Environmental dependence of the galaxy stellar mass function in the Dark Energy Survey Science Verification Data

4.6 MB·

by  J. Etherington

Mon.Not.R.Astron.Soc.000,000–000(0000) Printed24January2017 (MNLATEXstylefilev2.2)
Environmental dependence of the galaxy stellar mass function in the
Dark Energy Survey Science Verification Data
J. Etherington1,∗ D. Thomas1,2, C. Maraston1,2, I. Sevilla-Noarbe3, K. Bechtol4,5,
7
1 J.Pforr6,P.Pellegrini7,8,J.Gschwend7,8,A.CarneroRosell7,8,M.A.G.Maia7,8,L.N.da
0 Costa7,8, A. Benoit-Le´vy9,10, M. E. C. Swanson11, W. G. Hartley12, T. M. C. Abbott13,
2
F. B. Abdalla14,15, S. Allam16, R. A. Bernstein17, E. Bertin18,9, D. Brooks14, E. Buckley-
n
a Geer16, M. Carrasco Kind19,20, J. Carretero21,22, F. J. Castander21, M. Crocce21,
J
1 C. E. Cunha23, S. Desai44, P. Doel14, T. F. Eifler26,27, A. E. Evrard28,29, A. Fausti Neto8,
2
D. A. Finley16, B. Flaugher16, P. Fosalba21, J. Frieman16,30, D. W. Gerdes29,

] D. Gruen23,31, R. A. Gruendl19,20, G. Gutierrez16, K. Honscheid32,33, D. J. James13,
A
G K. Kuehn34, N. Kuropatkin16, O. Lahav14, M. Lima15,8, P. Martini32,36, P. Melchior37,
. R.Miquel38,22,J.J.Mohr25,24,39,B.Nord16,R.Ogando8,7,A.A.Plazas27,A.K.Romer40,
h
p E.S.Rykoff23,31,E.Sanchez41,V.Scarpine16,M.Schubnell28,R.C.Smith13,M.Soares-
-
o Santos16, F. Sobreira42,8, G. Tarle29, V. Vikram43, A. R. Walker13, Y. Zhang16
r
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[ 24January2017

1
v
ABSTRACT
6
Measurementsofthegalaxystellarmassfunctionarecrucialtounderstandtheformationof
6
0 galaxies in the Universe. In a hierarchical clustering paradigm it is plausible that there is a
6 connectionbetweenthepropertiesofgalaxiesandtheirenvironments.Evidenceforenviron-
0 mental trends has been established in the local Universe. The Dark Energy Survey (DES)
. provideslargephotometricdatasetsthatenablefurtherinvestigationoftheassemblyofmass.
1
In this study we use ∼ 3.2 million galaxies from the (South Pole Telescope) SPT-East field
0
7 intheDESscienceverification(SV)dataset.FromgrizYphotometrywederivegalaxystellar
1 massesandabsolutemagnitudes,anddeterminetheerrorsonthesepropertiesusingMonte-
: Carlo simulations using the full photometric redshift probability distributions. We compute
v
galaxyenvironmentsusingafixedconicalapertureforarangeofscales.Weconstructgalaxy
i
X environment probability distribution functions and investigate the dependence of the envi-
ronmenterrorsontheapertureparameters.Wecomputetheenvironmentcomponentsofthe
r
a galaxy stellar mass function for the redshift range 0.15 < z < 1.05. For z < 0.75 we find
that the fraction of massive galaxies is larger in high density environment than in low den-
sityenvironments.Weshowthatthelowdensityandhighdensitycomponentsconvergewith
increasingredshiftuptoz ∼1.0wheretheshapesofthemassfunctioncomponentsareindis-
tinguishable.Ourstudyshowshowhighdensitystructuresbuilduparoundmassivegalaxies
throughcosmictime.
Keywords: galaxies:evolution–galaxies:formation–galaxies:clusters:general–galaxies:
photometry–galaxies:statistics
1 INTRODUCTION Measurementsofthegalaxystellarmassfunctionthroughcosmic
timefordifferentpopulationsofgalaxiesandasafunctionofen-
Establishing an understanding of the assembly of mass in galax-
vironmentarevitaltoinspectthenatureoftheassemblyandalso
ies is a key goal in modern extragalactic physics and cosmology.
constrainmodelsofthephysicalprocesses.
It is widely assumed that dark matter accumulated and col-
∗ E-mail:[email protected] lapsed in a hierarchical fashion (White & Frenk 1991). Lambda
(cid:13)c 0000RAS
2 J.Etheringtonetal.
Cold dark matter simulations (Boylan-Kolchin et al. 2009) are to a redshift of ∼0.6. The massive end of the mass function was
abletoemulatetheclusteringofstructureobservedinlargescale found to be consistent with passive evolution in agreement with
galaxysurveysinthelocalUniverse(Springeletal.2006).How- otherworks(Pozzettietal.2010;Ilbertetal.2010,2013).
ever there are unresolved issues. The observed pattern of “down- PencilbeamsurveyssuchastheDEEP2(Newmanetal.2013)
sizing”(Cowieetal.1996)remainsachallengeeventhoughsome andzCOSMOS(Lillyetal.2007)surveyshavetypicallycaptured
aspects of it can be understood in ΛCDM models assuming that data for no more than a few square degrees of the sky but they
there is some threshold of halo mass for efficient star formation arecompletetorelativelyhighredshifts.Theseanalysesexploitthe
(Conroy&Wechsler2009).Severalflavours(Fontanotetal.2009) measurementsof1000stoseveraltensof1000sofgalaxies.Some
of downsizing have now been observed: chemo archaeological studiesfocusonthemassfunctionsforthetotalgalaxypopulation
(Wortheyetal.1992),archaeological(Thomasetal.2005;Thomas whereas others have also investigated the contributions made by
etal.2010),downsizinginthestarformationrate(Conseliceetal. differentgalaxytypes;splitbymorphologyandcolour.Thereare
2007), stellar mass (Pozzetti et al. 2007; Maraston et al. 2013), relatively few works that have examined the role of galaxy envi-
metallicity(Maiolinoetal.2008),nuclearactivity(Cristianietal. ronmentonthestellarmassfunction.Theearliestofthesestudies
2004; Hasinger et al. 2005) and most recently black hole growth split galaxies into two types: field or cluster (Balogh et al. 2001;
(Hirschmannetal.2012). Kodama&Bower2003).Morerecentstudieshavequantifiedthe
Thequestionofgalaxyassemblyisundoubtedlytiedtotheold environments and then examined the mass function for different
adage:“naturevsnurture”.Disentanglingtheinternalandexternal environmentbinsforthelocalUniverse(McNaught-Robertsetal.
