Spatial and luminosity distributions of galactic satellites

0.96 MB·English

by  Quan Guo

Mon.Not.R.Astron.Soc.000,000–000 (0000) Printed16January2013 (MNLATEXstylefilev2.2)
Spatial and luminosity distributions of galactic satellites
Quan Guo, Shaun Cole, Vincent Eke, Carlos Frenk, John Helly
Institute forComputational Cosmology, Department of Physics, Durham University,Science Laboratories, South Rd, Durham DH1 3LE.
16January2013
3
1
0
ABSTRACT
2
We investigate the luminosity functions (LFs) and projected number density profiles

n of galactic satellites around isolated primaries of different luminosity. We measure
a these quantities for model satellites placed into the Millennium and Millennium II
J
dark matter simulations by the GALFORM semi-analytic galaxy formation model

4 for different bins of primary galaxy magnitude and we investigate their dependence
1 on satellite luminosity. We compare our model predictions to the data of Guo et

al. from the Sloan Digital Sky Survey Data Release 8 (SDSS DR8). First, we use a
]
O mock light-cone catalogue to verify that the method we used to count satellites in
the SDSS DR8 is unbiased. We find that the radial distributions of model satellites
C
are similar to those around comparable primary galaxies in the SDSS DR8, with
h. only slight differences at low luminosities and small projected radii. However, when
p splitting the satellites by colour, the model and SDSS satellite systems no longer
- resemble one another, with many red model satellites, in contrast to the dominant
o
blue fraction at similar luminosity in the SDSS. The few model blue satellites are
r
t also significantly less centrally concentratedin the halo of their stackedprimary than
s
their SDSS counterparts. The implications of this result for the GALFORM model
a
[ are discussed.

1 Key words: galaxies: dwarf, galaxies: structure, (galaxies:) Local Group, Galaxies:
v fundamental parameters,galaxies: statistics
4
3
1
3
. 1 INTRODUCTION one primary to another. This conclusion was supported by
1
Guo et al. (2011) who applied a semi-analytic galaxy for-
0
WhilethestandardΛColdDarkMatter(ΛCDM)modelhas mation model to thesame simulation. Thus,a large, statis-
3
been shown to be in good agreement with observations of tically representative sample of primary galaxies is clearly
1
largescalestructure,theverificationofthismodelatsmall, needed to test cosmological and galaxy formation models.
:
v galactic scales remains less certain. One reason for this is Suchan approach also avoids thedifficulty of havingto de-
i theincreased importanceof astrophysical processes relative finequitewhat is meant bya Local Group.
X
to gravity in this strongly non-linear regime. The study of
The construction of large galaxy redshift surveys, such
r
the properties and distribution of galactic satellite galaxies
a astheTwoDegreeFieldGalaxyRedshiftSurvey(2dFGRS,
providesanopportunitytotestΛCDMonsmallscaleswhile
Colless et al.2001),theSDSS(York et al.2000),theGalaxy
alsoconstrainingdifferentaspectsofgalaxyformationmod-
and Mass Assembly (GAMA,Driveret al. 2009, 2011) Sur-
elsrelatedtotheratesatwhichsatellitesformstars,become
vey and the Deep Extragalactic Evolutionary Probe 2
disrupted and merge with the central galaxy.
(DEEP2, Davis et al. 2003) Survey,has led to the accumu-
The Local Group satellite system within the haloes of lation of external galaxy samples covering large volumes.
theMilky Way(MW) andM31 isoften thefocus ofstudies Manystudiesoftheluminosityfunction(LF),spatialdistri-
ofgalacticsatellitesbecauseitisherewherethelowestlumi- butionand kinematics of bright satellites havebeencarried
nositysatellitescanbedetected.Whilethissystemhasbeen outusingtheseandevenearlierdatasets(e.g.Zaritsky et al.
used in attempts to constrain the cosmological model (e.g 1993, 1997; van den Bosch et al. 2004; Conroy et al. 2005;
Bullock et al. 2000; Benson et al. 2002; Klypin et al. 2002; van den Bosch et al. 2005; Chen et al. 2006; Koposov et al.
Lovell et al.2012;Wang et al.2012),itisnotclearthatitis 2009; Busha et al. 2010; Prescott et al. 2011). The inclu-
typicalofthepopulationasawhole.Usingthetechniqueof sion of a statistical background subtraction in the satel-
abundance matching in the Millennium II simulation (MS- lite system estimators has allowed fainter satellites to be
II),alarge-volume, high-resolution dark mattersimulation, studied using deeper photometric galaxy catalogues (e.g
Boylan-Kolchin et al.(2010)concludedthatthereshouldbe Lorrimer et al.1994;Liu et al.2008,2011;Lares et al.2011;
significantscatterinthepropertiesofsatellitesystemsfrom Guo et al.2011;Nierenberg et al.2011;Tal & vanDokkum
(cid:13)c 0000RAS
2 Guo et al
2011;Guoet al.2012;Jiang et al.2012;Strigari & Wechsler sets. Section 3 contains summaries of the methods we use
2012; Tal et al. 2012; Wang& White 2012). By extending to select primaries and determine the satellite luminosity
the regime over which the satellite distributions have been function and the projected number density profile. These
quantified, a more stringent test of the models can be per- two satellite galaxy distributions, upon which we will fo-
formed. cus in this paper, were calculated for the SDSS samples by
While some studies have attempted to make model Guo et al. (2011, hereafter Paper I) and Guo et al. (2012,
predictions using cosmological hydrodynamic simu- hereafter Paper II). A verification that our estimators are
lations (e.g Libeskind et al. 2007; Okamoto & Frenk unbiasedisperformed usingthemodelgalaxysamples.The
2009; Okamoto et al. 2010; Wadepuhl& Springel 2011; results of the comparison between model satellite systems
Parry et al. 2012), these efforts are limited to very few and those around similarly isolated SDSS primaries is pre-
primary galaxies because of the high computational cost. sented in Section 4. Implications for the model drawn from
Thebestwaytomakeastatisticalsampleofmodelgalaxies these comparisons are discussed in Section 5; we conclude
isbycombininglargecosmological darkmattersimulations, in Section 6. Throughout the paper we assume a fiducial
such as the Millennium Simulation (MS, Springel et al. ΛCDM cosmological model with ΩM = 0.3, ΩΛ = 0.7 and
2005) or the MS-II (Boylan-Kolchin et al. 2009), with a H0=70 km s−1Mpc−1.
