The ALHAMBRA survey: accurate merger fractions derived by PDF analysis of photometrically

15 Pages·2015·2.77 MB·English

A&A576,A53(2015) Astronomy
DOI:10.1051/0004-6361/201424913 &
(cid:13)c ESO2015 Astrophysics
The ALHAMBRA survey: accurate merger fractions derived by PDF
analysis of photometrically close pairs(cid:63),(cid:63)(cid:63)
C.López-Sanjuan1,A.J.Cenarro1,J.Varela1,K.Viironen1,A.Molino2,N.Benítez2,P.Arnalte-Mur3,B.Ascaso4,2,
L.A.Díaz-García1,A.Fernández-Soto5,6,Y.Jiménez-Teja7,I.Márquez2,J.Masegosa2,M.Moles1,2,M.Povic´2,
J.A.L.Aguerri8,9,E.Alfaro2,T.Aparicio-Villegas7,2,T.Broadhurst10,J.Cabrera-Caño11,F.J.Castander12,J.Cepa8,9,
M.Cerviño2,8,D.Cristóbal-Hornillos1,A.DelOlmo2,R.M.GonzálezDelgado2,C.Husillos2,L.Infante13,
V.J.Martínez6,14,J.Perea2,F.Prada2,andJ.M.Quintana2
1 CentrodeEstudiosdeFísicadelCosmosdeAragón,PlazaSanJuan1,44001Teruel,Spain
e-mail:[email protected]
2 InstitutodeAstrofísicadeAndalucía(IAA-CSIC),Glorietadelaastronomías/n,18008Granada,Spain
3 InstituteforComputationalCosmology,DepartmentofPhysics,DurhamUniversity,SouthRoad,DurhamDH13LE,UK
4 GEPI,ObservatoiredeParis,CNRS,UniversitéParisDiderot,61Avenuedel’Observatoire,75014Paris,France
5 InstitutodeFísicadeCantabria,AvenidadelosCastross/n,39005Santander,Spain
6 ObservatoriAstronòmic,UniversitatdeValència,C/CatedráticoJoséBeltrán2,46980Paterna,Spain
7 ObservatórioNacional,COAA,RuaGeneralJoséCristino77,20921-400RiodeJaneiro,Brazil
8 InstitutodeAstrofísicadeCanarias,víaLácteas/n,LaLaguna,38200Tenerife,Spain
9 DepartamentodeAstrofísica,FacultaddeFísica,UniversidaddelaLaguna,38200LaLaguna,Spain
10 DepartmentofTheoreticalPhysics,UniversityoftheBasqueCountryUPV/EHU,48040Bilbao,Spain
11 DepartamentodeFísicaAtómica,MolecularyNuclear,FacultaddeFísica,UniversidaddeSevilla,41080Sevilla,Spain
12 InstitutdeCiènciesdel’Espai(IEEC-CSIC),FacultatdeCiéncies,CampusUAB,08193Bellaterra,Spain
13 DepartamentodeAstronomía,PontificiaUniversidadCatólica,Santiago,782-0436Macul,Chile
14 Departamentd’AstronomiaiAstrofísica,UniversitatdeValència,46100Burjassot,Spain
Received3September2014/Accepted10December2014
ABSTRACT
Aims.Ourgoalistodevelopandtestanovelmethodologytocomputeaccurateclose-pairfractionswithphotometricredshifts.
Methods.Weimprovedthecurrentlyusedmethodologiestoestimatethemergerfraction f fromphotometricredshiftsby(i)using
m
thefullprobabilitydistributionfunctions(PDFs)ofthesourcesinredshiftspace;(ii)includingthevariationintheluminosityofthe
sourceswithzinboththesampleselectionandtheluminosityratioconstrain;and(iii)splittingindividualPDFsintoredandblue
spectraltemplatestoreliablyworkwithcolourselections.WetestedtheperformanceofournewmethodologywiththePDFsprovided
bytheALHAMBRAphotometricsurvey.
Results.ThemergerfractionsandratesfromtheALHAMBRAsurveyagreeexcellentlywellwiththosefromspectroscopicworkfor
boththegeneralpopulationandredandbluegalaxies.Withthemergerrateofbright(M ≤−20−1.1z)galaxiesevolvingas(1+z)n,
B
thepower-lawindexnishigherforbluegalaxies(n = 2.7±0.5)thanforredgalaxies(n = 1.3±0.4),confirmingpreviousresults.
Integratingthemergerrateovercosmictime,wefindthattheaveragenumberofmergerspergalaxysincez=1isNred=0.57±0.05
m
forredgalaxiesandNblue=0.26±0.02forbluegalaxies.
m
Conclusions.Ournewmethodologystatisticallyexploitsalltheavailableinformationprovidedbyphotometricredshiftcodesand
yieldsaccuratemeasurementsofthemergerfractionbyclosepairsfromusingphotometricredshiftsalone.Currentandfuturephoto-
metricsurveyswillbenefitfromthisnewmethodology.
Keywords.galaxies:evolution–galaxies:interactions–galaxies:statistics
1. Introduction Since then, the role of mergers in galaxy evolution has been
recognizedandstudiedsystematically,bothobservationallyand
Intheirpioneeringstudy,Toomre&Toomre(1972)wereableto theoretically. To constrain the role of mergers in galaxy evolu-
explain the tails and distortions of four peculiar galaxies as the tion, two observational approaches are needed: understanding
intermediatestageofamergereventbetweentwospiralgalaxies. preciselyhowinteractionsmodifythepropertiesofgalaxiesand
thefateofthemergerremnants,andmeasuringthemergerhis-
(cid:63) Based on observations collected at the German-Spanish tory of different populations over cosmic time to estimate the
Astronomical Center, Calar Alto, jointly operated by the Max- integratedeffectofmergers.
Planck-InstitutfürAstronomie(MPIA)atHeidelbergandtheInstituto
deAstrofísicadeAndalucía(CSIC). Regarding the first approach, it is widely accepted today
(cid:63)(cid:63) The catalogues, probabilities, and figures of the ALHAMBRA that the major merging (the merger of two galaxies with sim-
closepairsdetectedinSect.5.1areavailableathttps://cloud.iaa. ilar masses, M2/M1 ≥ 1/4) of two spiral galaxies is an effi-
csic.es/alhambra/catalogues/ClosePairs cient mechanism to create new bulge-dominated, red-sequence
ArticlepublishedbyEDPSciences A53,page1of15
A&A576,A53(2015)
galaxies(Naabetal.2006;Rothberg&Joseph2006a,b;Hopkins
1.0
et al. 2008; Rothberg & Fischer 2010; Bournaud et al. 2011),
whilemajorandminormergershavebeenproposedasthemain
0.8
mechanism in the mass and size evolution of massive galaxies
(e.g.,Bezansonetal.2009;López-Sanjuanetal.2012).Inaddi- F 0.6
tion,whentheseparationr betweengalaxiesinclosepairsde- D
p
creases,thestarformationrate(SFR)isenhanced(Bartonetal. P
0.4
2000;Lambasetal.2003;Robainaetal.2009;Knapen&James
2009;Pattonetal.2011)andthemetallicitydecreases(Kewley
0.2
etal.2006;Ellisonetal.2008;Scudderetal.2012).
