CFHTLenS: The Environmental Dependence of Galaxy Halo Masses from Weak Lensing

0.51 MB·English

by  Bryan R. Gillis

Mon.Not.R.Astron.Soc.000,1–16(2013) Printed1February2013 (MNLATEXstylefilev2.2)
CFHTLenS: The Environmental Dependence of Galaxy
Halo Masses from Weak Lensing
3
Bryan R. Gillis1⋆, Michael J. Hudson1,2, Thomas Erben3, Catherine Heymans4,
1
0 Hendrik Hildebrandt3,5, Henk Hoekstra6,7, Thomas D. Kitching4, Yannick Mellier8,
2
Lance Miller9, Ludovic van Waerbeke5, Christopher Bonnett10, Jean Coupon11,
n
a Liping Fu12, Stefan Hilbert13,3, Barnaby T.P. Rowe15,26,
J
0 Tim Schrabback3,13,6, Elisabetta Semboloni6, Edo van Uitert6,3,
3 and Malin Velander9,6.

] 1Department of Physics and Astronomy, University of Waterloo, Waterloo, ON N2L 3G1, Canada.
O 2PerimeterInstitute for Theoretical Physics, 31 Caroline St. N., Waterloo, ON, N2L 2Y5, Canada.
C 3Argelander Institute for Astronomy, Universityof Bonn, Auf dem Hu¨gel71, 53121 Bonn, Germany.
4Scottish UniversitiesPhysicsAlliance, Institute for Astronomy, Universityof Edinburgh, Royal Observatory, Blackford Hill,
.
h Edinburgh, EH9 3HJ, UK.
p 5Department of Physics and Astronomy, University of BritishColumbia, 6224 Agricultural Road, Vancouver, V6T 1Z1, BC, Canada.
- 6Leiden Observatory,Leiden University,Niels Bohrweg 2, 2333 CA Leiden, The Netherlands.
o 7Department of Physics and Astronomy, University of Victoria, Victoria, BC V8P 5C2, Canada.
r 8Institut d’Astrophysique de Paris, Universit Pierre et Marie Curie - Paris 6, 98 bisBoulevard Arago, F-75014 Paris, France.
t
s 9Department of Physics, Oxford University,Keble Road, Oxford OX1 3RH, UK.
a 10Institut de Cienciesde lEspai, CSIC/IEEC, F. de Ciencies, Torre C5 par-2, Barcelona 08193, Spain.
[ 11Institute of Astronomy and Astrophysics, Academia Sinica, P.O. Box 23-141, Taipei 10617, Taiwan.
1 12Key Lab for Astrophysics, Shanghai Normal University,100 Guilin Road, 200234, Shanghai, China.
v 13Kavli Institute of Particle Astrophysics and Cosmology (KIPAC), Stanford University,452 Lomita Mall, Stanford, CA 94305, and
1 SLAC National Accelerator Laboratory, 2575 Sand Hill Road, M/S 29, Menlo Park, CA 94025, UnitedStates of America.
2 14Max-Planck-Institut fu¨rAstrophysik,Karl-Schwarzschild-Straße 1, D-85748, Garching, Germany
4 15Department of Physics and Astronomy, UniversityCollege London, Gower Street, London WC1E 6BT, U.K.
7 16California Institute of Technology, 1200 ECalifornia Boulevard, Pasadena CA 91125, USA.
.
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i ABSTRACT
X
We use weak gravitational lensing to analyse the dark matter halos around satellite
r galaxiesin galaxygroups in the CFHTLenS dataset. This datasetis derived from the
a CFHTLS-Wide survey, and encompasses 154 deg2 of high-quality shape data. Using
the photometric redshifts, we divide the sample of lens galaxies with stellar masses
in the range 109M⊙ to 1010.5M⊙ into those likely to lie in high-density environments
(HDE) and those likely to lie in low-density environments (LDE). Through compari-
son with galaxy catalogues extracted from the Millennium Simulation, we show that
the sample of HDE galaxies should primarily (∼ 61%) consist of satellite galaxies
in groups, while the sample of LDE galaxies should consist of mostly (∼ 87%) non-
satellite (field and central) galaxies. Comparing the lensing signals around samples
of HDE and LDE galaxies matched in stellar mass, the lensing signal around HDE
galaxies clearly shows a positive contribution from their host groups on their lensing
signalsatradiiof∼500–1000kpc,thetypicalseparationbetweensatellitesandgroup
centres. More importantly, the subhalos of HDE galaxies are less massive than those
around LDE galaxies by a factor 0.65±0.12, significant at the 2.9σ level. A natural
explanation is that the halos of satellite galaxies are stripped through tidal effects
in the group environment. Our results are consistent with a typical tidal truncation
radius of ∼40 kpc.
Key words: gravitationallensing: weak, galaxies: clusters: general
2 Bryan R. Gillis et al.
1 INTRODUCTION 2001; Parker et al. 2005; Mandelbaum et al. 2006;
Johnston et al. 2007; Hamana et al. 2009; Leauthaud et al.
In the standard picture of hierarchical structure formation, 2010; Ford et al. 2012) have shown that the group lensing
larger dark matter halos are built up through the accre- signal can be measured and is on average consistent with
tion, stripping, and mergers of smaller halos. At the ex- an NFW density profile. However, it is unclear how much
tremes of the halo mass spectrum, namely isolated field of this signal results from a central halo, and how much
galaxies and galaxy clusters, we have a relatively good pic- is due to the contributions of satellites (Gillis et al. 2012).
ture of how the mass within these structures is organized. As such, it is necessary to measure the lensing signals
Forisolatedgalaxies,mostofthemassiscontainedwithina around satellites themselves to get a full picture of the
halo of dark matter, as confirmed by galaxy-galaxy weak mass distribution. Only limited work has been done in the
gravitational lensing measurements (Brainerd et al. 1996; group regime to date. For example, Suyu& Halkola (2010)
Hudson et al. 1998; Guzik & Seljak 2002; Hoekstra et al. studied a strong-lensing system and determined that tidal
2003,2004;Mandelbaum et al.2006;van Uitert et al.2012; stripping did seem to occur around the satellite studied,
Velanderet al. 2012). Simulations have shown that the which lies in a group of mass on the order of 1012M⊙.
shapeofthishalocanbewell-approximatedbyanNFWden- While this result is promising, a broader base of data will
sity profile(Navarro et al. 1997),which has been confirmed be needed to develop a general understanding of the dark
observationally (Kleinheinrich et al. 2003; Hoekstra et al. matter properties of satellite galaxies in galaxy groups.
