Stellar populations of galaxies in the ALHAMBRA survey up to z ~ 1

31 Pages·2015·2.35 MB·English

A&A582,A14(2015) Astronomy
DOI:10.1051/0004-6361/201425582 &
(cid:2)c ESO2015 Astrophysics
Stellar populations of galaxies in the ALHAMBRA survey up
∼
to z 1
I. MUFFIT: A multi-filter fitting code for stellar population diagnostics
L.A.Díaz-García1,A.J.Cenarro1,C.López-Sanjuan1,I.Ferreras2,J.Varela1,K.Viironen1,D.Cristóbal-Hornillos1,
M.Moles1,3,A.Marín-Franch1,P.Arnalte-Mur4,B.Ascaso5,3,M.Cerviño3,6,7,R.M.GonzálezDelgado3,
I.Márquez3,J.Masegosa3,A.Molino8,3,M.Povic´3,E.Alfaro3,T.Aparicio-Villegas9,3,N.Benítez3,
T.Broadhurst10,11,J.Cabrera-Caño12,F.J.Castander13,J.Cepa6,7,A.Fernández-Soto14,15,C.Husillos3,L.Infante16,
J.A.L.Aguerri6,7,V.J.Martínez4,17,15,A.delOlmo3,J.Perea3,F.Prada3,18,19,J.M.Quintana3,andN.Gruel20
(Affiliationscanbefoundafterthereferences)
Received24December2014/Accepted26May2015
ABSTRACT
Aims.WepresentMUFFIT,anewgenericcodeoptimizedtoretrievethemainstellarpopulationparametersofgalaxiesinphotometricmulti-filter
surveys,andcheckitsreliabilityandfeasibilitywithrealgalaxydatafromtheALHAMBRAsurvey.
Methods.Makinguseofanerror-weightedχ2-test,wecomparethemulti-filterfluxesofgalaxieswiththesyntheticphotometryofmixturesoftwo
singlestellarpopulationsatdifferentredshiftsandextinctions,toprovidethemostlikelyrangeofstellarpopulationparameters(mainlyagesand
metallicities),extinctions,redshifts,andstellarmasses.Toimprovethediagnosticreliability,MUFFITidentifiesandremovesfromtheanalysis
thosebandsthataresignificantlyaffectedbyemissionlines.ThefinalparametersandtheiruncertaintiesarederivedbyaMonteCarlomethod,
usingtheindividual photometricuncertainties ineach band. Finally,wediscusstheaccuracies, degeneracies, andreliabilityof MUFFITusing
bothsimulatedandrealgalaxiesfromALHAMBRA,comparingwithresultsfromtheliterature.
Results.MUFFIT is a precise and reliable code to derive stellar population parameters of galaxies in ALHAMBRA. Using the results from
photometric-redshiftcodesasinput,MUFFITimprovesthephotometric-redshiftaccuracyby∼10–20%.MUFFITalsodetectsnebularemissions
ingalaxies,providing physicalinformationabout theirstrengths. ThestellarmassesderivedfromMUFFITshow excellent agreement withthe
COSMOS and SDSS values. In addition, the retrieved age-metallicity locus for a sample of z ≤ 0.22 early-type galaxies in ALHAMBRA at
differentstellarmassbinsareinverygoodagreementwiththeonesfromSDSSspectroscopicdiagnostics.Moreover,aone-to-onecomparison
betweentheredshifts,ages,metallicities,andstellarmassesderivedspectroscopicallyforSDSSandbyMUFFITforALHAMBRArevealsgood
qualitativeagreements inallthe parameters, hence reinforcing thestrengths of multi-filtergalaxy dataand optimized analysis techniques, like
MUFFIT,toconductreliablestellarpopulationstudies.
Keywords.galaxies:stellarcontent–galaxies:photometry–galaxies:evolution–galaxies:formation–galaxies:high-redshift
1. Introduction front,itisworthnotingtheLicksystemofindices(Gorgasetal.
1993;Wortheyetal.1994),whichforthepastdecadeshasbeen
Studyingthestellarcontentofgalaxiesiscrucialtounderstand- the standard for most spectroscopic studies in stellar popula-
ingtheirstarformationhistories(SFH),whichinturnprovides tions in the optical (e.g. Trager et al. 1998; Jørgensen 1999;
uswithvaluableinformationaboutthepossibleevolutivepaths Kuntschneretal.2001;Thomasetal.2005;Bernardietal.2006;
from their formationat high redshiftdown to the presenttime. Sánchez-Blázquez et al. 2006a; Gorgas et al. 2007). The com-
Despite the strong efforts and advances achieved in this topic bination of a certain number of absorption lines mainly sensi-
duringthepastdecades,itstillremainsasoneofthemostchal- tive to age, such as the Balmer lines, or to the metallicity, as
lengingandpromisingwaystounderstandgalaxyevolution. tracedbycertainelementssuchasFe,Mg,Ti,C,Ca,andNa,
Early attempts to study the stellar content of early-type wereproventobeanefficientwaytobreakthewellknownde-
galaxies were based on colours from wide and narrow band generacybetweenthesetwoparameters,atleasttosomeextent
photometry (Baum 1959; Tifft 1963; Wood 1966; McClure & (Worthey1994).Thewaytomeasurethesefeaturesisdelicately
vandenBergh1968;Faber1973)andonempiricalsynthesisof chosentobeverysensitivetoaparameterofinterest,focusingits
thepopulationsusingtheobservedcoloursofnearbyearly-types study on narrow spectralranges. By construction,line-strength
asbasis.Theseearlymethodscanbeconsideredasthepioneers indices are quite insensitive to the influence of extinction, and
of the current photo-spectral fitting techniques, which are the by fine-tuningtheir definition or combining the sensitivities of
maintopicofthepresentpaper.Theabovemethodsweregrad- different indices, some of them may end up being almost in-
ually displaced by techniques based in more specific features dependentofotherparameters,suchasmetallicity(Vazdekis&
(Faber1973;Pritchet1977)thatweredefinedinnarrowspectral Arimoto1999;Cervantes&Vazdekis2009)andα-elementover-
ranges. abundances(Thomasetal.2003).