method to include galaxies. This approach was adopted by
van den Bosch et al. (2005), who used the conditional lu-
minosity function technique that simultaneously optimizes 2 OBSERVED AND MODEL GALAXIES
the model match to the abundance and clustering of low
In this section we briefly review the data being used from
luminosity galaxies in order tostudy thesatellite projected
the SDSS, which were described in more detail in Paper I
number density profile. Chen et al. (2006) investigated the
andPaperII,beforeintroducingtheproceduretoconstruct
same statistic by assigning luminosities to dark matter
mock galaxy catalogues to compare with these data.
structuresso astomatch thesimulated cumulativecircular
velocity function to the SDSS cumulative galaxy LF. A
similar subhalo abundance matching method was used
2.1 SDSS galaxies
by Busha et al. (2011) to study the frequency of bright
satellites around MW-like primaries. Galaxiesfromboththespectroscopicandphotometricsam-
Semi-analytic models provide a more physically mo- ples in the SDSS DR8 are used for this study. Isolated pri-
tivated approach to including galaxies into dark matter mary galaxies, as defined in Paper I and Paper II, are se-
simulations and have been shown to match a wide va- lected from the spectroscopic survey, whereas satellites can
riety of observational data (e.g Kauffmann et al. 1993; come from either the spectroscopic or photometric surveys.
Lacey et al. 1993; Cole et al. 1994; Kauffmann et al. 1999; With the relatively poorly constrained distances provided
Somerville & Primack 1999; Cole et al. 2000; Benson et al. by the photometric redshifts, a statistical background sub-
2002; Baugh et al. 2005; Bower et al. 2006; Croton et al. traction is performed to obtain an estimate of the satellite
2006;Guo et al.2011).Alargenumberofstudieshaveused galaxypopulationaroundeachoftheprimaries,asdescribed
this technique applied to simulations such as the MS-II, in Section 3 below.
Aquarius (Springel et al. 2008) and others to study vari-
ous aspects of the galaxy population predicted in a ΛCDM
2.2 Model galaxies
model (e.g Mun˜oz et al. 2009; Cooper et al. 2010; Li et al.
2010;Maccio` et al.2010;Font et al.2011;Wanget al.2012; The model galaxy catalogues were created using a combi-
Wang & White 2012). In particular, the mock catalogues nation of large dark matter simulations to define the mass
constructed by Guo et al. (2011) were tested against data distribution and a semi-analytic model to place the galax-
from the SDSS in two studies. Sales et al. (2012) showed ies within this density field. Either the Millennium Simula-
thattheabundanceofsatellitegalaxies asafunctionofpri- tion (MS, Springel et al. 2005) or the Millennium-II Simu-
marystellarmassintheSDSSDR7spectroscopiccatalogue lation (MS-II,Boylan-Kolchin et al. 2009) was used to pro-
wasingood agreementwiththismodel.Consideringfainter videthemassdistribution.Theformercoversalargevolume
dwarfsatellites,Wang & White(2012)studiedtheluminos- and hence contains many suitable isolated primaries, while
ity,colourdistributionandstellarmassfunctionusingSDSS the latter traces the mass distribution in a smaller volume,
DR8 data, concluding that, apart from the model satellites thusresolvingstructurescontaininglowerluminositygalax-
becomingredtooquicklywhenenteringthehaloofthepri- ies. While the two simulations trace the same number of
mary galaxy, many of the observed trends were reproduced particles (∼ 1010), the MS and MS-II simulation cubes are
in themodel. 714Mpcand143Mpclongrespectively.Thecorresponding
In this paper, we will test the ΛCDM model particle masses are ∼1.23×109 M⊙ and 9.9×106 M⊙.