2004; Mandelbaum et al. 2008). In galaxy clusters, most of
In principle, it is possible to study tidal strip-
themassalsoseemstoliewithinanNFWdarkmatterhalo,
ping using spectroscopically-derived group catalogues
with the constituent galaxies contributing only small per-
(Pastor Mira et al. 2011; Gillis et al. 2012). Spectroscopic
turbations to the density profile (Mandelbaum et al. 2006,
data allow one to more accurately identify whether a given
2008).Gravitationallensingmeasurementshaveshownthat
galaxyisa“central”ora“satellite’.Byusingvelocityinfor-
the halos around individual galaxies within clusters are
mation in addition to projected separation, it is also possi-
significantly smaller than the halos around comparably-
ble to assess statistically whether a satellite is falling in for
luminousfieldgalaxies,andthiseffectismoreextremewith
the first time, or has passed pericentre and hence is tidally
galaxies closer to the centres of clusters (Limousin et al.
stripped(Oman et al.2013).However,suchanalysesrequire
2007;Natarajan et al. 2009).
a large galaxy sample with both spectra and deep imag-
However,betweentheextremesoffieldgalaxiesandrich ing data, and such data are expensive to acquire. However,
clusters, the picture is less clear. Since multiple galaxies photometric redshifts are often available alongside imaging
must merge together to eventually form clusters, at some data.Duetotheirlargeuncertainties,photometricredshifts
point the mass in the galaxies’ individual halos must mi- have the drawback that groups are difficult to detect, and
grate into a shared halo. This process most likely occurs group-centralgalaxiesareverydifficulttoidentify.Thisthen
through tidal stripping: when two galaxies pass near each callsforastatisticalapproach,calibratedbysimulations,to
other, the particles in the halo of the less massive galaxy simultaneously fit boththesatellites’ and groups’ contribu-
will tend to be “stripped” from it and thus join the more tions to the stacked lensing signal. This is the approach we
massive galaxy’s halo. This effect has been demonstrated will takein this paper.
in various N-body dark matter simulations (Hayashi et al. A similar approach was taken by Mandelbaum et al.
2004; Kazantzidis et al. 2004; Springel et al. 2008). Tidal (2006), who investigated a large selection of galaxies from
stripping is also expected to remove hot gas from less the SDSS, selected by environment. They tested for the
massive galaxies, which will have the effect of cutting off presence of stripping by fitting models for the lensing sig-
their supply of cold gas and quenchingtheir star formation nal to the galaxies in high-density environments (HDE)
in a process known as “strangulation” (Tinsley & Larson and low-density environments (LDE). The authors found
1979; Balogh & Morris 2000). Galaxies in dense environ- no significant evidence of tidal stripping, but did not com-
ments are known to be significantly redder on average pletely rule it out, either. This was also later attempted
than field galaxies (Dressler 1980; Butcher& Oemler 1984; by vanUitert et al. (2011), who used the overlap between
Moore et al.1996;Balogh et al.1999,2004),andtidalstrip- RCS2 and SDSS, but they were similarly unable to get a
ping may contribute to the quenching of star formation, so cleardetectionoftidalstripping.Herewewillusedatafrom
there is a strong motivation to understand the mechanics the CFHTLenS collaboration, which is significantly deeper
and timing of tidal stripping (van den Bosch et al. 2008; thantheSDSS,andhenceshouldprovideastrongerlensing
Kawata & Mulchaey 2008). It remains unclear, however, signal. We also apply a new environment estimator, which
whether this process is rapid or gradual. This question can is tuned to work for photometric redshifts (see Section 2.2)
in part be investigated through analysis of the group and andamodified halomodel designedtowork with thisenvi-
cluster scales on which tidal stripping can be observed to ronment estimator (see Section 3).
occur. InSection 2of thispaper,wediscussthedatasetsused
Inthispaper,wefocusongalaxygroups,anintermedi- intheanalysisandthealgorithmforestimatinggalaxyenvi-
atemass scale between fieldgalaxies and clusters (typically ronments.InSection 3,wedetailthemodelsforthelensing
structures in the mass range 1012 M⊙ < Mhalo <1014 M⊙ signalsandtheprocedureusedtofitthemodelstothemea-
are considered groups, and more ma∼ssive stru∼ctures are sured signals. In Section 4, we present the results of the
considered clusters). Weak gravitational lensing provides analysis and discuss possible sources of error. We conclude
the only practical tool to measure the density profiles and in Section 5.
massesofdarkmatterhalosaroundsatellitegalaxieswithin For consistency with theMillenium Simulation, we use
groups. Lensing analyses of groups (Hoekstra et al. the following cosmological parameters: H0 = 73 km s−1
3
Mpc−1, Ωm = 0.25, ΩΛ = 0.75, and Ωb =0.045. All stated rough agreement with deeper data such as WIRDS, which
magnitudesareintheABsystem.Sincethereisnocleardi- includes NIRfilters (Bielby et al. 2012),up to z=0.8.
visionbetweengalaxygroupsandgalaxyclusters,weusethe Since we perform a differential measurement between
terminology “galaxy groups” throughout this paper, even samples, an overall bias in the stellar masses would not af-
though some of thestructures we refer to as such would be fect our results. It is possible, however, for a relative bias
more commonly deemed clusters. When masses are quoted inthestellarmassestimates ofredandbluegalaxies toim-
inthispaper,M isusedtorefertothetotal(halo+stellar) pact our results. This possibility is investigated further in
mass of a galaxy or group, and m is used to refer to the Section 4.4.1.
stellar mass of a galaxy, unless otherwise specified. When For this paper, we use take all unmasked galaxies with
radial measurements are used in this paper, R refers to a photometric redshifts in the range 0.2<z <0.8 as lens
phot
projected, 2D proper distance. All masses are in units of candidates. WedividetheseintoHDEand LDEsamples as
M⊙ unless otherwise specified. described next.
