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submittedtotheAstrophysicalJournal PreprinttypesetusingLATEXstyleemulateapjv.04/03/99 WHERE ARE THE MISSING GALACTIC SATELLITES? Anatoly A. Klypin, Andrey V. Kravtsov, and Octavio Valenzuela AstronomyDepartment, NewMexicoStateUniversity,Box30001, Dept. 4500,LasCruces,NM88003-0001 Francisco Prada Instituto deAstronomia,ApartadoPostal877,22900Ensenada, Mexico submitted to the Astrophysical Journal ABSTRACT 9 9 According to the hierarchical clustering scenario, galaxies are assembled by merging and accretion of 9 numeroussatellitesofdifferentsizesandmasses. Thisongoingprocessisnot100%efficientindestroying 1 all of the accreted satellites, as evidenced by the satellites of our Galaxy and of M31. Using published data, we have compiled the circular velocity (V ) distribution function (VDF) of galaxy satellites in n circ the Local Group. We find that within the volumes of radius of 570 kpc (400 h−1 kpc assuming the a J Hubble constanta h = 0.7) centered on the Milky Way and Andromeda, the average VDF is roughly 1 approximated as n(> Vcirc) 45(Vcirc/10 km s−1)−1h3Mpc−3 for Vcirc in the range 10 70 km s−1. ≈ ≈ − 2 TheobservedVDFiscomparedwithresultsofhigh-resolutioncosmologicalsimulations. Wefindthatthe VDFinmodelsisverydifferentfromtheobservedone: n(>V ) 1200(V /10km s−1)−2.75h3Mpc−3. 2 CosmologicalmodelsthuspredictthatahaloofthesizeofoucrircGa≈laxyshouclirdchaveabout50darkmatter v satelliteswithcircularvelocity>20km s−1andmass>3 108M⊙withina570kpcradius. Thisnumber 0 × is significantly higher than the approximate dozen satellites actually observed around our Galaxy. The 4 difference is even larger if we consider abundance of satellites in simulated galaxy groups similar to the 2 LocalGroup. Themodelspredict 300satellitesinsidea1.5 Mpcradius,whilethereonly 40satellites 1 are observed in the Local Group.∼The observed and predicted VDFs cross at 50km s∼−1, indicating 0 9 that the predicted abundance of satellites with Vcirc >50 km s−1 is in reasonab≈ly good agreement with 9 observations. ∼ / We conclude, therefore, that unless a large fraction of the Local Group satellites has been missed in h observations, there is a dramatic discrepancy between observations and hierarchical models, regardless p of the model parameters. We discuss severalpossible explanations for this discrepancy including identi- - o ficationof some satellites with the HighVelocity Clouds observedinthe LocalGroup,and the existence r of dark satellites that failed to accrete gas and form stars due either to the expulsion of gas in the t s supernovae-driven winds or to gas heating by the intergalactic ionizing background. a v: aAssumingH0=100hkms−1Mpc−1. i Subject headings: cosmology: theory – galaxy formation – methods: numerical X r a 1. INTRODUCTION historyofthesatellitesshowsremarkablediversity: almost every galaxy is a special case (Grebel 1998; Mateo 1998). Satellitesofgalaxiesareimportantprobesofthedynam- Thisdiversitymakesitverydifficulttocomeupwithasim- ics and masses of galaxies. Currently, analysis of satellite ple general model for formation of satellites in the Local dynamics is one of the best methods of estimating the Group. Because of the generally low star formation rates, masses within large radii of our Galaxy and of the Local it is not unexpected that the metallicities of the satellites Group (e.g., Einasto & Lynden-Bell 1982; Lynden-Bell et arelow: from 10−2 forDracoandAndIIIto 10−1 for al. 1983; Zaritsky et al. 1989; Fich & Tremaine 1991), ≈ ≈ NGC 205 and Pegasus (Mateo 1998). There are indica- as well as the masses of other galaxies (Zaritsky & White tions that properties of the satellites correlate with their 1994; Zaritsky et al. 1997). Although the satellites of distance to the Milky Way (MW) or Andromeda, with the Milky Way and Andromeda galaxy have been studied dwarf spheroidals and dwarf ellipticals being closer to the for a long period of time, their number is still uncertain. central galaxy (Grebel 1997). Overall, about 40 satellites More and more satellites are being discovered (Irwin et in the Local Group have been found. al. 1990; Whiting et al. 1997; Armandroff et al. 1998; Formation and evolution of galaxy satellites is still an Karachentseva & Karachentsev 1998) with a wide range open problem. According to the hierarchical scenario, of properties; some of them are relatively large and lumi- small dark matter (DM) halos should on average collapse nous and have appreciablestar formation rates (e.g., M33 earlierthanlargerones. Tosomedegree,thisissupported and the Large Magellanic Cloud; LMC). Exempting the by observations of rotation curves of dark-matter dom- strange caseof IC10,which exhibits a highstar formation rate (0.7M⊙yr−1; Mateo 1998), most of the satellites are inated dwarfs and low-surface-brightness galaxies. The curves indicate that the smaller the maximum circular dwarf spheroidals and dwarf ellipticals with signs of only mild star-formation of 10−3M⊙yr−1. The star formation velocity, the higher the central density of these galaxies. 