and the semi-analytic galaxy formation model GAL- The model galaxies populate the dark matter struc-
FORM (Bower et al. 2006), by comparing the properties of tures according to thegalaxy formation model GALFORM
model galactic satellite systems with those measured from (Bower et al.2006),whichincludesreionizationathighred-
the SDSS DR8 spectroscopic and photometric galaxy cata- shiftandenergyinjectionfromsupernovaeandstellarwinds
logues.WewillintroduceanewseriesofGALFORMmodel in order to prevent the overproduction of low luminosity
galaxy catalogues based on MS-II that will allow us to ex- galaxies.Theluminositiesofthemostluminousgalaxiesare
tendthepredictionsfrom theMS tolessluminousgalaxies. curbedbyfeedbackfromAGN.Parametersinthetreatment
In Section 2 we describe the SDSS and model galaxy ofthegalaxy formation processes havebeenchosen soasto
catalogue data that we use, and compare these two data produceasgoodamatchaspossibletotheobservedKband
(cid:13)c 0000RAS,MNRAS000,000–000
Statistics of Galactic Satellites 3
0 M = 21.0
GAMA (z<0.1) 7 c −
MS Estimated r200 (Model)
3Mpc)−−12 MSDSS-ISI NYU-VAGC mber65 REsetaiml ra20t0e (dM ro20d0e (lS)DSS)
u
dM−3 ed N4
(dN/−4 maliz3
g 2
o r
l o
−5 N1
−6 0
-14.0 -16.0 -18.0 -20.0 -22.0 -24.0 1.8 2.0 2.2 2.4 2.6 2.8 3.0
M log(r /kpc)
r 200
M = 22.0
Figure1.TheluminosityfunctionsofallgalaxiesintheMS(blue 7 c −
dashed line) and MS-II (black solid line) cubes compared with Estimated r (Model)
200
(otbhseerzve<d l0u.m1isnuobsisteyt ffuronmctioLnosveodfaygaelatxaiel.s2in01t2h,ereGdApMoiAntss)uravnedy er6 Real r200 (Model)
SDSS(Blantonetal.2005,greenpoints).Theobservedluminosity mb5 Estimated r200 (SDSS)
functionsarek-corrected(SDSS)orshifted(GAMA)toz=0. u
N4
d
e
z3
ali
LF of local galaxies. Fig. 1 shows the luminosity functions m
2
of all galaxies in theMS and MS-II simulation cubes. They or
N
match quitewell with both theobserved r band luminosity 1
functionofGAMAgalaxies (Loveday et al.2012)shiftedto
z =0 by applying the offset r =0.1r−0.22 (Blanton et al. 0
1.8 2.0 2.2 2.4 2.6 2.8 3.0
2005),andtheLFfromtheSDSS(Blanton et al.2005).The log(r /kpc)
200
drop in the MS LF at low luminosities reflects the resolu-
tion limit, which correspondsroughly toMr =−16. Galax- M = 23.0
ies placed into the MS-II should be complete significantly 7 c −
Estimated r (Model)
beyond thisand thussuitable for studyingfaint satellites. 200
For the MS, in addition to having the GAL- er6 Real r200 (Model)
FORMmodelgalaxiespopulatingthesimulationcube,flux- mb5 Estimated r200 (SDSS)
limited light-cone mock catalogues, either with or without u
the peculiar velocity included in the line-of-sight ‘redshift’, d N4
have also been constructed (Merson et al. 2012). These e
z3
galaxies cover the redshift range z =0.0−2.0. To simulate ali
m
the photometric redshifts in the SDSS DR8 catalogue, we 2
r
assign a photometric redshift with a random error to every No
1
galaxy that is fainter than mr =17.7.
UsingboththeMSandMS-IIcubesofgalaxies,wecan
0
test how robust our results are to the numerical resolution 1.8 2.0 2.2 2.4 2.6 2.8 3.0
of the dark matter simulations. Comparison of the results log(r200/kpc)
obtained from the MS cube with those obtained from the
light-cone mock catalogue, provides a test of the accuracy Figure 2. The distribution of estimated r200 values for model
of our background removal and satellite distribution esti- primary galaxies (solid lines), real r200 values for their associ-
mation procedures. Finally, the light-cone mock catalogue ated parent haloes (dashed lines) and estimated r200 values for
is intended to mimic the SDSS survey and provide a direct primariesselectedfromtheSDSS(dottedlines).Fromtoptobot-
test of themodel. tom,thepanelsshowresultsforprimarymagnitudebinscentred
When calculating scaled satellite number density pro- onMc =−21.0,−22.0and−23.0 respectively. Thevertical lines
arethemeansofthecorrespondingdistributions.
files, it is necessary to determine the value of r200 (defined
as the radius enclosing a mean total overdensity of 200
times the critical cosmic value) associated with each pri-
mary galaxy.Following PaperII,r200 is estimated from the primaries respectively,with thedifferentpanelsshowingre-
stellar mass, inferred from the luminosity and colour of the sults for different luminosity primaries. Vertical lines show
primary. This is converted to a halo mass, M200, using the themeanvaluesofthedistributions,whichdifferbynomore
abundance matching technique of Guo et al. (2010), from thanabout 15 percent in all cases. This similarity between
whichr200 follows.ThesolidanddottedlinesinFig.2trace estimated satellite system sizes in themock and SDSSsug-
the distributions of r200 estimated from the MS and SDSS gests that scaling the satellite number density profiles by
(cid:13)c 0000RAS,MNRAS000,000–000
4 Guo et al
SDSS MS Lightcone (r<17.7)
1.0 1.0
0.8 0.8
0.6 0.6
r r
− −
g g
0.4 0.4
0.2 0.2
0.0 0.0
−14 −16 −18 −20 −22 −24 −14 −16 −18 −20 −22 −24
M M
r r
MS Snapshot (z=0) MS-II Sanpshot (z=0)
1.0 1.0
0.8 0.8
0.6 0.6
r r
− −
g g
0.4 0.4
0.2 0.2
0.0 0.0
−14 −16 −18 −20 −22 −24 −14 −16 −18 −20 −22 −24
M M
r r
Figure3.Colour-magnitudediagramsofspectroscopicgalaxiesinSDSS(topleft)andofgalaxiesintheMSmocklight-cone(topright)
andthetwodifferentsimulationcubes (MS,bottom leftandMS-II,bottom right).Contours representlinesofconstant galaxynumber
densityandthestraightlinesindicatethecolourcuts usedtodefineredandblueprimaries.ThesamecutisusedforboththeMSand
MS-II.
the system size should not create any large systematic dif- magnitude diagram is shifted along the g − r axis com-
ferences between thereal and mock results. pared to that of the model galaxies. Thus, while we choose
The distributions of real r200 values, inferred from the a0.n0d(gb−lure)ScpuDtoSpSu=lat0i.o1n5s−in0.t0h2e4MSDrSaSstthheislibnoeudnidvaidryingistphleacreedd
dwaitrhk mdaasthteedr dliinstersibiuntiFoing.in2.thFeorsimthuelaltoiwonerculubme,inaorseitsyhopwrin- at0.0(g−r)McuSt,MS−II=−0.28−0.04Mr forthemodelgalaxy
populations.Thesecutsareshowninthe4panelsofFig. 3,
maries, the real and estimated r200 distributions are sim- wheretheeffect onthecolour magnitudedistributionof in-
ilar. However, in the bottom panel of Fig. 2 it is appar-
cluding the survey flux limit can be seen for the MS. This
entthatthereisasignificant population ofphysicallysmall
removes the bulk of the low luminosity galaxies that are
haloessurroundingprimarygalaxieswhosestellarmasscor-
presentinthez =0snapshotandmakestheresultinglight-
responds to a larger halo. As pointed out in Paper II, this
cone galaxy population significantly more like that in the
isprobablyduetothefactthatthestellarmassvarieslittle
with halomassfor thesemost luminoussystems.Thus,any SDSS. The fraction of the −21 < Mr < −19 model light-
cone galaxies that are defined as red is 0.51, the same as
smallscatterinstellarmassgivesrisetoalargechangeinthe
that for the SDSS. Had we adopted the SDSS colour cut,
value of r200 inferred from abundance matching. This is an themodelwouldonlyhavehadaredgalaxyfractionof0.28.