2.2 Determining Environment: The P3 Algorithm
2 DATA AND SIMULATIONS
It is not a trivial matter to determine which galaxies are
Inthissection,wediscussthedatasetsusedandhowgalaxies
members of groups. Even when spectroscopic redshifts are
are selected for the HDE and LDE samples. In Section 2.1,
available, the peculiar velocities of galaxies make it impos-
we discuss the CFHTLenS survey,from which we draw our
sibletodeterminethemembershipsofgroupswithabsolute
data. In Section 2.2, we discuss the algorithm used to esti-
certainty (Robotham et al. 2011). When only photometric
mate the local density around galaxies in the sample. Sec-
redshiftsareavailable,thebestwecandoistoselect galax-
tion 2.3 describes how the sample is divided into matched
iesthatarelikelytobemembersofgroups.Todoso,weuse
high-density and low-density subsamples, and presents the
a modified version of the Photo-z Probability Peaks (P3)
statistics of the galaxies in the HDE and LDE samples. In
algorithm (Gillis & Hudson 2011). The P3 algorithm gen-
Section 2.4, we discuss the simulations we have run to test
erates a 3-D density field by smoothing the distribution of
ourmethodsandthestatisticsofthegalaxysampleswithin
galaxies in the redshift direction according to the probabil-
these simulations.
itydistributionfunction oftheirphotometricredshifts. The
algorithm identifies peaks in the pseudo-three-dimensional
field with group centres. Herewedo not usethegroup cen-
2.1 Observations
tres, but rather use the entire P3 density field to identify
CFHTLenS is a 154 deg2 survey (125 deg2 after mask- overdenseregions.Ratherthanusethelocal P3overdensity
ing) (Erben et al. 2012), based on the Wide component itself,werestrictourselvestoregionsinwhichwehavehigh
of the Canada-France-Hawaii Telescope Legacy Survey confidenceintheoverdensity,andinstead usethesignal-to-
(Heymanset al. 2012), which was observed in the period noise (S/N) of the local overdensity, under the assumption
from March 22nd, 2003 to November 1st, 2008, using the that galaxies in overdense regions of space are more likely
MegaCam instrument (Boulade et al. 2003). It consists of to bein groups than galaxies in underdenseregions.
deep, sub-arcsecond, optical data in the u∗g′r′i′z′ filters. We now briefly review the technical details of the P3
CFHTLS-Wide observations were carried out in four high- algorithm. To determine the S/N of a given test galaxy,
galactic-latitude patches: the P3 algorithm compares the density of galaxies within
a circular aperture (R = 0.5 Mpc) surrounding each test
W1: 72 pointings; RA=02h18m00s, Dec= 07d00m00s
• W2: 25 pointings; RA=08h54m00s, Dec=−04d15m00s galaxy to the density of galaxies within a larger annulus
• W3: 49 pointings; RA=14h17m54s, Dec=−+54d30m31s (Rinner = 1 Mpc, Router = 3 Mpc) surrounding each test
• W4: 25 pointings; RA=22h13m18s, Dec=+01d19m00s. galaxy (to approximate the background density). The con-
• tributionofeachgalaxytothismeasurementisweightedby
Shapes have been measured with the LensFit shape the probability that this galaxy lies at the same redshift as
measurement algorithm for galaxies with i′ < 24.7 the test galaxy (by taking the integral of the photo-z prob-
(Miller et al. 2012), giving an effective galaxy density of 11 ability distribution function overa thinredshift slice). This
sources/arcmin2 in the redshift range 0.2 < z < 1.3 gives theoverdensity:
phot
(Heymanset al. 2012). Photometric redshifts are available δ= ρap−ρannu, (1)
for the entire survey, with a typical redshift uncertainty of ρannu
0.04(1+z) (Hildebrandt et al. 2012). We use all fields
∼in the survey,not simply those that passed the systematics where ρap and ρannu are the weighted densities of galaxies
withintheapertureandannulussurroundingthetestgalaxy,
testsforcosmicshearmeasurements(Heymanset al.2012).
respectively. This value can take the range 1 < δ < ,
It has been demonstrated that fields with systematics that − ∞
which negative values corresponding to regions less dense
may affect cosmic shear have no effect galaxy-galaxy lens-
than the background density, and positive values to over-
ing measurements (Velanderet al. 2012), and the analysis
dense regions. We then estimate the noise in this value by
inthispaperrequiresasmanylens-sourcepairsaspossible.
assuming a Poisson distribution for galaxies:
We use the stellar mass estimates described by
Velanderet al. (2012), obtained by fitting spectral energy
distribution (SED) templates, following the method of σPoisson = ρap 2+ ρannu 2, (2)
Ilbert et al.(2010).Thesestellarmasseswerefoundtobein s nap nannu
(cid:18) (cid:19) (cid:16) (cid:17)
4 Bryan R. Gillis et al.
wherenapandnannuarethenumbersofgalaxiesintheaper- HDE LDE
ture and annulus respectively with more than a threshold
weight1. From this, we calculate the S/N δ/σPoisson for logm z fred fblue fred fblue
≡
each test galaxy. Note that this S/N can take negative val- 9–9.5 0.57 0.13 0.73 0.08 0.80
ues, assuming δ is negative. The distribution of galaxies’ 9.5–10 0.56 0.28 0.60 0.18 0.70
10–10.5 0.56 0.54 0.30 0.44 0.38
S/Nsthatresultsfromthiscalculationdependsonthechoice
10.5–11 0.57 0.78 0.10 0.72 0.13
ofthresholdweightused,soourchoicesofS/Nlimitsarenot
11–11.5 0.57 0.95 0.02 0.90 0.03
universally applicable. We picked limits of S/N > 2 for the
high-densitysampleandS/N<0forthelow-densitysample 9–10.5 0.56 0.43 0.43 0.33 0.51
based on an analysis of the simulated galaxy catalogues to
maximize the expected signal for tidal stripping.2 Table 1.Statisticsofgalaxiesinvariousstellarmassbinsinthe
Since this environment estimator provides us with CFHTLenS survey, as a function of environment. z is the mean
galaxy samples biased to lie in high- and low-density en- redshift of the bin. fred is the fraction of galaxies that are red,
vironments, we cannot use the standard halo model (eg. and fblue is the fraction that are blue, determined by the best-
fit photometric templates and defined in the same manner as
Mandelbaum et al. 2006; Velanderet al. 2012) for fitting
by Velanderetal. (2012). Fractions do not add to unity as not
ourlensingsignals.Instead,themodelsweusearecalibrated
all galaxies are classified as “red” or “blue.” See Velanderetal.
from simulations and are detailed in Section 3.
