Where are the missing galactic satellites?

10 Pages·0.29 MB·English

by  Anatoly A. Klypin

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 numer-
ical 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 dif-
ference 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 mas-
sive 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 circu-
lar 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 frac-
tion. 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 sim-
ulation 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 hierar-
chical 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).
REFERENCES
Armandroff,T.E.,Davies,J.E.,Jacoby,G.H.1998, AJ,116,2287 Lin,D.N.C.,Lynden-Bell,D.,1982, MNRAS,198,707
Barkana,R.,&Loeb,A.1999,ApJ,submitted(astro-ph/9901114) Lynden-Bell, D., Cannon, R.D., Godwin, P.J. 1983, MNRAS, 204,
Blitz,L.,Spergel,D.,Teuben,P.,Hartmann,D.,Burton,W.B.,1998, 87
ApJ,submitted, astro-ph/9803251 MacLow,M.-M.,&Ferrara,A.1998,ApJ,submitted
Col´ın,P.,Klypin,A.A.,Kravtsov,A.V.,Khokhlov,A.M.1998,ApJ, Mateo,M.L.1998, ARA&A,36,435
submitted(astro-ph/9809202) Moore,B.,Katz,N.,&Lake,G.1996,ApJ,457,455
Einasto,J.,Lynden-Bell,D.,1982,MNRAS,199,67 Navarro, J.F., Frenk, C., & White, S.D.M. 1997, ApJ, 490, 493
Dekel,A.,&Silk,J.1986,ApJ,303,39 (NFW)
Efstathiou,G.1992,MNRAS,256,43 Navarro,J.F.,&Steinmetz, M.1997,ApJ,478,13
Einasto,J.,&Lynden-Bell,D.1982,MNRAS,199,67 Peebles,P.J.E.,Melott,A.,Holmes,M,Jiang,L.R.,1989,ApJ,345,
Fich,M.,&TremaineS.1991,ARA&A,29,409 108
Ghigna, S., Moore, B., Governato, F., Lake, G., Quinn, T., Stadel, Peterson,R.C.,&Caldwell,N.1993, AJ,105,1411
J.1998, MNRAS,submitted(astro-ph/9801192) Press,W.H.,&Shechter, P.1974,ApJ,187,425
Governato, F., Moore, B., Cen, R., Stadel,J., Lake, G., Quinn,T., Quinn,T.,Katz,N.,&Efstathiou,G.1996,MNRAS,278,P49
1997,NewAstronomy,2,91 Rees,M.J.1986,MNRAS,218,25
Grebel,E.K.1997, ReviewsofMod.Astronomy,10,29 Somerville, R.S., & Primack, J.R. 1998, MNRAS, in press
Grebel, E.K. 1998, To appear in the proceedings of the XVIIIth (astro-ph/9802268)
Moriond conference on ”Dwarf Galaxies and Cosmology”, Les Stark, A.A., Gammie, C.F., Wilson, R.W., Bally, J., Linke, R.A.,
Arcs,March1998,T.X.Thuanetal.(eds.(astro-ph/9806191) Heiles,C.,&Hurwitz,M.1992,ApJS,79,77
Grebel,E.K.,Guhathakurta, P.1998,ApJL,511,inpress Summers,F.J.,Davis,M.,&Evrard,A.E.1995, ApJ,454,1
Hirashita,H.,Kamaya,H.,&Takeuchi,T.T.1998,ApJ,504,L83 Thoul,A.A.,&Weinberg,D.H.1996, ApJ,465,608
Irwin,M.J.,Bunclark,P.S.,Bridgeland,M.T.,McMahon,R.G.1990, vanKampen,E.1995, MNRAS,273,295
MNRAS,244,16P Wakker,B.P.,vanWoerden,H.1991, A&A,250,509
Johnston, K.V.,Spergel,D.,Hernquist,L.,1995,ApJ,451,598 Wakker,B.P.,vanWoerden,H.1997, ARA&A,35,217
Karachentseva, V.E.,&Karachentsev, I.D.1998,A&AS,127,409 Wakker, B.P., van Woerden, H., Gibson, B.K. 1999, to appear in
Kauffmann, G., Nusser, A., & Steinmetz, M. 1997, MNRAS, 286, Stromlo Workshop on High Velocity Clouds, B.K. Gibson and
795 M.E.Putman(eds.),(astro-ph/9901029)
Klypin,A.A.,&Holtzman,J.1997,preprintastro-ph/9712217 (see Weinberg,D.H.,Hernquist,L.,Katz,N.1997, ApJ,477,8
alsohttp://astro.nmsu.edu∼aklypin/pmcode.html) Whiting,A.B.,Irwin,M.J.,Hau,G.K.T.1997,AJ,114,996
Klypin,A.A.,Gottlo¨ber,S.,Kravtsov,A.V.,Khokhlov,A.M..1998, White,S.D.M.1976, MNRAS,177,717
ApJaccepted (astro-ph/9708191) (KGKK) Weinberg,D.,Hernquist,L.,Katz,N.,1997, ApJ,477,8
Knebe, A., Kravtsov, A.V., Gottlo¨ber, S., Klypin, A.A. 1999, in Widrow,L.M.,&Dubinski,J.1998,ApJ,504,12
preparation Yepes, G., Kates, R., Khokhlov, A., & Klypin, A. 1997, MNRAS,
Kormendy,J.,&Freeman,K.C.1998,BulletinAAS,193,2105 284,235
Kravtsov,A.V.,Klypin,A.A.,Khokhlov,A.M.1997, ApJS,111,73 Zaritsky, D., Olszewski, E.W., Schommer, R.A., Peterson, R.C.,
Kravtsov, A.V., Klypin, A.A., Bullock, J.S., Primack, J.R. 1998, Aaronson,M.,1989, ApJ.,345,759
ApJ,502,48 Zaritsky,D.,White,S.D.M.,1994,ApJ.,435,599
Kroeker,T.,&Carlberg,R.,1991,ApJ,376,1 Zaritsky,D.,Smith,R.,Frenk,C.,&White,S.D.M.,1997,ApJ.,478,
Kuhn,J.R.,1993ApJ,409,L13 39