Regardingthesecondapproach,themergerhistoryofagiven 0.0
populationisestimatedbymeasuringitsmergerfraction f ,that 0.2 0.4 0.6 0.8 1.0
m z
is, the fraction of galaxies in a sample that undergoes a merg-
ing process, both by morphological criteria (highly distorted
galaxies are merger remnants, e.g., Conselice 2003; Conselice Fig.1. Probability distribution function (PDF) of an ALHAMBRA
et al. 2008; Cassata et al. 2005; De Propris et al. 2007; Lotz source (black solid line) with I = 22.8 and its Gaussian approach
et al. 2008, 2011; López-Sanjuan et al. 2009a,b; Jogee et al. (zp=0.329±0.147,reddashedline).Bothdistributionsarenormalised
totheirmaximumprobability.
2009;Bridgeetal.2010),orbyclose-pairstatistics(twogalax-
ies close in the sky plane, r ≤ rmax, and in redshift space,
p p
∆v ≤ 500kms−1,thatwillleadtoamerger,e.g.,LeFèvreetal. However, the previous methods have several shortcomings
2000;Pattonetal.2000,2002;Patton&Atfield2008;Linetal. thatshouldbeaddressed:
2004,2008;DeProprisetal.2005,2010;deRaveletal.2009;de
Raveletal.2011;López-Sanjuanetal.2011,2013;Tascaetal. – The PDFs of galaxies with a low signal-to-noise ratio are
2014). poorly approximated by a Gaussian function. We illustrate
Severaleffortshavebeenconductedintheliteraturetostudy this point in Fig. 1. The Gaussian approach of the PDF in
close companions in photometric surveys. Photometric surveys this example is zp = 0.329 ± 0.147, notably worse than
arelimitedbythe∆vcondition:The500kms−1differencetrans- the actual PDF that presents two main narrow peaks at
latesintoaredshiftdifferenceof|z −z | ≤ 0.0017(1+z),with z ∼ 0.33 and z ∼ 0.61. Several studies have proven that
1 2
thebestphotometricredshifts(z )fromcurrentbroad+medium- thePDFsarethebestapproachtodealwithphotometricred-
p
bandsurveysreachingaprecision∼0.01(1+z)(e.g.,Ilbertetal. shifts (e.g., Fernández-Soto et al. 2002; Cunha et al. 2009;
2009; Pérez-González et al. 2013; Molino et al. 2014). Next- Wittman2009;Myersetal.2009;Schmidt&Thorman2013;
generation large photometric redshift surveys will cover huge CarrascoKind&Brunner2014).
sky areas ((cid:38)5000 deg2) with broad-band filters, such as the – The luminosity, stellar mass, or star formation rate of a
DarkEnergySurvey(DES,grizY;Flaugher2012)andtheLarge source depend on its redshift. Even in the Gaussian ap-
Synoptic Survey Telescope (LSST, ugrizY; Ivezic et al. 2008), proach, previous studies assumed the properties of galaxies
andwithnarrow-bandfilters,suchastheJavalambre-Physicsof tobeconstantwithredshift,andtheysetthemtothevalues
the accelerated universe Astrophysical Survey (J-PAS, 56 opti- ofthebestphotometricredshiftsolution.Thisisacrudeap-
calfiltersof∼145Å;Benítezetal.2014),providingphotometric proximation that affects the sample selection as well as the
redshifts for hundreds of million sources. Thus, a suitable and luminosityandmassdifferencebetweengalaxypairs.
robustmethodologytoestimatethemergerfractionfromphoto- – Thecolourselectionisblurredbyphotometricerrors.When
metric close pairs is fundamental to exploit the current and the bluegalaxiesspillovertheredlocusandviceversa,thedif-
ambitiousfuturephotometricsurveys. ferencesbetweenthetwopopulationsdiminishforthegalax-
ieswithalowsignal-to-noiseratio.
The most extended approach to explore the redshift condi-
tionisestimatingthenumberofrandomcompanions.Itcanbe
Weheresolvetheseshortcomingsbygeneralisingandextending
estimated by either searching for close companions in random
the LS10 methodology. The new method (i) uses the full PDFs
positions in the sky, providing the number of expected com-
ofthesourcesinredshiftspace;(ii)includesthevariationinthe
panions found by chance in a given catalogue (e.g., Kartaltepe
luminosityofthesourceswithzinthesampleselectionandlu-
etal.2007;Williamsetal.2011;Mármol-Queraltóetal.2012;
minosityratioconstraint;and(iii)splitsindividualPDFsintored
Xu et al. 2012; Díaz-García et al. 2013; Ruiz et al. 2014), or
andbluespectraltemplatestoreliableattendtothecolourselec-
integrating the observed luminosity or mass function over the
tions.Wetakeadvantageoftheuniquedesign,depth,andphoto-
searchareaaroundthecentralgalaxy(e.g.,LeFèvreetal.2000;
metricredshiftaccuracyoftheAdvanced,Large,Homogeneous
Rawat et al. 2008; Hsieh et al. 2008; Bluck et al. 2009; Bundy
Area, Medium-Band Redshift Astronomical (ALHAMBRA1)
et al. 2009). Then, the observed number of companions is de-
photometric survey (Moles et al. 2008) to develop and test our
contaminated by the random one to obtain the number of real
newmethodology.
companions.
The paper is organised as follows: in Sect. 2 we present
A probabilistic approach was presented in López-Sanjuan the ALHAMBRA survey and its photometric redshifts. We de-
etal.(2010,LS10hereafter)todealwiththeredshiftcondition. velopthemethodologytomeasureaccuratemergerfractionsby
Theyassumedthattheprobabilitydistributionfunction(PDF)of PDF analysis of photometrically close pairs in Sect. 3. We test
thephotometricredshiftsiswelldescribedbyaGaussian.Then, our new methodology by comparison with spectroscopic stud-
they estimated the overlap between the PDFs of close galaxies ies in Sects. 4 and 5, and in Sect. 6 we summarise our work
intheskyplanetoderivethenumberofpairsperclosesystem. and present our conclusions. Throughout this paper we use a
In this approach, each system has a probability of being a real
closepair. 1 http://alhambrasurvey.com
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C.López-Sanjuanetal.:TheALHAMBRAsurvey.Accuratemergerfractionsderivedfromphotometricallyclosepairs
Table1.ALHAMBRAsurveyfields.
Field Overlapping RA Dec Sub-fields/area
name survey (J2000) (J2000) (#/deg2)
ALHAMBRA-2 DEEP2(Newmanetal.2013) 013016.0 +041540 8/0.377
ALHAMBRA-3 SDSS(Aiharaetal.2011) 091620.0 +460220 8/0.404
ALHAMBRA-4 COSMOS(Scovilleetal.2007) 100000.0 +020511 4/0.203
ALHAMBRA-5 GOODS-N(Giavaliscoetal.2004) 123500.0 +615700 4/0.216
ALHAMBRA-6 AEGIS(Davisetal.2007) 141638.0 +522450 8/0.400
ALHAMBRA-7 ELAIS-N1(Rowan-Robinsonetal.2004) 161210.0 +543015 8/0.406
ALHAMBRA-8 SDSS(Aiharaetal.2011) 234550.0 +153505 8/0.375
Total 48/2.381
standard cosmology with Ωm = 0.307, ΩΛ = 0.693, H0 = mergerfractionstudiesasdemonstratedbyLópez-Sanjuanetal.
100hkms−1Mpc−1,andh = 0.678(PlanckCollaborationXVI (2014).
2014). Magnitudes are given in the AB system (Oke & Gunn
1983).