important source of potential bias when trying to measure
concentrationsofsatellitedistributionsaroundthemost lu- For galaxies in the magnitude range −20<Mr <−19, the
red fractions are 0.46 and 0.38 for the model and SDSS re-
minousprimaries.Inthiscase,aconcentrationderivedusing
spectively,whenusingthecutsshowninFig.3.Thus,apart
thevalueofr200 estimatedfrom stellar masseswill notnec- fromamagnitude-dependentshiftinthecoloursofgalaxies,
essarily reflect the concentration as defined with respect to
which we can correct for with the different colour cuts, the
thehalo mass.
global red galaxy fractions are quitesimilar between model
Finally, as we will be investigating the colour depen- andSDSSdatasetsatmagnitudesthatwewillbeconsider-
dence of the results, in Fig. 3 we compare the colour dis- ing for thesatellite galaxies.
tributions of galaxies in the SDSS and model galaxy cat-
alogues. The distribution of SDSS galaxies in the colour- The MS and MS-II simulations, once populated with
(cid:13)c 0000RAS,MNRAS000,000–000
Statistics of Galactic Satellites 5
galaxies according to the semi-analytic model, contain very is straightforward. For the jth magnitude bin, the average
similar galaxy populations. Thus, it is appropriate to use satellite LF is estimated using
theminterchangeablydependinguponwhichismoreimpor-
tant: having a large volume containing many primaries, or Nreal sat = ΣiNireal sat(Mj), (1)
beingabletoresolvelow luminosity satellite galaxies. How- j Njreal prim
ever, if we want to compare results from the MS-II cube
where Nreal sat is the number of satellites around primary
of galaxies with those from the SDSS flux-limited survey, i
i and Nreal prim is the number of primaries contributing to
then we still need to demonstrate, using the MS, that our j
thejth bin of theLF.
methodsrecoverfromthelight-conemocksurveysthesame
Whileweneednocorrectionforinterlopersinrealspace,
satellitedistributionsasarepresentinthesimulationcubes.
the process of estimating the mean projected number den-
sity of satellite galaxies is such that a fair comparison with
light-conedatastillrequiresthesubtractionofabackground
estimated from anouterarea. Hence,theprojected number
3 METHOD densityprofilesofsatellitesbrighterthanMtruninrealspace
are determined using all galaxies within a cylinder of pro-
Inthissectionwebrieflyreviewtheprocedureusedtodeter-
jected radius Router and length 2Router, centred on the pri-
mine the satellite LF and projected number density profile
mary.Thesegalaxiesareprojectedontoaplaneandprovide
for SDSS, described more fully in Papers I and II, before
the sources for the potential satellites/background for pro-
detailing how these distributions are determined from the
jected radii less/greater than Rinner.The projected number
variousdifferenttypesofmodelgalaxycatalogue.Thequal-
density profile is determined using
ity of the recovery of these distributions is quantified by
cwoimthptahrionsge ftrhoomsetdheetflerumx-inliemditferdommotchkelMigShtc-cuobneeosfurgvaelayxs.ies Σi(rjann)= PiNij(AMptrun) − PiANoibuctekr, (2)
i ij i i
Primary galaxies are selected to have spectroscopic
P P
redshifts in the SDSS and to have magnitudes, Mp, sat- where Nij is the number of galaxies brighter than Mtrun
isfying Mc − ∆Mbin < Mp < Mc + ∆Mbin. We choose within a projected distance Rinner of the ith primary and
Mc = −21.0,−22.0,−23.0 and ∆Mbin = 0.5. Further, the inthejthprojectedannulus,andNibck isthecorresponding
primaries should be isolated in the sense that no other numberofgalaxies intheprojected outerannulus,Rinner <
galaxy within ∆Mfaint = 0.5 magnitudes lies within a pro- r<Router.Apij istheareacontributedbytheithprimaryto
jected distance of 2Rinner and is sufficiently close in red- the jth annulus for the detection of satellites brighter than
shift. ‘Sufficiently close’ is defined as a difference in spec- Mtrun,
twsrhioitfshtcoowuptiitcharinesdpsαehcPitfσrtoP∗so,cfowlpehiscserrteehdaαsnPhi∆ft=z,sw2=.i5th0a.0an0d2phσooP∗rt,ofimsoretthgraieclaprxheideos-- Apij(Mtrun)=(cid:26) 0Aij MMttrruunn ><MMiilliimm , (3)
tometric redshift error defined in Paper II. Rinner repre- where Aij is the area of the jth annulus surrounding the
sents the projected radius within which satellites may re- ithprimaryandMlim istheabsolutemagnitudethatcorre-
i
side, and the variable Router defines the outer edge of an sponds to the apparent magnitude limit of the mock cata-
annulus within which the local background is estimated. logue. Aouter isthecorresponding areain theouterannulus
i
Weadopt thesame values of (Rinner,Router) as in Paper II: surroundingtheith primary.
