtasnrueievgsseehsmr.ttyhipsesaminsoaenoml,oseathnmodcwaoupsmspetiphntoehgnettoesontaactmlooeslvoumerfrasapctchapeleienb,sgrkeitgyxochtecthnpoaelttosfrsdoosrfcrmtaohlimen,amaetlxealpsccetophftmetfphotoertntrahelesnflotmsluvaxteopd(gioestfsuthtbihensertt.rerugeAcsrtloaulltrvemeedsad,pflwssuuhxsbehsirtoserwuntcheteuahreelys, where the surface brightness in units of the main halo’s diffuse emission, and use the same mapping to color scale, except for the map of the resolved substructures, where the 1s.9urtfiamcsceasbletrhiegexhtitennnteedsgssrtaiontecudsocnnflaistluisedxeorxfarttoebhnlmyedsfmtahtioaenictnmeorhnasaiunildorehf’asraacldbeoil)fby.frufiFagsiehnttaenelmerlsysis,su.strhifoaecneb, oabtnrtidogmhutsnreeisgtsh.et psanmeel smhaopwpsintghetotoctoalosrusrcfaclee, berxicgehptnt efsosr fthroemmalpl coofmthpeorneesnotlsvetodgseutbhsetrr.uActlulrmesa,pwshsehroewthtehe scale extends to considerably fainter surface brightness. suscrfaaleceexbtreingdhstnteosscoinsuidneirtsabolfytfhaeinmtearisnuhrfaalcoe’sbdriigffhutsneesesm. ission, and use the same mapping to color scale, except for the map of the resolved substructures, where the scale extends to considerably fainter surface brightness. Indirect Detection If the halo is smooth: Smooth halo flux = Particle Physics x Astrophysics If there is sub-structure: Total flux = [Smooth halo Flux] x [Substructure Boost] Annihilation Signals + Halo Kinematics 7.1 7.2 7.3 7.4 -5 -4 Combine-3 MCMC -2code that-1 determines0 0 2 4 6 8 10 best fitting halo parameters with a DM log10 [M0.3 (M!!")] particle modelbeta rs [kpc] Provides robust bounds on the DM properties, accounting for astrophysics 90% c.l. lower bound Can either use ``CDM” or ``non- CDM” based models by marginalizing over varying ranges of the inner and outer slopes 7 Prior Data 0.8 0.9 1.0 1.1 1.2 15.0 15.5 16.0 16.5 16.0 16.5 17.0 17.5 18.0 18.5 Scale radius 2 3 2 -6 log Draco L.O.S. Integral [GeV2 2 cm-5-5] inner slope log10 ["0 rs (M!!" kpc )] log10 [L (GeV cm )] Scale density FIG. 2: The allowed region in the ρs − rs plane for the six dSphs after marginalizing over the stellar velocity dispersion −1 anisotropy parameter β. Solid lines correspond to contours with Vmax of 5, 10, 20, 40, 80, 150 km s . Long-dashed lines represent the ρs − rs relation as derived from the field halo relation, and the 2-σ scatter above the median concentration vs. mass relation. Dot-dashed lines represent the ρs − rs relation as derived from the tidally-stripped halo relation, and the 2-σ scatter below the median concentration vs. mass relation. not well-defined, in all of the cases the data does approx- ing the relation that is 2-σ above the median for field ha- imately fix the density at the mean radii r! of the stellar los in ΛCDM [38] and the lower (dash-dotted) lines show distribution [69]. Calculating the total mass of the dark the relation implied by the the tidally-stripped Vmax-rmax matter within this characteristic radius, for all galaxies relation with a 2-σ scatter below the median c(M) rela- 7 the minimum implied dark matter mass 10 M!, which tion [52, 53]. We consider both the field and stripped ∼ occurs for the lowest implied values of ρs rs in each case. relation because the degree of tidal stripping experienced This is at least an order of magnitude− greater than the by each dSph is uncertain, depending sensitively on the contribution to the total mass in stars in all cases. precise orbital information and/or redshift of accretion, two quantities that set the amount of tidal mass loss [40]. Over-plotted in Fig. 2 are lines of constant Vmax in The region where the CDM predictions cross with the the ρs rs plane. Phrasing the dark matter halo prop- − observationally-allowed values of ρ and r in Fig. 2 de- erties in terms of Vmax allows for a direct comparison s s to CDM models, which provide predictions for the cu- fines a preferred model for the structure of these dark matter