2.1. BayesianphotometricredshiftsinALHAMBRA
WereliedontheALHAMBRAphotometricredshiftstocompute
the merger fraction. The photometric redshifts used throughout
2. ALHAMBRAsurvey
werefullypresentedandtestedinMolinoetal.(2014),andwe
summarisetheirprincipalcharacteristicsbelow.
The ALHAMBRA survey provides a photometric data set
The photometric redshifts of ALHAMBRA were estimated
over 20 contiguous, equal-width (∼300 Å), non-overlapping,
with BPZ2.0, a new version of the Bayesian Photometric
medium-band optical filters (3500–9700 Å) plus 3 standard
Redshift (BPZ; Benítez 2000) estimator. This is an SED-fitting
broad-bandnear-infrared(NIR)filters(J,H,andK )overeight
s methodbasedonaBayesianinference,whereamaximumlike-
differentregionsofthenorthernsky(Molesetal.2008).Thesur-
lihoodisweightedbyapriorprobability.Thelibraryof11SEDs
veyhastheaimofunderstandingtheevolutionofgalaxiesalong
that comprises four ellipticals (E), one lenticular (S0), two spi-
cosmic time by sampling a large enough cosmological fraction
rals (S), and four starbursts (SB), and the prior probabilities
oftheUniverse,forwhichreliablespectralenergydistributions
used by BPZ2.0 in ALHAMBRA are detailed in Benítez (in
(SEDs)andprecisephotometricredshiftsareneeded.Thesimu-
prep.).ALHAMBRAreliedontheColorProsoftware(Coeetal.
lationsofBenítezetal.(2009),whichrelatetheimagedepthand
2006) to perform PSF-matched aperture-corrected photometry,
accuracy of the photometric redshifts to the number of filters,
whichprovidedbothtotalmagnitudesandisophotalcoloursfor
suggestedthatthefiltersetchosenforALHAMBRAcanachieve
the galaxies. In addition, an homogeneous photometric zero-
aphotometricredshiftprecisionthatisthreetimesbetterthana
point recalibration was made using either spectroscopic red-
classicalsetof4–5opticalbroad-bandfilters.Thisexpectationis
shifts (when available) or accurate photometric redshifts from
confirmedbytheresultspresentedinMolinoetal.(2014).The
emission-line galaxies (Molino et al. 2014). Sources were de-
finalsurveyparametersandscientificgoals,aswellasthetech-
tected in a synthetic F814W filter image, noted I in the fol-
nical properties of the filter set, were described by Moles et al. lowing, defined to resemble the HST/F814W filter. The areas
(2008). The survey has collected its data for the 20+3 optical- oftheimagesaffectedbybrightstarsandthosewithlowerexpo-
NIR filters with the 3.5 m telescope at the Calar Alto observa-
suretimes(e.g.,theedgesoftheimages)weremaskedfollowing
tory, using the wide-field camera Large Area Imager for Calar
Arnalte-Muretal.(2014).Thetotalareacoveredbythecurrent
Alto (LAICA) in the optical and the OMEGA–2000 camera in
ALHAMBRAdataaftermaskingis2.38deg2(Table1).Finally,
theNIR.Thefullcharacterisation,description,andperformance a statistical star/galaxy separation is encoded in the variable
oftheALHAMBRAopticalphotometricsystemwerepresented
Stellar_Flag of the ALHAMBRA catalogues, and we kept
inAparicio-Villegasetal.(2010).Asummaryoftheopticalre-
ALHAMBRAsourceswithStellar_Flag≤0.5asgalaxies.
ductioncanbefoundinCristóbal-Hornillosetal.(inprep.),the
The photometric redshift accuracy, as estimated by com-
NIRreductionisreportedinCristóbal-Hornillosetal.(2009).
parison with ∼7200 spectroscopic redshifts (z ), is encoded in
s
TheALHAMBRAsurveyhasobservedeightwell-separated thenormalisedmedianabsolutedeviation(NMAD)ofthepho-
regions of the northern sky. The wide-field camera LAICA tometric versus spectroscopic redshift distribution (Ilbert et al.
has four chips with a 15(cid:48) × 15(cid:48) field of view per chip 2006;Brammeretal.2008),
(0.22 arcsec/pixel). The separation between chips is also 15(cid:48).
Thus,eachLAICApointingprovidesfourseparatedareasinthe (cid:18)|δ −median(δ )|(cid:19)
σ =1.48×median z z , (1)
sky.Currently,sixALHAMBRAregionscomprisetwoLAICA NMAD 1+z
s
pointings.Inthesecases,thepointingsdefinetwoseparatestrips
in the sky. In our study, we assumed the four chips in each where δ = z − z . The fraction of catastrophic outliers η is
z p s
pointing to be independent sub-fields. The photometric cali- defined as the fraction of galaxies with |δ |/(1+z ) > 0.2. In
z s
bration of the field ALHAMBRA-1 is currently ongoing, and thecaseofALHAMBRA,σ =0.011forI ≤22.5galaxies
NMAD
the fields ALHAMBRA-4 and ALHAMBRA-5 comprise one withafractionofcatastrophicoutliersofη = 2.1%.Wereferto
pointing each (see Molino et al. 2014, for details). We sum- Molinoetal.(2014)foramoredetaileddiscussion.
marise the properties of the seven ALHAMBRA fields used in Theoddsqualityparameter,notedO,isaproxyforthepho-
Table1.Attheend,thedataweusedcomprise48sub-fieldsof tometricredshiftreliabilityofthesourcesandisalsoprovidedby
∼180 arcmin2 each, which can be assumed as independent for BPZ2.0. The O parameter is defined as the redshift probability
A53,page3of15
A&A576,A53(2015)
10 E/S0 1.0
]
˚A S/SB
/
0.8
2
m 1
/c F 0.6
s D
/ 0.1
g P
r 0.4
e
[
Fλ 0.01 0.2
103 104 105 0.0
0.2 0.4 0.6 0.8 1.0
λ[A˚] z
Fig.2. Spectral energy distributions of the red (T = E/S0) and blue 1.0
(T =S/SB)templatesinBPZ2.0.Thetemplatesarenormalisedatλ=
4000Åforclarity.(Colourversiononline.) 0.8
F
enclosedona±K(1+z)regionaroundthemainpeakinthePDF D 0.6
of the source, where the constant K is specific for each photo- P
metricsurvey.Molinoetal.(2014)foundthatK =0.0125isthe R z 0.4
optimalvalueforALHAMBRAsincethisistheexpectedaver-
0.2
agedaccuracyformostgalaxiesinthesurvey.Thus,O ∈ [0,1],
and it is related to the confidence of the photometric redshifts,
0.0
makingitpossibletoderivehigh-qualitysampleswithbetterac- 0.2 0.4 0.6 0.8 1.0
z
curacy and a lower rate of catastrophic outliers. For example,
anO≥0.5selectionforI ≤22.5galaxiesyieldsσ =0.009
NMAD
and η = 1%, while σNMAD = 0.006 and η = 0.8% if galaxies Fig.3.Partialprobabilitydistributionfunctions(toppanel)andthecu-
with O ≥ 0.9 are selected (see Molino et al. 2014, for further mulativedistributionfunctions(bottompanel)ofthesourcepresented
details).López-Sanjuanetal.(2014)setO ≥ 0.3astheoptimal inFig.1.TheblacksolidlinesmarkthetotalPDF,thereddashedlines
selectionformergerfractionstudiesinALHAMBRA.Westudy mark the red templates, PDFred = PDF(z,E/S0), and the blue dotted
theimpactofthisOselectioninSect.3.3.1. lines mark the blue templates, PDFblue = PDF(z,S/SB). This galaxy
countsas0.65redand0.35blueintheanalysis(bottompanel).