1 2 KLYPIN ET AL. This is expected from the hierarchical models in which galaxies (KGKK; Ghigna et al. 1997; Col´ın et al. 1998). the smaller galaxies collapse earlier when the density of Encouraged by this success, we have undertaken a study the Universewas higher (Kravtsovet al. 1998;Kormendy of the survival of satellites in galaxy-size halos. & Freeman 1998). Thus, it is likely that the satellites Dynamically, galactic halos are different from cluster- of the MW galaxy were formed before the main body of size halos (mass >1014h−1 M⊙). Clusters of galaxies are the MW was assembled. Some of the satellites may have relativelyyoungs∼ystemsin whichmostofthe satellite ha- survived the very process of the MW formation, whereas los have had time to make only a few orbits. Galaxies are others may have been accreted by the MW or by the Lo- on average significantly older, enabling at least some of cal Group at later stages. Indeed this sequence forms the their satellites to orbit for many dynamical times. This basis of the currently popular semi-analytical models of increases the likelihood of the satellite being destroyedei- galaxy formation (e.g., Somerville & Primack 1998, and ther from numerical effects of the simulation or the real references therein). processes of dynamical friction and tidal stripping. The There have been a number of efforts to use the Local destruction of the satellites is, of course, counteracted by Group as a cosmological probe. Peebles et al. (1989) accretion of the new satellites in an ongoing process of modeled formation of the Local Group by gravitational galaxy formation. It is clear, therefore, that to predict accretion of matter onto two seed masses. Kroeker & the abundances and properties of galactic satellites, one Carlberg (1991) found pairs of “galaxies” in cosmologi- needs to model self-consistently both the orbital dynam- calsimulationsandusedthemtoestimate the accuracyof icsofthesatellitesandtheformationprocessoftheparent traditional mass estimates. Governato et al. (1997) stud- haloinacosmologicalsetting. Inthispaperwepresentre- ied the velocity field around Local Group candidates in sultsfromastudyofgalacticsatelliteabundancesinhigh- different cosmologicalmodels and Blitz et al.(1998) simu- resolutionsimulations of two popular variants of the Cold lated a group of galaxies and compared their results with Dark Matter (CDM) models. As will be described below, the observations of the high-velocity clouds in the Local the dissipationless simulations used in our study are large Group. enough to encompass a cosmologically significant volume Nevertheless, despite significant effort, theoretical pre- and, at the same time, have sufficient resolution to make dictions of the abundance and properties of the satel- the numerical effects negligible. lites are far from been complete. One of the difficulties The paper is organized as follows. In 2 we present the § is the survival of satellites inside halos of large galaxies. datathatweusetoestimatetheobservedvelocityfunction This numerically challenging problem requires very high- ofsatellitesofourGalaxyandM31. Cosmologicalsimula- resolution simulations in a cosmological context and has tions are presented and discussed in 3. We compare the § beenaddressedindifferentways. Intheclassicalapproach predicted and observed velocity functions in 4 to show § (e.g.,Lin&Lynden-Bell1982;Kuhn1993;Johnstonetal. that the models predict considerably more lower mass 1995),oneassumesarealisticpotentialfortheMW,aden- satellites than is actually observed in the Local Group. sity profile for the satellites (usually an isothermal model In 5 and 6 we discuss possible interpretation and impli- § with a central core), and numerically follows a satellite cations of our results and summarize our conclusions. as it orbits around the host galaxy. This approach lends many valuable insights into the physical processes oper- 2. SATELLITESINTHELOCALGROUP ating on the satellites and alleviates some of the numerical problems. It lacks, however, one important feature: There are about 40 known galaxies in the Local Group connection with the cosmological background. The host (Mateo 1998). Most of them are dwarf galaxies with ab- galaxyisimplicitlyassumedtobestableovermanybillions solute magnitudes of MV 10 15. While more and ≈ − − of years which may not be realistic for a typical galaxy moregalaxiesarebeingdiscovered,mostofthenewgalax- formed hierarchically. Moreover, the assumed isothermal ies are very small and faint making it seem unlikely that density profile of the satellite is different from profiles of toomanylargersatelliteshavebeenmissed. Therefore,we typical dark matter halos formed in hierarchical models have decided to consider only relatively massive satellites (Navarro, Frenk & White 1997). Last but not least, the withestimatedrotationalvelocityorthree-dimensionalve- abundances of the satellites can only be predicted if the locity dispersion of stars larger than 10 km/s. In order to formationofthesatellitesandoftheparentgalaxyismod- simplify the situation even further, we estimate the num- elled self-consistently. Thus, more realistic cosmological ber of satellites per central galaxy. There is a number of simulations are necessary. argumentswhythisisreasonable. First,itmakescompar- Unfortunately, until recently numerical limitations pre- isonwithcosmologicalmodelsmuchmorestraightforward. vented the usage of cosmological simulations to address This is justified to some degree by the fact that the satel- satellite dynamics. Namely, dissipationless simulations lites in the Local Group cluster around either the MW or seemed to indicate that DM halos do not survive once M31 and there are only a few very remote ones of unclear they fall into larger halos (e.g., White 1976; van Kampen associationwithacentralgalaxy. Wealsobelievethatthe 1995;Summersetal. 1995). Itappears,however,thatthe estimate of the satellite abundance per galaxy is more ac- prematuredestructionoftheDMsatellitesinsidethevirial curate because it is relatively straightforward to find the radius of larger halos was largely due to numerical effects volume of the sample, which would be more difficult if we (Moore, Katz, Lake 1996; Klypin et al. 1997 (KGKK)). were to deal with the Local Group as a whole1. Indeed, recent high-resolution simulations show that hun- Using published results (Mateo 1998), we have com- dreds of galaxy-size DM halos do survive in clusters of piled a list of satellites of the Milky Way and of the M31 with estimated circular velocities above the threshold of 1Oneoftheproblemswouldbechoiceoftheouter boundaryofthesamplevolume. WHERE ARE GALACTIC SATELLITES? 