halos within the context of CDM. mulative number distribution of halos at a given Vmax. Although the high Vmax solutions are plausible by consid- ering the data alone, comparison to CDM models show that it is improbable that all of these halos have Vmax IV. FLUXES FROM DWARF SPHEROIDAL in the high end of the allowed regime [40, 70, 71, 72] GALAXIES (although this solution may be viable for some smaller fraction [73]). Typical CDM halos have 1 system as A. Smooth Halo large as 60 km s−1. ∼ ∼ Dashed and dash-dotted lines in Fig. 2 enclose the The flux of γ-rays originating from the annihilation 2 3 predicted ρs-rs relation (including scatter) for cold dark of dark matter particles is sensitive to ρsrs (recall that 2 3 matter halos as determined from numerical simulations. ρsrs , see also Eq. (6)). Even though ρs and rs indi- In order to provide a conservative range for the CDM ex- Lvidually∼ can vary by orders of magnitude and still satisfy pectation, the upper (long-dashed) lines are obtained us- the observed velocity dispersion profile (see Fig. 2), the Cross Section/Lifetime Bounds ] -1 s 3 [cm Lifetime [s] Annihilation Cross Section Dark matter mass [GeV] Dark matter mass [GeV] Essig, Sehgal, Strigari 2009 Sommerfeld Effect in dSphs 5 Robertson & Zentner If sommerfeld effect explains PAMELA, flux detectable within about 1 year with Fermi [Essig, Sehgal, Strigari 2009] FIG. 3: Radial enhancement in the DM annihilation rate owing to a Sommerfeld-like velocity-dependent cross section and the radially-dependent halo velocity dispersion σv. Shown are the products of cross section and velocity averaged over the local velocity distribution function and normalized to their values absent any Sommerfeld effect, !σv"/(σv)0 = S(v)f(v)dv. Position is given in units of halo scale radii, x = r/rs. The annihilation enhancement is plotted for MW-like (left! panels) and Ursa Minor-like (right panels) halos with NFW (1st and 3rd columns) and Einasto (2nd and 4th columns) halo profiles, using either the Arkani-Hamed et al. [13] or Lattanzi and Silk [22] DM parameters. form of the interaction and the masses of particles, this the Sommerfeld factor averaged over the relative veloc- method can be applied to any model of particle inter- ity distribution functions for dark matter halo models actions. The qualitative features we describe hold for at each position within the halo. We show halo models Sommerfeld-enhanced annihilation in general. representative of the MW and the Ursa Minor satellite Figure 2 shows the dependence of the Sommerfeld en- for the dark matter parameters chosen by Arkani-Hamed hancement on the dark matter particle masses and rel- et al. [13] and Lattanzi and Silk [22]. ative velocities (the right panels of Fig. 2 reproduce the The behavior of the annihilation enhancement results in Figures 2 and 3 of Ref. [22]). Sommerfeld fac- σv /(σv)0 depends on the halo kinematical structure tors can clearly be quite large for reasonable parameter $and% the details of the particle model. If the DM parti- values. The upper panels of Fig. 2 show examples of cle mass is near resonance, the Sommerfeld enhancement − resonant capture at specific values of mDM. The lower increases faster than S(v) v 1 and the decline of the panels show that the Sommerfeld factor becomes unim- halo velocity dispersion with∝ radius leads to a large in- portant as v/c 1 and saturates according to Eq. (10). crease in the annihilation rate between the radii x 1 → 2 ∼ For α > v/c > αmV /mDM the Sommerfeld factor ex- and x 0 in addition to the expected Γ ρ depen- −1 ∼ ∝ hibits∼ a strong∼ " relative speed dependence. S(v) v dence. The relative increase is larger for the Milky Way −∝2 3 for models away from resonance while S(v) v near ( σv x∼0/ σv x∼1 10 for Arkani-Hamed et al. [13] ∝ $ % $ % ∼ resonances [13, 22]. DM with mass mDM 650 GeV) than for Ursa Minor ≈ ( σv x∼0/ σv x∼1 30) because the velocity dispersion