physicalprocessesinvolvedisataxingbusiness.Modernworksare 2014),intermediateredshifts(Bundyetal.2006;Bolzonellaetal.
providingclues;somebyexaminingtheenvironmentaldependence 2010;Vulcanietal.2011)andhighredshiftsMortlocketal.(2015).
ofcentralandsatellitegalaxiesseparately(e.g.forgroups-Carollo Themainfindingoftheseworksisthemassiveendofthegalaxy
etal.2013;Cibineletal.2013;Pipinoetal.2014).Themass,ei- stellar mass function is dominated by galaxies that reside within
ther the stellar mass or the total mass of the dark matter halo, is highdensityenvironmentsatlowandintermediateredshiftsbutat
widelythoughttobetheprimarydriverofgalaxyevolution.Thisis higherredshiftsthemassfunctionisindependentofenvironment.
asecularchannelofevolutionchampioningthe‘nature’argument. Davidzon et al. (2016) show the weakening of the environmental
Inthehierarchalclusteringparadigmwhereatreeofhalosmerge dependenceofthemassfunctionbetweenredshiftsof0.5and0.9.
andaccreteforminglargerstructuresitmayfollowthatagalaxy’s Futurestudiesofthegalaxystellarmassfunctionrequiresur-
environmentalsohasaroletoplay. veysoflargercosmologicalvolumes.Thisiscurrentlyonlyfeasi-
Galaxiesaresubjecttoseveralexternalphysicalprocessesin- blewithlargescalephotometricsurveysasspectroscopicsurveys
cluding ram pressure stripping (Boselli & Gavazzi 2014; Fuma- withasimilarvolumetoDESforexample,wouldbetoocostlyand
galli et al. 2014) galaxy harassment (Farouki & Shapiro 1981), slow.Largenumberstatisticsthereforecomeatthecostofredshift
strangulation (Larson et al. 1980) and cannibalism (Nipoti et al. precision.
2003).Theseprocessesarecertainlycapableofstrippinggas,shut- Theaimofthisworkistostudythecontributionstothestellar
tingdownstarformationandtransformingagalaxy’smorphology. massfunctionfromdifferentenvironmentsasafunctionofredshift
ButtowhatdegreearetheseprocessesubiquitousintheUniverse? exploitingtheDESSV(scienceverification)datatakenbeforethe
In a hierarchical scenario it is clear that a galaxy’s environ- firstseasonofthesurvey’soperation.
ment is not constant through cosmic time. It is in fact changing. The paper consist of six sections. In Section 2 we describe
Thekeyparametermaythereforebethegalaxy’sintegratedenvi- the data and the galaxy parameters. In Section 3 we present the
ronmentthroughtime.Devisinganobservationalproxyforthisis galaxyenvironmentmeasurements.InSection4weshowthemass
challenging, perhaps even intractable with the snapshot observa- function analysis. In Section 5 we discuss the robustness of the
tionswecapturewithmoderngalaxysurveys.Theproblemisnot mainresultsandlastlyinSection6wepresentourconclusions.
merelyoneofdatacollectionbutalsoofdefinition.Insimulations InthisworkwehaveassumedaSalpeter(Salpeter1955)ini-
forexample,howdoyoudefineorevenidentifyagalaxysenviron- tialmassfunction,acosmologywithΩm = 0.286,ΩΛ = 0.714
mentwhenitsconstituentpartshavenotyetassembled? andH0 = 70 kms−1Mpc−1 andhaveadoptedcomovingcoordi-
Galaxy surveys such as the SDSS have revolutionised the nates(e.g.Cooperetal.2006)tocalculatethedistancesbetween
study of the galaxy population at low redshift (Blanton & Mous- galaxies.
takas2009).Surveyinglargeareasprovideslargestatisticsandre-
ducestheerrorassociatedwithcosmicvariance.Thefirstmeasure-
mentsofthegalaxystellarmassfunctionofthelocalUniversewere
2 DATAANDGALAXYPARAMETERS
obtainedbyconvertingluminosityfunctionsbysimplemodelling
oftheM/Lofgalaxies(Coleetal.2001;Belletal.2003;Kodama The DES is a multi-band (g, r, i, z, Y) photometric survey per-
&Bower2003).Therearenowseveralmeasurementsofthegalaxy formed with the Dark Energy Camera (DECam, Flaugher et al.
stellarmassfunctionforthelocalUniverse(Baldryetal.2008;Li 2015) mounted on the 4-meter Blanco Telescope at Cerro Tololo
&White2009;Baldryetal.2012)basedonstellarmassesderived Inter-American Observatory (CTIO), aimed at imaging 5000 sq.