The arrival of absorption line-strength indices to study the Inthepastfifteenyears,thedevelopmentofstellarlibraries
stellar content of galaxies (Burstein et al. 1984; Faber et al. inspectralrangesotherthantheopticalhasdriventhedefinition
1985) brought a significant breakthrough in the field. On this ofnewindicesthatallowedthiskindofstudytobeextendedto
ArticlepublishedbyEDPSciences A14,page1of31
A&A582,A14(2015)
otherregionswithunexploredsensitivities(Cenarroetal.2002; providingcompleteandhomogeneoussetsofgalaxySEDsdown
Mármol-Queraltóet al. 2008).In addition,the indexsystem of to a certain magnitude depth. Although there are several SED-
referenceintheopticalspectralrangehasbeenrevisitedandim- fittingcodesavailable,tocopewiththecalibrationparticularities
proved(see e.g.Vazdekiset al. 2010)thanksto the availability ofmulti-filtersurveys(seee.g.Molinoetal.2014),andgiventhe
ofmuchbetterstellarlibrariesatmuchbetterspectralresolution. vast amountof high-qualityphotometricdata already available
It was with the arrivalof improvedstellar libraries,such as intheliteratureandstilltocomeinthenextyears,inthispaper
CaT (Cenarro et al. 2001a,b), ELODIE (Prugniel & Soubiran wepresentMUFFIT(MUlti-FilterFITtingforstellarpopulation
2001),STELIB(LeBorgneetal.2003),INDO-US(Valdesetal. diagnostics),acodespecificallydesignedforanalysingthestel-
2004), Martins et al. (2005), and MILES (Sánchez-Blázquez larcontentofgalaxieswithavailablemulti-filterdata.
etal.2006b;Cenarroetal.2007),andtheconsequentevolution- This paper mainly aims to describe the code and its func-
arystellarpopulationsynthesismodels(e.g.Bruzual&Charlot tionalities, set the accuracy and typical uncertainties in the re-
2003;Vazdekisetal.2003,2010,2012;GonzálezDelgadoetal. trievedstellar populationparameters,anddemonstrateitsrelia-
2005;Marastonetal.2009;Conroy&vanDokkum2012),that bility compared with already existing stellar population results
fittingtechniquesoverthefullspectralenergydistribution(SED) intheliterature.MUFFITwasdevelopedwithintheframework
of galaxies appeared as an alternative to line-strength indices. of the ALHAMBRA survey (see Sect. 2), so even though the
SED-fitting can also be used to derive severalphysical proper- codeisgenericandcanbeeasilyemployedforanykindofpho-
tiesof galaxies(Mathisetal. 2006;Kolevaetal. 2008;Coelho tometricsystem, manysectionsin thispaperare specific to the
et al. 2009;Walcher et al. 2011;Liu et al. 2013).In fact, there ALHAMBRA dataset. This allows us to show the code’s per-
is a growing number of public codes specifically devoted to formanceonrealgalaxydata, whichis ultimatelythe bestsan-
carryingout SED-fitting with differentprocedures,such as hy- ity check for any stellar population code. Even though in this
perz(Bolzonellaetal. 2000),Le PHARE (Arnoutsetal. 2002; paper we use galaxy data from ALHAMBRA, it is not our in-
Ilbert et al. 2006), STARLIGHT (CidFernandes et al. 2005), tention to scientifically exploit the dataset here. In subsequent
STECKMAP(Ocvirketal.2006),VESPA(Tojeiroetal.2007), papersinthisseries,wewillprovideandexploitthestellarpop-
ULySS (Koleva et al. 2009), FAST (Kriek et al. 2009), and ulationparametersretrievedforthewholegalaxysampleinthe
SEDfit(Sawicki2012). ALHAMBRAsurvey.
Nowadays, there is an increasing number of present and Thispaperisorganizedasfollows.Section2presentsaquick
future multi-filter surveys, including COMBO-17 (Wolf et al. overview of the ALHAMBRA survey, that is, the photometric
2003),MUSYC(Gawiseretal.2006),COSMOS(Scovilleetal. dataset employed to develop the present work. In Sect. 3, we
2007), ALHAMBRA (Moles et al. 2008), CLASH (Postman summarisethemaintechnicalaspectsofourcode,MUFFIT,as
et al. 2012), SHARDS (Pérez-González et al. 2013), J-PAS well as the processes for obtaining photometric colour predic-
(Benitez et al. 2014), and J-PLUS (Cenarro et al., in prep.), tions from models of single stellar populations (SSP) and the
eachofthemwithavastvolumeofhigh-qualitymulti-filterdata. MilkyWay(MW)extinctioncorrections.Weshowtheaccuracy
Thesekindsofsurveyspursuediversegoalswithacommonfea- andreliabilityofthestellarpopulationparametersretrievedwith
ture:samplingtheSEDsofgalaxiesusingtop-hatand/orbroad- our code, together with the uncertainties and degeneracies ex-
band filters that mainly cover the optical range. Owing to this pected for ALHAMBRA data in Sect. 4. Section 5 presents a
configuration,the retrieved SEDs are half-way between classi- comparison study of the results retrieved from ALHAMBRA
cal photometry and spectroscopy, because in practice they are galaxy data using MUFFIT with previous studies, including
likealow-resolutionspectrumwhoseresolutiondependsonthe spectroscopiconesand data fromthe literature,therebytesting
filtersystem(e.g.R∼20forALHAMBRA;R∼50forJ-PAS). the reliability of our results. Finally, we provide the summary
Although multi-filter observing techniques suffer from the andconclusionsofthisresearchinSect.6.
lack of high spectral resolution,their advantagesover standard ThroughoutthispaperweassumeaΛCDMcosmologywith
spectroscopyareworthnoting:(i)thegalaxysamplesofmulti- H0 =71kms−1,ΩM =0.27,andΩΛ =0.73.
filtersurveysdonotsufferfromselectioncriteriaotherthanthe
photometricdepth in the detectionband of the survey,because
alltheobjectsinthefieldofviewareobserved.Forafixedob-
2. TheALHAMBRA survey
servationaltimeandsimilartelescopes,thisleadstomuchlarger
galaxysamplesthaninmulti-objectspectroscopy,whereachiev- Thestellarpopulationcodethatwepresentinthispaperisgener-
ing multiplexitiesgreater than ∼1000is a challengeat present. ically designed for all types of multi-filter surveys. However,
(ii)Unlikestandardspectroscopy,theSEDofgalaxiesobserved we makeuse of the data in the ALHAMBRA survey1 to prove
inmulti-filtersurveysdoesnotsufferfromthetypicaluncertain- and test the reliability of our techniques, as in fact this code
ties in the flux calibration that lead to systematic colourterms, will be employed to analyse the stellar population properties
since the photometriccalibrationofeach individualbandis in- of ALHAMBRA galaxies in forthcoming papers (Díaz-García
dependentoftherest.Thisadvantageiscrucial,becauseitisthe et al., in prep.). Throughout this work, therefore, we mainly
overall continuum of the stellar population that in most cases presentresultsfrombothsimulationsandrealobservationsthat
dominatesthediagnosticwithSED-fittingtechniques.(iii)With are based either on the ALHAMBRA data or on its technical
similar telescopes, the depth of multi-filter surveys is usually setup.Inthefollowingparagraphswepresentashortsummary
much greater than for spectroscopic survey, since direct imag- oftheALHAMBRAsurvey.