(2012) for further explanation. All average values and fractions
assumegalaxiesareweightedbytheirstellarmasses.
2.3 Galaxy Matching
weightequalthenumberofmatcheswefound.(Thisweight
2.3.1 Matching Algorithm
is later applied when we stack lensing signals together, and
We use the S/N values obtained for each galaxies in Sec- this modification is necessary to ensure the mass distribu-
tion2.2toformtwosamplesofgalaxiesfromthecatalogues. tions of the HDEand LDE samples are comparable.)
Aswecannotensurethatapairofrandomsamplesofgalax- (vi) We assign all match galaxies to the LDE sample. If
iesinhigh-andlow-densityenvironmentswillhavethesame they were not already in the LDE sample, we set each of
distribution of stellar mass and redshift as each other, we their weights to 1. Otherwise, we increase their weights by
perform a matching between galaxies with S/N > 2 and 1.
galaxies with S/N < 0 as follows:
The resultant mass and redshift distributions of this
(i) For each galaxy with S/N > 2, we search through all scheme are assessed in Section 2.3.2 and Section 2.4.1.
galaxies with S/N < 0 within thesame pointing3.
(ii) For each S/N < 0 galaxy, if its stellar mass differs
from the stellar mass of the S/N > 0 galaxy by more than 2.3.2 Statistics of Galaxy Selection
20% of thelatter’s mass, weexcludeit as a possible match.
Fig. 1 shows the distributions of stellar mass and redshift
(iii) For each remaining S/N < 0 galaxy, we calculate a
for the HDE and LDE samples of lens galaxies in the
quality-of-match value:
CFHTLenS.Thematchingschemeresultsinanearlyidenti-
caldistributionofstellarmassesforHDEandLDEgalaxies,
d= zH−zL 2+(10(logmH logmL))2 (3) and a very similar distribution of redshifts.
r zH − Table1showsstatisticsforlensgalaxiesintheHDEand
(cid:16) (cid:17)
where zH and zL are the redshifts of the S/N > 2 and S/N LDE samples in the CFHTLenS, for various stellar mass
< 0 galaxies, respectively, and mH and mL are their stellar bins. The HDE sample contains a higher fraction of red
masses. This form significantly prioritizes a match in mass galaxies than the LDE sample, as expected, but the dif-
overredshift. ference is at most 10% for a given stellar mass bin. This
(iv) WeselectthefourS/N<0galaxieswiththelowestd difference in the fractions of red and blue galaxies could in
valuesasmatchesforthisS/N>2galaxy.Iftherearefewer principlelead toaspuriousdetection ofstrippingifthereis
thanfourmatchcandidates,weassign themall asmatches. arelativebiasinthestellarmassestimatesbetweenredand
(v) Assumingatleastonematchwasfoundforit,weadd bluegalaxies.ThisissueisdiscussedfurtherinSection4.4.1.
this S/N > 2 galaxy to the HDE sample, and we set its
2.3.3 Measuring the Lensing Signal
1 We useathreshold weight hereof a>0.001% chance of lying
withinaredshiftof0.01ofthetestgalaxy. To calculate the lensing signal around the HDE and LDE
2 In a rough approximation, the expected signal-to-noise lens galaxies, we stack together all galaxies in a particular
of a stripping measurement is proportional to (fsat,HDE − sample and stellar mass bin4. We then bin all lens-source
fsat,LDE) NH−D1E+NL−D1E,wherefsat,HDE andfsat,LDE arethe pairs (only using pairs where zphot,source > zphot,lens+0.1)
fractionsofsatellites intheHDEandLDE samplesrespectively, basedontheprojecteddistancebetweenthelensandsource,
and NHDpE and NLDE are the number counts of galaxies in the calculated at the redshift of the lens. For each pair, we cal-
HDEandLDEsamplesrespectively.Wecalculatedthisvaluefor culate the tangential ellipticity of the source relative to the
various S/N cuts, and the combination of S/N > 2for the HDE
sample and S/N < 0 for the LDE sample provided the best ex-
pectedsignal-to-noiseforastrippingmeasurement. 4 This process is performed one pointing at a time due to com-
3 Matching only within the same pointing is done to conserve putational limitations, and all pointings are stacked together in
computational time. theend.
5
50000
0 0
0.2 0.4 0.6 0.8
Figure 1.Thedistributionsofstellarmass(leftpanel)andredshift(rightpanel)forthesamplesofHDE(solidline)andLDE(dashed
line)galaxies, which, because of our matching algorithm,arevirtuallyidentical. Theredshiftdistributionsdiffer slightlybetween HDE
andLDEgalaxies,butthereisnoapparenttrendtothedeviation.
60000
40000
20000
0
Figure 2. The distributions of the types of galaxies classified as HDE and LDE in the simulations (left), and, of those classified as
satellites,thedistributionsofthemassesofthegroupsinwhichtheyreside(right).
lens, gt, and convert this into units of surface mass density This measurement relates to the projected mass of the lens
gradient: through (Mandelbaum et al. 2005):
∆Σ=Σcritgt, (4)
∆Σ(R) =Σ(<R) Σ(R), (6)
where h i −
Σcrit = c2Ds , (5) where Σ(<R) is the surface density averaged for all points
4πGD D
ls l contained within radius R, and Σ(R) is theaverage surface
and Ds is the angular diameter distance to the source, Dl density at radius R. This prescription works even for mass
is the angular diameter distance to the lens, and D is distributionsthatarenotaxisymmetric,aslongasallpoints
ls
the angular diameter distance from the lens to the source. in a given annulus around a lens object are stacked. We
6 Bryan R. Gillis et al.
HDE LDE
logm M z fsat ffield fcen Mhost fsat ffield fcen Mhost
9–9.5 17 0.37 0.54 0.42 0.05 4700 0.14 0.79 0.07 1635
9.5–10 32 0.45 0.62 0.25 0.13 4000 0.15 0.61 0.24 1500
10–10.5 80 0.51 0.64 0.10 0.26 4300 0.13 0.32 0.54 1900
10.5–11 390 0.50 0.45 0.02 0.53 5600 0.09 0.12 0.79 3400
9–10.5 63 0.48 0.63 0.16 0.21 4300 0.14 0.43 0.43 1800
Table2.StatisticsofgalaxiesintheMillenniumsimulationforvariousstellarmassbins,usingourmodelsforestimatinghalomassand
environment.logmisthestellarmassbin.M isthemeanhalomassofthegalaxiesinthisbininunitsof1010M⊙,andz istheirmean
redshift.fsat,ffield,andfcen arethefractionsofgalaxiesthataresatellites,fieldgalaxies,andgroupcentrals,respectively.Mhost isthe
meanmassofthehostgroupforsatellitegalaxiesinunitsof1010M⊙.Allvaluesassumegalaxiesareweightedbytheirstellarmasses.