fromgalaxyphotometry.TheGAMAsurveyhasaugmentedSDSS deg of the southern sky out to redshift ∼1.4. The survey started
with additional spectroscopic data to obtain mass complete sam- in February 2013 but from November 2012 to February 2013,
plesto∼108M(cid:12)yieldingthecurrentstateoftheartmassfunction DEScarriedoutaScienceVerification(SV)survey.Theseobser-
measurementsinthelocalUniverse(Baldryetal.2012). vations provide science quality data for more than 250 deg2 at
Investigations of the redshift evolution of the stellar mass close to the main survey’s nominal depth (i-band 2-arcsec aper-
functionhaveuntilrecentlybeenrestrictedtodatacollectedfrom turemagnitude(cid:39) 24mag)for standardsurvey fields(e.g. SPT-E
spectroscopicpencilbeamsurveys.HowevertheBOSSsurveyen- field)and/ordeeperfields(usedforcalibrationand/orsupernovae
abledMarastonetal.(2013)tostudytheevolutionofthemassive studies).AnumberofanalysesoftheSVdatahavenowbeenre-
endofthestellarmassfunctionusingasampleof400,000LRGs leased (Dark Energy Survey Collaboration et al. 2016; Palmese
(cid:13)c 0000RAS,MNRAS000,000–000
EnvironmentaldependenceofthegalaxystellarmassfunctionintheDarkEnergySurvey 3
Figure1.EdgesandholesoftheSPT-Efield.Thefieldhasauniformdepthof23magini-bandintegratedapparentmagnitude.
et al. 2016) including weak lensing shear measurements (Jarvis spectroscopic redshifts obtained from existing datasets including
etal.2016),CMBlensingtomography(Giannantonioetal.2016), VVDS Deep (Le Fe`vre et al. 2005, 2013), VVDS Wide (Garilli
systematics(Crocceetal.2016;Leistedtetal.2015),LRGselec- et al. 2008), SDSS/BOSS (Strauss et al. 2002; Eisenstein et al.
tion (Rozo et al. 2016) and a study of the galaxy populations in 2001;Ahnetal.2012),ACES(Cooperetal.2012),and2dFGRS
massiveclusters(Hennigetal.2016). (Collessetal.2001)thatmatchedtheDESSVphotometry.Sa´nchez
ThedatastoredinthecatalogueoftheSVcoaddedimaging etal.(2014)foundthattwoofthetrainingmethods,onebasedon
createdbytheDESDataManagement(DESDM)pipeline(Mohr artificial neural networks (ANNz) (Collister & Lahav 2004) and
etal.2012,Sevillaetal.2011,Desaietal.2012)werethenthor- the otheron prediction treesand random forests,called Trees for
oughlytestedandanalysedbyateamofDESscientists,whowere Photo-z or TPZ (Carrasco Kind & Brunner 2013), performed the
able to construct a new photometric catalogue, called the SV An- best. The scatter of the difference between the photometric red-
nual1(SVA1)Goldcatalogue,containing25,227,559objectsand shiftsandthetestsetofspectroscopicredshiftsforthesemethods
extendingoveranarea∼250deg2.Thiscatalogueisnowpublicly wasδ68 =0.08.
available1. InthispaperweutilisetheoutputfromtheTPZcodebecause
In this work we use the Portsmouth COnstant Mag MOdel in addition to the best estimate of the redshift this code provides
DepthOriginatedREgion(COMMODORE)galaxycatalogue(see photometric redshift probability distribution functions (PDFs) for
Capozzietal.,inprep.),asubsampleoftheGoldSVA-1catalogue. each galaxy. The photo-z PDFs consist of 200 bins spanning the
TheCOMMODOREcataloguewasconstructedtohavehomoge- redshiftrange:0-1.8.Eachbinhasawidthof0.009inredshift.
neous depth (i-band integrated magnitude = 23 mag) so that it We computed the 1 sigma width of each photo-z PDF and
could be used for galaxy evolution studies and a bright end limit identifiedthegalaxiesatthe16th,50th and84th percentilesinthe
(i-bandintegratedmagnitude=16mag)toaidstar-galaxysepara- distribution of widths. The half-widths at these percentiles are:
tion.Thetotalareacoveredbythiscatalogueis∼155deg2.How- 0.041, 0.055 and 0.079 respectively. We note that the 1 sigma
everthisareaisnotcontiguousandforgalaxyenvironmentstudies width of the photo-z PDFs as measured here for all of the SPT-
whichrequireareacontiguity,asubsampleoftheCOMMODORE E galaxies is a different quantity from the scatter (δ ) measured
68
cataloguemustbeselected.InthispaperweselectfromtheCOM- betweenthepeaksofthePDFsandthespectroscopicredshiftsmea-
MODOREcatalogueonlythegalaxiesintheSPT-E(∼130deg2) suredinSa´nchezetal.(2014).
field(whichisthelargestfieldintheSVdataset)toensurethecon- Inthispaperweareinterestedinthepropagationofthered-
tiguityrequirementismet.Fig1showstheperimeteroftheSPT-E shift errors into the derived galaxies properties: mass, absolute
fieldandtheholesinthedata(duetobrightstars)afterallofthe magnitudeandgalaxyenvironment.Thisinturnenablesustoquan-
processingstepshavebeenapplied. tify errors on the environment components of the galaxy stellar
massfunction.
2.1 Photometricredshifts
There are two types of methods used to measure photometric 2.2 K-corrections,absolutemagnitudesandstellarmasses
redshifts: template methods and training methods. Sa´nchez et al.
