Halo masses for optically-selected and for radio-loud AGN from clustering and galaxy-galaxy lensing

20 Pages·2008·0.55 MB·English

Mon.Not.R.Astron.Soc.000,1–20(2008) Printed24October2008 (MNLATEXstylefilev2.2)
Halo masses for optically-selected and for radio-loud AGN
from clustering and galaxy-galaxy lensing
Rachel Mandelbaum1⋆, Cheng Li2,3†, Guinevere Kauffmann2‡, Simon D. M. White2
1Institute for Advanced Study, EinsteinDrive, Princeton NJ08540, USA
2Max-Planck-Institute for Astrophysics, Karl-Schwarzschild-Str. 1, D-85741 Garching, Germany
3MPA/SHAO Joint Centerfor Astrophysical Cosmology at Shanghai Astronomical Observatory, Nandan Road 80, Shanghai 200030, China
8
0
0
2 Accepted ........Received........;inoriginalform........

t
c
O ABSTRACT
We compute two-point correlation functions and measure the shear signal due to
4
galaxy-galaxy lensing for 80 000 optically identified and 5 700 radio-loud AGN from
2
Data Release 4 (DR4) of the Sloan Digital Sky Survey. Halo occupation models are

used to estimate halo masses and satellite fractions for these two types of AGN. The
]
h largesamplesizeallowsustoseparateAGNaccordingtothestellarmassoftheirhost
p galaxies. We study how the halo masses of optical and radio AGN differ from those
o- of the parent population at fixed M∗. Halo masses deduced from clustering and from
r lensing agree satisfactorily. Radio AGN are found in more massive halos than optical
st AGN: in our samples their mean halo masses are 1.6 ×1013 and 8× 1011h−1M⊙,
a respectively. Optical AGN follow the same relation between stellar mass and halo
[ mass as galaxies selected without regard to nuclear properties, but radio-loud AGN

deviate significantly from this relation. The dark matter halos of radio-loudAGN are
2
abouttwiceasmassiveasthoseofcontrolgalaxiesofthesamestellarmass.Thisboost
v
9 is independent of radio luminosity, and persists even when our analysis is restricted
8 to field galaxies. The large-scale gaseous environment of the galaxy clearly plays a
0 crucialroleinproducingobservableradioemission.Thedarkmatterhalomassesthat
4 we derive for the AGN in our two samples are in good agreement with recent models
. in which feedback fromradio AGN becomes dominant in halos where gascools quasi-
6
0 statically.
8
Key words: galaxies: active – galaxies: haloes – galaxies: formation – gravitational
0
lensing – dark matter –large-scale structure of Universe
:
v
i
X
r
a 1 INTRODUCTION ing a variety of different methods. Models that describe
the evolved, non-linear dark matter distribution in terms
It is now widely accepted that galaxies form by the cool-
of its halo building blocks (so-called halo models, e.g.
ingandcondensationofbaryonswithinamerginghierarchy
Peacock & Smith 2000; Seljak 2000; Berlind & Weinberg
of dark matter halos (White & Rees 1978). Processes other
2002; Cooray & Sheth 2002; Yang et al. 2003) or direct N-
thancoolingalsoinfluencetherelationshipbetweengalaxies
body simulations (e.g. Kauffmann et al. 1997; Jing et al.
andtheirhalos.“Feedback,”bothfromsupernovaexplosions
1998;Kauffmann et al.1999;Benson et al.2000;Yang et al.
and from energy liberated during the accretion of material
2003), can be used in conjunction with the measured clus-
onto a central supermassive black hole, is currently under
tering amplitude of galaxies to constrain the relationship
considerable scrutiny and debate, because it is believed to
betweenthegalaxiesandtheirhosthalos.Theseconstraints
playaveryimportantroleinregulatingthefractionofavail-
should be regarded as indirect, in part because of the need
able baryons that end up in galaxies.
for a cosmology-dependent conversion from galaxy bias to
Over the past few years, considerable effort has been
halo mass.
devoted to obtaining quantitative constraints on the rela-
tionship between galaxies and their dark matter halos us- Weak lensing around galaxies (or galaxy-galaxy lens-
ing, hereafter g-g lensing) provides a direct probe of the
dark matter that surrounds galaxies (for a review, see
Bartelmann & Schneider 2001). Gravitational lensing in-
⋆ E-mail:[email protected],HubbleFellow
† E-mail:[email protected] duces tangential shear distortions of background galaxies
‡ E-Mail:[email protected] aroundforegroundgalaxies, allowing directmeasurementof
(cid:13)c 2008RAS
2 Mandelbaum et al.
the galaxy-mass correlation function around galaxies. The extendedtoredshiftsz>3byShenet al.(2007)andz<0.6
individual distortions are small (of order 0.1 per cent), but byPadmanabhan et al.(2008).Thelack ofevolution of the
byaveragingoverallforegroundgalaxieswithinagivensub- halo masses from the ∼ 1012h−1M⊙ scale is all the more
sample, we obtain high signal to noise in the shear as a remarkable considering that the nonlinear mass evolves by
function of angular separation from the galaxy. If we know well over a factor of ten over the full redshift range probed
thelensredshifts,theshearsignalcanberelatedtothepro- bythese studies.
jectedmassdensityasafunctionofproperdistancefromthe Clusteringmeasurementsofradio-loudAGNhavebeen
galaxy. Thus we can observe the averaged DM distribution considerablylessaccuratebecausemanyfewerredshiftshave
around any given galaxy sample. been available. Studies of the angular clustering of radio
These techniques have been applied to study how sourcesdrawnfromthewide-areasurveyssuchastheNRAO
galaxies with different properties such as luminosity, stel- VLA Sky Survey (NVSS) or the Faint Images of the Radio
lar mass, colour, spectral type and morphology populate SkyatTwenty-centimetres(FIRST)surveyshowthatradio-
darkmatter halos ofdifferent masses (Hoekstra et al. 2005; loud AGN are considerably more strongly clustered than
Heymanset al.2006;Mandelbaum et al.2006).Thederived quasars. The estimated halo masses are typically around
relationsserveasimportantconstraintsonmodelsofgalaxy 1013 −1014M⊙ (Overzier et al. 2003). Magliocchetti et al.