2.2. ProbabilitydistributionfunctionsinALHAMBRA
In practice, the red templates have T ∈ [1,5.5] and the blue
This section is devoted to the description of the PDFs of the templates have T ∈ (5.5,11] in the ALHAMBRA catalogues.
ALHAMBRA sources. The probability of a galaxy i to be lo- Thisisamajorstepforwardinthemethodology,whichisableto
cated at redshift z and have a spectral type T is PDFi(z,T). reliablyworkwithcoloursegregationswithoutanypre-selection
This probability function is the posterior provided by BPZ2.0. ofthesources(Fig.3).
Theprobabilityofthegalaxyitobelocatedatredshiftzisthen The B-band absolute magnitude of a galaxy with observed
(Fig.1) magnitudeI =20andspectraltypeT thatislocatedatredshiftz
(cid:90) isnotedasM20(z,T),whichisalsoprovidedbyBPZ2.0.Weare
PDFi(z)= PDFi(z,T)dT. (2) interestedinMB Basafunctionofz.WeestimateMB(z)as
(cid:82)
Moreover, the total probability of the galaxy i of being located M20(z,T)×PDF(z,T)dT
atz1 ≤z≤z2is MB(z)= B (cid:82) +(I−20). (6)
(cid:90) z2 PDF(z,T)dT
P (z ,z )= PDF (z)dz. (3)
i 1 2 i TheaverageB-bandabsolutemagnitudeofagalaxyisthen
z1
ThedistributionfunctionPDF(z,T)isnormalisedtoonebydef- (cid:82)
M (z)×PDF(z)dz
inition,meaningthatthereisonegalaxyspreadovertheredshift (cid:104)MB(cid:105)= B(cid:82) . (7)
andtemplatespaces.Formally, PDF(z)dz
(cid:90) (cid:90)(cid:90)
1= PDF (z)dz= PDF (z,T)dTdz. (4) Thanks to the probability functions defined in this section, we
i i
are able to statistically use the output of current photometric
The definition of red and blue galaxies takes advantage of the redshift codes without losing information. This is important to
profuse information encoded in the PDFs. Instead of selecting perform accurate and robust studies of the merger fraction and
galaxiesaccordingtotheirobservedcolourortheirbestspectral theenvironmentwithphotometricredshifts.
template, we split each PDF into “red” templates (T = E/S0),
notedPDFred,and“blue”templates(T = S/SB),notedPDFblue
2.3. Sampleselection
(Fig.2).Formally,
Throughoutthispaper,wefocusouranalysisonthegalaxiesin
PDF (z) = PDFred(z)+PDFblue(z)
i i i the ALHAMBRA first data release2. This catalogue comprises
(cid:90) (cid:90)
= PDF (z,E/S0)dT + PDF (z,S/SB)dT. (5)
i i 2 http://cloud.iaa.es/alhambra/
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C.López-Sanjuanetal.:TheALHAMBRAsurvey.Accuratemergerfractionsderivedfromphotometricallyclosepairs
∼500 k sources and is complete (5σ, 3(cid:48)(cid:48) aperture) for I ≤ 24.5 primarysample.Withthepreviousdefinitions,themergerfrac-
galaxies(Molinoetal.2014). tionis
We performed our study in a given redshift range z ∈
[zmin,zmax) and in samples selected with B-band luminosity. To f = Np, (10)
define the galaxy samples under study, we first estimated the m N
1
B-bandselectionfunction,S(z),as
where N is the number of sources in the primary sample and
(cid:40) 1
S(z)= 1, if MBbri < MB(z)+Qz≤ MBsel, (8) Np the number of close pairs. This definition applies to spec-
0, otherwise, troscopic volume-limited samples, but we relied on photomet-
ric redshifts to compute f . In the following, we expand the
m
whereM (z)istheB-bandluminosityofthegalaxyfromEq.(6), methodologypresentedbyLS10touseanarbitraryPDFinred-
B
thetermQzaccountsfortheevolutionoftheluminosityfunction shiftspaceandtotakeintoaccountthevariationofgalaxyprop-
withredshift(e.g.,Linetal.2008), Msel istheselectionmagni- ertieswithz.
B
tudeofthesample,and Mbri imposesamaximumluminosityin
B
thestudy.WeassumedMbri =−22toavoidthedifferentcluster- 3.2. PDFanalysisofphotometricclosepairs
B
ingpropertiesofthebrightestgalaxies(Pattonetal.2000,2002;
Lin et al. 2008). Then, we kept as galaxies in the sample the Inthissection,wedetailthestepsofcomputingthemergerfrac-
sourceswith tion in photometric redshift surveys. The primary and the sec-
ondarysamplesweredefinedaccordingtothe B-bandselection
(cid:90) zmaxPDFi(z)×Si(z)dz>0. (9) fsuanmcptiloenanindtSrod(uzc)efdorintheSescetc.o2n.d3a,rynostaemdpSle1.(z) for the primary
2
zmin
The samples we studied comprise galaxies brighter than MB = 3.2.1. Initiallistofprojectedcompanions
−19 at the redshift ranges of interest. Given the depth of
the ALHAMBRA data, these samples are volume-limited, and Todefinetheinitiallistofprojectedclosecompanions,weesti-
thereforenocompletenesscorrectionisneeded. mated the maximum angular separation possible in the first in-
We note that Eq. (8) defines a B-band luminosity selection, stance,notedθtop.Thisangularseparationisdefinedas
but the selection function can be defined in the same way for
mass-selected samples if the stellar mass M (z) of the sources rmax
isknown. (cid:63) θtop = d (pz )· (11)
A min
Then, for each galaxy in the primary sample, we searched for
3. Measuringthemergerfractioninphotometric galaxies in the secondary sample with θ ≤ θ . We ended this
top
samplesbyPDFanalysis first step with a list of systems composed of a principal source
anditsprojectedcompanions.
In this section, we first recall the methodology to compute the
Toillustratetheperformanceofourmethodandforthesake
merger fraction from spectroscopically close pairs (Sect. 3.1)
ofclarity,wepresentaparticularALHAMBRAsystemasanex-
and then extend the method to the photometric redshift regime
ampleinthefollowing.Wedefinedtheprimarysamplewithab-
(Sects. 3.2 and 3.4). The statistical weights devoted to correct-
ingfortheselectioneffectsinthephotometriccasearedefinedin soluteB-bandmagnitude MBse,1l =−20andthesecondarysample
Sect.3.3.Finally,theoutputofthecodeisdetailedinSect.3.5. with Msel = −18.5, and assumed an evolution in the selection
B,2
of Q = 1.1. We used rmin = 10 h−1 kpc as the smallest search
p
radius,rmax =50h−1 kpcasthelargestsearchradius,z =0.4
3.1. Mergerfractioninspectroscopicsamples p min
asthelowestredshift,andz =1asthehighestredshift.These
max
The linear distance between two sources can be obtained from parameters are similar to those used in Sect. 5. The principal
their projected separation, r = θd (z ), and their rest-frame galaxy of the “system zero” is located at α = 188.7021 and
p A 1 1
relativevelocityalongthelineofsight,∆v=c|z −z |/(1+z ), δ = 61.9441. We found θ = 13.32(cid:48)(cid:48) with the assumed pa-
2 1 1 1 top
where z and z are the redshift of the central (the most lumi- rameters.Wesearchedforcompanionsinthesecondarysample
1 2
nous galaxy in the pair) and the satellite galaxy, respectively; andfoundthreeprojectedcompanions(Fig.4).Wenotethatthe
θ is the angular separation, in arcsec, of the two galaxies companionsaandbarealsointheprimarysample.