ing is much more efficient than spectroscopy. (iv) Multi-filter The ALHAMBRA survey provides a photometric dataset
surveys provide spatially resolved photo-spectra, similar to an of20contiguous,medium-band(FWHM ∼ 300Å),top-hatfil-
integralfieldunit(IFU),allowingustoperform2Dstellarpopu- ters,thatcoverthecompleteopticalrangeλλ3500–9700Å(see
lationstudiesingalaxieswhoseapparentsizesarenotdominated AparicioVillegasetal.2010,forfurtherdetails)overeightnon-
bythepointspreadfunction(PSF)ofthesystem. contiguousregionsof the northernhemisphere,amountingto a
Itisthereforeclearthatmulti-filtersurveysopenaprofitable
way to advance in our understanding of galaxy evolution by 1 http://www.alhambrasurvey.com
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totalareaof4deg2 ofthesky(includingareasincommonwith COMBO-17.Theyofferahugeamountofphotometricdatathat
othercosmologicalsurveyssuchasCOSMOS,see Molinoetal. wecanexploittostudytheevolutionofgalaxies,openinganew
2014,forotheroverlappingareas).Allfiltersintheopticalrange pathtoexploringthestellarpopulationofgalaxies,overallatin-
have very steep side transmission slopes, close to zero overlap termediateandhighredshifts.Althoughthese photometricdata
in wavelength,a flat top, and transmissions of 80–95%(Moles arelikelow-resolutionspectra,thesetechniquespresentremark-
et al. 2008).The magnitudelimit is m ∼ 24 (5-sigma, mea- able advantagesin comparisonwith spectroscopy.Theycango
AB
sured on 3(cid:5)(cid:5)) for the 14 filters ranging from 3500 to 7700 Å, deeperwithabetterfluxcalibration(thecalibrationofeachfilter
decreasingsmoothlyin the six reddestfilters reachingdown to isindependentoftherestofthem),wecanstudythestellarcon-
m ∼21.5inthereddestone(Molinoetal.2014),whichiscen- tentineachresolutionelement(similartoIFUtechniques)with
AB
tred at 9550 Å. The optical coverageis supplementedwith the oneexposure,andwecanworkwithlargergalaxysamples;asa
standardNIRJ,H,andK filters,whichhavea50%detectionef- result, it wouldbe a pitynotto take advantageofthese studies
s
ficiencydepth(point-likesources,ABmagnitudes)ofJ ∼ 22.4, andnotexploitalltheopportunitiesthattheyoffer.
H ∼ 21.3,and K ∼ 20.0,analysedinCristóbal-Hornillosetal. The collection of analysis techniques, routines, and other
s
(2009).TheALHAMBRAfilterset2 isdesignedtooptimizethe tools that we are using, are collected under the code name
accuracyofphotometricredshifts(photo-z,Benítezetal.2009), MUFFIT, which is written in Python language, and it mainly
but due to their characteristics, it also provides low-resolution focuses on retrieving the stellar populations of galaxies whose
photo-spectracomposedof23bands,correspondingtoaresolv- SEDsaredominatedbytheirstellarcontent.
ingpowerR ∼20intheoptical.Alltheobservationsweredone Thissectionissubdividedintwoextendedsections.Onthe
undera qualitycriterionofseeing <1.6(cid:5)(cid:5) andairmass<1.8,us- one hand, we show in Sect. 3.1 the main ingredients or inputs
ingthe3.5mtelescopeintheCalarAltoObservatory3(CAHA) requiredtodeveloptheanalysis.Thesepreliminaryelementsare
with two cameras, the imager LAICA in the optical range and basicallycomposedoftheSSPmodels,thephotometricsystem,
Omega-2000 for the NIR filters. The actual area for this work andthe selectionof a dustextinctionlaw to treatthe impactof
is 2.8 deg2 with a total on-target exposure time of ∼700 h dust on the modelSEDs properly.On the other hand,the code
(∼608 h were dedicated for the optical bands, and ∼92 h for is described in Sect. 3.2, emphasizing the description of some
theNIRones)becausepartoftheALHAMBRAfieldshavenot specifictasks.
beenimagedyet,althoughtherestofthefieldswillbecompleted InFig.1,weoutlinethemainstructureofthecodebyabrief
reachingtheexpectedtotalareaof4deg2. flowchartthatsummarisesthemainfeaturesofthefollowedpro-
The ALHAMBRA Gold catalogue4 (Molino et al. 2014, cesses to set constraints on the stellar populations. We caution
hereafter Gold catalogue), is the reference catalogue for that the purposes of the flowchart are to help the reader fol-
this work. As explained in Molino et al. (2014), synthetic low the developmentof Sects. 3.1 and 3.2 and to support the
F814W images were created, as a linear combination of indi- schematiccomprehensionoftheseveralstages.
vidual filters, to be used for both detection and completeness Thereaderwhoisprimarilyinterestedeitherinthereliabil-
purposes,emulatingthe F814W bandoftheAdvancedCamera ityofthecodeorinthecomparisonwithresultsretrievedfrom
for Surveys (ACS) in the Hubble Space Telescope (HST). the literature may skip this section to continue with the self-
Therefore,theGoldcatalogueprovides23+1photometricAB containedSects.4and5.
magnitudes(Oke & Gunn 1983) and errors for ∼95000 bright
galaxies (17 < m < 23), which are complete up to
F814W 3.1.Mainingredientsofthestellarpopulationcode
m = 23.Throughoutthiswork,thesyntheticF814W pho-
F814W
tometryisremovedfromtheanalysis.Duetotheexistenceofa In this section we describe the main input ingredients and
PSF variability among different filters, the photometry is cor- preparatorytasks that are considered for developingthe stellar
rected for PSF and aperture effects. In addition, and for the populationanalysis codethat is presentedin this paper.In par-
specificALHAMBRAcase,wequadraticallyaddanextrauncer- ticular, ourcode requiresan inputset of referenceSSP models
taintyof∼0.025(ABmagnitudes)ineachphotometricmeasure- (Sect. 3.1.1), the photometric system of the data (Sect. 3.1.2),
menttoaccountforpotentialcalibrationissuesoruncertainties. alongwith a set of recipesto take the intrinsic and MilkyWay
For further details of the ALHAMBRA survey, we refer extinctionintoaccount(Sect.3.1.3).Theredshiftsofthe target
readerstoMolesetal.(2008)andMolinoetal.(2014). galaxydatacanbemanagedasaninputingredientoranoutput
of the code, as explained in Sect. 3.1.4. The flowchart on the
left-handsideofFig.1particularlyillustratesthemainingredi-
entsandpreliminaryworkcarriedoutbythecodebeforestarting
3. Thecode
withtheanalysisofthedata.
Although there are many public codes devoted to carrying out
SED fitting in manydifferentways, e.g. hyperz,STARLIGHT,
3.1.1. TheSSPmodels
ULySS, VESPA, Le PHARE, FAST, or SEDfit; we are per-
forming our own analysis techniques to retrieve stellar pop- The code has been designed to use SSP models as input tem-
ulation parameters from photometric SEDs, specifically de- platesforthecomparativeanalysisof thestellar populationsof
signed for analysing the stellar content of galaxies from the galaxies.Currently,thecodeisreadytoaccountfortheBruzual
ALHAMBRAsurvey,butbeinggenericandeasilyadaptableto & Charlot (2003, hereafter BC03)5 and MIUSCAT6 (Vazdekis
anymulti-photometricsurvey.Secondarily,thereisanincreasing et al. 2012;Ricciardelli et al. 2012)SSP models, althoughany
number of large-scale multi-filter surveys; e.g. ALHAMBRA, otherSSPspectraldatasetcanbeeasilyimplemented.