(0.3,0.6),(0.4,0.8)and(0.55,0.9)Mpcforprimariesinmag- The comparison of the projected number density pro-
nitudebinsMc =−21.0,−22.0and−23.0respectively.Only files, before and after background subtraction, with that
galaxies brighter than mlim=20.5 are considered. formed bysimply projecting thegalaxies within asphereof
r
Only sufficiently close galaxies in redshift are included radius Rinner of the primary galaxy is shown in Fig. 4. The
when counting the potential satellites within the pro- results indicate that the projected profile after subtracting
jected radius Rinner and making the local background es- the background very accurately recovers that estimated di-
timate from the surrounding annulus out to Router. The rectly from the galaxies within the inner area (r < Rinner).
background-subtractedsatellitesystemsarestackedforpri- Theimpactofthebackgroundsubtractionissmallandlim-
maries ineach absolutemagnitudebintoprovideestimates itedtoradiineartoRinner.Thisestablishesthatthemethod
forthemeansatelliteLFsandprojectednumberdensitypro- forcalculatingthebackgroundsubtractedprojectednumber
files of satellites more luminous than a particular absolute density profile from a real space light-cone survey provides
magnitude, as described more fully in Papers I & II. an unbiased estimate of that produced when only satellites
The procedure described above is applied to the SDSS within a 3D distance Rinner are used. We can now compare
itselfandalsototheMSredshiftspacelight-conemockcat- theserealspaceprofileswiththosefromredshiftspacelight-
alogue. However, different estimation procedures are used cones.
forthelight-conemockwithrealspace(ratherthanredshift Having described the three different types of model
space)galaxycoordinatesandthegalaxypopulationsinthe galaxy catalogues made using the MS and how the satel-
simulationcubes.Withtherealspacepositions,itispossible lite distributions are determined from each of them, we are
to define isolated primaries as having no bright neighbours nowinapositiontotesttheaccuracyofourestimationpro-
within a sphere of radius 2Rinner. The satellites within a cedure. Fig. 5 shows the satellite LF and projected number
sphere of radius Rinner can also be determined without any densityprofilesestimatedfromeachofthemodelgalaxycat-
need for background subtraction. Using only the real space alogues: simulation cube, real space light-cone and redshift
satellites, theestimation ofthesatellite luminosityfunction space light-cone. The agreement between the two different
(cid:13)c 0000RAS,MNRAS000,000–000
6 Guo et al
3.5 2
M = 21.0
3.0 Mc=−22.0
Mc=−23.0
)2.5 1 c −
2 )
c M
p
M2.0 d
/
) N 0
r
(1.5 d
Σ (
log(1.0 log−1
Rtrun=R Sphere
0.5 inner
Rtrun=R Cylinder
outer
0.0 −2
-3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0
log(r/Mpc)
∆M
r
Figure 4. The comparison of real space projected number den- 3.5
sityprofilesestimatedbydifferentmethods.Theblacklineisthe M = 21.0
profileestimatedbyprojectingthesatelliteswithinspheresofra- 3.0 Mc=−22.0
dius Rinner around primaries. The dashed blue curve shows the ) 2.5 Mcc=−−23.0
projected number density profile of all galaxies within a line-of- 2c 2.0
sight distance Router of a primary. The solid blue curve is the p
M
background-subtracted case, where the background is estimated 1.5
fromtheouterannuluswithRinner<r<Router.Verticaldashed (r) 1.0
linesshowRinner andRouter. Σ
g( 0.5
o
l 0.0 MMMtttrrruuunnn=== 111999...000
satellite distributionsmeasuredfrom all threecatalogues at sss −−−
Mc =−21.0,−22.0 and −23.0 providesstrong support that −0.5
our results are unbiased, and that our technique for back- −1.0
ground subtraction is appropriate. Given that the isolated -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0
log(r/Mpc)
primariesareaspecially selected subsetofthedifferentially
clustered galaxy population, one would expect that a local,
rather than global, background subtraction would be ap- Figure 5. Satellite LFs (top) and number density profiles (bot-
propriate. The fact that the results from the MS light-cone tom)estimatedfromlight-conemockcataloguesanddirectlyfrom
mock match well with those from the MS cube of galaxies theMScube.Theresultsforprimarymagnitudebinscentred at
suggests that we can use results from the MS-II simulation Mc = −21.0,−22.0,−23.0 are shown in black, blue and red re-
spectively.Solidanddashedlinescorrespondtoresultsfromred-
cubeatz=0whencomparingwithlowluminositygalaxies
shift and real space light-cones respectively, whereas the points
in theSDSSDR8.
showtheresultsforthewholevolumeinthesimulationcube.
4 RESULTS
densityprofilesofsatellitesbrighterthanMtrun =−19.0for
sat
Having verified that the model galaxies have similar distri-
thedifferentprimarysamples.Thislimitischosen,following
butions of luminosity and colour to those in the SDSS and
PaperII, toensurethat theprofiles for different luminosity
that our local background subtraction procedure produces
bins are measured from a large enough sample. In all cases
unbiased estimates of the satellite LF and projected num- the profile approximately follows Σ(r) ∝ r−1.5, with the
berdensityprofile,wenowcomparethemodelandobserved
amplitude reflecting the fact that more luminous primaries
satellite systems in more detail.
host more satellites. For most radii, the model reproduces
the amplitude observed in SDSS. In detail though, there is
4.1 Dependence on primary and satellite a factor 2 difference at ∼30 kpc for both Mc =−21.0 and
−23.0.Themodelunderproducessatellitesatthisradiusfor
luminosity
theleastluminousprimariesandoverproducesthemforthe
The top panel of Fig. 6 shows the satellite LFs for the pri- most luminous primaries.
mary magnitude bins Mc = −21.0,−22.0,−23.0 estimated Oncerescaledinbothradiusandprojectednumberden-
from both the SDSS and MS-II mock data. For ∆Mr < 5, sity, as shown in the bottom panel of Fig. 6, the model
themodelandSDSSsatelliteluminosityfunctionsgenerally and SDSS profiles line up well outside the region at 0.05∼<
agreewell.However,thereisasteepeningoftheLFforlower r/r200 ∼<0.1.AsnotedinPaperII,theslightdeficitofsatel-
luminositysatellite galaxies intheSDSSthatisnotpresent litegalaxiesintheinnerregionsoftheSDSSforMc =−23.0
in the model. The MS-II was used for this comparison, so primaries,relativetothemodel,mayreflectdifficultiesiden-
a lack of numerical resolution should not be responsible for tifying low luminosity satellites in regions where the back-
this deficit. ground light subtraction is significant (Aihara et al. 2011).