of$ Ursa% Minor$ % near∼ x 1 is already approaching the IV. THE ENHANCEMENT OF velocity at which the Sommerfeld∼ boost saturates. The VELOCITY-DEPENDENT DARK MATTER faintest known Local Group dwarfs such as SEGUE 1 ANNIHILATION IN GALACTIC HALOS [33] or Coma Berenices [34] with very low velocity dis- persions (σv < 10 km/s, see Martinez, Strigari, Bullock Figure 3 shows the enhancement of the annihilation et al. in prep)∼ will have a radially-dependent cross sec- cross section owing to the Sommerfeld effect as a func- tion enhancement only if the saturation velocity is very −5 tion of position in dark matter halos. We show the quan- low (v/c < 10 ). When mDM is such that the inter- tity σ(v)v /(σv)0 = S(v)f(v)dv, which amounts to actions are∼ far from resonance, the effects are much less $ % ! Supersymmetry predictions Segue 1 G. Martinez et al. 2009 Marginalizes over all CMSSM parameters (SuperBayes, Ruiz de Austri et al. 2006) Marginalizes over all astrophysical parameters, including Boost 14 Milky– 23 – Way/Local Group Mass Fig. 1.— OrbitalFigure poles of Milkyfrom Way Metz satellite & Kroupa galaxies as 2008 derived from their measured proper motion and radial velocities. The directions are shown in an aitoff projection in Galactocentric coordinates. The solid lines give the projected arc-segments derived from the uncertainties of the measured proper motions. Different symbols mark data derived by different methods: circles: HST, diamonds: ground-based measurements, and hexagons: the weightedUpdated mean applications values from Table 1. of The Timing filled star symbolargument marks the imply mean spherical Local Group mass of 5 x 1012 Msun and MW direction l of the directions of12 the angular momenta of the satellites excluding Sagittarius and Sculptur,mass of and 2 the x solid 10 loopMsun gives the spherical[van der standar Mareld deviation & Guthalakurta of this sample. The 2008, Li & White 2008] smaller, open star symbol marks the mean spherical direction as before, but now treating the LMC/SMC as a bound system whose barycentre is moving with the velocity of the LMC, assuming Ground-based an LMC/SMC mass proper ratio of motions: 5/1. The dashed Scholz loops & indic Irwinate regions 1994, with Schweitzer 15◦ et al. 1997, Ibata et al. 1997, Dinescu et al. 2005 and 30◦ from the direction of the normal to the plane fitted to the 11 classical Milky Way satellites Space-based (the DoS pole). proper Note the proximity motions: of l to Piatek the normal et al. of the 2002-2007 DoS. Satellite proper motions ``Perspective rotation”; see Feast, Thackeray, & Wesselink MNRAS 1961 Line-of-sight velocities in some cases better Walker, Mateo, & Olszewski ApJL 2008 than HST proper motions Sagittarius: Constraints on the shape of the MW halo Is Leo I bound to the MW? LMC, SMC? [Kaplinghat & Strigari ApJL 2008] HST error The core/cusp ``problem” • CDM predicts NFW/Einasto cuspy profiles • WDM or some alternatives predict shallower central densities • Current data from MW dwarf spheroidals are unable to conclusively establish whether these galaxies have cores or cusps Figure 4-9. The projected 100 error on the log-slope of the DM density profile of Draco at the King core radius as a function of the number of 80 proper motions. From top Projections to bottom, the curves as- sumed that the errors on the transverse velocities are 10, 60 7, 5, 3 km/s. Beta/log-slope degeneracy precludes measurement of central Percent Error on Log–Slope 40 density profile See Wilkinson et al. MNRAS 2002 for 20 0 200 earlier400 modeling600 800 1000 Number of Proper Motions Figure 4-10. A demonstra- available for 1000 stars in a 1 tion of the ability to recover particular dSph (top panels). 