on the sky plane; and d (z) is the angular diameter distance,
A
in kpcarcsec−1, at redshift z. Two galaxies are defined as a
close pair if rmin ≤ r ≤ rmax and ∆v ≤ ∆vmax. To ensure 3.2.2. RedshiftprobabilityZ
p p p
clearly de-blended sources and to minimise colour contamina-
Intheinitiallistdefinedabove,agalaxycanhavemorethanone
tioninground-basedsurveys,theminimumsearchradiusisusu-
projected companion. In that case, we took each possible pair
ally rpmin ≥ 5 h−1 kpc. With rpmax ≤ 100 h−1 kpc and ∆vmax ≤ separately,thatis,ifthecompaniongalaxiesa,b,andcareclose
500 kms−1,50% to 70%of theselected closepairs willfinally totheprincipalgalaxyX(Fig.4),westudiedthecentral-satellite
merge (Patton et al. 2000; Patton & Atfield 2008; Bell et al. pairs X–a, X–b, and X–c independently. This defines the initial
2006;Jianetal.2012). list of projected close pairs. We note that if the galaxies X and
To compute the merger fraction, one defines a primary and a are both in the primary sample, the close pairs X–a and a–X
asecondarysample.Theprimarysamplecomprisesthepopula- couldbepresentintheinitiallist.Wecleanedtheinitiallistfrom
tionofinterestandonelooksforthosegalaxiesinthesecondary duplicatesbeforestartingthestudyintheredshiftspace,keeping
sample that fulfil the close pair criterion for each galaxy of the thegalaxywithlower(cid:104)M (cid:105)asthecentralgalaxyinthepair.
B
A53,page5of15
A&A576,A53(2015)
15 1.0
((aa))
0.8 NNzz ==00..7722
10
F
0.6
D
P
5
z 0.4
R
)
00( 0.2
0
δ
∆ 0.0
0.2 0.4 0.6 0.8 1.0
−5 z
1.0
((bb))
−10
0.8 NNzz ==00..0011
F
0.6
−15 D
−15 −10 −5 0 5 10 15 P
∆ α (00) z 0.4
R
Fig.4. Postage stamp of a particular ALHAMBRA system composed 0.2
ofaprincipalsource(redcross)anditsthreeprojectedcompanionsin
theskyplane(orangeletters)intheIband.Northisupandeasttothe 0.0
left. The axes show the right ascension (α) and declination (δ) offset 0.2 0.4 0.6 0.8 1.0
z
with respect to the position of the principal source (α = 188.7021,
1
δ = 61.9441).Theredcirclemarkstheangularseparationinthesky 1.0
1
planeforrmax=50h−1kpcatz =0.4,θ =13.32(cid:48)(cid:48). ((cc))
p min top
0.8 NNzz ==00
F
0.6
Foreachprojectedclosepairintheinitiallist,wedefinedthe D
redshiftprobabilityfunctionZas P
z 0.4
R
2×PDF (z)×PDF (z) PDF (z)×PDF (z)
Z(z)= 1 2 = 1 2 , (12)
PDF (z)+PDF (z) N(z) 0.2
1 2
where
0.0
0.2 0.4 0.6 0.8 1.0
PDF (z)+PDF (z) z
N(z)= 1 2 · (13)
2
Fig.5. Cumulative distribution function of the principal galaxy (red
We multiplied the PDFs of the central galaxy (PDF ) and its
1 solid line), its projected companions (blue dashed lines), and the
satellite (PDF ) to obtain the shape of the function Z, and we
2 Z function of the close pairs (purple dotted lines). The letter in each
normalised by the number of potential pairs (two galaxies per
(cid:82) panelreferstothecompaniongalaxyinFig.4.Thenumberofpairsin
pair)ateachredshift,notedN(z).Wenotethat N(z)dz=1by eachsystem,N,islabelledinthepanels.
z
construction. This normalisation is crucial in the methodology
becauseitbringstheclose-pairsystemstoacommonscale,with
Z(z)beingthenumberofclosepairsinthesystematredshiftz.
at the scale of the velocity condition, and a limited impact on
Thus,theintegralofthefunctionZprovidesthetotalnumberof
the results is expected. We find that the convolution modifies
pairsinthesystem,N .Weonlykeptprojectedclosepairswith
N =(cid:82) Z(z)dz>0inzthesubsequentanalysis. themeasuredmergerfractionsbylessthan1%,confirmingour
z initial guess, but increases the computational time by a factor
We note that the velocity condition ∆v ≤ 500 km s−1 used
of 100. The convolution with a top-hat function can therefore
in spectroscopic studies (Sect. 4) is not included in the defini-
beomittedinALHAMBRA,butwouldbeimportantforfuture
tionofthefunctionZ.Toaccountforthevelocitycondition,we
medium-band photometric surveys, such as J-PAS, which will
should convolve the PDFs of the galaxies with a top-hat func- reachaprecisionof∼1000kms−1.
tion.Formally,
The cumulative PDFs and the derived Z functions for the
(cid:90) three projected close pairs in the “system zero” are shown in
PDF∆v(z)= W(z,∆vmax)×PDF(z(cid:48))dz(cid:48), (14) Fig.5.ThePDFofthecentralgalaxyisthesameinallthepan-
els, with the best photometric redshift z = 0.604. The first
p,1
whereWisatop-hatfunctionofwidth2∆v atredshiftz.Then, companion,panela,hasaphotometricredshiftz = 0.630and
max p,2
we used the PDF∆v functions instead of the original PDFs in the overlap of the PDFs is evident, with Nz = 0.72. The sec-
Eq. (12). The accuracy of the ALHAMBRA photometric red- ondcompanion,panelb,hasz = 0.350andthePDFsoverlap
p,2
shifts is ∼3000 kms−1, higher that the typical ∆v condition. marginally,withN = 0.01.Despitethelowprobabilityofthis
max z
This implies that the ALHAMBRA PDFs are already smooth closepair,wekeptitinthesubsequentanalysisbecauseN >0.
z
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C.López-Sanjuanetal.:TheALHAMBRAsurvey.Accuratemergerfractionsderivedfromphotometricallyclosepairs
20 secondpair,panelb,hasθ =10.46(cid:48)(cid:48) andfulfilstheangularcon-
ditionintworedshiftranges,0.071 < z < 0.663andz > 4.099
(outside the plotted redshift range). We focused here on z < 1,
15
but the method has been developed to study close pairs in the
) fullredshiftspace.
00( 10
θ
3.2.4. PairselectionmaskMpair
5
Inthissectionwedefinethepairselectionmask,notedMpair(z).