ThemiddlepanelofFig.6showstheprojectednumber This had the effect of slightly decreasing the fitted concen-
(cid:13)c 0000RAS,MNRAS000,000–000
Statistics of Galactic Satellites 7
2 22.5<M < 21.5
Mr = 21.0 3 − p −
Mcr =−22.0
Mcr =−23.0
M) 1 c − 2pc) 2 −−2119..00<<MMss<<−−1197..00
d M
/
N 0 ) 1
d r
g( Σ(
o (
l g
−1 o 0
l
−2 −1
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0
∆M log(r/Mpc)
r
22.5<M < 21.5
3 3 − p −
)
) 2 )0 2
2c r20
p <
M 1 r 1
r) N(
(Σ( 0 r)/ 0
g (
o Σ
l−1 Mstrun=−19.0 og(−1
l
−2 −2
-2.5 -2.0 -1.5 -1.0 -0.5 0.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5
log(r/Mpc) log(r/r )
200
2 22.5<M < 21.5
3 − p −
<r))200 1 <r))200 2 −−−21111975....0000<<<<MMMMsss<<<<−−−11119753....0000
N(r 0 N(r 1 −−13.0<Mss<−−11.0
log(Σ(r)/−1 Mstrun=−19.0 log(Σ(r)/−01
−2 −2
-2.0 -1.5 -1.0 -0.5 0.0 0.5 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5
log(r/r ) log(r/r )
200 200
Figure 6. Model (MS-II, solid lines) and SDSS (points) satel- Figure 7. The dependence of the scaled and unscaled satellite
lite LFs (top), projected number density profiles (middle) and densityprofiles onsatelliteluminosityforprimariesinthe range
normalizedprofiles(bottom). Theresultsforprimaryluminosity −22.5<Mp<−21.5.Unscaled(top)andscaled(middle)profiles
binsMc=−21.0,−22.0,−23.0areshowninblack,blueandred, ofsatellitesareshownfortwodifferentluminositybands:−21.0<
respectively. Ms <−19.0 (black) and −19.0<Ms <−17.0 (blue). The solid
linesandpoints correspondtoresultsfromthemodelandSDSS
respectively. The bottom panel shows scaled profiles for lower
luminositysatellitesinthemodel.
trationofsatellitesaroundthemostluminousprimariesrel-
ative to thelow luminosity primary bins.
The dependenceof the satellite projected numberden- lite projected numberdensity profiles before and after scal-
sityprofileonsatelliteluminosityforprimarieswith−22.5< ingrespectively.Whilegenerallyingoodagreement,thereis
Mp <−21.5 is shown in Fig. 7. Satellites are split into two an excessof lower luminosity satellites in theSDSSrelative
bands of luminosity: −21.0 < Ms < −19.0, representing to themodel at ∼30 kpc.
the objects that contributed to the profile in Fig. 6, and The ‘bump’ in the projected number density profile in
−19.0<Ms<−17.0, showing thebehaviouroflower lumi- theSDSSdataispresentonlyforthelowerluminositysatel-
nosity satellites. The top and middlepanelsshow thesatel- lites. One is therefore tempted to ask if it is present at any
(cid:13)c 0000RAS,MNRAS000,000–000
8 Guo et al
satelliteluminosityinthemockcatalogues. Thisquestionis 22.5<M < 21.5
answered in thebottom panelof Fig. 7,where nocompara- 2 − p −
Blue prims SDSS
ble deviations are seen for satellites with Ms <−13, which Blue prims MS-II
have indistinguishable profiles from those of brighter satel-
1 Blue prims MS
lites. The profile for satellites with −13<Ms <−11 shows M) Red prims SDSS
aslight changeinshapeoveralargerange ofscales relative
d Red prims MS-II
totheothersetsof satellites, butnothingas pronouncedas N/ 0 Red prims MS
is seen in theSDSS. d
(
g
o
l−1
4.2 Dependence on primary and satellite colour
As a further test of the galaxy formation model, which has
so far largely succeeded in reproducing thesatellite LF and −2
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0
projected number density distributions, we now split the ∆M
r
primariesandsatellitesbycolourusingtheslightlydifferent
colourcutsdescribedinSection2.2forthemodelandSDSS.