computetheerrorinthisvalueempirically from thescatter in the HDE sample remains roughly constant with stellar
in calculated ∆Σ values for each lens-source pair. mass, and decreases slightly with stellar mass in the LDE
Forthecalculationsoferrorinourmodelfits,weassume sample.Forbothsamples,thefraction ofcentralsriseswith
thenoise in all radial annuliis independent.Strictly speak- stellar mass, while the fraction of field galaxies falls. Nei-
ing, this isn’t true, as there is a small correlation between ther sample shows any significant change with stellar mass
theellipticitiesofnearbysources,butthiseffectisnegligible in the mean mass of the host groups for satellites, except
except at extremely large radial annuli. For computational for a rise in the most massive stellar mass bin tested. HDE
simplicity, we do not apply the c2 correction5 to source el- satellitesareobservedtoresideingroupsof 4 1013 M⊙.
∼ ×
lipticities in our analysis. Because galaxy-galaxy measure- In contrast, for the small fraction of LDE galaxies that are
ments stack lens-source pairs over all position angles, they satellites, the characteristic host halo mass is 1.8 1013
∼ ×
are insensitive to this correction(see Velander et al. 2012, M⊙.
for further explanation and justification of this). Moreover,
hereweareinterestedinadifferentialmeasurementbetween
galaxy-galaxy lensingsamples, andsoweexpectourresults
to behighly robust to this effect.
2.4.2 Simulated Lensing Signals
InordertosimulatelensingsignalsfortheMillenniumSimu-
2.4 Simulated Galaxy Catalogues
lationcatalogues,weusethesamemethodsasinGillis et al.
We require simulations in order to calibrate the frac- (2012).Inshort,weassumeallgalaxiesandgroupcentresare
tions of satellite and central galaxies in our samples, and surroundedbysphericaltruncatedNFWhalos(Bartelmann
to test our methods for modelling the lensing signals 1996; Hamana et al. 2009), using the model of Baltz et al.
around galaxies. The simulations are based on the semi- (2009), and estimating halo mass from stellar mass by us-
analytic models of DeLucia & Blaizot (2007) which are ing equation 3 from Guo et al. (2010) (to better match the
based on the Millenium Simulation (Springelet al. 2005; stellar-dark mass ratio in theCFHTLenS):
Lemson & Virgo Consortium2006).Weuseforouranalysis
asetofthirty-two16deg2“lightcone”fieldsbyHilbert et al.
(2009). We assign photo-z errors consistent with those in −0.926
m m
CFHTLenS and apply the P3 algorithm to the simulated 0.129 halo = halo
data. This allows us to select galaxies in the same manner × mstellar (cid:18)1011.4M⊙(cid:19)
as is done with theCFHTLenS dataset. 0.261 2.44
m
+ halo . (7)
(cid:18)1011.4M⊙(cid:19) !
2.4.1 Statistics of Simulated Catalogues
Weform twoversionsofthesimulated shearcatalogue,
Fig. 2 shows the distributions of galaxy types for the mock
oneinwhichwesimulatetheeffectsofstrippingbydecreas-
HDEandLDEsamplesdrawnfromtheMillenniumSimula-
ing the truncation radii of satellite galaxies’ halos and al-
tion, and, for the satellite galaxies within each sample, the
locating thelost mass to group centres’ halos (“Stripping”)
distribution of the masses of the groups in which they re-
andoneinwhichwedonot(“NoStripping”).Theamountof
side. We classify galaxies as “central” (the most massive in
strippingis assumed todepend on distance from thecentre
a group), “satellite” (in a group but not the most massive)
of the host halo and is given by equation (5) of Gillis et al.
or “field” (not in a group). Table 2 shows the distributions
(2012), which is based on data in figure 15 of Gao et al.
of galaxy types for the HDE and LDE samples for various
(2004). With this prescription, we find that the mean re-
stellar mass bins. This shows that the fraction of satellites
tainedmassafterstrippingisapproximately40%oftheini-
tialmass.Wethencalculateshapesforallbackgroundgalax-
5 The c2 correction is an empirical correction to the e2 compo- iesbyassuminginitiallyzeroellipticityinbothcomponents,
nentofsourceellipticity,basedontheassumptionthatthemean then applying shear due to each nearby halo between the
e2acrossagivenfieldshouldbeclosetozero. source galaxy and theobserver.
7
where ∆ΣUD is the “underdensity” term, which is the ef-
fectivecontributionfromthefactthatgalaxies inanunder-
dense environment will see a negative contribution to their
lensing signal at large radii. This effect is analogous to the
offset grouphalo term,exceptarising from an underdensity
instead of an overdensity.
Wecanbestcomparethelensingsignalsthatresultfrom
stacksof HDEandLDEgalaxies by fittingthesignals with
amodelprofile,andcomparingthesefits.Themodelprofile
fortheHDEsampleincludesjustthe“one-halo”and“offset
grouphalo”terms.Sincethe“underdensity”and“two-halo”
terms are only significant at relatively large radii, we can
safely ignore them if we do not fit the profiles out to large
radii. We discuss this furtherin Section 4.4.2.
These components are discussed in the subsections be-
low, and we discuss the procedure we use to fit a model to
thedata in Section 3.4.