(a) The pair selection mask simultaneously imposes three condi-
0 tions: the selection of the primary sample, the selection of the
0.2 0.4 0.6 0.8 1.0
companionsample,andtheluminosityratiobetweenthegalax-
z
iesinthepair.Thelastconditionisneededtodefinemajorand
minorcompanions.Formally,thegeneralformofthepairselec-
20
tionmaskis
00() 1105 Mpair(z)=10,, oifthM∆MeMrBbBbwrriiBi<<s(ez,M)M≤BB,,1−2((2zz)).5++loQQgzz10≤≤µ,MMBsBsee,,1l2l,, (16)
θ
where ∆M (z) = |M (z) − M (z)| and µ = L /L is
5 the B-bandBluminosityBr,a2tio. TypiBc,a1lly, µ ≥ 1/4 (∆MB,2 ≤B,11.5)
B
(b) defines major mergers, and µ < 1/4 defines minor mergers
0 (e.g., López-Sanjuan et al. 2011). We recall that we assumed
0.2 0.4 0.6 0.8 1.0 Mbri = −22 (Sect. 2.3). We note that Eq. (16) focuses on a
z B
B-bandluminosityselection,butthepairselectionmaskcanbe
defined in the same way for mass-selected pairs if the stellar
Fig.6. Angular separation θ as a function of redshift. The solid lines
massM (z)ofthesourcesisknown.
markthemeasuredangularseparationoftheclosepairs,θ = 7.36(cid:48)(cid:48) in (cid:63)
panel a) and θ = 10.46(cid:48)(cid:48) in panel b). The letter in each panel refers The MB(z)functionoftheprincipalgalaxyanditscompan-
to the companion galaxy in Fig. 4. The grey area marks the angular ionsinthe“systemzero”areshowninFig.7,thederivedlumi-
separationsbetweenθ (z)andθ (z)(reddashedlines).Thevertical nosityratiosinFig.8.Weassumedµ=1/4toselectmajorcom-
min max
dashed lines mark the redshift range under study, 0.4 ≤ z < 1. The panions.Thefirstcompanion,panelainbothfigures,isfainter
redshiftsatwhichtheangularmaskMθisequaltoonearemarkedwith than the central galaxy at each redshift with ∆M ∼ 0.6. This
B
thethickgreenline. value is higher than the luminosity difference derived from the
best-fitsolution,∆M =0.47.Wenotethattheprincipalgalaxy
B
fulfilstheprimaryselectionatz>0.52.Thesecondcompanion,
Thethirdcompanion,panelc,hasz =0.988andthePDFsdo
p,2 panel b in both figures, is brighter than the principal galaxy at
notoverlap,withN =0.Thus,wediscardthisclosepairinthe
z eachredshiftwith∆M ≥ 1.2,farfromthebest-fitsolutionra-
following. B
tio, ∆M = 0.22. The principal galaxy has a lower (cid:104)M (cid:105) than
B B
thecompanionandwasassumedtobethecentralgalaxyofthe
3.2.3. AngularmaskMθ pair(Sect.3.2.2).However,thestudyof M (z)revealsthatthe
B
companionisindeedthecentralgalaxy,andtheprincipalgalaxy
The function Z defined in the previous section only accounts
of the “system zero” its satellite. In consequence, the compan-
for the overlap of the central and the satellite galaxy probabili-
ion has to fulfil the primary selection and the principal galaxy
tiesinredshiftspace.However,thedefinitionofaclosepairalso
thesecondaryselectioninEq.(16).Thiscaseillustratesthepos-
includesconditionsontheprojecteddistancer andonthelumi-
p siblecomplexityofthesystemsunderstudyandtheimportance
nosityofthesources.Thus,thenextstepwastodefineredshift
ofanalysingthephysicalvariablesintheredshiftspace.
masks, noted M(z), to account for the other conditions of in-
terest. These masks complement the function Z and are equal
to one at redshifts where a particular condition is fulfilled and 3.2.5. Pairprobabilityfunction
equaltozerootherwise.
Finally,eachclose-pairsystemhasanassociatedpairprobability
The first mask that we computed is the angular mask Mθ.
functiondefinedas
Thefunctiond changeswithredshift,whichmeansthataclose
A
pairintheskyplaneatzmin(Sect.3.2.1)mightnotbeaclosepair PPF(z)=Z(z)×Mθ(z)×Mpair(z), (17)
at higher redshifts. Thus, we estimated the functions θ (z) =
min
rpmin/dA(z)andθmax(z)=rpmax/dA(z),andimposedthecondition whereZistheredshiftprobabilityfunction(Sect.3.2.2),Mθ is
θmin(z)≤θ≤θmax(z).Formally, the angular mask (Sect. 3.2.3), and Mpair is the pair selection
(cid:40) mask (Sect. 3.2.3) of the system. The PPF is a new probability
Mθ(z)= 1, ifθmin(z)≤θ≤θmax(z), (15) function3 that encodes the relevant information about the close
0, otherwise. pairs in the survey. The PPFs are used to define the number of
Themeasuredangularseparationoftheclosepairsinthe“sys- 3 Formally, the PPF is not a probability density function because its
tem zero” are shown in Fig. 6. The first pair, panel a, has normalisationisdifferentfromone.However,theintegralofthePPFisa
θ = 7.36(cid:48)(cid:48) and fulfils the angular condition at z > 0.106. The probability.Thereforewekeeptheattributeprobabilityinthefollowing.
A53,page7of15
A&A576,A53(2015)
−23
(a) (a)
−22 1.5
−21
B
B M 1.0
M
−20
∆
−19 0.5
−18
0.0
0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1.0
z z
−23
(b) (b)
−22 1.5
−21
B
B M 1.0
M
−20
∆
−19 0.5
−18
0.0
0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1.0
z z
Fig.7.B-bandabsolutemagnitudeMBasafunctionofredshift.Thered Fig.8.Absolutemagnitudedifferencebetweenthegalaxiesinthepair,
andbluesolidlinesmarktheabsolutemagnitudeoftheprincipalandthe ∆M (z)=|M (z)−M (z)|,asafunctionofredshift(thickgreenline).
B B,2 B,1
companiongalaxy,respectively,atredshiftswithPDF(z)>0.Theletter TheletterineachpanelreferstothecompaniongalaxyinFig.4.The
ineachpanelreferstothecompaniongalaxyinFig.4.Thedarkgrey dashed lines mark the major merger limit, ∆M = 1.5. The red solid
B
areamarkstheselectionoftheprimarysample,andthetwogreyareas linesmarkthe∆M computedwiththeabsolutemagnitudesestimated
B
mark the selection of the secondary sample (i.e., the primary sample atthebestphotometricredshifts.
is included in the secondary one). The vertical dashed lines mark the
redshiftrangeunderstudy,0.4≤z<1.Theredshiftsatwhichthepair
selection mask Mpair is equal to one are marked with the thick green We defined the odds sampling rate (OSR) as the ratio of
line.(Colourversiononline.) galaxieswithO≥0.3withrespecttothetotalnumberofgalax-
ies (i.e., those with O ≥ 0). The OSR mainly depends on the
I-band magnitude because the quality of the photometric red-
shifts decreases according to the signal-to-noise ratio. We used
pairs (Sect. 3.4), but are also crucial for subsequent studies of the redshift information encoded in the PDFs to estimate the
properties of galaxies with a close companion, such as the star OSRinourrangeofinterest.Formally,theoddssamplingrate
formation rate. We will explore the potential of the PPFs in a oftheALHAMBRAsub-field jisestimatedas
futurework. (cid:80) (cid:82)zmaxPDFj(z)dz
OSRj = (cid:80)i,O≥0.3(cid:82)zzmmianxPDFji(z)dz , (18)
3.3. Correctionforselectioneffects i,O≥0 zmin i
ThePPFsdefinedintheprevioussectionaremainlyaffectedby whereiindexeseverygalaxyinthesub-field j.
twoselectioneffectsinALHAMBRA:theselectionintheodds The current ALHAMBRA release comprises 48 sub-fields.