22.5<M < 21.5
Fig. 8 shows how the satellite luminosity function and 3 − p −
Blue prims SDSS
projected number density profile depend upon the colour
Blue prims MS-II
of the primary around which they are being measured, and
) 2 Blue prims MS
compares the results from the model and the SDSS for pri- 2c Red prims SDSS
maries with −22.5 < Mp < −21.5. For the adopted colour Mp Red prims MS-II
cuts, the vast majority of primaries are classified as red in ) 1 Red prims MS
both the model and SDSS. Given that when not split by (r
Σ
colour the model produces a good match to these satellite (
g
distributions, it is nosurprise that thesatellite populations o 0
l
around red primaries agree well between model and obser-
vations.However,theblueprimariesinthemockcatalogues
aredeficientinsatellitesbyafactorof2−3.Theexcesssatel- −1
-2.5 -2.0 -1.5 -1.0 -0.5 0.0
lites around SDSS primaries span the range of luminosities
log(r/Mpc)
andradiibeingconsideredhere,withaslighttendencytobe
at lower luminosity and nearer to the primary than for the
22.5<M < 21.5
satellites present around the model primaries. The scaled 2 − p −
profiles in the bottom panel of Fig. 8 show that satellites Blue prims SDSS
around blueSDSSprimaries are slightly moreconcentrated )) Blue prims MS
than those around model primaries. 200 1 Red prims SDSS
r Red prims MS
In the top two panels of Fig. 8 results for both theMS <
and MS-II are shown. Because of its limited resolution the (r
LF in the MS becomes incomplete at ∆M ∼ 5.5, but the N 0
/
LF in the MS-II is well resolved down to ∆M ∼ 7. On the r)
(
other hand, in the smaller volume of the MS-II, there is a Σ
(−1
relatively small number of primaries and, as a result, the g
o
projected number density profile of satellites brighter than l
Ms =−19 is noisy (and it is therefore omitted in thelower −2
panel of the figure). In the regions where both simulations -2.0 -1.5 -1.0 -0.5 0.0 0.5
log(r/r )
are well resolved and sampled, theirresults are consistent. 200
The satellites themselves can be divided into red and
blue subsets and their distributions around primaries with Figure8.Thedependenceonprimarygalaxycolourofthesatel-
−22.5<Mp <−21.5 are shown in Fig. 9. Once again both liteLF(top),unscaled(middle)andscaled(bottom)numberden-
MSandMS-IIresultsareshowninthetoptwopanels,while sity profiles for primary galaxies of magnitude −22.5 < Mp <
thenoisyMS-IIresultsarenotpresentedforthescaledpro- −21.5.Solidanddashedlinesshowmodelresultsforprimariesin
jectednumberdensityprofilesinthebottompanel.Thefact theMSandMS-IIrespectively,whereasthepointsareforSDSS.
that the colour cuts in the model and SDSS samples yield AllprofilesareforsatellitesmoreluminousthanMs=−19.0.
completely different red and blue fractions is immediately
apparent in the satellite LFs, with the model satellite sys-
tems dominated by red satellites to a coincidentally simi-
lar extent as the blue satellites dominate around SDSS pri-
maries.Forthemostluminoussatellites,theSDSSblueand
redfractionsconverge,whereasthisdoesnothappenforthe thebottompanelofFig.9.However,thisisnotthecasefor
model. thebluesatellites,whichhaveamuchlessconcentrateddis-
Theshapeoftheprojecteddensityprofilesofredsatel- tribution around model primaries. For real systems of blue
litesareverysimilar forthemodelandSDSSsystems,once satellites, the distribution is only slightly less concentrated
thedifferenceinamplitudehasbeenscaledaway,asshownin than it is for the red satellites.
(cid:13)c 0000RAS,MNRAS000,000–000
Statistics of Galactic Satellites 9
22.5<M < 21.5 filesareuptoafactor2discrepantwithin∼30kpc,butthe
2 − p − agreement is generally good.
Blue sats SDSS
Tal et al. (2012) also studied the radial distribution of
Blue sats MS-II
satellitesystemsaroundbrightprimarygalaxiesusingSDSS
1 Blue sats MS
) data.TheirprimarieswereLRGsat0.28<z<0.40withno
M Red sats SDSS
isolationcriteriaappliedandhenceofteningroupsofbright
d Red sats MS-II
/ galaxies, and thus are different to those studied here in a
N 0 Red sats MS
d few respects that may well be important. They found the
(
g projectednumberdensitywaswellfittedbyacombinationof
o
l−1 aprojectedNFWprofile(Navarro et al.1996,1997)forlarge
radii and a central steeper profile that follows the stacked
light profile of the LRGs. This central bump is similar to
−2 thatseenforthelower luminositysatellites aroundprimary
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0
galaxies shown in Fig. 7, but is, in contrast, most apparent
∆M
r in the high luminosity satellites around theLRGs.
The differences between the model and SDSS satel-
22.5<M < 21.5
3 − p − lite systems are greater when the colour of the satellites is
Blue sats SDSS considered. Even the distribution of galaxies in the colour-
Blue sats MS-II
magnitude plane shows that the model has too high a frac-
2) 2 Blue sats MS tionoflowluminosityredgalaxiesrelativetotheSDSS.The
c Red sats SDSS
p modelbluesatellitesarebothsignificantlydepletedandvery
M Red sats MS-II
much less concentrated relative to either blue or red SDSS
) 1 Red sats MS
r satellites,whichhaveaprojectednumberdensityprofilelike
(
Σ
that of the red model satellites. These pieces of evidence
(
g
o 0 point tothemodel beingtoo ready toconvert low luminos-
l
ity bluegalaxies to red ones.
Weinmann et al. (2012) suggest that galaxy formation
−1 models have a generic problem with maintaining sufficient
-2.5 -2.0 -1.5 -1.0 -0.5 0.0 gastoformstarsinlowermassgalaxiesatlowredshift.The
log(r/Mpc)
satellite galaxies we are considering are somewhat larger
than those studied by Weinmann et al. (2012), and our
22.5<M < 21.5
2 − p − choiceofdifferentcolourcutsfordefiningredandbluegalax-
Blue sats SDSS iesinthemodelandSDSSsamplesreducesglobalsystematic
)) Blue sats MS colour differences. For instance, the overall fraction of blue
200 1 Red sats SDSS galaxies in the model, at the magnitudes of the satellites
r
< Red sats MS thatwefocuson,isverysimilar tothatintheSDSS.Satel-
(r lite galaxies in ourstudyconstitute only asmall fraction of
N 0
thetotalpopulationofgalaxies.Thus,adramaticchangein
/
r) the satellite properties will leave very little imprint on the
(
Σ global LF.
(−1
g Alternatively, it could be that semi-analytical galaxies
o
l turn red too rapidly after accretion into larger haloes. This
−2 idea was investigated by Font et al. (2008), who changed
-2.0 -1.5 -1.0 -0.5 0.0 0.5 the GALFORM treatment of gas stripping from subhaloes
log(r/r )
200 as they enter the virial radius of large primary galaxies.