formation, but they do not directly constrain the physical (2004) computed the redshift-space correlation function for
processes that are responsible for creating the relations in 820 nearby radio sources with redshifts from the 2dF, and
thefirst place. derivedacharacteristichalomassof1013.4M⊙.Nodifference
For example, Yanget al. (2005) use the occupation wasfoundintheclusteringpropertiesofAGNwithdifferent
statistics of a group catalogue to show that the mean lu- radio luminosities.
minosity of halo central galaxies scales with halo mass as Thispaperfocusesonasampleof80000opticallyiden-
Lc ∝ M2/3 for halos less massive than 1013h−1M⊙ , and tifiedAGNand5700radio-loudAGNdrawnfromtheData
flattens to a much shallower relation (L ∝M1/4) for more Release 4 (DR4) of the Sloan Digital Sky Survey. We com-
c
massive halos. It has been proposed that this characteristic putetwo-point correlation functions and measure the shear
scale reflects theimprint of feedback from radio-loud AGN, signal due to g-g lensing for these two samples. The large
whichheatthegasinmassivehalosandpreventitfromcool- samplesizeallows ustosplit theAGNintodifferentbinsin
ing and condensing onto the central galaxy. In the models stellar mass and study how the dark matter halo masses
of Croton et al. (2006) and Bower et al. (2006), this “radio of optical and radio AGN differ at a fixed value of M∗.
mode” feedback operates in halos with masses greater than Nearby radio-loud AGN have been shown to have signifi-
∼ 3×1011h−1M⊙, where cooling times are long compared cantly higher stellar masses than optically-identified AGN
to the free-fall time and gas cools quasi-hydrostatically. On at the same redshift (Best et al. 2005b), so it is important
the other hand, the work of Springel et al. (2005a) and tounderstandwhetherthederivedhalomassessimplytrack
Hopkinset al.(2005b,a)hasfocusedontheroleofoptically thisdifferenceorwhetherthedarkmatterhaloaffectseither
luminous AGN in expelling gas from galaxies and regulat- theabilityofanaccretingblackholetoproduceajetorthe
ing the rate at which they are able to form stars. In these detectability of thejet at radio wavelengths.
models,themajorgrowthphasesofblackholesandthetrig- We also create control samples of non-AGN that are
gering of optically luminous AGN occur when two galaxies matched in stellar mass, redshift and morphology, and we
that contain sufficient cold gas merge with each other. The use these control samples to investigate whether the halo
triggering thusdoesnotdependdirectly onthemass ofsur- masses of active galaxies differ from those of their counter-
roundingdark matterhalo. parts chosen irrespective of their level of nuclear activity.
In order to constrain the importance of these pro- Finally, the fact that the clustering and weak lensing anal-
cesses, it is important to understand how the AGN them- ysesarecarried out onthesameset ofgalaxies allows usto
selves are related to the surrounding dark matter distri- evaluate the consistency of our constraints on dark matter
bution. The large-scale clustering amplitude of luminous halo mass obtained using the two methods.
quasars has been accurately measured using tens of thou- We begin by outlining the theory behind the lensing
sands of such objects drawn from the 2dF and Sloan Dig- andclusteringmeasurementsinsection 2.Wethendescribe
ital Sky Survey. Croom et al. (2005) use a sample based the data used for the analysis, and the analysis procedure,
on the 2dF to conclude that quasars from 0.5 < z < 2.5 in section 3. The results for optical and radio-loud AGN
inhabit dark matter halos with a characteristic mass of are presented in section 4, including lensing and clustering
∼ 3 × 1012h−1M⊙, and that this mass does not depend separately,followed byajoint analysis. Wethensummarize
on redshift or on quasar luminosity. Myerset al. (2007a) the key results and discuss their implications in sections 5
use a photometrically-identified quasar sample from SDSS and 6, respectively.
over a similar redshift range to estimate a typical mass of
∼5×1012h−1M⊙,withoutarobustdetectionofluminosity-
dependent bias at fixed redshift (for which there is only a 2 THEORY
marginal detection in the 2dF sample, Porciani & Norberg
2006). Several studies (Hennawi et al. 2006; Myers et al. 2.1 Galaxy-galaxy lensing
2007b, 2008) have also probed the very small-scale cluster-
Galaxy-galaxy weaklensingprovidesasimpleway toprobe
ing of quasars, using pairs of binary quasars, which are a
theconnection betweengalaxies andmatterviatheircross-
probe of how the local environment affects quasar activity,
correlation function
though no clear consensus arises from these studies. The
Croom et al.(2005)resultsabouthalomasseswererecently ξ (~r)=hδ (~x)δ (~x+~r)i (1)
gm g m
(cid:13)c 2008RAS,MNRAS000,1–20
Halo masses of AGN 3
where δ and δ are overdensities of galaxies and matter, assume that all central galaxies in our sample have a sin-
g m
respectively, and in practice the mean is taken over some gle halo mass M , and that all satellite galaxies are dis-
cent
surveyvolume (in theory it is theaverage overa whole dis- tributed in halos with M > 3M with the number in a
cent
tribution,butwecanonlyestimateitsvalueusingthefixed halo of given mass above this threshold ∝M. Tests of this
volumesthatareavailableinreality).Wewillinterchangably halomodelformulationusingthelensingsignalfromN-body
expresscorrelation functionsasfunctionsofvectors(~r)and simulations(Mandelbaum et al.2005b)clearlyindicatethat
scalars (r)becauseoftheassumption ofstatistical isotropy. thebest-fittingM andαrecoverthetruevaluestowithin
cent
This cross-correlation can be related to the projected ∼10percent,providedthatthedistributionofcentralhalo
surface density massesisrelativelynarrow(FWHMtypicallyafactorof6or
less). For a broader distribution of central halo masses, the
Σ(R)=ρ 1+ξ R2+χ2 dχ (2) best-fittingM lies between themedian and themean of
gm cent
Z h (cid:16)p (cid:17)i thedistribution, butmay differfrom eitheronebyas much
(forr2 =R2+χ2),whereweignoretheradialwindow,which asafactoroftwo.Formoredetailsofthishalomodelandits
is much broader than the typical extent of the lens. This assumptions, see Mandelbaum et al. (2005b). In this work,
surface density is then related to the observable quantity we use this halo model without applying any correction for
for lensing, the(unknown)scatterbetweengalaxystellarmassanddark
matter halo mass, but we will discuss the extent to which
∆Σ(R)=γ (R)Σ =Σ(<R)−Σ(R), (3)
t c our assumptions about the width of the central halo mass
where the second relation is true only for a matter distri- distribution are likely to be correct.