ThegalaxypropertiesusedinourstudyaretakenfromtheCOM-
(2014) performed extensive tests on the SV data using 13 differ-
MODORE catalogue, which provides both galaxy physical prop-
entphotometricredshiftcodes.Thecodesweretrainedwith∼6000
erties (e.g. age, star formation history and stellar mass) and de-
tectability related properties (e.g. k-correction, maximum acces-
1 http://des.ncsa.illinois.edu/releases/SVA1. sible volumes and completeness factors as function of apparent
(cid:13)c 0000RAS,MNRAS000,000–000
4 J.Etheringtonetal.
magnitudeandsurfacebrightness).Thephysicalpropertiesareob- 2.3.1 SamplingTests
tainedviaSpectralEnergyDistribution(SED)fitting,usingthirty
Toinvestigatethevariabilityduetothephotometricredshifterrors
two sets of theoretical templates (as in Maraston et al. 2006 and
wegenerated100realizationsoftheSPT-Ecataloguedrawingred-
Capozzietal.2016)constructedwiththeevolutionarystellarpop-
shiftsfromthephoto-zPDFs.Todothisweconstructedthephoto-z
ulationsynthesismodelsbyMaraston(2005)andMarastonetal.
cumulativedistributionfunctionsfromthephoto-zPDFsforeach
(2009) under the assumption of a Salpeter (Salpeter 1955) Initial
galaxy. The cumulative distribution function maps the range 0 to
MassFunction(IMF).Thesetemplatesconsistoffourtypesofstar
1tothepossibleredshiftsforagalaxy.Wedrewrandomnumbers
formationhistoriesincluding:singlebursts(SSPs),exponentially-
fromauniformdistributionspanning0to1andusedthemappings
declining, truncated star formation rate (SFR) and constant SFR.
toobtainredshiftdraws.
The SED fitting was performed by means of the template fitting
Toverifythatthesampledredshiftdrawswererepresentative
code HYPERZ (Bolzonella et al. 2000), using the DES photome-
ofthephoto-zPDFswecalculatedsummarystatistics.Weobtained
tryandfixinggalaxyredshiftsatthephotometricvaluesprovided
the “true” mean and variance of each photo-z PDF. The mean is
bytheTPZcode.Foreachgalaxywethencalculateddetectability
simplytheexpectationofthedistribution:
usingtherealobserved-framemagnitudescalculatedatgivenred-
shiftforthegalaxy’sbestfittingmodelfoundabove.Weusetables2
whichprovideforeachofthe32setsoftemplates,theirobserved- µ=E(z)=Σz p . (1)
i i
framemagnitudes(assumingastandardcosmology)forafinegrid
of redshifts including z = 0. The difference between the model Itisthesumoftheredshiftmidpositionsofthebarsmultiplied
magnitudeatgivenzandthesameatz =0isthentheexactvalue bytheprobabilities(heights)ofthebars.Thevarianceistheexpec-
ofthefaintingorbrighteningtobeappliedintheexactfilter,with- tationofthesquareddistributionminustheexpectationsquared:
outgoingthroughapproximatedk-corrections.These∆’sarethen
appliedtothei-bandabsolutemagnitudes. σ2 =E(z2)−(E(z))2, E(z2)=(cid:88)z2p . (2)
In evolutionary studies it is important to estimate the com- i i
pleteness of the galaxy sample in absolute magnitude and stellar Themeanoftherandomlygeneratedredshiftdrawswascal-
massasafunctionofredshift.Todothiswefollowasimilarpro- culatedusing:
cedureasdescribedinPozzettietal.(2010).Weobtainthecom-
pleteness limits by computing the 90th percentiles of the limiting
1 (cid:88)
stellar mass and absolute magnitudes within redshift bins for the zˆ= z (3)
N
faintandbrightendsofthesample.Limitsareconstructedforthe draws
bright end in addition to the faint end because of the i-band ap- andthevarianceoftheredshiftdrawswascalculatedusing:
parentmagnitudeselection(seeSection2)appliedtoconstructthe
COMMODOREcatalogue.WereferthereadertoCapozzietal.(in σˆ2 = 1 (cid:88)(z−zˆ)2. (4)
prep.),wherethePortsmouthCOMMODOREcatalogue,thecom- N −1
draws
pletenesslimitsandthegalaxypropertycalculationsarepresented
Therangeof5-100drawsofeachgalaxywasinvestigated.
indetail.
Using these summary statistics the biases and root mean
squared errors (RMSE) between the “true” statistics (mean and
variance) and the statistics from the samples as a function of the
2.3 Erroranalysis numberofdrawswerecalculated.ThebiasandRMSEofthemean
aregivenby:
The main aim of this Section is to quantify the errors on the de-
rivedgalaxyproperties,i.e.thestellarmassesandthei-bandabso-
lutemagnitudesduetotheerrorsonthephotometricredshifts.We 1 (cid:88)
Biasofthemean= (µ−zˆ), (5)
adopt a Monte-Carlo approach and generate many realizations of Ngal
theSPT-Ecataloguebydrawingredshiftsfromthephoto-zPDFs.
An alternative is to start with the errors on the photometry itself (cid:115)
1 (cid:88)
andpropagatethemforwards(e.g.Tayloretal.2009).Weusethe RMSEofthemean= (µ−zˆ)2 (6)
N
photo-zPDFsasthismakesourstudyeasiertoreproduceormod- gal
ifyastheSVphoto-zPDFsarepubliclyavailable(seeSection2).
andthebiasandRMSEofthevariancearegivenby:
SincetheTPZphoto-zPDFsareconstructedusingthephotometric
errorstheseapproachesarecomparable.