J-PLUSandJ-PAS,SHARDS,CLASH,MUSYC,COSMOS,or BC03isperfectlysuitedtoSEDfittinggiventhelargespec-
tralcoverageofthemodels,from91Å to160μm, allowingus
2 http://svo2.cab.inta-csic.es/theory/fps3/
3 www.caha.es 5 http://bruzual.org/
4 http://cosmo.iaa.es/content/alhambra-gold-catalog 6 http://miles.iac.es/
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Fig.1.Flowchartsofthephotometricmodelpredictions(left)andtheanalysistechniques(right).Amoredetailedexplanationofeachstepcan
befoundinSects.3.1.2,3.1.3,and3.2.Thedashedrowindicateswherebothprocessesarerelated.Flowchartsymbolsrepresentstandardtasks:
ovals,start/endofaprocess(red);arrows,thedirectionoflogicflowintheprocess; parallelograms,input/ouput operation(cyan);diamonds, a
decisionorbranchtobemade(yellow);andrectangles,aprocessingstep(green).
to cope with most kinds of multi-filter galaxy data, irrespec- butconcentrateon the performanceof the code on the basis of
tive of the redshift. For the present work, we assume ages up thetwoSSPmodelsetsmentionedabove.
to14Gyrandmetallicities[Fe/H]= −1.65,−0.64,−0.33,0.09,
and0.55,Padova1994tracks(forfurtherdetailsandreferences,
seeBruzual&Charlot2003),andaChabrier(2003)initialmass 3.1.2. Photometricsystemandsyntheticphotometry
function(IMF).
ForapropercomparisonbetweeninputSSPmodelsandgalaxy
MIUSCATprovidesasampleofSEDswithaspectralrange data, it is essential to build a reliable estimation of the syn-
λλ 3465–9469 Å and a resolution of FWHM ∼ 2.5 Å, almost thetic magnitudes (or integrated fluxes) of the SSP template
constantwithwavelength(Falcón-Barrosoetal.2011).Despite models in the same photometric system of the galaxies as the
the great colour calibration of these models, its spectral range onethatneedsto be analysed.Thisis computedby convolving
is not enough for galaxies at intermediate redshift and further, the SSP model or galaxy reference spectra with the response
missing the observed ALHAMBRA colours in the UV range. functions of the photometric system. In addition to taking the
Forthispurpose,weextendthelowerendofMIUSCATmodels empirical filter transmission curves into account, in order to
up to 1860 Å (A. Vazdekis2015,priv.comm.),using the Next obtain a reliable photometric prediction it is advisable to ac-
GenerationSpectralLibrary(NGSL,Heap& Lindler2007).In countforspecificcharacteristicsoftheobservingconditionsand
addition, we complement these models with their photomet- the instrumental setup employed for the photometric observa-
ric predictions for J, H, and K, which are adapted to predict tions of the galaxiesto be analysed, for example,the transmit-
the ALHAMBRA NIR bands. Throughout this work, we use tance of the optical system and/orthe sky absorptionspectrum
the models up to 14.13 Gyr with metallicities [Fe/H] = −1.31, wheretheobservationsweredone.Thewavelengthdependence
−0.71,−0.40,0.0,and0.22.WeassumeaKroupaUniversal-like ofthe quantumefficiencyofcharge-coupleddevices(CCDs) is
initialmass function(Kroupa2001),eventhoughits universal- remarkable,sincetypicallylesssensitiveinthebluerandredder
ity is a currentmatter of debate(see, e.g. Ferrerasetal. 2013). ends. If not accounted for properly,this effect modifies the ef-
In future works, we will shed light on the systematic variation fectivewavelengthofsuchfilterbandpasses,creatingafictitious
of the IMF for the more massive galaxiesin the ALHAMBRA colourterminthesyntheticphotometryofthereferencemodels.
database. Figure 2 presents the response functions of the ALHAMBRA
By construction, the code can also use not only any other photometric system. It consists of 20 optical bands (left-hand
set of SSP models, but also any other kind of reference tem- side)andtheALHAMBRAJ,H,andKs NIR-bands(right-hand
plate spectra; for example, as long as their main stellar popu- side). In this figure, all the effects explained above are already
lation parameters (age, metallicity, IMF, extinction, and over- embedded.
abundances), the spectra of real galaxies are assigned by the Wecomputethesyntheticphotometryfollowingthemethod-
user. Throughoutthis paper we do not present this possibility, ologydescribedinPickles&Depagne(2010),whichisbasedon
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Fig.2.ResponsecurvesoftheALHAMBRAfiltersetfortheCCD1intheopticalrange(LAICAcamera;onecolourfrombluetoredperband),
togetherwiththeALHAMBRAJ,H,andK filters(Omega-2000camera;darkred)tomakethemodelsyntheticphotometry.
s
1.0
0.9
] 0.8
s
nit 0.7
u
0.6
y
ar 0.5
r
t
bi 0.4
r
A 0.3
[
λ 0.2
F
0.1
350 550 750 950 1150 1350 1550 1750 1950 2150
λ [nm]
Fig.3. Synthetic photometry of a SSPusing the ALHAMBRA photometric system. Theblack lineis the SSPflux, the colour squares are the
expectedpassbands,andthehorizontalbarsrepresenttheFWHMofeachfilter.
theHSTsynphot7packageandinBessell(2005).Sincecurrent where fν is the flux in ergs cm−2 Hz−1 s−1. To transform the
detectorsarephoton-countingdetectors,thenumberofphotons weighted mean photon flux density into AB magnitudes, we
detectedacrossapass-bandXis compute the magnitude of the flux in the STMAG system
(cid:2) (system for calibrating HST stars, Stone 1996), which can be
λ
NXph = hcFλRX(λ)dλ, (1) einatseirlymetrdainastefosrtmepedistonetcheessAaBrymbeacganuitsuedtehesywsteeimgh(teEdq.m(e5a))n.pThhois-
tonfluxdensityisestablishedperunitwavelength,whereasthe
whereFλisthespectrumtoconvolve,andRX(λ)istheresponse AB magnitude system is given per unit frequency.The magni-
functionofthefilter X (alsocalled sensitivityfunctioninsome
tudeacrossthebandpassXintheSTMAGsystem,mST,X,andin
previouswork).NormalizingEq.(1),wegettheweightedmean
theABsystem,mAB,X,is
photonfluxdensity,
FXph = (cid:3)(cid:3)λλFRλR(Xλ()λd)λdλ· (2) mmSATB,,XX == −m2ST.5,Xlo−g510loFgXp1h0−λp2iv1o.t1+, 18.692, ((54))
X
whereλ is the source-independentpivotwavelength,which
pivot
SomecataloguesprovidephotometryinABmagnitudes,defined isdefinedas
(cid:4)(cid:5) (cid:3)
as
λR (λ)dλ
mAB =−2.5log10 fν−48.6, (3) λpivot = (cid:3) RX(Xλ)dλ/λ· (6)
7 http://www.stsci.edu/institute/software_hardware/ To illustrate this, Fig. 3 shows an example of a SSP spec-
stsdas/synphot trum taken from the model set of BC03 (rest frame, solar
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metallicity, intermediate age of 5 Gyr, Chabrier IMF, and no observedgalaxy,whichisredshiftedwiththegalaxysystem;on
intrinsic extinction) along with its synthetic photometry us- theother,theforegrounddustoftheMW,whichreddentheob-
ing the ALHAMBRA filter set. The spectrum synthetic pho- servedgalaxySEDintheobserver’sreferencesystem.Itisim-
tometry was computed following the process explained above, portanttonotethatthislocalMWextinctioncannotbecorrected
where ea(cid:3)ch bandpass(cid:3)is centred at their effective wavelengths with the intrinsic galaxy reddening as the emitted flux is red-
(λeff = λRX(λ) dλ/ RX(λ) dλ) and the horizontal bars rep- shifted beforebeingscattered by the dustin our galaxy.As we
resent the FWHM of each filter. This example is also useful presentbelow,weseparatelydealwithbothextinctioneffects.