bution that is axisymmetric along the line of sight. This
observable quantitycan beexpressed as theproduct of two
factors, a tangential shear γt and a geometric factor, the 2.2 Galaxy clustering
critical surface density
Theclusteringofgalaxiesisusuallyquantifiedusingthetwo-
Σ = c2 DS (4) pointcorrelationfunction(2PCF,e.g.Peebles1980),defined
c 4πGDLDLS(1+zL)2 by
whereDLandDS areangulardiameterdistancestothelens dP =n¯2[1+ξ(~r)]dV dV . (5)
12 1 2
and source, D is the angular diameter distance between
LS
thelens and source, and the factor of (1+z )−2 arises due Here n¯ is the mean number density of galaxies, and dV
L 1
toouruseofcomovingcoordinates.Foragivenlensredshift, anddV arethevolumesoftwoinfinitesimallysmallspheres
2
Σ−c1 rises from zero at zs = zL to an asymptotic value at centeredat~x1 and~x2 withdistanceof~r=~x2−~x1.Bydefi-
zs ≫zL; that asymptotic value is an increasing function of nition,dP12isthejointprobabilitythatagalaxyliesineach
lens redshift. of the spheres, and so the 2PCF ξ(r) represents the excess
In practice, we measure the g-g weak lensing signal probabilityoffindingtwogalaxiesseparatedbyadistance~r,
around a stacked sample of lenses to obtain the average comparedwiththeresultobtainedforauniformrandomdis-
∆Σ(R) for the whole sample. This stacked lensing signal tribution.Ifξ(r)>0,thengalaxies aresaidtobeclustered.
canbesplitintotwotermsthatdominateondifferentscales. Ingalaxyredshiftsurveys,the2PCFismeasuredinredshift
The1-haloorPoissonterm,whichisdeterminedbythedark spaceandusuallyexpressedasfunctionsofseparationsper-
matter halo in which the galaxy lives, dominates on scales pendicular(r )andparallel(π)tothelineofsight.Inmany
p
typically below ∼ 1h−1Mpc. The halo-halo term, which is cases, the projected two-point correlation function, wp(rp),
determined by correlations between the galaxy and other is the more useful quantity, because it does not suffer from
dark matter halos, dominates on larger scales. The 1-halo redshift-spacedistortions,andisthusdirectlyrelatedtothe
termcanbefurthersplitintotwocontributions.Forcentral real-space correlation function. The 2PCF is also simple to
galaxies, which reside at the peak density of a dark matter compute and can be easily compared with the predictions
halothatisnotcontainedwithinanotherhalo(ahosthalo), of theoretical models.
thePoissontermissimplydeterminedbythematterdensity The amplitude of the correlation function on scales
of that host halo, ρ(r). For satellite galaxies, which reside largerthanafewMpcprovidesadirectmeasureofthemass
in dark matter subhalos, there is a contribution from the of thedark matterhalos that host thegalaxies through the
densityofthedarkmattersubhalo,butthereisalso aterm halo mass - bias relation. As shown in Li et al. (2008a,b),
onhundredsofkiloparsecscalesduetothecross-correlation the amplitude of the correlation function on scales . 100
between thegalaxy position and thehost darkmatterhalo. kpccanserveasaprobeofphysicalprocessessuchasmerg-
Consequently, the lensing signal on <∼ 0.3h−1Mpc scales ers and interactions. On intermediate scales, the shape of
tells us about the dark matter halo in which the galaxy re- thecorrelation function is sensitive to how galaxies are dis-
sides; the signal from ∼ 0.3 – 1h−1Mpc reveals the local tributed withintheir dark matter halos.
environment of the galaxy; and the signal on larger scales The clustering signal must also be interpreted using
indicates the large-scale correlations of thegalaxy sample. someformofhalomodel.Followingtheapproachadoptedin
Weinterpretthelensingsignalstatisticallyusingahalo our previous work, we interpret clustering results using the
model, which allows us to determine both the typical halo modelsofLi et al.(2006a)andWanget al.(2006)whichare
mass M for central galaxies in our galaxy sample, and basedon directN-bodysimulations. Wehaveconstructeda
cent
also the satellite fraction α (the fraction of the sample lo- setof100mockgalaxycataloguesfromtheMillenniumSim-
catedinsubhaloswithinsomemoremassivehostdarkmat- ulation (Springelet al.2005b)with exactlythesameobser-
ter halo). In this simple formulation of the halo model, we vationalselectioneffectsastheSDSSDR4.TheMillennium
(cid:13)c 2008RAS,MNRAS000,1–20
4 Mandelbaum et al.
Simulationuses1010 particlestofollowthedarkmatterdis- 3 DATA AND SIGNAL MEASURES
tribution in a cubic region 500h−1 Mpc on a side. The cos-
3.1 Overview of SDSS
mological parameters assumed are Ω = 0.25, Ω = 0.75,
m Λ
σ8 =0.9andh=0.73. Weadoptedthepositionsandveloc- ThedatausedhereareobtainedfromtheSDSS(York et al.
ities of the galaxies given in the catalogue of Croton et al. 2000), an ongoing survey to image roughly π steradi-
(2006), who implemented asemi-analytic modelin orderto ans of the sky, and follow up approximately one million
track the formation and evolution of galaxies in the sim- of the detected objects spectroscopically (Eisenstein et al.