3.1 One-halo term
Fortheone-haloterm,weassumethatallgalaxiesresideina
darkmatterhalothatcanbeapproximatedwithatruncated
Figure 3. An illustration of how the one-halo term varies with
NFW density profile, as formulated by Baltz et al. (2009).
satellitemass(topleft);andhowtheoffsetgrouphaloterm(equa-
tion(12))varieswithgroupmass(topright),satelliteconcentra- This model has three free parameters: the halo mass M200,
tion(bottomleft),anddensitythreshold(bottomright).Plotted concentrationc,andthetruncationparameterτ rtrunc/rs.
≡
valuesoftheparameters,withitalicizedparametercorresponding In practice, we have found that the signal is not strong
to the value used for other plots: Msat = 1010, 1011, 1012 M⊙; enough to simultaneously constrain all three parameters.
Mgroup = 1013, 1014, 1015 M⊙; csat = 2.5, 5, 7.5, Σt = 0, Therefore,forsimplicity,inourdefaultfitsdiscussedbelow,
10, 20 M⊙/pc2. Increasing lineweight corresponds to increasing we fit M200, with c fixed by:
the varying parameter. The fraction of satellites which reside in
−0.11
groupsisnotillustrated,asitisasimplescalingofthegrouphalo c=4.67 M200 , (10)
term;itisfixedto0.6fortheseplots. × 1014h−1M⊙
(cid:18) (cid:19)
takenfromNeto et al.(2007),andwealsofixτ =2c,which
3 MODELS AND SIGNAL FITTING isareasonablevalueforunstrippedhalos(Hilbert & White
2010; Oguri & Hamana 2011).
We expect the lensing signal around galaxies in the HDE
InSection4.3.2,weinvestigatealternativefitsinwhich
sampletobereasonablywell-describedbythefollowinghalo
c or τ are allowed to bedepend on environment.
model (see eg. Velanderet al. 2012):
∆Σ=∆Σ1h+fsat∆ΣOG+∆Σ2h (8)
3.2 Offset group halo term
where ∆Σ1h is the “one-halo” term, fsat is the fraction of
galaxies in the sample that are satellites ∆ΣOG is the “off- Since the P3 algorithm biases our galaxy selection such
set group halo” term, and ∆Σ is the “two-halo” term, as that the HDE sample predominantly consists of galaxies
2h
described below: within groups, we cannot use the standard halo model
(eg. Velanderet al. 2012) to calculate the contributions of
(i) One-halo term: The lensing signal that results from
nearby groups. Instead, we make the assumption that the
thegalaxy’s own dark matter halo.
sample consists of a fraction fsat satellites, and the rest are
(ii) Offset group halo term: This is the contribution to
eithercentralorfieldgalaxies.Thecentralandfieldgalaxies
the lensing signal a satellite caused by the presence of its
willonlyhaveaone-halocomponentintheirlensingsignals,
group’s halos.
while satellites will have both the one-halo component and
(iii) Two-halo term: Galaxies will typically reside near
a contribution from their host groups. In order to model
other massive structures, which results in a contribution to
theaveragecontributionofgrouphalostothelensingsignal
thelensing signal at large radii.
aroundgalaxiesintheHDEsample,weassumethatittakes
Sincegalaxies in theHDEsample are morelikely liein thefollowing form:
overdense regions, we cannot apply exactly the same halo
∆ΣOG(R)=∆Σhost(R,Rs)P(Rs)dRs, (11)
model aseg. Velanderet al. (2012), whouseall galaxies in-
dependent of environment. This primarily affects the offset whereRS istheprojectedseparationbetweenasatelliteand
group halo term. See Section 3.2 below for an explanation the group centre, ∆Σhost(R,Rs) is the contribution of the
of how we modify ourhalo model to account for this. grouphalotothelensingsignalaroundapointatprojected
ForLDEgalaxies, weexpectthesignal tobedescribed distance R from the group centre:
by theform:
∆Σ=∆Σ1h+∆ΣUD (9) ∆Σhost(R,Rs)=Σhost(<R,Rs) Σhost(R,Rs)
−
8 Bryan R. Gillis et al.
= πR12 R2πR′ 2πΣhost(Rg)dθdR′ hcoanlocetnetrrmastiovnaricessatwainthdtthheregsrhooulpdhsuarlofamceadssenMsigtryouΣp,t.satellite
Z0 Z0
2π
1
−2π Σhost(Rg)dθ, (12) 3.3 Underdensity signal
Z0
where Σhost(Rg) is the projected surface density of Galaxies in the LDE sample are selected to lie in S/N < 0
the host group’s halo at projected radius Rg = regions, which are underdense (δ < 0) compared to a sur-
√R′2+Rs2 R′Rscosθ; and P(Rs) is the probability that roundingannuluswith innerradius1Mpcandouterradius
−
a satellite in the sample will reside a distance Rs from its 3 Mpc. Similarly to how galaxies in groups have a posi-
host group’s centre. Weassume P(Rs) takesthe form: tivecontributiontotheirlensingsignalfromtheoffsetover-
densityinwhich theyreside, galaxies inunderdenseregions
1
P(Rs)= 2πRsΣ(Rs,Mgr,csat)PHDE(Rs), (13) will have a negative contribution to their lensing signal on
MN larger scales due to the fact that their local environment is
where MN is a normalization factor, Σ(Rs,Mgr,csat) is the lessdensethanthesurroundingenvironment.Thiseffecthas
projected surface density of an NFW halo with mass equal beenobservedinboththeCFHTLenSdataset,aswellasin
to the mass of the host group, Mgr, but a concentration thesimulations.
csat, differentfrom thedark matter concentration c.Analy- The expected form of this negative lensing signal has
ses of thesatellite density in groups and clusters (Lin et al. not been well-studied, so there is no functional form which
2004;Budzynskiet al.2012)haveindicatedthatthespatial we expect it to take. We have attempted to fit this signal
distribution of satellites can be well-modelled in this way, withthesamefunctionalform asthegrouphaloterm,mul-
assuminganNFWdensityprofilewithconcentration 2.5, tiplied by a negative free term, but this failed to provide
∼
which is lower than the typical concentration of the dark a suitable fit to either the simulated or to the CFHTLenS
matter halo by a factor of 2. data. Note in the right panel of Fig. 5 that the minimum
∼
ThetermPHDE(Rs)istheprobabilitythatasatelliteat valuefortheLDEsignalisatahigherprojectedradiusthan
a distance Rs from thehost group’s centre will be included thepeak of theoffset group halo term.
in the HDE sample. The form of PHDE(Rs) is determined To handle this effect, for the LDE sample, we only fit
bytheselectioneffectsinherentintheP3algorithm.Tofirst thelensingsignalforR<400kpc,wheretheone-haloterm
order,P3selectsgalaxiesinregionsofhighprojectedsurface dominates thesignal.
density for the HDE sample. We thus model PHDE(Rs) as
a smooth cut-off based on the projected surface density of
3.4 Fitting Procedure
the group. We wish for it to converge to PHDE(Rs)=1 for
Σ(Rs) Σt, and converge to PHDE(Rs) = 0 for Σ(Rs) For all fits, we use radial bins of 25 kpc< R < 2000 kpc.