for showing that the main, broader spectral features are easily Following a given extinction law, the intrinsic extinction is
distinguished after convolving, emphasizing the power of the applied to the SSP template models before they are redshifted
ALHAMBRA photo-spectraashalfwaybetweenclassicalpho- and convolved with the photometric system. Throughout this
tometryandspectroscopy. work the values of AV range from 0.0 to 3.1 (in bins of 0.1 in
For the specific case of ALHAMBRA, and because of therange0.0–1.0,andinbinsof0.3from1.0–3.1).Theintrinsic
the configuration of LAICA, we computed four photometric extinctioncanbeaddedas
databasesfortheopticalbands,oneperCCD,becausethereare Fλ = Fλ,0×10−0.4Aλ, (7)
discrepancies among CCD sensitivities and each CCD has its
ownsetoffilters.FortheNIR-filtersJ,H,andKs,werepeatthis whereFλ,0istheSSP-model/templatefluxatrestframeFλafter
processtakingtheOmega-2000configuration(onlyonedetector adding extinction, and Aλ is determined by the extinction law,
plate).InbothopticalandNIRsyntheticphotometry,wetakethe which can be chosen by the user. Since it is not clear how R
V
filtertransmissioncurvesintoaccount,thequantumefficiencyof varieswithinahostgalaxyandamongstdifferenttypesofgalax-
everyCCD/camera,theskyabsorptionspectrumatCAHA,and ies,wekeepthevaluetoR =3.1constant,i.e.themeanvalue
V
the reflectivity of the 3.5 m-telescope primary mirror with the in the MW. This helpsto avoid degeneraciesand to reduce the
transmittanceoftheopticalsystem. numberoffreeparameters,whichisalreadyveryhighandtime
Owing to boththe largenumberof inputmodelparameters consuming. Even though the different reddening laws have in-
(ages, metallicities, extinctions, IMF slopes, and redshifts) and trinsicdifferences(seeFitzpatrick1999),we donotassumeer-
the intermediate-high spectral resolution of current SSP mod- rorsintheSSPtemplatemodelsowingtosuchuncertainties.
els, it is in general more efficient to build up our set of con- We use the dust maps of Schlegel et al. (1998, hereafter
volved models once at the beginning, rather than recomputing SFD), in order to deal with the MW reddening in the line of
themodelsyntheticphotometryeverytimethecodeisrun.After sightofeachgalaxyinoursample.TheSFDdustmapsprovide
computing the synthetic photometry of all models, the photo- E(B−V) valuesin differentpositionsof the sky by estimating
metricpredictions(fluxesandmagnitudes),alongwiththemain the dust column density.These estimations were calibrated us-
characteristics of each model, are stored in a structured query inggalaxiesandassumingastandardreddeninglawtoinferthe
language (SQL) database. A straightforward flowchart of the existenceofgalacticdustbetweentheobserverandthesources
processforestimating photometricpredictionsis shown on the beyond the MW limits. Since the spatial resolution of SFD is
left-handsideofFig.1. low, FWHM ∼ 6.1(cid:5) and pixel size (2.372(cid:5))2, MUFFIT makes
a bilinear interpolation in the E(B−V) grid for all the galaxy
coordinatesinthesample.
3.1.3. Dust-extinction MUFFITappliesaforegroundextinctioncorrectionforeach
individualgalaxyphoto-spectrumusingan extinctionlaw fora
Stellar population diagnostic techniques based on SED fitting value of E(B− V) and R . The simplest way to deredden the
V
overa broad spectralcoverage,as in this case, requirethe red-
photo-spectrumofagivengalaxyistocomputetheextinctionin
dening by extinction to be thoroughly considered to avoid po- theeffectivewavelengthsofthedifferentfiltersandthencorrect
tentialmisinterpretationsoftheintegratedcoloursofthepopula-
thesourcephotometryusingtheequation
tion,e.g.olderagesorhighermetallicities,aswellastoderive
reliablestellarmasses. Fλ,c = Fλ,red×100.4Aλ, (8)
Manyauthorshavetriedtoparametrizetheshapeofthedust
extinction curve (e.g. Prevot et al. 1984; Massa 1987; Mathis where Fλ,c is the flux correctedfor MW extinction for a given
1990;Cardellietal.1989;Calzettietal.2000;O’Donnell1994; wavelength, Fλ,red is the observed flux (reddened), and Aλ the
extinction factor given for a extinction law. Since the trans-
Fitzpatrick1999),overallonthebluerpartswherethedustred-
mission curves of the filters are not completely flat and the
deningismorecomplex.Thedustextinctioncurveisreproduced
shapeofthecontinuumissourcedependent,thisapproximation
well using the parameter R ≡ A /E(B − V) (Cardelli et al.
V V may be inappropriatefor those filters that exhibit a gradientin
1989),which varies between 2.2 and 5.8 dependingon the en-
their transmission curves(e.g. the lower and upper ends of the
vironmental characteristics of the diffuse inter stellar medium
ALHAMBRAopticalbands,seeFig.2),especiallyinthespec-
(ISM).AlthoughthevaluesofRV maychangedependingofthe tral rangeswhere the observed spectrum is not flat. This effect
line ofsight, throughoutthisworkwe assume thatthe valueof wouldbeinterpretedasashiftinthefiltereffectivewavelength
thisparameteris R = 3.1,whichis the meanvaluein thedif-
V (Fitzpatrick 1999) and, finally, as a colour term in the spectral
fuseISMoftheMW(Cardellietal.1989;Schlafly&Finkbeiner
regionswithstronggradientsinflux,suchasthe4000Å-break.