ulation. Physical properties of the galaxies, such as stel- 2001; Richardset al. 2002; Strauss et al. 2002). The imag-
lar masses and AGN status, are not taken from the semi- ing is carried out by drift-scanning the sky in photo-
analytic model, however, but instead are assigned to each metric conditions (Hogg et al. 2001; Ivezi´cet al. 2004), in
model galaxy using parametrized functions. The main such fivebands (ugriz) (Fukugitaet al. 1996; Smith et al. 2002)
functionrelatesthestellarmassofthegalaxytothemassof using a specially-designed wide-field camera (Gunn et al.
the halo at the epoch when the galaxy was last the central 1998). These imaging data are used to create the source
dominant object in its own halo, including scatter in that cataloguethatweuseinthispaper.Inaddition,objectsare
relation. Tests have shown that this procedure allows us to targeted for spectroscopy using these data (Blanton et al.
match accurately both the stellar mass function of SDSS 2003c) and are observed with a 640-fiber spectrograph
galaxies and the shape and amplitude of their two-point on the same telescope (Gunnet al. 2006). All of these
correlations as a function of stellar mass (Li et al. 2006a; data are processed by completely automated pipelines
Wang et al. 2006). that detect and measure photometric properties of ob-
jects, and astrometrically calibrate the data (Lupton et al.
2001; Pier et al. 2003; Tuckeret al. 2006). The SDSS has
In Liet al. (2006b, hereafter L06), we adapted this had seven major data releases (Stoughton et al. 2002;
halomodeltointerprettheclusteringof optically-identified Abazajian et al. 2003, 2004, 2005; Finkbeineret al. 2004;
AGN.Inthatpaper,wecomputedthecorrelation functions Adelman-McCarthy et al. 2006, 2007, 2008). In this pa-
ofAGNandofcontrolsamplesofinactivegalaxiesthathad per we use data from the fourth of these releases(DR4;
the same redshift and stellar mass distribution as the ac- Adelman-McCarthy et al. 2006).
tivegalaxies. Wefound thaton scales between100 kpcand
1 Mpc, AGN are clustered more weakly than the inactive
sample. We then introduced a simple model in which the 3.2 The AGN and control samples
probability of a galaxy of given stellar mass to be an AGN
3.2.1 Optically-identified AGN
is enhanced if it is the central galaxy of its own halo, and
showedthatthismodelcouldprovideagoodfittothedata. The sample of optically-identified AGN is the same as that
Inthebest-fittingmodel,84percentofallopticalAGNare analyzedinL06andLi et al.(2008b),inwhichtheclustering
located at the centres of their own dark matter halos (i.e., of AGN on a variety of different scales was studied.
fcen = 0.84), whereas this is true for only 73 per cent of The base sample is composed of ∼ 4×105 objects for
inactive galaxies. which data are publicly available through DR4 and which
have been spectroscopically confirmed as galaxies with r-
band magnitudes in the range 14.5 < r < 17.6, redshifts
We emphasize that while in principle, it would be easy in the range 0.01 < z < 0.3, and absolute magnitudes in
to assume that α derived from the lensing analysis is sim- the range −23 < M < −17. Here r is the r-band Pet-
0.1r
ply1−f from theclustering analysis, therelationship is rosian apparent magnitude corrected for foreground extinc-
cen
notasstraightforwardasthis.Theclusteringanalysisstarts tion,and M0.1r isther-bandabsolute magnitudecorrected
fromtheassumptionthattheAGNandcontrolsamplesde- toitsz =0.1valueusingthek-correctcodeofBlanton et al.
rive from a parent population which matches the statisti- (2003a)andtheluminosityevolutionmodelofBlanton et al.
cal properties of galaxies as a function of stellar mass (i.e., (2003b). A sample of ∼ 80,000 AGN are selected from the
thestellar massfunctionandtheclusteringasafunction of subset of these galaxies with S/N > 3 in the four emission
mass).Anyhalomodelparameterssuchasf arethenin- lines [O iii]λ5007, Hβ, [N ii]λ6583 and Hα, following the
cen
troducedasawayofmatchingtheobservedAGNclustering criteriaproposedbyKauffmann et al.(2003).Inthefollow-
bymodifyingtheprobabilitythateachgalaxyintheparent inganalysis, we occasionally divideoursample into“weak”
populationisanAGN.Incontrast,thelensinganalysisdoes and“powerful”AGNusingthequantityL[OIII]/M ,where
bh
not assume that the AGN and control samples stem from L[OIII] is the extinction-corrected [OIII] line luminosity of
identical parent populations. In future analyses with larger the AGN and M is the black hole mass estimated from
bh
datasets, we will jointly model clustering and lensing with thevelocitydispersionofthegalaxyusingtherelationgiven
the same assumptions at the outset; here, we simply use in Tremaine et al. (2002). As discussed in Heckman et al.
pre-existing analysis pipelines that output quantities that (2004), this quantity can beviewed as a measure of theac-
shouldbereasonably(butnotexactly)comparable.Evenin cretion rate onto the black hole relative to the Eddington
the absence of a completely unified approach to modeling, rate.
therearemanyvaluableconclusionsthatcanbedrawnfrom Wehavealsoconstructedtwosetsof20differentcontrol
thelensingandclusteringsignals(e.g.,ifboththeclustering samplesfromthefullparentsampleofgalaxiesbymatching
andlensingsignalsforaparticularsamplearecomparableto anumberofphysicalparametersregardlessofnuclearactiv-
thesignalsforthecontrols,oriftheyarebothquitedifferent ity. For the first set, four physical parameters are matched:
from the signals for thecontrols). redshift (z), stellar mass (M∗), concentration (R90/R50),
(cid:13)c 2008RAS,MNRAS000,1–20
Halo masses of AGN 5
and stellar velocity dispersion (σ∗). For the second set, the of the lensing signal, such as the sky subtraction uncer-
4000 ˚Abreakstrength(D )isalso matched.Thematch- tainties,intrinsicalignments,magnificationbias,star-galaxy
4000
ing tolerances are ∆cz < 500 km s−1, ∆logM∗ < 0.1, separation, and seeing-dependent systematics. The overall
∆σ∗ < 20 km s−1, ∆R90/R50 < 0.1 and ∆D4000 < 0.05.1 calibration uncertainty was estimated to be eight per cent
In thefirst case, 28 percent of thecontrol galaxies are also (Mandelbaum et al. 2005a), though the redshift calibration
included in the AGN sample; in the second case, the over- componentofthissystematicerrorbudgethasrecentlybeen
lap fraction ishigher, 37 percent.Inboth cases, thematch decreasedduetotheavailability ofmorespectroscopicdata
fraction is a slightly increasing function of stellar mass. (Mandelbaum et al. 2008). With a total estimated lensing
calibration uncertainty of ∼ 5 per cent, this systematic is
subdominant compared to the statistical error and to the
3.2.2 Radio-loud AGN uncertainty derived from the model used to interpret the
lensing signal.