≫ ≪
Σt, and so we choose the following functional form, which Wetested constraining thefitsto alower maximum radius,
has these properties: and this had no noticeable effect on thefitted satellite halo
PHDE(Rs)= Σ(RΣs()R2s+)2Σ2t, (14) mfitatsesdWesge.rFouuistpetimnagatswtsoo,-amstlaoekpwienprgrmoitcaelxdeisumsruewmetollr-aficdotinutshstreoanimnlyeodda.eltlesretodtthhee
where Σ(Rs) is the projected surface density for a satellite lensing signals. Because our models are relatively simple,
at distance Rs from a group centre and Σt is the threshold they are not perfect fits to the data. So, we first attempt
density. As we have no prior justification for any specific todetermine theamount of error inherent in our modeling,
densitythresholdtouse,weleavethisparameterfree,tobe inordertoassignmoreconservativeuncertaintiestothefit-
fit by ouralgorithm. tedparameters, aswe will nowdescribe.Wefirstperform a
For the HDE sample, we fix fsat to the value found steepest-descent χ2 minimization to obtain best-fitting pa-
in the mock HDE sample from the Millennium Simulation. rametersforthemodel.Atthispoint,iftheχ2 valueforthe
red
We do not expect this simulated result to perfectly match fitisgreaterthan1,weassumethatthisisduetosomeerror
the fraction of satellites we might find in the CFHTLenS inthemodeling,whichweparametrizeasσm.Weuniformly
dataset, and we investigate what impact a different fsat add this value in quadrature to the measured uncertainties
might have in Section 4.4.2. For the LDE sample, we don’t in all radial bins, such that the adjusted χ2 = 1 for the
red
include this term, as the form of the measured lensing sig- best fit. We then repeat this process, finding new best-fit
nal in both simulated and CFHTLenS data shows that the valuesand recalculating σm untilconvergence.
underdensitysignal dominates at large radii. Sincethisprocedureeffectivelyincreasestheerrorinall
We choose to model the offset group halo term as if radialbins,thisprocesshastheresultofincreasingthemea-
all groups are of the same mass. We tested using a distri- surederrorsonallfittedparameters.Ifthemodelisinitially
bution of group masses, and the resulting signal was not a good fit (χ2 1) to the data, the increase is negligible,
red ≈
appreciablydifferentfromthesingle-masssignal.Theuseof but if the model is a poor fit to the data, the estimated er-
a distribution of group masses did tend to increase the re- rorsforthefittedparameterswillbesignificantlyincreased.
sultant signal (the difference scaling with the spread of the As such, this process allows us to place more conservative
mass distribution), even when the mean mass is fixed, and limitson ourresults, basedon thequalityofthemodel’s fit
sothesingle-massmodelwilllikelyunderestimatethemean to thedata.
host halo mass. Additionally, since the model error is uniformly added
Fig. 3illustrates howthemodeled one-halotermvaries to the errors in all radial bins, it prevents the fitting algo-
withsatellitehalomass,aswellashowthefittedoffsetgroup rithm from over-weighting the fit to the high-radius bins,
9
which otherwise have significantly lower errors, and thus
typically contribute more to the χ2 value of the fit if the 40
model isn’t a perfect fit tothe data.
For the models we tested, we typically found for the
HDE samples that σm <0.5M⊙/pc2, which is <5% of the
measuredlensingsignal∼∆Σ.FortheLDEsampl∼es,mostfits 30
were initially of χ2 1, and so no model error term was
red ≈
necessary.
Oncethemodelerrorisdetermined,werunanMCMC
algorithmtohelpdeterminetheerrorsofthefittedparame- 20
ters. Since only themass of satellite halos is relevant to us,
we marginalize over all other parameters to get the mean
valueand errors for thesatellite mass.
10
4 RESULTS AND ANALYSIS
Inthissection,wepresenttheresultsofthefitsanddiscuss 0
their implications. In Section 4.1, we discuss the predicted
results from the simulations, for both the “No Stripping” 50 100 500 1000
and “Stripping” models. Section 4.2 presents the main re-
sults of our analysis of the CFHTLenS dataset and discuss
their implications. In Section 4.3, we discuss alternative in- Figure 5.Measured lensingsignal and model fits for data from
the CHFTLenS survey, including all galaxies with 109 < m <
terpretations of the data, and which of the one-halo mass,
concentration, and truncation radius might plausibly con- 1010.5M⊙. HDE (red) and LDE (blue) lensing signals and fits
are illustrated, as well as the HDE data with the fitted offset-
tribute to the observed differences between the HDE and
group-halo term subtracted off (orange). The dashed line shows
LDEsamples. Section 4.4 discusses potential systematic ef-
the one-halo model fit to the HDE sample, and the dotted line
fects. showstheHDEoffset-group-haloterm.Theone-halomassfitfor
the HDE sample is found to be significantly lower than for the
LDEsample.