ToestimatetheglobalOSRinALHAMBRA,wecomputed
parameter(Sect.3.3.1)andtheincompletenessinthesearchvol-
umeneartheimageboundaries(Sect.3.3.2).Inthenextsections, (cid:80) wj (cid:80) (cid:82)zmaxPDFj(z)dz
wseeledcetifionneetffheecststa.tisticalweightsdevotedtocorrectingforthese OSRALH = (cid:80)j wdejn (cid:80)i,O≥0.3(cid:82)zzmmianxPDFji(z)dz , (19)
j den i,O≥0 zmin i
wherewj istheinverseofthenumberdensityinthesub-field j.
3.3.1. oddssamplingrate den
ThisdensityweightavoidstheglobalOSRtobedominatedby
thedensestALHAMBRAsub-fields.
Followingspectroscopicstudies,weshouldcorrecttherawPPFs
for the selection effects in our sample. As shown by Molino We computed the OSRALH in bins of 0.5 magnitudes in the
I band at 0.4 ≤ z < 1 and interpolated the results to obtain
etal.(2014),aselectionintheOparameterensureshigh-quality
OSR (I).Wecheckedthatourinterpolatedfunctiondescribes
photometric redshifts and a low rate of catastrophic outliers. ALH
the OSR properly estimating it in bins of 0.1 magnitudes
López-Sanjuan et al. (2014) set O ≥ 0.3 as the optimal selec- ALH
(Fig.9).Finally,wedefinedtheoddsweightofthegalaxyias
tionformergerfractionstudiesinALHAMBRA.Ifthegalaxies
withO < 0.3areincludedinthesamples,theprojectioneffects 1
wi = · (20)
becomestrongandthemergerfractionisoverestimated. osr OSR (I)
ALH i
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1.0 Table2.ALHAMBRAclose-paircatalogue.
0.9
0.8 Column Description
R 0.7 PID Identificationnumberofthepair
S ID1 ALHAMBRAIDoftheprincipalgalaxy
0.6
O ID2 ALHAMBRAIDofthecompaniongalaxy
0.5 RA1 Rightascensionoftheprincipalgalaxy
Dec1 Declinationoftheprincipalgalaxy
0.4
RA2 Rightascensionofthecompaniongalaxy
0.3 Dec2 Declinationofthecompaniongalaxy
17 18 19 20 21 22 23 24 25 theta Angularseparation(arcsec)
z1 Bestphotometricredshiftoftheprincipalgalaxy
I
z2 Bestphotometricredshiftofthecompaniongalaxy
PPF Integratedpairprobabilityfunction
Fig.9.Oddssamplingrate(OSR)inALHAMBRAasafunctionofthe
PPFw IntegratedPPFcorrectedforselectioneffects
I-bandmagnitude.DotsaretheOSRestimatedat0.4≤z<1inbinsof
I1 F814Wmagnitudeoftheprincipalgalaxy
0.1magnitudes.Thesolidlineisthefunctionalparametrisationofthe
I2 F814Wmagnitudeofthecompaniongalaxy
OSRusedinthepaper.
wosr1 Oddsweightoftheprincipalgalaxy
wosr2 Oddsweightofthecompaniongalaxy
Theoddsweightonlydependsonthe I-bandmagnitudeofthe warea Averageareaweightofthepair
galaxy,andwecheckedthatitslightlydependsonredshiftinour MB1 M oftheprincipalgalaxyatz1
B
rangeofinterest. MB2 MBofthecompaniongalaxyatz2
(cid:80)
3.3.2. Bordereffectsintheskyplane number of close pairs and Ni the number of primary galax-
i 1
ies. To estimate the observational error of f , noted σ , we
m f
When we search for a primary source companion, we define a usedthejackknifetechnique(Efron1982).Wecomputedpartial
volumeintheskyplane-redshiftspace.Iftheprimarysourceis standard deviations for each system k, δ , taking the difference
k
neartheboundariesofthesurvey,afractionofthesearchvolume between the measured f and the same quantity after remov-
liesoutsideoftheeffectivevolumeofthesurvey.Wedefinedthe ing the kth pair from themsample, fk, such that δ = f − fk.
m k m m
areaweightofaclosepairsystemas For a redshift range with N systems, the variance is given by
p
σ2 =[(N −1)(cid:80) δ2]/N .
w (z)= 1 , (21) f p k k p
area f (z)
area
3.5. Outputofthecode
where f isthefractionofthesearchareathatiscoveredbythe
area
ALHAMBRAsurvey.Thesearchareaisaringcentredat(α ,δ ) Inadditiontothemergerfraction,thedevelopedcodealsopro-
1 1
anddefinedbyrmin andrmax.Thesearcharea,andthereforethe videsvaluableoutputsforfuturestudies.Thecodecreatesthree
p p
areaweight,dependsonredshiftbecauseofthevariationofthe files:
angulardiameterdistanced withz.
A – Theclosepaircatalogue.Itsummarisesthemainproperties
of the pairs, as shown in Table 2. The reported values are
3.3.3. Pairweightw eitherintegratedoverz andz orthevaluesforthebest
pair min max
photometricredshift.However,weencouragetheuseofthe
Foreachobservedclosepairwedefinedthepairweightas
PDFsandthePPFsasoutlinedthroughoutthepaper.
w (z)=w ×w ×w (z), (22) – The close pair probabilities. The relevant merger probabil-
pair osr,1 osr,2 area ities of the systems listed in the close-pair catalogue are
wherewosr,1 = wosr(I1)istheoddsweightofthecentralgalaxy, storedinahdf5file.WereportthePPFandthewpairofeach
w = w (I ) is the odds weight of the satellite galaxy, and closepair.ThecomputationandthestorageofthePPFswere
osr,2 osr 2
w is the area weight of the pair. The pair weight is always madewithPyTables4(Altedetal.2002).
area
equal to or larger than unity and is applied to volume-limited – Acompletegraphicaloutputwiththesummaryofeachclose
samples. pair with Npair ≥ 0.01. This summary includes the stamp
of the merger system in the synthetic I band, the relevant
information from the close-pair catalogue, the PDFs of the
3.4. MergerfractioninphotometricsamplesbyPDFanalysis principal and companion galaxies, the function Z, and the
Themergerfractionintheredshiftrangez =[z ,z )is angularandthepairselectionmasks.Wepresentanexample
r min max
ofthegraphicaloutputofthecodeinFig.10.
(cid:80) (cid:82)zmaxwk (z)×PPF (z)dz (cid:80) Nk
fm = (cid:80)i(cid:82)zkzmminazxmwiniosr×pairPDFi(z)×kSi1(z)dz = (cid:80)kiNp1aiir, (23) 4. MergerfractioninALHAMBRA
where k indexes the close pair systems, i indexes the galax- 4.1. Reliablemeasurementofthemergerfractionin
ies in the primary sample, PPF is the pair probability function ALHAMBRA
(Sect.3.2.5),w isthepairweight(Sect.3.3.3),w istheodds
pair osr As demonstrated by López-Sanjuan et al. (2014), the 48
weightoftheprimarygalaxies(Sect.3.3.1),andS istheselec-
1 ALHAMBRA sub-fieldscan be assumedto be independent for
tion function of the primary galaxies (Sect. 2.3). Equation (23)
(cid:80)
isthephotometricanalogueofEq.(10),with Nk beingthe 4 http://www.pytables.org/
k pair
A53,page9of15
A&A576,A53(2015)
Table3.MergerfractioninALHAMBRAasafunctionofBbandluminosity.