TheNational Radio AstronomyObservatory (NRAO)Very
LargeArray(VLA)SkySurvey(NVSS;Condon et al.1998)
and the Faint Images of the Radio Sky at Twenty centime- 3.3.2 Lensing signal computation
ters (FIRST) survey (Beckeret al. 1995) are two radio sur-
Herewebriefly describethecomputation of thelensing sig-
veys that have been carried out in recent years using the
nal;formoredetail,seeMandelbaum et al.(2005a).Foreach
VLA radio synthesis telescope at a frequency of 1.4 GHz.
lens, we identify sources within 46 logarithmically-spaced
Best et al. (2005b) identified radio-emitting galaxies within
annuli around the lens (in comoving transverse separation)
the main spectroscopic sample of the SDSS data release 2
from 20 h−1kpc to 2 h−1Mpc. The tangential ellipticity of
(DR2) by comparing these galaxies with a combination of
the source relative to the lens is measured, in order to es-
these two surveys. The use of two radio surveys allowed a
timate the tangential shear. Lens-source pairs are assigned
radio sample to be constructed that was both reasonably
weights according to the error on the shape measurement
complete(∼95percent)andhighlyreliable (itisestimated
via
that∼99percentofthesourcesinthecataloguearegenuine
radio galaxies rather than false matches). In this paper, we Σ−2
w = c (6)
use an updated catalogue of 5 712 radio galaxies based on ls σ2+σ2
s SN
theSDSSdatarelease4(DR4).Thesamplespansthesame
where σ2 is the intrinsic shape noise and σ is the mea-
redshift rangeasthesampleofoptically-selected AGN,and SN s
surementerroronthesourcegalaxyellipticity.Thefactorof
the radio luminosities of the AGN range from 1023 to 1026
Σ−2 optimally weightsthesignal bythenoisein ∆Σrather
W Hz−1 (i.e., they are mainly FRI typesystems). c
than in the shear.
Wehaveused theparentgalaxy catalogue toconstruct
Oncewehavecomputedtheseweights,wecomputethe
a set of five control samples that are closely matched in
lensing signal in each radial bin as a summation over lens-
redshift, stellar mass and stellar velocity dispersion. The
source pairs via:
matching tolerances are the same as used to construct the
opticalAGNcontrolsamples.Wedonotadditionallymatch w e(ls)Σ
∆Σ(R)= ls ls t c (7)
in D , because almost all galaxies at the relevant stellar
4000 2R w
masses are red, with a strong 4000 ˚A break. Of the control P ls ls
sample,10.3percentofthegalaxiesareradio-loudAGN;for wherethefactorPof2andtheshearresponsivityRrelateour
our higher stellar mass subsample (log(M∗/M⊙) > 11.44), definition of ellipticity to the shear, using the formalism in
theradio-loud AGN fraction is 16 percent,whereas for the Bernstein & Jarvis(2002).Inpractice,R≈1−e2rms≈0.86.
lower M∗ subsample, it is 7 percent. There are several additional procedures that must
be done when computing the signal (for more detail,
see Mandelbaum et al. 2005a). First, the signal computed
3.3 Lensing analysis around random points must be subtracted from the signal
around real lenses to eliminate contributions from system-
3.3.1 Lensing source catalogue
atic shear. In practice, this correction is negligible for the
scalesusedinthiswork.Second,thesignalmustbeboosted,
Thesource sample used for thelensing analysis is thesame
i.e. multiplied by B(R) = n(R)/n (R), the ratio of the
as that originally described in Mandelbaum et al. (2005a). rand
number density of sources relative to the number around
Thissourcesampleincludesover30milliongalaxiesfromthe
random points, in order to account for dilution by sources
SDSS imaging data with r-band model magnitude brighter
thatarephysicallyassociated withlenses,andthereforenot
than 21.8, with shape measurements obtained using the
lensed.
REGLENS pipeline, including PSF correction done via re-
To determine errors on the lensing signal, we divide
Gaussianization (Hirata & Seljak 2003) and with cuts de-
the survey area into 200 bootstrap subregions, and gen-
signed to avoid variousshear calibration biases. Inaddition
erate 2500 bootstrap-resampled datasets. These bootstrap-
to these, there are also uncertainties due to photometric
resampled datasets are also crucial for determining thesta-
redshiftsand/orredshift distributionsofbackgroundgalax-
tistical significance of differences between correlated sub-
ies, as well as due to other issues affecting the calibration
samples of galaxies, because fitting the signal to the halo
model on each resampled dataset allows us to determine
1 ThisprocedureisidenticaltothatinL06,exceptthatthecon- howmuchanyoverlapbetweentwogalaxysamplesleadsto
trolgalaxiesareselectedfromthefullparentsample,ratherthan acorrelationbetweenthebest-fittinghalomodelparameters
fromthesubsetofinactivegalaxies. for thetwo samples.
(cid:13)c 2008RAS,MNRAS000,1–20
6 Mandelbaum et al.
Figure 1.Thegalaxy-galaxylensingsignalforopticalAGN(top)andcontrolgalaxies(bottom)asafunctionoftransverseseparation.