1000 LOS information on the nature of A significant improvement 0 X X DM using observations of is derived from the addition B dSph stars, from analytical of 200 SIM Lite proper modeling by Strigari et al. motions providing 5 km/s –1 (2007a). Ellipses indicate precision transverse veloci- Cusp Core the 68 percent and 95 per- ties (bottom panels). The left –2 cent confidence regions for (right) panels correspond the errors in the measured to a cusp (core) halo model 1000 LOS + 200 SIM dark halo density profile for dSphs and the small ×’s 0 X X slope (measured at twice indicate the fiducially input B the King core radius) and model values. velocity anisotropy param- –1 eter B in the case where Proper motions probe DM halo profile only radial velocities are –2 0 1 2 0 1 2 3 in central regions Velocity Anisotropy Log-Slope Log-Slope Figure 4-11. Potential SIM given transverse velocity 400 Lite exploration of the Draco uncertainty: 3 km/s (green dSph would need to probe line), 5 km/s (red line), to V ~ M = 19 to derive a 7 km/s (blue line) and 100 sample of 200 red giants 10 km/s (magenta line). 300 as seen by its Washington (From Strigari et al., in M-band luminosity function preparation.) (black line and left axis). The colored lines represent the number of days (right axis) 200 10 necessary to observe all the Days stars to a given magnitude Integrated Count limit with SIM Lite and for a 100 1 0 17 18 19 20 M #(!04%2 '! , !#4) # $9.! -)# 3 ! .$ ,/#!, $!2+ -! 4 4 % 2 s 55 Error projections Figure 4-9. The projected 100 error on the log-slope of the DM density profile of Draco at the King core radius as a function of the number of 80 proper motions. From top to bottom, the curves as- sumed that the errors on the transverse velocities are 10, 60 7, 5, 3 km/s. 10 km/s error per star Percent Error on Log–Slope 40 3 km/s error per star 20 0 200 400 600 800 1000 Number of Proper Motions Figure 4-10. A demonstra- available for 1000 stars in a 1 tion of the ability to recover particular dSph (top panels). 1000 LOS information on the nature of A significant improvement 0 X X DM using observations of is derived from the addition B dSph stars, from analytical of 200 SIM Lite proper modeling by Strigari et al. motions providing 5 km/s –1 (2007a). Ellipses indicate precision transverse veloci- Cusp Core the 68 percent and 95 per- ties (bottom panels). The left –2 cent confidence regions for (right) panels correspond the errors in the measured to a cusp (core) halo model 1000 LOS + 200 SIM dark halo density profile for dSphs and the small ×’s 0 X X slope (measured at twice indicate the fiducially input B the King core radius) and model values. velocity anisotropy param- –1 eter B in the case where only radial velocities are –2 0 1 2 0 1 2 3 Log-Slope Log-Slope Figure 4-11. Potential SIM given transverse velocity 400 Lite exploration of the Draco uncertainty: 3 km/s (green dSph would need to probe line), 5 km/s (red line), to V ~ M = 19 to derive a 7 km/s (blue line) and 100 sample of 200 red giants 10 km/s (magenta line). 300 as seen by its Washington (From Strigari et al., in M-band luminosity function preparation.) (black line and left axis). The colored lines represent the number of days (right axis) 200 10 necessary to observe all the Days stars to a given magnitude Integrated Count limit with SIM Lite and for a 100 1 0 17 18 19 20 M #(!04%2 '! , !#4) # $9.! -)# 3 ! .$ ,/#!, $!2+ -! 4 4 % 2 s 55 Figure 4-9. The projected 100 error on the log-slope of the DM density profile of Draco at the King core radius as a function of the number of 80 proper motions. From top to bottom, the curves as- sumed that the errors on the transverse velocities are 10, 60 7, 5, 3 km/s. Percent Error on Log–Slope 40 20 0 200 400 600 800 1000 Number of Proper Motions Figure 4-10. A demonstra- available for 1000 stars in a 1 tion of the ability to recover particular dSph (top panels). 