3 Table 1 Satellites of the MW and Andromeda V Milky Way Andromeda Average Comments circ (km/s) 286/571kpc 286/571kpc 286/571kpc 10 11 /13 13 /15 12/14 Sculptor Carina Sextans LeoII AndI-III,V,VI, CAS Pegasus 15 7 /9 7 /8 7/8.5 Phoenix Fornax LeoI UrsMin Draco Sagit Lgs3 20 2 /3 6 /7 4/5 IC1613 30 2 /3 6 /6 4/4.5 SMC NGC6822 IC10 NGC147 NGC185 50 1 /1 3 /3 2/2 LMC 70 0 /0 3 /3 1.5/1.5 M33 M32 NGC205 10 km/s. In our estimate of abundances, we have not at- 10-20 km/s. Details of recent measurements of different tempted to decide whether a satellite is bound to its cen- properties of these satellites of the M31 can be found in tral galaxy or not. Satellites have been simply counted if Armandroff et al. (1998) and Grebel (1998). We also in- they lie within a certain radius from the center of their cluded CAS dSph (Grebel & Guhathakurta, 1998) in our parent galaxy. We have chosen two radii to make the list with V in the range (10 20) km s−1. One satel- circ − counts. The counts of DM satellites were made for the lite (AND II) can be formally included in both lists (MW same radii. The radii were chosen rather arbitrarily to be and M31). It is 271 kpc from the M31, but being at the 200h−1 kpc and 400h−1 kpc. For a Hubble constant of distance of 525 kpc from MW it is should also be counted h = 0.7 (H = 100h km/s/Mpc), which was assumed for as the MW satellite. Since this is the only such case, we 0 our most realistic cosmological model and which is con- have decided to count it only once – as a satellite of M31. sistent with current observational results, the radii are 286 kpc and 571 kpc. The smaller radius is close to a 3. COSMOLOGICALMODELSANDSIMULATIONS typicalvirialradiusofaMilkyWaysizehaloinoursimula- To estimate the satellite abundances expected in the tions. The largerradius allowsus to probe largervolumes hierarchical models, we have run simulations of two rep- (and, thus,givesbetterstatistics)bothinsimulationsand resentative cosmologies. Parameters of the models and in observations. Unfortunately, observational data may simulations are given in Table 2, where Ω is the density 0 become less complete for this radius. parameterof the matter at z =0, σ is the rms of density 8 Sincewecannotestimatetheluminositiesofgalaxiesas- fluctuationson8h−1Mpcscaleestimatedbythelinearthe- sociated with DM satellites in dissipationless simulations, oryatpresenttime usingthe top-hatfilter. Other param- wehavechosencircularvelocityVcirc tocharacterizeboth eters given in Table 2 specify the numerical simulations: the dark halos and the satellite galaxies. The circular mass of dark a matter particle, m , defines the mass particle velocity can be estimated for galaxies (with some uncer- resolution,numberoftime-stepsatthelowest/highestlev- tainties) and for the DM halos. For spiral and irregular els of resolution, size of the simulation box, and the num- galaxies we used the rotational velocity, which is usually ber of dark matter particles. Numbers on resolution refer measured from 21 cm HI observations. For ellipticals and tothesizeofthesmallestresolutionelements(cells)inthe dwarf spheroidals we used observed line-of-sight velocity simulations. dispersion of stars, which was multiplied by √3 to give The simulations have been performed using the Adap- an estimate of Vcirc. Using our numerical simulations we tive Refinement Tree (ART) N-body code (Kravtsov, confirmed that this gives a reasonably accurate estimate Klypin & Khokhlov 1997). The ART code reaches high of Vcirc with an error less than 10% 20%. Table force resolution by refining the mesh in all high-density ∼ − 1 lists the number of satellites with Vcirc larger than a regions with an automated refinement algorithm. The given value (first column) for the Milky Way galaxy (sec- ΛCDM simulation used here was used in Kravtsov et al. ond column) and M31 (third column). The forth column (1998) and we refer the reader to that paper for details givestheaveragenumberofsatellitesandthefifthcolumn and tests. Additional tests and comparisons with a more lists names of the satellites in given velocity bin. Figures conventionalAP3Mcode willbe presentedin Knebeet al. 4 and 5, discussed in detail below, present the cumulative (1999). TheCDMsimulationdiffersfromtheΛCDMsim- circular velocity distribution of the observed satellites in ulations only in the cosmological parameters and size of MWandM31within286kpcand571kpcradiusfromthe the simulation box. Our intent was to use the much more central galaxies. realistic ΛCDM model for comparisonswith observations, A few special cases should be mentioned. There are andtousetheCDMmodeltotestwhetherthepredictions no measurements of velocity dispersionfor AND I-III and dependsensitivelyoncosmologyandtosomewhatbroaden the other two satellites of M31, AND V and VI, do not the dynamical range of the simulations. Jumping ahead, have measured magnitudes. Given that they all seem to we note here that results of the CDM simulationare close have the properties of a dwarf spheroidal, we think it is to those of the ΛCDM simulation as far as the circular reasonable to expect that they have Vcirc in the range velocity function of satellites is concerned. This indicates 4 KLYPIN ET AL. Table 2 Parameters of simulations Model Ω h σ m N Resolution Box N 0 8 particle steps part (h−1M⊙) (h−1pc) (h−1Mpc) SCDM 1.0 0.5 1.0 2.05 106 650-40,000 150 2.5 1283 ΛCDM 0.3 0.7 1.0 1.66×107 650-40,000 450 7.5 1283 × that we are dealing