In Section 2.3.1 we present a series of tests on the redshift Biasofthevariance= 1 (cid:88)(σ2−σˆ2), (7)
drawsto:(i)verifythatthedrawsarerepresentativeofthephoto- Ngal
z PDFs and (ii) quantify the difference between the statistics of
the draws and the photo-z PDFs as a function of the number of (cid:115)
1 (cid:88)
catalogue realizations. We compute the stellar masses and i-band RMSEofthevariance= (σ2−σˆ2)2. (8)
N
absolutemagnitudesforthegalaxiesineachoftherealizationsof gal
theSPT-EcataloguesusingHYPERZasdescribedinSection2.2.In Fig2showsthebias(top)andRMSE(bottom)forthemean
Section2.3.2wepresentthedistributionsofthegalaxyproperties
(left) and variance (right) as a function of the number of redshift
andtheirerrors.
draws for each galaxy. Plots a) and b) show that the bias of the
meanandthevarianceareapproximatelyzero.Thisisexpectedas
these estimators are unbiased. The plots show the random errors
2 C.Maraston,inpreparation,availableuponrequest generated from the sampling process are of theorder of ∼ 10−5
(cid:13)c 0000RAS,MNRAS000,000–000
EnvironmentaldependenceofthegalaxystellarmassfunctionintheDarkEnergySurvey 5
Figure2.Top:Biasforthemean(left)andvariance(right)asafunctionofthenumberofdraws.Bottom:RMSEforthemean(left)andvariance(right)of
theredshiftdrawsasafunctionofthenumberofdraws.
centered on zero. The RMSE for the mean decreases as approx- for each galaxy as half the difference between the 84th and 16th
imately the square root of the number of redshift draws of each percentiles.
galaxy.TheRMSEforthevariancefallsoffslightlymorerapidly
Fig3showsthe(median)distributionsoftheredshifts,i-band
withthenumberofdraws,withapowerof−0.52.
absolutemagnitudesandstellarmassesinthefirstrow,thedistri-
For100randomcataloguestheRMSEofthemeanis0.0076
butionoferrorsonthepropertiesinthesecondrow,theTPZred-
and RMSE of the variance is 0.0028 as shown in Fig 2. In addi-
shift dependence of the property errors in the third row and the
tionwefoundthattheRMSEofthestandarddeviationforthe100
dependenceofthepropertyerrorsonthepropertiesthemselvesin
cataloguesis0.0082.Thesenumbersarebetween5and10times
the fourth row. The left hand column shows the galaxy redshifts.
smallerthanthetypicalwidthofthephoto-zPDFs.Individualex-
Themiddlecolumnshowsi-bandabsolutemagnitudesandtheright
ampleshavebeenexaminedandwith100drawsminoroffsetsbe-
handcolumnshowsthegalaxystellarmasses.Throughoutthispa-
tweenthestatisticsofthesamplesandthePDFscanbeintroduced.
pertheunitsofstellarmassissolarmassesandstellarmassisplot-
PDFs that have multiple peaks, separated by relatively large red-
tedonalogarithmicscale.Inthefirstrowtheverticalreddashed
shifts can be sampled less effectively with only a small number
lines show the median values and the vertical blue dashed lines
ofdraws.Nevertheless,theprecisionquotedhere,issufficientfor
showthe16th and84th percentilesoftheredshift,i-bandabsolute
thepurposesofthisstudy.Sincetheerrorsdecreaseapproximately
magnitudeandmassdistributions.Wequotetherangesoftheprop-
as the square root of the number of draws 4 times as many ran-
ertydistributionsintheplotsasthedifferencebetweenthe84thand
dom catalogues (i.e. 400 catalogues) would be required to halve
16th percentiles. In the second row the red vertical dashed lines
theRMSEs.
markthemedianpropertyerrors.Wequotethemedianerrorsfor
comparisonwiththerangesofthedistributionsthemselvesquoted
inthefirstrow.
2.3.2 Galaxyproperties:distributionsanderrors
The ranges of the distributions are: 0.56, 2.62 and 1.36 for
InthisSectionwepresentthecollatedresultsforthegalaxyprop- redshift, i-band absolute magnitude and stellar mass respectively
erties:redshifts,i-bandabsolutemagnitudesandstellarmassesde- and in the same order the median errors for these quantities are
rivedfromthe100Monte-Carlosimulations. 0.054, 0.256 and 0.118. The ratios of the ranges of the property
For each of the 3,207,756 galaxies in the SPT-E field we distributionstothemedianpropertyerrorsare:10.3,10.2and11.5
computedthemedian,16thand84thpercentiles(outofthe100val- forredshift,i-bandabsolutemagnitudeandmassrespectively.This
ues)ofthedrawnredshifts,computedi-bandabsolutemagnitudes quantificationsuggeststhatallthreeofthesepropertiescanbestud-
andstellarmasses.Wequotethe1-sigmaerror(foreachproperty) ied,asthemedianerrorduetothephotometricredshiftsisanorder
(cid:13)c 0000RAS,MNRAS000,000–000
6 J.Etheringtonetal.
Figure3.Firstrow:Propertydistributions,secondrow:errordistributions,thirdrow:TPZredshiftdependenceofthepropertyerrorsandfourthrow:property
dependenceoftheerrors.Thefirstcolumnisforredshift,thesecondcolumnisforthei-bandabsolutemagnitudeandthethirdcolumnisforthestellarmasses.
Stellarmasshasunitsofsolarmasses.Theredverticaldashedlinesshowthemedianvalues.Theblueverticaldashedlinesshowthe16thand84thpercentiles.
ofmagnitudesmallerthantherangesofthedistributionsofthese tiallyconstantat∼ 0.035acrosstheredshiftrange0 < z < 1.0.
properties. Theerroratz ∼0.7isslightlysmallercomparedtotherestofthe
range. This is around the peak of the redshift distribution shown
The third row of plots in Fig 3 shows the median errors (in inplota).Theerrorsonthei-bandabsolutemagnitudesandstel-
redshiftbins)onthepropertiesasafunctionofthegalaxies’TPZ lar masses behave in a similar way to each other. The errors are
redshifts.Theredshifterrorcorrectedbyafactorof1+zisessen-
(cid:13)c 0000RAS,MNRAS000,000–000
EnvironmentaldependenceofthegalaxystellarmassfunctionintheDarkEnergySurvey 7
particularlylargeforz < 0.25andincreaseastheredshiftisde- methodsarearguablyeasiertointerpretbecausetheycomputeden-
creased.Theerrorsstabiliseatlargerredshiftstovaluesof< 0.4 sitiesoverfixedscales,(ii)Shattowetal.(2013)showedthatfixed
and< 0.2forthei-bandabsolutemagnitudeandstellarmassre- aperturemethodsprovidemorerobustmeasurementsovercosmic
spectively.Thereisa“sweet”spotforbothpropertiesintheredshift timeand(iii)fixedaperturemethodsarecomputationallylessex-
range0.6<z <0.7wheretheerroris<0.2forthei-bandabso- pensivecomparedtoNthnearestneighbourmethods.