Pointsarethedata,andlinesarethebest-fittinghalomodels.Theleftpanelsshowthesamplesplitbystellarmassasfollows:logM∗<
10.6(blacksolid),10.66logM∗<11(reddotted), logM∗>11(bluedashed). Therightpanels showthesamplesplitbyL[OIII]/Mbh
intothelowerhalfofthesample(blacksolid)andupperhalf(reddotted).
Thelensingsignalispresentedincomovingcoordinates, 3.4 Clustering analysis
with angular diameter distances computed assuming a flat
3.4.1 The reference galaxy sample
ΛCDM universe with Ω = 0.3 and Ω = 0.7. The halo
m Λ
modelusedtointerpretthelensingsignalassumesσ8 =0.9. In this paper, the clustering of AGN (or control galaxies)
Intheunitsused,H0 scalesoutofeverything,soourresults is quantified by the projected two-point cross-correlation
areindependentofthisquantity.Thecentralhalomassdef- function (2PCCF), w (r ), which is estimated by cross-
p p
initionforthispaperisthemasswithinwhichthespherical correlating the AGN (or control) samples described above
overdensity is 200ρcrit, which is roughly 35 per cent lower with a reference sample of galaxies.2 The reference galax-
than the mass definition used for previous lensing analyses ies are selected from sample dr4 of the New York Uni-
usingthishalomodelformalism (Mandelbaum et al.2005b, versity Value Added Galaxy Catalogue (NYU-VAGC),
2006). This change in halo mass definition was made to which is based on SDSS DR4, publicly available at
match the mass definition for theclustering analysis.
2 We use the notation rp for the transverse separation in the
clustering analysis, and the notation R for the same quantity in
the lensing analysis. The main reason is to maintain notational
consistencywithinpreviouswork.
(cid:13)c 2008RAS,MNRAS000,1–20
Halo masses of AGN 7
http://sdss.physics.nyu.edu/vagc/, and is described in de-
tail in Blanton et al. (2005). The reference sample contains
292,782objectsthatareidentifiedasgalaxiesfromtheMain
sample and have 0.01 6 z 6 0.3, 14.5 < r < 17.6 and
−23 < M0.1r < −17. This sample has formed the basis of
our recent investigations of the clustering properties of dif-
ferent classes of galaxies (L06, Li et al. 2007a,2008a,b).
3.4.2 Clustering measures
Our methodology for computing correlation functions has
alsobeendescribedindetailinourpreviouspapers.Random
samples are constructed with the same selection function
as the reference sample, as described in detail in Li et al.
(2006a) (but note the slight differences mentioned here in
§3.2.1). The redshift-space 2PCCF ξ(r ,π) between AGN
p
(orcontrolgalaxies) andthereferencesampleisthencalcu-
lated using theestimator presented in L06,
N QD(r ,π)
ξ(r ,π)= R p −1, (8)
p N QR(r ,π)
D p
where r and π are the separations perpendicular and par-
allel topthe line of sight; N and N are the number of Figure 2.Thebest-fitting central halomasses Mcent (top) and
D R satellitefractionsα(bottom)asafunctionofstellarmassforthe
galaxies in thereference sample and in therandom sample,
opticalAGNandthetwocontrolsamplesaslabelledontheplot.
with N /N = 10 throughout this paper; QD(r ,π) and
R D p
QR(r ,π) are the cross pair counts between AGN/control
p
and the reference sample, and between AGN/control and shown,becausetheyarestatistically consistent withthere-
therandom sample, respectively. Finally, theredshift-space sults for the control samples where D is not matched.
4000
projected2PCCFw (r )isestimatedbyintegratingξ(r ,π) There are several clear trends in this figure. First, the
p p p
along theline-of-sight direction: g-glensingsignalonsmallscales(<0.3h−1Mpc)showsthat
thehalomassforcentralgalaxiesincreaseswithstellarmass
+πmax
wp(rp)= ξ(rp,π)dπ= ξ(rp,πi)∆πi. (9) anddecreases with L[OIII]/Mbh.This conclusion istruefor
Z−πmax i both theAGN and for thecontrol samples. Second, theg-g
X
lensing signal for AGN and controls in a particular sub-
Here π = 40h−1 Mpc, and the summation for comput-
max sample is quite similar; any differences are not statistically
ing w (r ) runs from π = −39.5 h−1 Mpc to π = 39.5
p p 1 80 significant.
h−1 Mpc, with ∆π = 1 h−1 Mpc. We have also corrected
i Wenowconsiderthehalomodelinterpretationofthese
carefully for the effect of fibre collisions; a description and
results,representedbythebest-fittingcentralhalomassand
tests of the method can be found in L06. As will be de-
satellite fraction foreach sample. Thesequantitiesareplot-
scribed in more detail in § 4.2.1, error estimates come from
tedfortheopticalAGNandthetwocontrolsamplesinFig.2
thevariance in w (r ) between 100 mock catalogues.
p p as a function of stellar mass. For reference, they are tabu-
The clustering computation assumes the same flat
latedforallopticalAGNandcontrolsubsamples,including
ΛCDM universe with Ω = 0.3, Ω = 0.7 and σ = 0.9 as
m Λ 8 thesplits by L[OIII]/M , in Table 1.
bh
for the lensing analysis. Our results are presented in units
Afewtrendsareevidentfromtheplotandtable.First,
of h−1 Mpc with h=1.
for the samples split bystellar mass, the differences in halo
model parameters for the AGN and control samples are
not statistically significant, as expected from Fig. 1. How-
4 RESULTS ever, the central halo mass shows a strong trend with stel-
lar mass, consistent with the lensing results for the general
4.1 Optical AGN
galaxypopulationdiscussedinMandelbaum et al.(2006).If
Resultsandinterpretationforthegalaxyclusteringsignalof wecompare against theresultsin that paperafter account-
the optical AGN have been presented in L06, and are also ingfor thedifferenthalo mass definitions,weconcludethat
brieflydescribedin§2.2.Consequently,herewepresentonly for the lower and middle stellar mass bins, the best-fitting
the galaxy-galaxy lensing signal and its interpretation for central halo mass is consistent (within the noise) with the
this sample. In section 5, we compare the halo masses and results for both early and late type galaxies, which have
satellite fractions estimated through lensing with the same similar mean halo masses below stellar masses ∼ 1011M⊙.
quantitiesestimated through clustering. Forthehigheststellarmassbin,ourbest-fittingcentralhalo
In Fig. 1,weshow theg-glensing signal for theoptical massismoreconsistentwiththeresultsforlate-typegalaxies
AGNsamplesplit bystellar mass andbytheaccretion rate (lower by a factor of a few than that for early-type galax-
per unit black hole mass (L[OIII]/M ). Results are shown ies). This result is consistent with the general tendency of
bh
for both the AGN and the control samples; results for the these narrow-line AGN to be associated with galaxies with
controlsampleswith thesamedistributionofD arenot ongoing star formation.