with general prediction of hierarchi- halos is < 2rs, only one halo (the more massive of the cal scenarios,not particular details of the ΛCDM model. two) is left in the catalog. A typical value for the search Nevertheless, we do expect that some details of statistics radius is (5 10)h−1 kpc. We set a lower limit for the − and dynamics of the satellites may depend on parameters number of particles inside the search radius N(<rs): ha- of the cosmologicalmodels. los with N(< rs) < 6 are not included in the catalog. The sizeofthe simulationboxis definedbythe require- We alsoexclude halos whichhave less than 20bound par- ment of high mass resolution and by the total number of ticles and exclude halos with circular velocity less than particles used in our simulations. DM halos can be iden- 10 km s−1. Some halos may have significant substructure tified in simulations if they have more than 20 particles in their cores due, for example, to an incomplete merger. ∼ (KGKK).SmallsatellitesoftheMWandAndromedahave Such cases appear in the catalogs as multiple (2-3) ha- masses of (1 5) 108M⊙. Thus, mass of a particle in los with very similar properties (mass, velocity, radius) at the simula∼tion−shou×ld be quite small: < 107M⊙. There- small separations. Our strategy is to count these as a sin- fore,thenumberofparticlesinoursimu∼lations(1283)dic- gle halo. Specific criteria used to identify such cases are: tates the box size of only a few megaparsec across. This (1)distancebetweenhalocentersis<30h−1 kpc,(2)their puts significantconstraints onour results. The number of relativevelocity in units of the rms∼velocity ofparticles in massive halos, for example, is quite small. In the CDM the halos ∆v/v is less than 0.15, and (3) the difference in simulation we have only three halos with circular velocity massis lessthanfactor1.5. Ifallthe criteriaaresatisfied, larger than 140 km s−1. The number of massive halos in only the most massive halo was kept in the catalog. the ΛCDM simulation is higher (eight). The box size of the simulations clearly puts limitations The important issue for our study is the reliable identi- onsizesandmassesofhalos. Inafewmegaparsecbox,one fication of satellite halos. The problems associated with does notfind largegroupsorfilaments. The meandensity halo identification within high-density regions are dis- inthesimulationboxes,however,isequaltothemeanden- cussed in KGKK. In this study we use a halo finding al- sityoftheUniverse,andthusweexpectoursimulationsto gorithmcalledBoundDensityMaxima(BDM;seeKGKK berepresentativeofthefieldpopulationofgalaxies(galax- and Col´ın et al. 1998). The source code and description iesnotinthevicinityofmassiveclustersandgroups). The of the version of the BDM algorithm used here can be LocalGroupandfield galaxiesarethereforeourmaintar- found in Klypin & Holtzman (1997). The main idea of gets. Nevertheless, even in the small boxes used in this the BDMalgorithmistofindpositionsoflocalmaximain paper, the number of halos is very substantial. We find the density field smoothed at a certain scale and to apply 1000 – 2000 halos of different masses and circular veloci- physicallymotivatedcriteriatotestwhethertheidentified ties in eachsimulation. This number is large enoughfor a site corresponds to a gravitationally bound halo. The al- reliable statistical analysis. gorithm then computes various properties and profiles for eachoftheboundhalosandconstructsauniformhalocat- 4. SATELLITES:PREDICTIONSANDOBSERVATIONS alogreadytobeusedforanalysis. Inthisstudywewilluse themaximumcircularvelocityasthehalo’sdefiningprop- Figure 1 presents the velocity distribution function, de- erty. This allows us to avoid the problem of ambiguous fined as the number of halos in a given circular velocity mass assignment(see KGKK for discussion) and makes it intervalper unit volume,in two ΛCDM simulations. The easier to compare the results to observations. smaller-boxsimulationistheonethatweuseinourfurther The density maxima are identified using a top-hat fil- analysis. To estimate whether the halo velocity function ter with radius rs (“search radius”). The search is per- is affected by the small-box size, we compare the small- formed starting from a large number of randomly placed box result with results from the larger, 60h−1 Mpc box, positions (“seeds”) and proceeds by moving the center of simulationusedinCol´ınetal. (1998). Thelatterfollowed mass within a sphere of radius rs iteratively until conver- the evolution of 2563 particles and had a mass resolution gence. In order to make sure that we use a sufficiently of1.1 109h−1 M⊙. Inthesmallbox,thetotalnumberof largenumber of seeds,we usedthe positionofevery tenth halosw×ithVcirc >10km s−1andVcirc >20km s−1is1716 particle as a seed. Therefore, the number of seeds by far (1066)for the lowestthresholdof20boundparticles. The exceeds the number of expected halos. The search radius numberschangeslightlyifamorestringentlimitof25par- rs alsodefinestheminimumalloweddistancebetweentwo ticlesisassumed: 1556(1052). Intheoverlappingrangeof halos. If the distance between centers of any of the two circular velocities Vcirc = (100 200) km s−1 the velocity − functionofthe smallboxagreesverywellwith thatofthe WHERE ARE GALACTIC SATELLITES? 