Sampleselection z=0.51 z=0.69 z=0.83 z=0.95
(0.4≤z<0.6) (0.6≤z<0.75) (0.75≤z<0.9) (0.9≤z<1)
M ≤−20 0.0118±0.0025 0.0160±0.0021 0.0180±0.0018 0.0224±0.0017
B
M ≤−19.5 0.0156±0.0021 0.0230±0.0017 0.0245±0.0014 0.0297±0.0014
B
M ≤−19 0.0220±0.0015 0.0271±0.0017 0.0297±0.0013 0.0359±0.0014
B
15 field=f05p01c03 3. We applied the maximum likelihood estimator (MLE) pre-
kpair=2
ID1=81451300487 sented in López-Sanjuan et al. (2014) to measure the aver-
ID2=81451300488
10 I1=20.62 agemergerfractioninALHAMBRAanditsuncertainty.The
I2=21.22
α1=188.7021deg MLEusesthemeasuredmergerfractionsandtheirerrorsto
5 δα12==6118.89.4649181dedgeg compute the median of the merger fraction distribution. It
δθ2==76.316.904��49deg alsoprovidesareliablemeasurementoftheintrinsicdisper-
δ()�� 0 zzpp,,12==00..660340 sion of the distribution, which is the cosmic variance. The
Δ MMBB,,12==−−2200..9592 ctaoislmbiycLvóaprieazn-cSeanfjourancloestea-lp.a(i2r0s1tu4d).ieWsewsatsresstsudthieadt tihnedree--
−5 zPPFk=0.72 portedALHAMBRAmergerfractionsareunaffectedbycos-
�zPPFkwpkair=0.88
w�osr,1=1.02 micvariance.
−10 w�wosakrr,e2a�==1.10.416
−15 4.2. MergerfractioninMB selectedsamples
−15 −10 −5 Δα0(��) 5 10 15 Wetestthereliabilityofournewmethodologybycomparingthe
1.0 NNNNNNNNNNNNNNNNNNNNNNzzzzzzzzzzzzzzzzzzzzzz======================0000000000000000000000......................60000000200000000000771100000158010340000002 20 11111111111111111110000000000000000000≤≤≤≤≤≤≤≤≤≤≤≤≤≤≤≤≤≤≤rrrrrrrrrrrrrrrrrrrppppppppppppppppppp[[[[[[[[[[[[[[[[[[[hhhhhhhhhhhhhhhhhhh−−−−−−−−−−−−−−−−−−−1111111111111111111kkkkkkkkkkkkkkkkkkkpppppppppppppppppppccccccccccccccccccc]]]]]]]]]]]]]]]]]]]≤≤≤≤≤≤≤≤≤≤≤≤≤≤≤≤≤≤≤55555555555555555550000000000000000000 merger fractions in the ALHAMBRA photometric survey with
0.8 15 those from previous spectroscopic work. Robust measurements
PDFz00�..46 θ()��10 ilnoctahleUBnbivaenrdsefrotomzsp∼ect1r,ospcroopviicdisnagmaplevsalauraebalevabileanbclhemfraormk tfhoer
0.2 5 ourpurposes.WeusedthehomogenisedcompilationfromLS10
to test the performance of the ALHAMBRA merger fractions.
0.0 0
0.2 0.4 z0.6 0.8 1.0 0.0 0.2 0.4 z0.6 0.8 1.0 This compilation comprises the merger fractions from Patton
et al. (2000) in the Second Southern Sky Redshift (SSRS2;
−−2232 MMMMMMMMMMMMBBBBBBBBBBBB,,,,,,,,,,,,121212121212≤≤≤≤≤≤≤≤≤≤≤≤−−−−−−−−−−−−212121212121080808080808............050505050505000000000000−−−−−−−−−−−−111111111111............111111111111zzzzzzzzzzzz 1.5 ΔΔΔΔΔΔMMMMMMBBBBBB≤≤≤≤≤≤111111......555555000000 da Costa et al. 1998) survey, LS10 in the Millennium Galaxy
Catalogue (MGC; Liske et al. 2003; see also De Propris et al.
MB−21 MB1.0 2005,2007)andGreatObservatoriesOriginDeepSurveySouth
−20 Δ
(GOODS-S; Giavalisco et al. 2004), Patton et al. (2002) in the
−19 0.5
CanadianNetworkforObservationalCosmology(CNOC2;Yee
−18
0.0 etal.2000)survey,Linetal.(2004)intheDEEP2redshiftsur-
0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0
z z
vey(Newmanetal.2013),andLinetal.(2008)inseveralofthe
Fig.10.Exampleofthegraphicaloutputofthecode.Toppanel:postage abovespectroscopicredshiftsurveys.
stampoftheclosepairintheIband.Theredcrossmarkstheprincipal
Following LS10, we defined three samples selected in
apgtaalziarm.xiMny,=idthd0el.e4b.lleTufehtepcartoenxsestl:atPhteDthcFeosrmiogfphatthnseiuopmnrimgnacalirapixsaeyls.aTtnhdheecmoremadipncapinrricoolpenemgrtaialeraskxosyfraptmnhadex −B-2b0a,n−d19lu.5m,iannodsi−ty1.9T,ahnedsenosaemvpolleustioanreindtehfienseedlewctiitohn,MQBse,=1l 0=.
thefunctionZofthesystem(Sect.3.2.2,Fig.5).Middlerightpanel: Weusedthesethreesamplesasprimaryandsecondarysamples
angular mask Mθ of the system (Sect. 3.2.3, Fig. 6). Bottom panels: (i.e., Msel = Msel),anddidnotapplyanyluminositycondition
B,2 B,1
pairselectionmaskofthesystem.Leftpanel:selectionoftheprimary betweenthegalaxiesinthepairs(µ=0).Wesearchedforclose
andsecondarysample(Sect.3.2.4,Fig.7),rightpanel:luminosityratio pairswith6h−1 kpc ≤ r ≤ 21h−1 kpctomimicthedefinition
p
constraintofthesystem(Sect.3.2.4,Fig.8).(Colourversiononline.) usedbyLS10.Weperformedthestudyat0.4 ≤ z < 1toensure
largeenoughvolumesatthelowerredshiftsandvolume-limited
samples at the higher ones. We summarise the ALHAMBRA
merger fraction studies. In addition, they set the optimal pa- merger fractions in Table 3 and show them in Fig. 11. We find
rameterstoobtainreliablemergerfractions.TheALHAMBRA that the merger fraction increases with redshift and that it is
mergerfractionswereportherewerecomputedasfollows: largerforfaintersamples.
LS10reportedthenumberofcompanionsN ,whichistwice
c
1. Theprimaryandsecondarysamplescomprisegalaxieswith the number of close pairs (two galaxies per pair). We show
O ≥ 0.3. This ensures high-quality photometric redshifts 0.5N thereforeinFig.11.Inaddition,wecomputedthemerger
c
and non-biased samples, as shown by López-Sanjuan et al. fraction in the deep part of the VIMOS VLT Deep Survey
(2014). (VVDS;LeFèvreetal.2005,2013)followingSect.3.1andthe
2. The methodology presented in Sect. 3 was applied in each completenesscorrectionsoutlinedindeRaveletal.(2009)and
ALHAMBRA sub-field to obtain the merger fraction f . López-Sanjuan et al. (2011). The ALHAMBRA merger frac-
m
Thisprovided48estimationsof f acrossthesky. tionsagreeexcellentlywellwiththespectroscopicvalues.These
m
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