lutemagnitudeand<0.1forthestellarmass. Several different aperture volumes have been used in previ-
ThefourthrowofplotsinFig3showstheaverage16th and ousstudiesincludingspheres(Crotonetal.2005),cylinders(Gal-
84th percentilepropertyerrorsasafunctionofthemedianvalues lazzietal.2009),annuli(Wilmanetal.2010),cones(Etherington
ofthepropertiesthemselves.Asexpectedtheredshifterrordepen- &Thomas2015)andellipsoids(Schawinskietal.2007;Thomas
denceonthemedianredshiftshowninplotj)issimilartothede- etal.2010).Inphotometricsurveystheerrorsintheredshiftmea-
pendenceontheTPZredshiftshowninplotg).Theerrordepen- surementsalongthelineofsightaremuchgreaterthantheerrors
dence for the i-band absolute magnitude and masses also mirror in the angular measurements. The most appropriate aperture for
eachother.Theerrorsarelargestfortheleastluminousandleast aphotometricsurveyisthereforeconicalinshapeasthisvolume
massivegalaxies.Thisisinlinewithexpectationasfaintergalax- mosteffectivelyencompassesadjacentlinesofsight.
ies are more difficult to measure. The i-band absolute magnitude The aperture that we adopt is approximately a conical frus-
errorisrelativelystableand< 0.25forgalaxieswithanabsolute tum,i.e.thevolumethatisleftwhenyousliceoffthetopofacone.
magnitude brighter than −20.0. Similarly the mass error is rela- Thevolumeisthereforecalculatedbytakingthedifferenceoftwo
tivelyconstantat<0.2forLog(M)>8.5. cones.Wecontrolthevolumeoftheaperturewithtwoparameters:
theradius(r)ofthecrosssectionoftheconeatthetargetgalaxy
andthe(∆z)half-lengthoftheaperture.Inthisstudyweinvestigate
arangeofradii:0.1−3.0Mpcandhalf-lengths:0.08−0.3(inred-
3 GALAXYENVIRONMENT
shift).Wecountthenumberofdensitytracinggalaxies(seeSection
InthisSectionwepresentthegalaxyenvironmentmeasurements. 3.1.2)withintheapertureandcomputeadensity.Aperturesthatare
We proceed with the Monte-Carlo approach and compute galaxy found to be devoid of galaxies are assigned a nominal minimum
environments for all 100 catalogue realizations to determine the densityof0.5galaxiesperaperture.Thedensityforeachgalaxyis
errorontheenvironmentmeasurementsofeachgalaxy.InSection thenturnedintoadensitycontrastwithrespecttothemeandensity
3.1wedescribethemethodweusetoquantifygalaxyenvironment. ρmusingtheequationbelow:
In Section 3.2 we study the environment measurements and their
errorsasafunctionoftheapertureparameters.InSection3.3we
δ=(ρ−ρ )/ρ (9)
m m
characterisetheenvironmentmeasurementsthatweemploylaterin
thegalaxystellarmassfunctionanalysis.InSection3.4wepresent Themeandensityρm iscalculatedwithinaredshiftwindow
theresultsoftheMonte-CarlosimulationsasenvironmentPDFs. centredonthetargetgalaxy.WecomputeLog(1+δ)andreferto
thisquantityasthegalaxyenvironment.
3.1 Environmentmeasurements
3.1.2 DensityDefiningPopulations
In preparation for photometric surveys there have been a num-
The distribution of stellar matter is a biased tracer (Kaiser 1984)
ber of studies that have investigated the impact of redshift preci-
ofthelargescalestructureintheUniverse.Mapsofthetotalmass,
siononmeasurementsofgalaxyenvironment.Cooperetal.(2005)
baryonicanddarkmattercombined,havenowbeencreatedusing
concluded that for pencil beam surveys such as DEEP2 redshift
weaklensingmeasurementsfromtheDES(Vikrametal.2015).
measurementswitherrors> 0.02wereunsuitabletomeasurelo-
We follow the approach that has been adopted in previous
calgalaxydensities.HowevermorerecentlyFossatietal.(2015)
galaxy environment studies (e.g Baldry & Balogh 2006; Thomas
showedusingasemi-analyticalmodelthatitispossibletomeasure
etal.2010;Pengetal.2010)anduseonlythegalaxydistribution
trendswithgalaxyenvironment.Etherington&Thomas(2015)ex-
andassumethisisanadequateproxytotracetheunderlyingdensity
aminedtheimpactofredshiftprecisionwithafocusonlarge-scale
field.
surveysusingSDSSdataandfoundthattheenvironmentalsignal
Populations of intrinsically faint galaxies are not detectable
inphotometricdatacanbemeasuredbutneedstobeoptimisedwith
throughtheentiresurveyvolume.Tofairlytracethegalaxydistri-
acarefulchoiceofapertureparametervalues.
butionweconstructedvolumelimitedsamples.Weemployedtwo
densitydefiningpopulationswhichwecalledthefaintandbright
tracersbecauseofthecutsontheabsolutemagnitudesofthegalax-
3.1.1 Method
ies.Weemployluminositycutsonthesample,ratherthancutsin
Galaxy environment has been measured with a variety of meth- stellar mass because luminosities are more closely related to the
ods(e.gCarolloetal.2013)includingVoronoiTessellation,fixed observationsandarelessmodeldependent.