1000 LOS information on the nature of A significant improvement 0 X X DM using observations of is derived from the addition B dSph stars, from analytical of 200 SIM Lite proper modeling by Strigari et al. motions providing 5 km/s –1 (2007a). Ellipses indicate precision transverse veloci- Cusp Core the 68 percent and 95 per- ties (bottom panels). The left –2 cent confidence regions for (right) panels correspond the errors in the measured to a cusp (core) halo model 1000 LOS + 200 SIM dark halo density profile for dSphs and the small ×’s 0 X X slope (measured at twice indicate the fiducially input B the King core radius) and model values. velocity anisotropy param- –1 eter B in the case where only radial velocities are Observational Estimates –2 0 1 2 0 1 2 3 Log-Slope Log-Slope Figure 4-11. Potential SIM given transverse velocity 400 Goal:Lite exploration 200+ of the Draco proper uncertainty: motions 3 km/s (green dSph would need to probe line), 5 km/s (red line), fromto V ~ M = 1+19 to derivedSphs a 7 km/s (blue line) and 100 sample of 200 red giants 10 km/s (magenta line). 300 as seen by its Washington (From Strigari et al., in M-band luminosity function preparation.) (black line and left axis). The colored lines represent the number of days (right axis) 200 10 necessary to observe all the Days stars to a given magnitude Integrated Count limit with SIM Lite and for a 100 1 0 17 18 19 20 M #(!04%2 '! , !#4) # $9.! -)# 3 ! .$ ,/#!, $!2+ -! 4 4 % 2 s 55 Hundreds+ Milky Way Satellites? Hundreds of Milky Way Satellites? 7 the observer’s position to vary over six specific locations, at (x, y, z) = (±8, 0, 0), (0, ±8, 0), and (0, 0, ±8) on the Via Lactea grid. We acknowledge that there are (contradictory) claims in the literature concerning whether satellite galaxies are preferentially oriented (either parallel or perpendicular) with respect to galaxy disks (Kroupa et al. 2005; Kuhlen et al. 2007; Wang et al. 2008; Faltenbacher et al. 2008), and equally contradictory claims regarding how disks are oriented in halos (Zentner et al. 2005; Bailin et al. 2005; Dutton et al. 2007). If there were a preferential orientation, then the appropriate sky- coverage correction factors would need to be biased accord- ingly, but for our correction, we make no assumptions about the orientation of the “disk”. Therefore, any uncertainty in the correct orientation of the disk is contained within the er- rors we quote on our counts. In the end, we produce 18576 equally-likely mock surveys each with their own correction factors, and use these to correct the Milky Way satellite lumi- nosity function for angular and radial incompleteness. For each of the mock surveys, we consider every DR5 satel- lite (i = 1, ..., 11, sometimes 12 ) with a helio-centric distance FIG. 6.— Luminosity function as observed (lower), corrected for only within Router = 417 kpc and determine the total number of SDSS sky coverage (middle), and with all corrections included (upper). Note objects of its luminosity that should be detectable. Specifi- that the classical (pre-SDSS) satellites are uncorrected, while new satellites An empirical correctioni to the luminosity function,have the cassumingorrection applie dthe. The Viashade dLacteaerror regio n1c oradialrrespond s to the 98% cally, if satellite i has a magnitude MV that is too faint to be distribution, gives i100-1000 satellites [Tolleruds petre aal.d ov eApJr our m 2008]ock observation realizations. Segue 1 is not included in this detected at Router (i.e. if MV ! −7), then we determine the correction. numbe rCorrectionsof Via Lactea sassumedubhalos, N (populationr < Rcomp, Ω of< satellitesΩDR5), resemblesTable 3). We therepr oknownduce tho spopulatione efficiencies in our Table 1, and that sit within an angular cone of size ΩDR5 and within a we assume ! = 1 for all of the classical satellites that are not helio-centric radius Rcomp(Mi). We then divide the total within the DR5 footprint. Explicitly, the cumulative luminos- 21 number of Via Lactea subhalos, Ntot by this “observed” count ity function for a given pointing is: and obtain a corrected estimate for the total number satellites