5 pleteness ofthe catalogsat these velocities wouldincrease the discrepancy between observations and models. Figure 2 provides a visual example of a system of satellites around a group of two massive halos in the ΛCDM simulation. The massive halos have V circ 280 km s−1 and 205 km s−1 and masses of 1.7 ≈ 1012h−1M⊙ and 7≈.9 1011h−1M⊙ inside the centr×al 100h−1 kpc. In Figure×3 the more massive halo is shown in more detail. To some extent the group looks similar to the LocalGroupthough the distance betweenthe halosis 1.05h−1Mpc, which is somewhat larger than the distance between the MW and M31. Yet, there is a significant difference from the Local Group in the number of satellites. In the simulation, there are 281 identified satellites with V > 10 km s−1 within 1.5 h−1Mpc sphere shown in circ Figur∼e2. The LocalGroupcontainsonly about 40known satellites inside the same radius. The number of expected satellites is therefore quite large. Note,however,thatthetotalfractionofmassbound to the satellites is rather small: M = 0.091 M , sat dm where Mdm = 7.8 1012h−1M⊙ is the total mas×s inside × the sphere. Most of the mass is bound to the two massive halos. There is another pair of massive halos in the simulation, which has even more satellites (340), but the central halo in this case was much larger than M31. Its circular velocity was V = 302 km s−1. We will discuss circ the correlation of the satellite abundances with the circular velocity of the host halo below (see Figs. 4 & 5). The fraction of mass in the satellites for this system was also small ( 0.055). ≈ Table 3 presents parameters of satellite systems in the Fig.1.—Differentialcircularvelocitydistributionfunction ΛCDM simulation for all central halos with V > of dark matter halos in the ΛCDM model. The solid curve 140 km s−1. The first and the second columns gicviercthe and the filled circles are results of the small-box (box-size of 7.5h−1Mpc) simulation. Open circles show the correspond- maximum circular velocity Vcirc and the virial mass of ingvelocityfunctioninlarger(box-sizeof60h−1Mpc)simula- the central halos. The number of satellites and the fraction. Error bars correspond to thePoisson noise. The dotted tion of mass in the satellites are given in the third and curve is the power-law with the slope of -3.75 motivated by fourth columns. All satellites within 200 (400) h−1 kpc the Press-Schechterapproximation (see §4 for details). from the central halos, possessing more than 20 bound particles, and with V > 10 km s−1 were used. The circ last two columns give the three-dimensional rms velocity large box. This shows that the lack of long waves in the ofthe satellites and the averagevelocity ofrotationofthe small-box simulationhasnot affected the number ofhalos satellite systems. with V <200 km s−1. Figures 4 and 5 show different characteristics of the circ In the range V 20 400 km s−1 the velocity func- satellite systems in the Local Group (see 2), and in the circ ≈ − § tion can be accurately approximated by a power law ΛCDMandtheCDMsimulations. Toppanelsintheplots dN/dVdV 3 104V −3.75h3Mpch−3/km s−1 mo- clearly indicate that the abundance and dynamics of the circ circ ≈ × tivated by the Press-Schechter(1974)approximationwith satellites depend on the circular velocity (and thus on assumptions of M v3 and of the power-law power spec- mass) of the host halo. More massive halos host more ∝ trum with a slope of n = 2.5. At higher circular veloc- satellites and the rms velocity of the satellites correlates ities (V > 300 km s−1)−the fit overpredicts the num- withhost’scircularvelocity,ascanbeexpected. Thenum- circ ber of halos because the above fit neglects the exponen- ber of satellites is approximatelyproportionalto the cube tial term in the Press-Schechter approximation. At small of the circular velocity of the central galaxy (or halo): Vcirc (<20km s−1)thepointsdeviatefromthe fit,which Nsat Vcirc3. This means that the number of satellites ∝ we attribute to the incompleteness of our halo catalog at is proportional to the galaxy mass N M because the sat thesecircularvelocitiesduetothelimitedmassresolution. halomassisrelatedtoV asM V ∝3. Thenumberof circ circ ∝ Indeed, comparison with the CDM simulation, which has thesatellitesalmostdoubleswhenthedistancetothecen- higher mass resolution, shows that the number of halos tralhaloincreasesbyafactoroftwo. Thisisverydifferent increases by about a factor of three when the threshold from the Local Group where the number of satellites in- for Vcirc changes from 20 km s−1 to 10 km s−1. We creases only slightly with distance. Note that the fraction thus estimate the completeness limit of our simulations of mass in the satellites (see Table 3) does not correlate to be Vcirc = 20 km s−1 for the ΛCDM simulations and with the mass of the central object. The velocity disper- Vcirc = 10 km s−1 for the CDM run. Note that for the sion decreases with distance, changing by 10% – 20% as issue of satellite abundance discussed below, any incom- 6 KLYPIN ET AL. Fig.2.—Distributionofdarkmatterparticlesinsideasphere Fig.3.—Distributionofdarkmatterparticlesinsideasphere of the radius of 1.5h−1Mpc (solid circle) for a small group of oftheradiusof0.5h−1 Mpc(solid circle) centeredonthemore dark matter halos (similar in mass to the Local Group) in the massivehaloshowninFigure2. Thesmallboxinthefigurehas ΛCDM simulation. The group consists of two massive halos size 20h−1 kpc. The color-coding is similar to that in Figure 2 withcircularvelocitiesof280km s−1 and205km s−1 (massesof except that the local density was obtained using top-hat filter 1.7×1012h−1M⊙ and 7.9×1011h−1M⊙ inside 100h−1 kpc ra- of 3h−1 kpcradius. dius) and 281 halos with circular velocities >10 km s−1 inside 1.5h−1Mpc. The distance between the halos is 1.05h−1Mpc. To enhance the contrast, we havecolor-coded DM particles on a grey scale according to their local density: intensity of each particle is scaled as the logarithm of the density, where the densitywasobtainedusingtop-hatfilterwith2h−1 kpcradius. theradiusincreasesfrom200h−1 kpc to400h−1 kpc. We side 400 h−1 kpc spheres around the massive host halos). wouldliketoemphasizethatboththe numberofsatellites ComparisonclearlyindicatesthattheVDFofthesatellite