aperture,Nthnearestneighbourmethodsandnumerousvariantsof Fig4showsanexampleofthesampleselectionofthegalax-
these.(seeMuldrewetal.(2012)andHaasetal.(2012)forcompi- iesfromtheSPT-Efieldusingthei-bandabsolutemagnitudesand
lations). in this example their TPZ redshifts. The colour bar indicates the
In this work we employ a fixed aperture method. In this number of galaxies in each grid cell. The upper and lower ma-
methodanumberdensityiscalculatedbycountingthenumberof genta curves mark the i-band absolute magnitude completeness
densitytracinggalaxies(seeSection3.1.2)foundwithinanaper- limits. The faint and bright tracers consist of the galaxies within
turecentredonthetargetgalaxy(thetargetgalaxyisnotincluded themagentarectangles.Thecompletenesslimitswereusedtode-
withinthecount)anddividingthisbythevolumeoftheaperture. termine the extremities of the tracers. The faint tracer has a red-
Therearethreereasonsforthischoiceofmethod:(i)fixedaperture shift range 0.15 < z < 0.75 and an i-band absolute magnitude
(cid:13)c 0000RAS,MNRAS000,000–000
8 J.Etheringtonetal.
Figure4.SampleselectionintheMi-redshiftplane.InthisexampletheTPZredshiftsareused.Theverticalmagentalinesmarktheredshiftbounds.The
numberofgalaxiesineach2-dimensionalbinisrepresentedwithacolourasindicatedinthecolourbar.Themagentacurvesmarkthelowerandupperi-band
absolutemagnitudecompletenesslimits.Themagentarectangularregionsenclosethefaint(lowredshift)andbright(highredshift)densitytracers.Thereisan
overlappingredshiftrangebetweenthefaintandbrighttracersthatenablescomparisons.Selectionforeachofthe100Monte-Carlosimulationsisperformed
inthesamewayusingtheredshiftsdrawnfromthephoto-zPDFsandthecorrespondingi-bandabsolutemagnitudes.
range −24.0 < M < −20.63. The bright tracer has a redshift
i Table1.Densitydefiningpopulationproperties
range 0.6 < z < 1.05 and an i-band absolute magnitude range
−27.91 < M < −22.37.Wepurposelydesignedanoverlapof
i Property FaintTracer BrightTracer
the redshift ranges of the two tracers to enable comparisons be-
tween the two tracers. Table 1 summarizes the properties of the z 0.15<z<0.75 0.6<z<1.05
faintandbrighttracers.Selectionforeachofthe100Monte-Carlo Mi −24.00<Mi<−20.63 −27.91<Mi<−22.37
Radius r=1.0Mpc r=1.4Mpc
simulationsisperformedinthesamewayusingtheredshiftsdrawn
Half-depth δz=0.1 δz=0.2
fromthephoto-zPDFsandthecorrespondingi-bandabsolutemag-
Range 0.36 0.42
nitudes.
Log(1+δ)
Median 0.096 0.11
∆Log(1+δ)
3.1.3 Surveyedgeandholes Ratio 3.8 3.8
Galaxy environment measurements require contiguous regions to
ensuredensitiesarenotunderestimated.Theboundariesoftheho-
mogenised SPT-E field are not regular and there are holes in the
datacausedbybrightstars.Itisthereforeimportantthattheedges Toensuretheperipheryofthedatadidnotimpacttheenvironment
ofthedataaredeterminedandappropriatelymanaged.Weusedthe measurementsweappliedaconservativecutanddiscardedgalaxies
HEALPix(Go´rskietal.2005)softwaretoidentifythepixelsthat thatwerelessthan0.1degreeawayfromanedgepointbutinside
containedgalaxiesandthosethatdidnot.Wepopulatedthecells thefootprint.Afterapplyingthiscuttheareaofthefootprintwas
withrandompoints.Thedensityofrandompointswas>10times 78.09deg2.
theaveragedensityofthegalaxies.Wethencomputedtheangular We manage the redshift boundaries by adjusting the depth
distancebetweenpointsthatwereinsidethedatafootprintandthe of the aperture in cases where the aperture would cross over the
pointsoutsideofthefootprint.Weidentifiedthesetofpointsthat boundary.Wereducethehalfdepthoftheaperture(oftheinfring-
wereinsidethefootprintbutweretheclosesttoanypointoutside inghalf)tobethecomovingdistancefromthetargettothebound-
ofthefootprint.Thissetofrandompointsdefinestheedgeofthe ary. This ensures the aperture fits inside the redshift range. The
SPT-Edatathatweusedinthescientificanalysis.Fig1showsthe depthoftheotherhalfoftheaperturethatresideswithintheredshift
positionsofthesetofpointsthatdefinestheedgesofthefootprint. rangeisnotchanged.
(cid:13)c 0000RAS,MNRAS000,000–000
EnvironmentaldependenceofthegalaxystellarmassfunctionintheDarkEnergySurvey 9
Figure5.Leftcolumn:rangeoftheenvironmentdistributions(differencebetweenthe84thand16thpercentiles)asafunctionoftheradiusanddepthofthe
aperture.Middlecolumnshowsthemedianerroroftheenvironmentmeasurementsasafunctionoftheradiusanddepth.Rightcolumnshowstheratioofthe
rangeoftheenvironmentdistributiontothemedianerrorasafunctionoftheradiusanddepth.Toprowisforthefainttracerandthebottomrowisforthe
brighttracer.Thecontourlinesinplotsc)andf)areforaratioof3.8.