4000
(cid:13)c 2008RAS,MNRAS000,1–20
8 Mandelbaum et al.
Table 1.Best-fittinghalomodelparametersforfitstotheopticalAGNg-gweaklensingsignal,with68percentCLerrors.
OpticalAGN Controls ControlswithD4000
Sample Mcent α Mcent α Mcent α
1012h−1M⊙ 1012h−1M⊙ 1012h−1M⊙
logM∗/M⊙<10.6,hM∗/(1010M⊙)i=2.3 0.13±0.08 0.26±0.04 0.31±0.16 0.27±0.05 0.29±0.15 0.33±0.05
10.66logM∗/M⊙<11,hM∗/(1010M⊙)i=6.5 0.86±0.21 0.18±0.04 0.77±0.20 0.22±0.05 0.79±0.21 0.19±0.05
logM∗/M⊙>11,hM∗/(1010M⊙)i=15.4 2.3±0.4 0.19±0.04 3.0±0.5 0.20±0.04 2.8±0.6 0.21±0.05
Lowerhalf,L[OIII]/Mbh 1.1±0.2 0.25±0.03 1.5±0.2 0.25±0.03 1.1±0.2 0.30±0.03
Upperhalf,L[OIII]/Mbh 0.47±0.13 0.16±0.03 0.39±0.14 0.22±0.03 0.52±0.16 0.17±0.03
tral halo mass distribution. This plot is shown in Fig. 3.
Asshown, theFWHM of thedistribution for the two lower
stellar mass bins is within the factor of ∼ 6 needed for ac-
curate estimation of the mean central halo mass. However,
the distribution is sufficiently broad for the highest stellar
mass bin that our estimate from the lensing signal is likely
anunderestimateofthemean,possiblybyasmuchas50per
cent. We do not apply a correction to determine the mean
centralhalomass foreithertheAGNorthecontrols inthis
bin, since there is significant systematic uncertainty in the
correction factor itself.
4.2 Radio AGN
4.2.1 Galaxy Clustering
Wehavemeasuredtheprojected2PCCFw (r )oftheradio
p p
AGN with respect to the reference galaxies, and compared
this to the average result of the five control samples. The
results are shown in Fig. 4 for the whole sample (circles in
the left panel) and for two different ranges in stellar mass
M∗.
Figure3.Thedistributionsofcentralhalomassinthemockcat-
Radio AGN are more strongly clustered than control
aloguesthatareabletoreproducetheclusteringsignalinLietal.
galaxies on all scales. The difference in w (r ) amplitude is
(2006b)inourthreestellarmassbins. p p
aconstantfactoronscalessmallerthan∼1Mpc,thenrises
slightlyonlargerscales.Fig.4alsoshowsthattheclustering
The satellite fractions decrease slightly from the low- amplitude of radio AGN increases with the stellar mass of
est to middle stellar mass bin. Consistent with the results the host galaxy. This result is consistent with the fact that
from L06, we find slightly lower satellite fractions for the moremassivegalaxies aremorestrongly clustered (Li et al.
optical AGN than for the control samples. Unlike for the 2006a). We have also tested whether there is a dependence
galaxy clustering signal, this difference is not statistically of the clustering amplitude on the radio luminosity of the
significant. AGN, and we find that at fixed M∗, there is no significant
Thereisclearlyasignificantdifferenceinthemeancen- effect. This finding is consistent with the recent results of
tral halo mass and satellite fraction for the samples split Kauffmann et al. (2008), who show that radio-loud AGN
at the median value of L[OIII]/M . However, this quan- are in denser environments than control radio-quiet galax-
bh
tity is itself correlated with stellar mass, so some of the ies, but that there is no dependence of local density on the
trend derives from that correlation. For the lower half of radio luminosity of the AGN.
the sample in OIII luminosity, the mean stellar mass is Wenow useourmock catalogues (see §3) to model the
hM∗i=9.1×1010M⊙;fortheupperhalf,itis7.3×1010M⊙. observed clustering measurements of radio AGN. We first
The results for the control samples with the same stellar tried to vary the fraction of radio AGN assigned to central
mass distribution suggest that the difference in best-fitting versus satellite galaxies (as was done for theoptical AGN).
centralhalomassescanbeexplainedsolelybythisdifference WefoundthatifradioAGNarepreferentiallyfoundinsatel-
in stellar mass distributions. litegalaxies,wecanfitthedataonscalessmallerthanafew
Finally, we discuss the broadness of the central halo Mpc, but the model then underpredicts the clustering am-
massdistribution.Aswehavealreadynoted,abroadcentral plitudeonlargerscales.Aswehavediscussed,theamplitude
halomassdistributionwouldleadtothebest-fittingcentral of the correlation function on scales larger than a few Mpc
halomasses beingan overestimateof themedian mass, and provides a direct measure of the mass of the dark matter
underestimateofthemeanmass.Toassesswhetherthismay halos hosting the radio AGN. Motivated by the models of
be the case, we use the halo occupation models of L06 for Croton et al. (2006) and Bower et al. (2006), we impose a
optical AGN (see §2.2) which can be used to derive a cen- lower threshold in halo mass, Mmin, as a second free pa-
h
(cid:13)c 2008RAS,MNRAS000,1–20
Halo masses of AGN 9
Figure 4. Projected cross-correlation function wp(rp) for radio AGN (green filled circles) in different stellar mass ranges compared
to results for control samples selected without regard to AGN properties (black open symbols). Results for the best-fitting model are
indicated as red (AGN) and blue (controls) shaded regions, where the width of the shaded regions corresponds to the 1−σ variance
between200mockcatalogues. Errorbarsaresignificantlycorrelated(>10percent) betweenradialbinsabove ∼1h−1Mpc.