2011).Amongsttheavailableextinctionlawsinourcode(Prevot
To geta morereliablecorrectionin thissense, the codecarries
etal.1984;Cardellietal.1989;Fitzpatrick1999;Calzettietal.
outthedereddeningprocessofthedatainthreesteps:
2000),throughoutthisworkwehavechosentheFitzpatrickred-
deninglaw(Fitzpatrick1999)becauseitreproducestheextinc- – First, we pick up a set of models from BC03 (29 ages,
tion observed for MW stars well with a preferred mean value from 0.1 to 10 Gyr, four metallicities, [Fe/H] = −0.64,
aroundRV =3.1(Schlafly&Finkbeiner2011). −0.33,0.09,and0.56,andaChabrierIMF)toberedshifted
For extragalacticobjects,thereare two mainsourcesof ex- (redshiftbin0.01)andconvolvedwiththesurveyphotomet-
tinctiontoaccountfor:ontheonehand,thedustintrinsictothe ric system. Before redshifting and computing the synthetic
A14,page6of31
L.A.Díaz-Garcíaetal.:MUFFIT:Amulti-filterfittingcodeforstellarpopulationdiagnostics
photometry, we add the intrinsic extinction (A from 0.0 3.2.ThecoreoftheMUFFITanalysistechniques
V
to1.0,inbinsof0.2)totherest-frameBC03models.Then,
we carry out an error-weighted χ2 test to find the best fit This section is devoted to the main technical features and pro-
cesses carried out by our code to constrain the stellar popula-
betweentheabovemodelsandtheobservedgalaxyphotom-
tionparametersofgalaxiesinmulti-filterdatasamples.Wefirst
etry.Theaimofthisstepisnottoderivephysicalparameters
describetheway inwhichthe χ2 minimizationis performedin
fromthebestfitting,buttosetconstraintsontheshapeofthe
Sect.3.2.1,withtheadditionofamixtureofSSPsgivingremark-
continuum.
able improvement, which was specifically computed for each
– Second,were-normalizetheBC03spectroscopicmodelas-
galaxy,inordertosetmorepreciseconstraintsonthestellarpop-
sociated to the best-fitting photo-spectrum. The synthetic
ulations.InSect.3.2.2weexplaintheprocessofdetectingthose
photometryofthisre-normalizedmodelhastoreproduceall
bands that may be affected by strong emission lines in detail,
theobservedphotometricbandsexactly.
helping to understand the overall fitting process. Section 3.2.3
– Finally,weapplyEq.(8)tothere-normalizedmodelderived
explainshowthestellarmassesarecalculatedfromthefittings.
inthepreviousstep,inordertoobtainadereddenedspectrum
Inaddition,aMonteCarloapproachisusedtosetconstraintson
that we convolve with its related filter response curve. We
theconfidenceintervalsoftheparametersprovidedbythecode,
usetheFitzpatrick(1999)extinctionlawstocalculateAλ,the
valueE(B−V)providedbySFDandR =3.1,toderedden detailedinSect.3.2.5.Finally,wedescribehowwemanagethe
V k-correctionsasaresultofthefittingsinSect.3.2.6.Thecontent
allthegalaxiesofoursample.
ofthissectionisoutlinedontheright-handsideoftheflowchart
(seeFig.1).
Inparticular,theFitzpatrick(1999)extinctionlawwasbuiltfrom
the superposition of the extinction curves derived for a set of
stars.Consequently,thisextinctionlawcontainsintrinsicuncer- 3.2.1. Theχ2 minimizationandmixtureofSSPs
tainties, although we would accurately know the values of R
V Our stellar population analysis technique is based on error-
andE(B−V).Weaccountfortheparticularuncertaintiesofthis weighted χ2 tests between the multi-filter galaxy data and the
law,addinganerrortothedereddenedphotometryofMWdust,
template SSP models of choice. Since SSP models are usually
Fλ,c,followingthemethodologyexplainedinFitzpatrick(1999) normalizedtoainitialstellarmassandboththegalaxydistance
andassumingσ =0.
RV and its luminosityare uncertainin a generalcase (in fact these
Cosmological fields, often the targets of multi-filter photo- are parameters generally derived from the fit), it is required to
metricsurveys,usedtoberegionsoftheskywithlowextinction add a normalization term, ε, in the classical χ2 equation. This
values.IntheparticularcaseofALHAMBRA,ourmaingalaxy termminimisestheχ2 valueforeverymodel-galaxypairandit
sample has MW extinction values of E(B − V) down to 0.04 takes all observed bandsand associated errors into account, so
(AV <0.12forRV =3.1)inallthecases.Thecolourtermdueto that the result is only colour dependent. It is more robust for
theMWdustintheALHAMBRAsurveymayreachamaximum multi-filter surveys because, at most, they only contain a few
ofΔmAB ∼ 0.15,andthestellarmassesmaybeunderestimated dozenfilters(e.g.23inALHAMBRA).Thisway,allthemean-
by3%(8%)ifweusetheKs(R)filtertoestimateit.Althoughthe ingful filters contribute to determining the best solution of the
stellarmassisnotprimarilyaffectedbyMWextinctioninthese fitting(withoutgivinguponeofthebestbandsinordertonor-
fields,thecolourtermmightchangetheretrievedstellarpopula- malise), and there is no risk that the normalisation band is af-
tionsandconsequentlythederivedstellarmass(seeSect.3.2.3). fectedbyemissionlinesorcosmeticdefects.
InALHAMBRAtherearenogalaxiesatlowGalacticlatitudes, Because the number of reliable bands in each source may
|b| < 5, where the MW temperature structuresare not duly re- bedifferentfromoneobjecttothenext(forsomeobjects,some
solvedintheSFDmaps(Schlegeletal.1998). filters may be rejected for observational, cosmetic, or calibra-
tionproblems),ingeneralwedivideeveryχ2 bythenumberof
available,safefiltersineachcase.Dependingonwhetherweare
3.1.4. Redshifts working with bandpass fluxes or magnitudes, the χ2 definition
canbeexpressedas
Togetherwiththemassandthestellarpopulationparametersof
(cid:7) (cid:8)
tmhaetigoanlaoxfyt,htehephcootdoe-zi.sItgiesnweroicrtahllnyoptirnegp,ahreodwteoveprr,othvaidtethainsceosdtie- χ2 = 1 (cid:6)Np OmX −(εm+mX) 2,and (9)
is not intended to be a photo-z code. The large number of po- m Np X=1 σmX
tsehnifttiailsmseotdaeslapacroammpelteetresltyhfartetehepacroadmeeptelaryisnwthiethfiwttihnegnpthroecreesds-, χ2 = 1 (cid:6)Np ⎡⎢⎢⎢⎢⎣OfX −εffX⎤⎥⎥⎥⎥⎦2, (10)
means that there is a slight degeneracy with other parameters f N σf
p X=1 X
(likeextinction;seeSect.4.4)thattendstooverestimatethede-
rivedphoto-z.Toovercomethiseffect,thecodeisalsoprepared whereNpisthenumberofavailablefiltersinanobservedgalaxy,
to accept a list of redshift values for each target galaxy as ini- Om,f is the observed X-filter(magnitudeor flux),σm,f its error,
X X
tial constraint: either a list of nominal redshift values, so that m (f ) the X-filter model prediction (single SSP or SSP mix-
X X
the code only performsthe fitting process at exactly these red- ture, more details below) and ε (ε ) the normalization term.