3.2 Environmentsasafunctionoftheapertureparameters asthevolumeoftheapertureincreases.Probingenvironmentson
largescaleshomogenisesthemeasurementsaslocalcontrastsare
Toinvestigatetheimpactoftheapertureparametersontheenviron-
smoothed out. The median error is also small for radii less than
mentmeasurementswetestedapertureswithradiiof0.1−3.0Mpc
0.3 Mpcforthefainttracerandlessthan0.6 Mpcforthebright
at0.1Mpcincrementsandhalf-depthsof0.08−0.3at0.02incre-
tracer. These scales are approaching or beneath the average sam-
mentsinredshift.
pling scale of the tracing populations. The small environment er-
Fig5showstherangeoftheenvironmentdistributionofthe
rorsatthesescalesareanartificialeffectandthesescalesshould
galaxiesinthedensitydefiningpopulationasafunctionoftheaper-
notbeemployedforscientificanalysis.
tureparametersintheleftcolumn;themedianerroroftheenviron-
The ideal scenario is to have a large environment range and
mentmeasurementsasafunctionoftheapertureparametersinthe
smallmeasurementerrors.Howeverthetrendsofincreasingrange
middlecolumnandtheratiooftherangetotheenvironmenterror
anddecreasingerrordependontheapertureparameters,especially
asafunctionoftheapertureparametersintherightcolumn.The
theradiusinacounteractingfashion.
top row is for the faint, low-z tracer. The bottom row is for the
bright,high-ztracer.Wedefinetherangeoftheenvironmentdistri- Therightcolumnshowstheratioofthetracingpopulationen-
butionasthedifferencebetweenthe84thand16thpercentilesofthe vironmentrangetothemedianenvironmenterrorasafunctionof
distribution. theapertureparameters.Theblacklinesover-plottedmarkacon-
Therangeoftheenvironmentdistributionofthedensitydefin- stant ratio of 3.8. The black crosses mark the aperture parame-
ingpopulationdependsstronglyonapertureradiusandweaklyon ters that we select to employ later. The plots show that the ratio
the aperture half-depth for both the faint and bright tracers. For increases with increasing depth and radius for both the faint and
both tracers the environment range becomes larger as the radius bright tracers. However the trend is stronger for the faint tracer,
decreasesfrom3.0 Mpc.Thistrendcontinuesforthefainttracers illustrated with the stronger colour gradient. On the one hand it
until a radius of 0.2 Mpc and for the bright tracer until a radius is desirable for this ratio to be as large as possible to minimize
of0.6 Mpc.Apertureswithradiismallerthanthesevaluespoorly contaminationbetweenenvironmentbinsbutontheotherhandit
samplethetracingpopulation,becausemanyaperturesaredevoid isnecessarytoprobesignalfromthescaleswhereenvironmental
ofgalaxies.Alargerapertureisrequiredforthebrighttracerbe- processeshavearole.
causethistracersamplesthedensityfieldmoresparsely. Previous studies have reported that environmental processes
Themiddlecolumnshowsthatthemedianenvironmenterror occurmostreadilyonscalesof∼1Mpcorless(Blanton&Berlind
is a smooth function of both the aperture radius and half depth. 2007; Wilman et al. 2010). For scientific analysis employing the
Thegeneraltrendisthatthemedianenvironmenterrordecreases fainttracerwethereforeoptforaradiusof1 Mpc.Thechoiceof
(cid:13)c 0000RAS,MNRAS000,000–000
10 J.Etheringtonetal.
Figure6.a)environmentdistribution,b)distributionofenvironmenterror,c)TPZredshiftdependenceoftheenvironmenterrorandd)environmenterrorasa
functionofenvironmentforthefaint(black)andbright(blue)tracers.
depthforthefainttracerisatradeoffbetweenmaximisingtheratio environmentmeasurementsthereforehaveadistinguishingpower
(betweentherangeoftheenvironmentdistributionandthemedian thatisonlyabout3timeslessthantheotherparameters.
environment error) and the goal of measuring local environment.
We opt for a half-depth of 0.1 (in redshift). The ratio with these
apertureparametervaluesis∼3.8.Thechoiceforthebrighttracer 3.3 Environmentcharacterisation
ismoreconstrained.Forthepurposesofcomparisonbetweenthe
faintandbrighttracerswechooseapertureparametervaluesforthe Wenowcharacteriseinmoredetailtheenvironmentmeasurements
brightthatleadtoasimilarratio.Forthebrighttracerwetherefore obtainedwiththeapertureparameterschoseninSection3.2.The
choose a radius of 1.4 Mpc and a half-depth of 0.2 (in redshift) keyproperties,suchastheredshiftranges,apertureparametersand
whichalsogivesaratioof∼3.8.Wenotethatwiththischoiceof environmentpropertiesarelistedinTable1.
parametersthehalf-depthsoftheapertureareatleasttwiceaslarge Fig 6 shows the environment distribution in the top left; the
as the 1-sigma photometric redshift errors (see Fig. 3) across the medianenvironmenterrordistributioninthetopright;themedian
whole range of redshifts we study and this ensures that the envi- environmenterrorasafunctionoftheTPZredshiftinthebottom
ronmentmeasurementsarenotseverelyaffectedbysignaltonoise leftandthemedianenvironmenterrorasafunctionofthemedian
issues.Thenumberofaperturesthataredevoidofdensitydefining environment in the bottom right for the faint (black) and bright
populationgalaxiesislessthan0.2and4.0percentforthefaintand (blue)tracers.
brighttracersrespectively. Theenvironmentdistributionsforboththefaintandthebright
tracers are approximately Gaussian and have widths of 0.36 and
Theratiobetweentherangeofthedistributionandtheaver- 0.42respectively.Theaperturesaresufficientlylargethatanegligi-
ageerrorfortheothergalaxyproperties(redshift,massandi-band blenumberaredevoidofgalaxiesandthedistributionsareroughly
absolute magnitude) was ∼10-12 as shown in Section 2.3.2. The symmetrical.Theshapeandrangeofthefaintandbrightenviron-
(cid:13)c 0000RAS,MNRAS000,000–000