and the velocity dispersion have large real fluctuations by halos has the same shape as the VDF of the field halos a factor of two around their mean values. with the only difference being the amplitude of the satel- The bottom panels in Figures 4 and 5 present the cu- lites’ VDF. There are more satellites in the same volume mulativevelocitydistributionfunction(VDF)ofsatellites: closetolargehalos,butthefractionoflargesatellitesisthe the number of satellites per unit volume and per central same as in the field. We find the same result for spheres object with internal circular velocity larger than a given of 200h−1 kpc radius. value of V . Note that the VDF is obtained as the un- The velocity distribution function can be roughly ap- circ weighted average of the functions of individual halos in proximated by a simple power law. For satellites of the the interval V 150 300 km s−1. This was done Local Group the fit at V >10 km s−1 gives circ circ ≈ − to improve the statistics. However, it is easy to check −1 V that the amplitude of the VDF corresponds to the satel- n(>V)=300 (h−1Mpc)−3, (1) lite abundance around 200 km s−1 halos. For instance, (cid:18)10 km s−1(cid:19) ≈ theaverageVDFshowninFigure5predicts 50satellites within the radius of 400h−1 kpc, while the u≈pper panel of and this figure shows that this is about what we observe for V −1 n(>V)=45 (h−1Mpc)−3, (2) 200 km/s hosts. (cid:18)10 km s−1(cid:19) ≈ The right y-axis in the lower panels of Figures 4 and 5 showsthecumulativenumberofsatellitesinallhosthalos for R < 200 h−1 kpc and R < 400 h−1 kpc, respectively. in the ΛCDM simulation. Error bars in the plots corre- FortheΛCDM simulationatVcirc >20km s−1weobtain: spond to the Poisson noise. The dashed curve in Figure −2.75 V 5 shows VDF of all non-satellite halos (halos located out- n(>V)=5000 (h−1Mpc)−3, (3) (cid:18)10 km s−1(cid:19) WHERE ARE GALACTIC SATELLITES? 7 Fig. 4.— Properties of satellite systems within 200 h−1 kpc Fig. 5.— The same as in Figure 4, but for satellites within from the host halo. Top panel: The three dimensional rms ve- 400h−1 kpcfromthecenterofahosthalo. Inthebottompanel locity dispersion of satellites versusmaximum circular velocity we also show the cumulative velocity function for the field ha- of the central halo. Solid and open circles denote ΛCDM and los(halosoutsideof400h−1 kpc spheresaroundsevenmassive CDMhalos,respectively. Thesolidlineisthelineofequalsatel- halos), arbitrarily scaled up by a factor of 75. The difference litermsvelocitydispersionandthecircularvelocityofthehost at large circular velocities Vcirc > 50 km s−1 is not statisti- halo. Middle panel: The number of satellites with circular ve- cally significant. Comparison between these two curves indi- locitylargerthan10km s−1 versuscircularvelocityofthehost cates that the velocity functions of isolated and satellite halos halo. The solid line shows a rough approximation presented areverysimilar. Asforthesatelliteswithincentral200h−1 kpc in the legend. Bottom panel: The cumulative circular velocity (Figure 4), the number of satellites in the models and in the distribution (VDF) of satellites. Solid triangles show average Local Group agree reasonably well for massive satellites with VDF of Milky Way and Andromeda satellites. Open circles Vcirc >50km s−1, but disagree by a factor of ten for low mass present results for the CDM simulation, while the solid curve satellites with Vcirc10−30 km s−1. represents the average VDF of satellites in the ΛCDM simulation for halos shown in the upper panels. To indicate the statistics, the scale on the right y-axis shows the total number of satellite halos in the ΛCDM simulation. Note that while thenumbersofmassive satellites (>50 km s−1)agrees reason- ablywellwithobservednumberofsatellitesintheLocalGroup, modelspredictaboutfivetimesmorelowermasssatelliteswith Vcirc<10−30 km s−1. V −2.75 velocities. The numbers of observed satellites and satel- n(>V)=1200(cid:18)10 km s−1(cid:19) (h−1Mpc)−3, (4) lite halos cross at around Vcirc = (50 60) km s−1. This − means that while the abundance of massive satellites again,for R<200h−1 kpc andR<400h−1 kpc, respec- (Vcirc > 50 km s−1) reasonably agrees with what we find tively. This approximation is formally valid for V > in the MW and Andromeda galaxies, the models predict circ 20 km s−1, but comparisons with the higher-resolution an abundance of satellites with Vcirc > 20 km s−1 that is CDMsimulationsindicatesthatitlikelyextendstosmaller approximatelyfive times higher than that observedin the 8 KLYPIN ET AL. Table 3 Satellites in ΛCDM model inside R=200/400h−1 kpc from central halo Halo V Halo Mass Number of Fraction of mass V V circ rms rotation (km/s) (h−1M⊙) satellites in satellites (km/s) (km/s) 140.5 2.93 1011 9/15 0.053/0.112 99.4/94.4 28.6/15.0 278.2 3.90×1012 39/94 0.041/0.049 334.9/287.6 29.8/11.8 205.2 1.22×1012 27/44 0.025/0.051 191.7/168.0 20.0/11.3 175.2 6.26×1011 5/10 0.105/0.135 129.1/120.5 41.5/45.2 259.5 2.74×1012 24/52 0.017/0.029 305.0/257.3 97.1/16.8 302.3 5.12×1012 37/105 0.055/0.112 394.6/331.6 39.4/15.7 198.9 1.33×1012 24/58 0.048/0.049 206.1/169.3 17.7/12.1 169.8 7.91×1011 17/26 0.053/0.067 162.8/156.0 9.3/5.0 × Local Group. The difference is even larger if we extrapo- beevenmoreDMsatellitesatthelimitV =10km s−1. circ late our results to 10 km s−1. In this case eq.(4) predicts Thecorrectionissignificantbecauseabouthalfoftheiden- that on average we should expect 170 halo satellites in- tified halos have cirlular velocities below 20 km s−1. Us- side a 200h−1 kpc sphere, which is 15 times more than ing eq.(3) we predict that the pair should host (280/2) the number of satellites of the Milky Way galaxy at that 22.75 = 940 DM satellites with V > 10 km s−1 withi×n circ radius. 