m f
shifts, or complete probability distribution functions (PDF) of Forourpurposes,ε andε arewrittenas
m f
redshifts. Then the code only accounts for the model redshifts ⎛ ⎞ ⎛ ⎞
wweithuisneththeePpDhFotion-tzerPvDalF.sBepcroauvsideeodfbthyethgeooAdLreHsAulMtsBwReAobGtaoilnd, εm =⎜⎜⎜⎜⎜⎜⎝(cid:6)Np OmXσ−m2mX⎟⎟⎟⎟⎟⎟⎠×⎜⎜⎜⎜⎜⎜⎝(cid:6)Np σ1m2⎟⎟⎟⎟⎟⎟⎠−1,and (11)
catalogueasinputredshiftconstraintsusingBPZ2.0throughout X=1 X X=1 X
⎛ ⎞ ⎛ ⎞
tbihminispartwoiovonerskotf(hMoeuqorulicanoloidtyeetwoafiltt.hh2eth0ie1n4pA)u.LtIpHthAiosMton-BoztRe(swAeoeprSthheoyctott.-hz4a.ct3o)tnh.setrcaoinmts- εf =⎜⎜⎜⎜⎜⎜⎝(cid:6)Np OσfXff2X⎟⎟⎟⎟⎟⎟⎠×⎜⎜⎜⎜⎜⎜⎝(cid:6)Np σffX22⎟⎟⎟⎟⎟⎟⎠−1, (12)
X=1 X X=1 X
A14,page7of31
A&A582,A14(2015)
which correspondrespectivelyto minimizingEqs. (9)and (10) 14
for each galaxy, i. e., ∂χ2m,f/∂εm,f = 0. As we show later
(Sect.3.2.3),byfindingthebeststellarpopulationsolutionsfor
eachgalaxy,wecanestimateitsstellarmassfromtheεvalues. 12
Equation (9) (the equation used throughout this work) as-
sumesthat the distributionof errorsis Gaussian, whenthe dis- 10
tribution of magnitudes is generally not Gaussian since these r]
y
are logarithmic measurements of flux. From certain signal-to- G
noiseratios,S/N >∼ 5(oruncertaintiesσm <∼ 0.22),themagni- [ 8
X P
tudeuncertaintiesarequasi-normallydistributed,andtherefore, S
S
this approach is valid. Consequently, we encourage potential
,L 6
MUFFIT users to take fluxes instead of magnitudeswhen sev- e
g
eralgalaxybandsarecompromisedbyverylowsignal-to-noise A
ratios,S/N <∼ 4–5.Itmustbealsotakenintoaccountthatacer- 4
tain minimum signal-to-noise ratio is required for determining
reliable stellar population parameterswithout being dominated
bydegeneracies,asshownlaterinthispaper. 2
Oncewehavedefinedhowtocomputethefittinggoodness,
thenextstepistocompareoursetofmodelstoretrievethemost
likelystellarpopulationparameters.Wecarryoutthisprocessin 0 2 4 6 8 10 12 14
twodifferentsteps. AgeL, mock [Gyr]
– First, we run the χ2-test described above with the set of Fig.4. Empirical relation between the luminosity-weighted ages of
SSP models selected by the user (base models), making a mockgalaxiesmadeofrandommixturesoftwoSSPs,AgeL,mock,and
first determination of the bands that may be affected by thebestagedeterminationforsuchmockgalaxiesderivedfromasin-
strong emissionlines. In short, foreach redshiftstep of the gleSSPfitting,AgeSSP.TheyellowcurveistheAgeL,mock medianfor
agivenvalueofAge ,anditrepresentsthetypicaloffsetinagethat
SSP models, the code looks for a flux excess in the galaxy SSP
onemayexpectwheninterpretingtheSEDofamixtureoftwoSSPsby
SEDwithrespecttotheSSPmodelSEDs,forallthosebands
fittingauniqueSSP.
thatcouldbeaffectedbyemissionlinesatthegivenredshift.
A moreextensiveexplanationofourtechniqueofdetection
ofemissionslinesin multi-filtergalaxydatais presentedin
twoSSPs,age ,andthebestagedeterminationforsuch
Sect. 3.2.2. When this is the case, those bands potentially L,mock
affectedbyemissionlinesareremovedfromthefittingpro- mock galaxiesderivedfrom a single SSP fitting, ageSSP. In
cess, and the χ2-test is repeated again without the affected Fig. 4 we present the result of this study. As expected, we
observethatage underestimatestherealage,inparticular
bands. In addition, rather than taking the parametersof the < SSP
forage ∼6Gyr.TheyellowcurveinFig.4represents
bestSSPfitting,wecarryoutaMonteCarlosimulationus- L,mock
age as a function of age . Once the age threshold is es-
ingthepropersignal-to-noiseratiosineachfilter(furtherde- T SSP
tablished, we generate all the possible SSP combinations
tailsinSect.3.2.5).Fromthesetofparametersretrieveddur-
(younger and older than age ), including the stellar mass
ingtheMonteCarloapproach,wemaptheparameterspace T
weightofeachcomponentasanewdegreeoffreedom.Fora
ofcompatiblesolutions(overallage,metallicity,extinction,
generalcasewithncomponentspermixture,eachmagnitude
redshift, stellar mass, and IMF), although at this stage we
inthebandXofthenewmixturemodelisexpressedas
onlyfocusonthe retrieveddistributionsofageandredshift
⎛ ⎞
tsoubcsaerqryueonuttStEhDe-nfietxtitnsgteppr:octheessm. ixture of two SSPs and its mX,mix =−2.5log10⎜⎜⎜⎜⎜⎝(cid:6)n αi10−0.4miX⎟⎟⎟⎟⎟⎠, (13)
– Second, according to the age and redshift distributions de-
i=1
rivedfromtheinitialSSPanalysis,wemakeanewdatabase (cid:6)n
of models consisting of a mixture of two individual base fX,mix = αifXi, (14)
SSPmodels.Themixtureisonlycomputedforthebestred-
i=1
shiftsolutionsdeterminedinthepreviousstep.Foreachred-
shiftvalue,thetwo-modelmixtureisconstrainedtocombine wheremi (fi)isthemagnitude(flux)inthebandX forthe
X X
two SSPs, younger and older than a certain age thresh- ith SSP model, and α the relative flux contribution of the
old, ageT, that is related to the most likely age, ageSSP, in- SSP model in the ith ciomponent, with (cid:21)n α = 1 and 0 ≤
ferredfromtheMonteCarloanalysisperformedinthe pre- i=1 i
vious step. This is a reasonable assumption given that the α ≤ 1. In our case, we are mixing two SSPs and conse-
i
stellar content of galaxies are usually the result of com- quentlyn=2.