Rather than hot gas being stripped from subhaloes imme-
Figure 9. Dependence of satellite distributions on the colour diately as they enter the virial radius, a more gradual loss
of the satellite galaxy. Symbols and line types have the same of gas is adopted in the Font et al. (2008) model. This al-
meaningasinFig.8. lows arelatively extendedperiod ofstarformation tooccur
and the possiblity of bluer satellites. We have performed
our analysis on a model galaxy population constructed us-
ing this particular variant of the Bower et al. (2006) GAL-
5 DISCUSSION
FORM model. While the typical colours of galaxies do be-
The comparison of galactic satellite systems in the model come slightly bluer, the number of blue satellites per pri-
with those in the SDSS shows that the dependence of the maryintheFont et al.(2008)modelincreasesonlyslightly,
satellite distributions on primary and satellite luminosity as can be seen in Fig. 10. The shape of the blue satellite
is captured quite well by the GALFORM model. This is a profile improves significantly, with the extra blue satellites
non-trivial success of the model since its parameters were beingfoundpreferentiallyatsmallradii.However,theabun-
adjustedmerelytomatchtheglobalK-bandLFofgalaxies, danceof red satellites is also increased bythis modification
withnodirectreferencetosatellitesystems.Thereisanex- to the GALFORM model, because satellites generally be-
cessofverylowluminositysatellitesaroundSDSSprimaries come more luminous as a result of the more extended pe-
relativetothemodel,andtheprojectednumberdensitypro- riod of star formation. As a result, the Font et al. (2008)
(cid:13)c 0000RAS,MNRAS000,000–000
10 Guo et al
2 tivelyonaspectsofthegalaxyformation model.Giventhat
Bower et al. model Mr = 21.0 the treatment of gas stripping can have the large impact
c −
Font et al. model Mr = 22.0 shown in Fig. 10, one is drawn to conclude that the ability
c −
1 SDSS Mcr =−23.0 of the default Bower et al. (2006) model to match the to-
) tal satellite LF and projected number density profile of the
M
d SDSSsystems was far from inevitable.
/
N 0
d
(
g
o
l
−1
6 CONCLUSIONS
−2
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0
∆M Usingmodelgalaxycataloguesconstructedusinglargedark
r
matter simulations and a semi-analytic galaxy formation
model, we have tested the accuracy of our procedures for
3 Bower et al. model measuringpropertiesofthedistributionofsatellitegalaxies
Font et al. model
around bright, isolated primary galaxies. We find that our
SDSS
) 2 local estimation of the abundance of background galaxies
2
c yields unbiased estimates of the satellite galaxy luminosity
p
M function and projected number density profile. The agree-
1
) mentbetweenresultsintheMSandMS-IIgalaxycatalogues
r
(
Σ in their region of overlap shows that our results are numer-
0
(
g ically convergedandallows ustoextendthedynamicrange
o
l−1 Mstrun=−19.0 of thCeommopdaerlinpgretdhiectmioonds.el predictions with those measured
for satellite systems in the SDSS, we find that the de-
−-22.5 -2.0 -1.5 -1.0 -0.5 0.0 pendence of the satellite LF is matched well for Mc =
log(r/Mpc) −21.0,−22.0,−23.0 and ∆Mr < 5. Lower luminosity satel-
litesareincreasinglyunderpredictedbythemodel.Thepro-
22.5<M < 21.5 jectednumberdensityprofileisalsowellreproducedatradii
3.0 − p − greater than ∼ 30 kpc. At smaller radii, deviations in the
2.5 Red satellites abundance by a factor of two are apparent. These differ-
) 2.0 Blue satellites ences between model and SDSS are seen most strongly in
2 the low luminosity satellites, which show an excess in the
c
Mp 1.5 SDSS relative to the extrapolation of the power law from
) 1.0 larger radii, which describes the inner regions of the model
r
( satellite systems.
Σ 0.5
( Splitting the sample into red and blue galaxies pro-
g
lo 0.0 duces more dramatic differences between the model and
SDSSresults.Themodelplacesafactor2−3fewersatellites
−0.5
around blue primaries than are present around comparable
−1.0 SDSS primaries. However, the discrepancy between model
-2.5 -2.0 -1.5 -1.0 -0.5 0.0
log(r/Mpc) and SDSS is even larger when considering the colours of
thesatellites.Themodelsatellitesarepredominantlyred,in
contrast to the blue-dominated SDSS satellite galaxy pop-
Figure 10.TheeffectonthemodelsatelliteLF(top)andnum-
ulation. Furthermore, what model blue satellites there are
berdensityprofiles(lowertwopanels)ofchangingthetreatment
haveasignificantlymoreextendeddistributionaroundtheir
of hot gas strippinginGALFORM for primarygalaxies of mag-
nitude −22.5 < Mp < −21.5. The points are the results mea- primary galaxy than is seen for either the SDSS blue satel-
sured from SDSS data, whereas solid and dashed lines are the lites or the red satellites in the model and SDSS.
resultsmeasuredfromcataloguesconstructedusingtheBoweret The generally successful comparison of the GAL-
al.(2006)andFontetal.(2008)GALFORMmodelsrespectively. FORMmodel with theSDSSdata performed hereprovides
Themiddlepanelshows theprofilesofallsatellites,whereasthe a non-trivial validation of the assumptions and framework
lowerpanelshowsthemsplitbycolour. of this kind of modelling. At the same time, the failure of
themodeltoaccountfortheobservedcolourdependenceof
the satellite properties demonstrates that the model is in-
model overproduces satellite abundances overall, as shown completeandthatimportantphysicalprocesses,almostcer-
in the upper two panels of Fig. 10. The overproduction is tainly related to the rapidity with which infalling satellite
most discrepant with thedata at low luminosities. galaxies turn red, are not being faithfully modelled. Since
Manyimportantastrophysicalprocessescombinetode- a similar shortcoming is present in the independent model
termine the distribution of low luminosity galaxies. There- ofGuo et al. (2011),thisproblem seems deep-rootedand is
fore thedistributions of satellite galaxies will depend sensi- worthy of further investigation.
(cid:13)c 0000RAS,MNRAS000,000–000