rameter of the model. In other words, radio-loud AGN are catalogue. The m×m matrix C = {C } (i,j = 1,...,m)
ij
only found in dark matter halos more massive than Mmin. is the covariance matrix of the measurements from the 200
h
Theprobabilityofagalaxytobearadio-loudAGNdepends mock catalogues, given by
not only on whether it is a central or satellite system, but
n
alsoonthemassofitsdarkmatterhalo.However,theprob- 1
C = (Y −hY i)(Y −hY i) (13)
ability that aparticulargalaxy isan AGNdoes notdepend i,j n−1" ki i kj j #
k=1
ontheAGNstatusofitsneighbors.Whilethisstepfunction X
where
in mass is undoubtedly an over-simplification, we adopt it
as a first attempt at modeling tosee if it is close enough to Y =w (r ) (14)
k,i p,k p,i model
reality that the observations can bemodeled in this way.
is themeasurement at theith radial bin from thekth mock
Wehavegenerated agrid of322 modelsbyvaryingthe
two parameters, f and Mmin, with f ranging from catalogue, and
cen h cen
0.40to0.84withastepsizeof0.02,andlog(Mhmin/h−1M⊙) 1 n
rangingfrom 10.0to13.25withastepsizeof0.25. Wehave hYii= n wp,k(rp,i)model (15)
constructed 200 mock catalogues of radio AGN for each k=1
X
of the models. We measure wp(rp) and its covariance ma- isthemeanmeasurementattheith radialbinoverallmock
trix C at each grid point, and we compare the measure- catalogues.
ments to the SDSS results. In order to identify the best-fit We define the best-fit model to be the one giving a
model, we first calculate the likelihood of each parameter minimum Λ computed as follows:
set, L(f ,Mmin), by
cen h Λ(f ,Mmin)=−2lnL(f ,Mmin) (16)
cen h cen h
L(fcen,Mhmin)= det[C((2fπ)−,mM/2min)]e−0.5χ2(fcen,Mhmin),(10) =χ2(fcen,Mhmin)+2ln{det[C(fcen,Mhmin)]}+mln(2π).
cen h Notethatthismaximumlikelihoodestimatediffersfromthe
where simple minimum of χ2 if the determinant of the covariance
χ2(f ,Mmin)=XTC−1X. (11) matrix det[C] varies with the parameters. This variation is
cen h demonstrated in Figure 5, where we plot ln[det(C)] in the
HereX={Xj} (j =1,...,m) is an m×1 vector with grid of the two model parameters, fcen and Mhmin. As can
beseen,thedeterminantofthecovariancematrixdoesvary
n
1 systematicallyfrommodeltomodel.Thisvariationisdueto
X = w (r ) −w (r ) , (12)
j n p,i p,j model p p,j SDSS the fact that the covariance depends on the two- and four-
!
Xi=1 point functions of the galaxy distributions, which clearly
where n = 200 is the number of mock catalogues, m is differacross thegridduetothedifferentwaysthehalos are
the number of radial bins over which w (r ) is measured, populated with AGN. However, the variation is relatively
p p
w (r ) is the clustering amplitude at the jth radial smooth, indicating that we have used enough mock cata-
p p,j SDSS
bin as measured from the SDSS, and w (r ) is the logues at each grid point (200) to determine thecovariance
p,i p,j model
result at the jth radial bin as measured with the ith mock matrix with a sufficiently small noise level.
(cid:13)c 2008RAS,MNRAS000,1–20
10 Mandelbaum et al.
Figure5.Determinantofthecovariancematrixofwp(rp)(seeEq.13),onthegridofthetwomodelparameters,fcen andMhmin.fcen
isthe fractionof radioAGN that arehosted by thecentral galaxy of their owndarkmatter halo, and Mmin isthe minimummass for
h
thehalosthatcanhostradioAGN.Thecontour levelsareindicatedattheright-handside.
We compare the measured w (r ) with the models in diuswaschosenbecausethedataatsmallerseparationsare
p p
four radial bins centered at r = 0.21, 0.65, 2.1 and 6.5 rathernoisy.
p
h−1Mpc, with a step size of ∆logr =0.5 (larger than the
p
radial bins shown in the plots). The choice of 4 radial bins
was motivated by tests showing that the covariance matri- Fig. 6plotsthecontoursof∆Λ=Λ−Λmin in thegrid
ces evaluated from the mock catalogues were well-behaved ofthetwoparameters,whenusingthewp(rp)measurements
in this case, whereas using a significantly larger number of forthefullradio-loudAGNsample(leftpanelofFig.4).The
radial bins causes the covariance matrices (a) to be noisier, 1,2, and 3σ confidence regions, computed for m = 4 and 2
and (b) to have peculiar patterns of correlations between parameters, are indicated using solid, dashed and dotted
bins suggestive of edge effects (in particular, strong corre- black lines. We have explicitly checked the distribution of
lations between certain adjacent pairs of radial bins that χ2 valuesfortheindividualmock catalogs toascertain that
arenotrepresentativeoftheoverallpatternofcorrelations). the Gaussian approximation for the likelihood is valid, and
Theseparticularradialbinswerechosentosampleseparate foundthatthecumulativedistributionofχ2matchestheex-
partsoftheHOD,namelythecentral1-haloterm,thesatel- pected distribution at extremely high confidence (using the
lite 1-halo term, the transition between the 1- and 2-halo Kolmogorov-Smirnov test) at all points on the grid. Conse-
terms,andthe2-haloterm(respectively).Theminimumra- quently, the method we have used to determine confidence
regionsisvalid.TheminimumΛ ,appearsatf =0.74
min cen
(cid:13)c 2008RAS,MNRAS000,1–20