1.5h−1 Mpc. A somewhat smaller number, 640 satellites, follows from eq.(4), if we double the number of satellites 5. WHEREARETHEMISSINGSATELLITES? totakeintoaccountthatwehavetwomassivehalosinthe Although the discrepancy between observed and pre- system. dicted satellite abundances appears to be dramatic, it is The number of HVCs in the Local Group is known too early to conclude that it indicates a problem for hi- rather poorly. Wakker & van Woerden’s (1991) all-sky erarchical models. Several effects can explain the discrep- survey,madewith1degreeresolution,listsapproximately ancy and thus reconcile predictions and observations. In 500 HVCs not associated with the Magellanic Stream. this section we briefly discuss two possible explanations: About 300 HVCs have estimated linewidths (FWHM) of the identification of the missing DM satellites with High >20 km s−1 (see Fig.1 in Blitz et al.1998), the limit cor- Velocity Clouds observedin the Local Group, and the ex- responding to 3D rms velocity dispersion of 15 km s−1. ∼ istenceofalargenumberofinvisiblesatellitescontaininga Starketal.(1992)found1312cloudsinthenorthernhemi- very small amount of luminous matter either due to early sphere, but only 444 of them are resolved. The angular feedback by supernovae or to heating of the gas by the resolution of their survey was 2 degrees, but it had better intergalactic ionizing background. velocity resolution than the Wakker & van Woerden com- pilation. Comparisonsof low andhigh resolutionobserva- 5.1. High Velocity Clouds? tions indicates that the existing HVC samples are proba- bly affectedby selectioneffects (Wakker etal. 1999). The As was recently discussed by Blitz et al. (1998), abun- abundance of HVCs thus depends on one’s interpretation dant High-Velocity Clouds (HVCs) observed in the Local of the data. If we take 1312 HVCs of Stark et al.(1992), Group may possibly be the observational counterparts of double the number to account for missing HVCs in the the low-mass DM halos unaccounted for by dwarf satel- southern hemisphere, we arrive at about 2500 HVCs in lite galaxies. It is clear that not all HVCs can be related the Local Group. This is more than three times the num- or associatedwith the DM satellites; there is a number of berofexpectedDMsatellites. ThislargenumberofHVCs HVCswithaclearassociationwiththeMagellanicStream also results in a substantial fraction of mass of the Local and with the disk of our Galaxy (Wakker & van Woerden Group confined in HVCs. Assuming the average masses 1997; Wakker, van Woerden & Gibson 1999; and refer- given by Blitz et al., this naive estimate gives the total ences therein). Nevertheless, there are many HVCs which massinHVCs 7.5 1011M⊙. Ifwe takemass ofthe Local may well be distant (> 100 kpc; Wakker & van Woerden Group to be 3 ×1012h−1 M⊙ (Fich & Tremaine 1991), 1997; Blitz et al. 1998). According to Blitz et al., stabil- ≈ × the fraction of mass in the HVCs is high: 0.2-0.25. This ity argumentssuggestdiametersandtotalmassesofthese is substantially higher than the fraction of mass in DM HVCs of ∼ 25 kpc and 3×108M⊙, which is remarkably satellites in our simulations ( 0.05). close to the masses of the overabundant DM satellites in ≈ Nevertheless,thereisanother,morerealisticinouropin- our simulations. ion, way of interpreting the data. While it is true that The number of expected DM satellites is quite high. Wakker & van Woerden (1991) may have missed many For the pair of DM halos presented in Figure 2, we HVCs,itislikelythatmostofthemissedcloudshavesmall have identified 281 DM satellites with circular velocities linearsize. Thus,themassshouldnotbedoubledwhenwe > 10 km/s. Since the halo catalog is not complete at ve- make correction for missed HVCs. In this case 500 HVCs locities <20 km s−1 (see 4),we expect thatthere should § ∼ WHERE ARE GALACTIC SATELLITES? 9 (as in Wakker & van Woerden sample studied by Blitz et Katz 1997; Navarro & Steinmetz 1997; Barkana & Loeb al.) withaveragedarkmattermassof3 108h−1 M⊙ give 1999). NumericalsimulationsbyThoul&Weinberg(1996) in total 1.5 1011h−1 M⊙ or 0.05 of th×e mass of the Lo- and by Quinn et al. (1996) show that the ionizing back- × cal Group. This is consistent with the fraction of mass ground can inhibit gas collapse into halos with circular in DM satellites which we find in our numerical simula- velocities <30km s−1. These results are in generalagree- tions. Itshouldbe keptinmindthatthe smallHVCsmay ment with∼more recent simulations by Weinberg et al. contribute very little to the total mass in the clouds. (1997) and Navarro & Steinmetz (1997). As we have shown above, the number density of DM As explained by Thoul & Weinberg, accretion of inter- satellites is a very strong function of their velocity: galactic gas heated by the ionizing backgroundinto dwarf dn(V)/dV V−3.75. If the cloud velocity function is as < 30km s−1 systems is delayed or inhibited because the ∝ steep as that ofthe halos,this might explainwhy changes g∼as has to overcome pressure support and is, therefore, of parameters of different observational samples produce much slower to turn around and collapse. If the collapse very large differences in the numbers of HVCs. The mass may be delayed until relatively late epochs (z <1), many of a DM satellite is also a strong function of velocity: low-massDMsatellitesmayhavebeenaccreted∼bytheLo- M V3. As the result, the total mass in satellites with calGroupwithouthavingachancetoaccretegasandform velo∝city less than V is V2.25. The conclusion is that stars. This wouldclearly explainthe discrepancybetween ∝ the mass is in the most massive and rare satellites. If the theabundanceofdark matterhalosinoursimulationsand sameis truefor the