4.1 Predictions from Simulations
Fig. 4 shows plots of the best-fit models for the simulated
together,asisthecasehere–thelensingsignalofanaverage
catalogues from the Millennium Simulation, for both the
of halos of varying mass is similar to thelensing signal of a
“Stripping” and “No Stripping models” (described in Sec-
singlehalowithamasssomewhatgreaterthantheaverageof
tion 2.4.2), for galaxies with 109M⊙ <m<1010.5M⊙. The
thesample.ThefittedgroupmassesfortheCFHTLenSdata
plotillustratesthatinthe“NoStripping”scenario,themea-
are additionally observed to be a factor of 2 larger than
sured lensing signals for the HDE and LDE samples are ∼
thegroupmasses forsimulateddata.Thisisnotsurprising,
nearly identical at verysmall radii. Ouralgorithm does not
as the halo masses in the simulated data are extrapolated
work perfectly for this mass bin,and in the“NoStripping”
fromthestellarmassesoftheirconstituentgalaxies,andthe
scenario, it fits a one-halo mass to the HDE sample that is
distribution of stellar masses in the Millennium Simulation
somewhat larger than the one-halo mass fitted to the LDE
does not match thedistribution in theCFHTLenS dataset.
sample, while for the “Stripping” scenario, the fitted HDE
These results from thesimulations implythat with the
one-halomassisslightlylowerthanthefittedLDEone-halo
CFHTLenSdata,acomparison oftheHDEandLDEfitted
mass.
one-halo masses can be used as an indication of whether or
Furthercomparisonsoffittedone-halomassesfordiffer-
not tidal stripping is occurring, but we must use a stellar
ent mass bins can be seen in Table 3 and Fig. 7. As can be
seenthere,forallmassbinsm<1010.5M⊙ withthe“Strip- mass upperlimit of ∼1010.5M⊙.
ping” model, as expected the fit yields a relatively lower
one-halo mass for the HDE sample compared to the LDE
4.2 Observational Results
sample than it does for the “No Stripping” model. Above
m = 1010.5M⊙, however, the fitted masses in the “Strip- Fig.5showsthelensingsignalsfortheHDEandLDEsam-
ping” and “No Stripping” scenarios are comparable. This ples taken from the CFHTLenS survey,including all galax-
is due to the fact that at high stellar masses, the fraction ies with 109M⊙ <m<1010.5 M⊙, with thebest-fit models
of galaxies in the HDE sample that are centrals increases plotted on top. For this broad mass bin, the fits show that
rapidly (see Table 2). Since mass stripped from satellites is theHDEone-halotermislowerthantheLDEterm,at2.5σ
added to the masses of central galaxies, then if too many significance(p=0.0113). However,thissimplefitisnotop-
central galaxies are included in the sample, stripping will timal.Inpart,thisisbecausewearecombininggalaxieswith
havelittle or nonet effect on thelensing signal. greatly varying masses. The resultant lensing signal of this
The fitted group masses for the simulated data seen combination does not perfectly resemble the lensing signal
in Table 3 are larger than the actual group masses by a of a single halo possessing the average mass of the sample,
factor of 1.5–2. Ourtestshaveshown that this can occur and the code compensates for this by fitting a higher σm,
∼
when halos from averybroad rangeof masses are averaged which results in larger errors for the best fit.
10 Bryan R. Gillis et al.
50 50
40 40
30 30
20 20
10 10
0 0
50 100 500 1000 50 100 500 1000
Figure 4. Lensing signals and fits for simulated lensing data for the “No Stripping” (left) and “Stripping” (right) scenarios (see
Section 2.4). The “No Stripping” scenario shows similar one-halo fits for the HDE and LDE samples, while the “Stripping” scenario
showsalowerone-halomassfitfortheHDEsamplethanfortheLDEsample.Errorbarsarenotshown,asshapenoiseisnotsimulated
forthesedatasets,andsothescatter isextremelysmall.
Table 3.Results ofthe fittingprocedure whenappliedtosimulated(top) andthe CFHTLenS(bottom) lensingdata invarious stellar
massbins.Allmassesareinunitsof1010 M⊙.logmisthestellarmassbin.fsat isthefractionofsatellitesweuseforthefitting,based
on data from the Millennium Simulation. MHDE and MLDE are the fitted one-halo masses for the HDE and LDE samples. Mgr is the
fittedmassoftheoffsetgrouphaloterm.RM istheratioofMHDE toMLDE.χ2red isthereducedχ2 parameterwithoutthemodelerror
term(seeSection3.4)included(for36degreesoffreedom;avaluecloseto1isideal).
“NoStripping”Model “Stripping”Model
logm fsat MHDE Mgr MLDE RM MHDE Mgr MLDE RM
9–9.5 0.53 20 12000 21 0.95 14 9800 19 0.74
9.5–10 0.60 46 11000 41 1.12 32 9700 39 0.83
10–10.5 0.63 140 7300 110 1.27 110 7200 120 0.94
10.5–11 0.48 930 9600 650 1.43 950 5900 660 1.44
CFHTLenSData
logm fsat MHDE χ2red,HDE Mgr MLDE χ2red,LDE RM
9–9.5 0.53 17.6± 4.8 2.31 20500±2300 24.9± 4.0 0.83 0.71+0.25
−0.18
9.5–10 0.60 16.5± 6.5 1.05 15060± 900 35.6± 6.2 0.80 0.46+0.25
−0.15
10–10.5 0.63 67 ± 12 0.65 14550± 550 95 ± 11 0.90 0.70+0.17
−0.12
10.5–11 0.45 287 ± 34 1.45 23100±4000 239 ± 38 1.41 1.20+0.30
−0.21
11–11.5 0.45 1090 ±120 0.81 20300±2000 530 ±110 1.29 2.05+0.65
−0.31
Fig. 6 shows the likelihood distributions for the fit- the CFHTLenS data, with the ratio of the fitted one-halo
ted satellite masses, host group mass, and surface density massfortheHDEsampletothatoftheLDEsampleplotted
threshold for the HDE sample of galaxies with 109M⊙ < against the galaxies’ stellar masses. Simulated data is not
m<1010.5M⊙.Theplotshowsthatthereisonlyaweakde- available for all mass bins plotted due to limitations of the
generacyofMsat withtheothertwoparameters,butthereis Milleniumcatalogue.Thesimulateddatademonstratesthat
a stronger degeneracy between Mhost and Σt. Nevertheless, for sufficiently high stellar mass bins, the “Stripping” HDE
whenmarginalized overtheotherparameters, M isvery massbecomescomparabletoorgreaterthanthe“NoStrip-
host
tightly constrained, and Msat is reasonably constrained. ping” HDE mass. This is due to the fact that, at high stel-
lar masses, the P3-identified HDE sample contains a large
We can more carefully analyze the data by splitting
numberofcentrals.Whentidalstrippingispresent,massis
the galaxy sample into smaller stellar mass bins. Fig. 7
transferredfromsatellitestocentrals,increasingtheirmass.
shows the results of this analysis for both simulated and