HVCs,weshouldnotdouble the mass observed luminous satellites in the Local Group. More when we find that a substantial number of small HVCs interestingly, a recent study by Barkana & Loeb (1999) were missed in a catalog. shows that gas in small (V < 20 km s−1) halos would circ To summarize, it seems plausible that observational be photoevaporated during the∼reionization epoch even if data on HVCs are compatible with a picture where ev- thegashadachancetocollapseandvirializepriortothat. ery DM satellite either hosts a dwarf galaxy (a rare case These results indicate that the ionizing background, of at small V ) or an HVC. This picture relies on the large theamplitudesuggestedbythelackoftheGunn-Peterson circ distances to the HVCs andcan be either confirmedor fal- effect in quasar spectra, can lead to the existence of nu- sified by the upcoming observations(Wakker et al. 1999). merous dark (invisible) clumps of dark matter orbiting Note, however, that at present the observed properties of around the Milky Way and other galaxies and thus war- HVCs (mainly the abundances,distances,andlinewidths) rants further study of the subject. It would be interesting are so uncertain that a more quantitative comparison is toexplorepotentialobservationaltestsfortheexistenceof impossible. dark satellites, given the abundances predicted in hierarchical models. One such feasible tests, examined recently 5.2. Dark satellites? byWidrow&Dubinski(1998),concernstheeffects ofDM Thereareatleasttwophysicalprocessesthathavelikely satellitesonmicrolensingstatisticsintheMilkyWayhalo. operated during the early stages of galaxy formation and 6. CONCLUSIONS could have resulted in the existence of a large number of dark (invisible) satellites. The first process is gas ejec- We have presenteda study of the abundance and circu- tion by supernovae-driven winds (e.g., Dekel & Silk 1996; lar velocity distribution of galactic dark matter satellites Yepes et al. 1997; Mac Low & Ferrara 1998). This pro- in hierarchical models of structure formation. Numerical cessassumesatleastoneinitialstarformationepisode,and simulations of the ΛCDM and CDM models predict that thusshouldproducesomeluminousmatterinsidethehost thereshouldbearemarkablylargenumberofdarkmatter DM satellites. Indeed, this process may explain the ob- satellites with circular velocities V 10 20 km s−1 circ ≈ − served properties of the dwarf spheroidal galaxies in the orbiting our galaxy – approximately a factor of five more Local Group (e.g., Dekel & Silk 1996; Peterson & Cald- than the number of satellites actually observed in the well 1993; Hirashita, Takeuchi & Tamura 1998). It is not vicinity of the Milky Way or Andromeda (see 4). This § clearwhetherthisprocesscanalsoproducenumerousvery discrepancy appears to be robust: effects (numerical or low mass-to-light ratio systems missed in the current ob- physical) would tend to produce more dark matter satel- servational surveys. It is likely that some low-luminosity lites, not less. For example, dissipation in the baryonic satellites have still been missed in observations,since sev- component can only make the halos more stable and in- eralfaintgalaxieshavebeendiscoveredintheLocalGroup crease their chance to survive. just during the last few years (see 1). What seems un- Althoughthediscrepancybetweentheobservedandpre- § likely, however,is that observations have missed so many. dicted satellite abundances appears to be dramatic, it is Thismaystillbethecaseifmissedsatellitesareveryfaint tooearlytoconcludethatitindicatesaproblemforhierar- (almost invisible), but more theoretical work needs to be chical models. Several effects can explain the discrepancy done to determine whether gas ejection can produce nu- and thus reconcile the predictions and observations. If merous very faint systems. The recent work by Hirashita we discard the possibility that 80% of the Local Group ≈ etal. (1998)showsthatthisprocessmaybecapableofpro- satellites have been missed in observations, we think that ducing very high mass-to-light ratio (M/L up to 1000) the discrepancy may be explained by (1) identification of systems of mass <108h−1 M⊙. ∼ the overabundant DM satellites with the High Velocity Another possib∼le mechanism is prevention of gas col- CloudsobservedintheLocalGrouporby(2)physicalpro- lapse into or photoevaporation of gas from low-mass sys- cessessuchassupernovae-drivenwindsandgasheatingby tems due to the strong intergalactic ionizing background the ionizing background during the early stages of galaxy (e.g.,Rees1986;Efstathiou1992;Thoul&Weinberg1996; formation (see 5). Alternative (1) is attractive because § Quinn, Katz & Efstathiou 1996; Weinberg, Hernquist & thesizes,velocitydispersions,andabundanceoftheHVCs 10 KLYPIN ET AL. appear to be consistent with the properties of the over- evolution of gas in low-mass dark matter halos. abundant low-mass halos. These properties of the clouds are deduced under assumptions that they are located at large (> 100 kpc) distances which should be testable in We are grateful to Jon Holtzman and David Spergel the nea∼r future with new upcoming surveys of the HVCs. for comments and discussions. This work was funded by Alternative(2)meansthatthehalosofgalaxiesintheLo- the NSF grant AST-9319970, the NASA grant NAG-5- cal Group (and other galaxies) may contain substantial 3842, and the NATO grant CRG 972148 to the NMSU. substructure in the form of numerous invisible clumps of Our numerical simulations were done at the National dark matter. This secondpossibility is interesting enough CenterforSupercomputingApplications(NCSA;Urbana- to merit further detailed study of the above effects on the Champaign, Illinois). 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