plexSFHswithmultiplestellarpopulations(Ferreras&Silk After mixing the SSP models as explained above,the code
2000;Kaviraj et al. 2007;Lonoce et al. 2014),and the age againsearchesforthebest-fittingsolution,repeatingthede-
solutionsderivedfromcomparisonswithsingleSSPscanbe tection of emission lines with the mixtureof modelsas ex-
considered to be, in first order, luminosity-weightedmeans plainedinSect.3.2.2.AsinthefirststepusingasingleSSP,
of the ages of the individual, true populations. To deter- we not only provide the best solution but also map the
mine the age value that allows us to define the limit be- compatible stellar-populationparametersby a Monte Carlo
T
tween youngerandolderSSP mixturesforeachgalaxy,we approach,treatingtheerrorsproperlyineachband.Thispro-
havestudiedthe empiricalrelationbetweentheluminosity- videsanextraadvantagewhencarryingoutastatisticaltreat-
weightedagesofmockgalaxiesmadeofrandommixturesof ment of the results. We devote Sect. 3.2.5 to explaining in
A14,page8of31
L.A.Díaz-Garcíaetal.:MUFFIT:Amulti-filterfittingcodeforstellarpopulationdiagnostics
detail how we explore the compatible space of derived pa- ALHAMBRA filters, so the AGN emission line detection cri-
rametersforeachgalaxy. teriainMUFFITmightfailorbeinaccurate.Itisveryimportant
tonotethatanexcessivelistofemissionlines,mostlywhenthey
With this method and two SSPs, one database of mixed SSPs arespreadinthebroadwavelengthranges,willeventuallyderive
is particularly created for each galaxy, because it is more ade- incorrectresults, sincetoomanybandsmightberemoved.Itis
quate and realistic than a single SSP fitting. As shown above, thereforeadvisabletorestrictthislisttothelinesthatcanpresent
foranon-parametricSFH,thisrepresentsasubstantialimprove- ameasurableexcessinflux,whichmainlydependsonboththe
ment over using only one SSP, which is not able to reproduce filter widths andthe line intensity.For thisreason, some bands
thecolourofanunderlyingmainredpopulationplusless mas- can be forced by the user to remain in the SED-fitting analy-
siveandlatereventsofstarformation.Themixtureoftwopop- sis irrespective of whether they can be potentially affected by
ulationsisareasonablecompromisethatsignificantlyimproves emissionlines.Forinstance,inALHAMBRAweexpectthatthe
the reliability of determining the stellar population parameters NIRbandsaretoowidetobesensitivetothepresenceofemis-
of multi-filter galaxydata (Ferreras& Silk 2000;Kaviraj et al. sion lines, so they are neverremovedduringthe fitting process
2007;Lonoceetal.2014).Infact,ithasbeendemonstrated(e.g. evenifthecodedetectsafluxexcessinanyofthem.
Rogers et al. 2010) that the mixture of two SSPs turns out to Once we specify the emission line list in the code, the
be the most reliable approach to describing the stellar popula- emission line detection process is carried out in two steps.
tionsofyoungearly-typegalaxies,aswellasaveryreasonable First, taking the modelredshiftinto account,we fit ourmodels
approachforoldergalaxieswherethelattercaseisonlyslightly (singleSSPorSSPmixture)withoutallthebandsthatcouldbe
surpassedbytheuseofchemicallyenrichedexponentialmodels. potentiallyaffectedbythespecifiedemissionlines,andexplore
ThetwoSSPmodelfittingapproachmaythereforebegenerally the residuals of the best fitting. If the residuals of any of the
consideredasareasonablemethodforanalysingthestellarpop- potentially affected bands present an excess in flux/magnitude
ulationsofmostkindsofgalaxiesinaconsistentway.Moreover, greaterthanalimitvalueprovidedbythecodeuser,Δm ,and
EL
giventhatMUFFITdoesnotimposeconstraintsonthemetallic- theseresidualsaredeviatedbeyondaband-errorfactor,σ ,the
EL
itiesofthetwo-SSPmixture,thiscanprovidehintsnotonlyof bandsareconsideredtobeaffectedbyemissionlinesandarere-
ageevolutionbutalsoofametallicitybuild-up.Thatbeingsaid, movedfromthefittingprocess.Bothconstraints,Δm andσ ,
EL EL
futureversionsofMUFFITwillalsoaccountfortheuseofdif- arerequired:thelattertoassurethattheexcessinfluxisnotdue
ferentsetsofSSPorτ-modelsforthebestchoiceoftheuser. to photometricuncertainties,andthe formerto avoidremoving
thosebandswithtinyobservationalerrorsthatpresentlittledis-
crepancieswithrespecttothemodels.Finally,werepeatthefit-
3.2.2. Emissionlines
ting withoutthe bandsidentifiedin the previousstep, gettinga
NebularemissionlinesappearfrequentlyintheSEDsofgalax- newsetofreliableχ2values,freeofnebularcontributions.
ies,evenifthesearedominatedbythelightcontributionoftheir FortheALHAMBRAcase,weuseΔm =0.1,becausefor
EL
stellar content. In particular, dealing with multi-filter galaxy lowercontributions,theaffectedbandsdonotsignificantlyaffect
data, filters affected by emission lines may present a substan- theSED-fittingresultsretrievedwith MUFFIT.Inaddition,we
tialexcessinfluxwithrespecttoanycombinationofSSPmod- setσ =2.5asareasonablestatisticalthresholdtodetectemis-
EL
els, because the latter typically do not account for the nebular sion lines over the noise. Figure 5 illustrates two SED-fitting
emission physics. To guarantee the accuracy and reliability of examplesoftwogalaxiesfromALHAMBRA.Thetoppanelof
thestellar populationparametersderivedduringthe fittingpro- Fig.5illustratesafittingofaquiescentgalaxyinALHAMBRA
cess, it is crucialto detect and removethose bands that can be without strong nebular emissions, whereas the bottom panel
significantly affected by emission. Not only because they are showsagalaxyforwhichMUFFITdetectsthatsomebandsmay
not comparable to SSP models, but also since filters contami- be affected by emission lines (yellow squares). The red curves
nated by strong emission lines tend to exhibitmuch higher lu- represent the observed photo-spectra, while the blue curve is
minositiesandlowerphotonicerrorsthantherestofbands,and the best-fitting modelafter the detection of emission lines pro-
therefore,thesebandswoulddominateourerror-weightedSED- cess.Theyellowsquaresarethebandswheretheinfluenceofan
fitting techniques (see Eqs. (9) and (10)). On the other hand, emission line is ticked, in this particular case Hβ, Hα+[Nii],
ii
it is worth recalling that the presence of strong emission lines and [S ]. The dashed black lines point out the wavelengths
may also provide fruitful information, since they contribute to for Hα, Hβ, and [Sii] at the galaxyphoto-z.Forthis case, the
restrictingthefeasibleredshiftintervalsofthegalaxy.Thered- detectionoftheemissionlinescontributeparticularlytostrongly
shift constraints due to nebular emissions are also considered constrainingtheredshiftrange.DespitetheALHAMBRAreso-
duringtheanalysis. lution(FWHM ∼300Å),wenotethatstrongemissionlinescan
Theemissionlinedetectionprocessofourcodedependson modifythefittingresults.Insomecases,evenHβshowssignif-
thespecificphotometricsystemofthegalaxysample,becauseit icantcontributionsintheALHAMBRAdataset.
only accountsfor those emission lines that are typically strong Sinceweareprovidingboththosebandsthatmaybeaffected
enoughtoaffectthephotometryofthegivenfilterset.Itisobvi- bystrongemissionlinesandtheresidualsfromtheSEDfittings,
ousthatthebroaderthespectralfilterwidth,thelargertheequiv- we can easily estimate the flux excesses in orderto later trans-
alent width (EW) of the line that may be potentially detected formthemtoEWs.Theadvantageofthismethodisthatourbest
ata fixedsignal-to-noise.In this sense, thecode isinitially fed SED-fittingsaremixturesofSSPs thatalreadyincludethe cor-
with a list of targetemission lines that dependsparticularlyon responding stellar absorptions, so the residuals can be directly
thefilterset,customizablebytheuser,withemissionlines,such relatedtotheabsolutenebularemission.Themainlimitation,in
as[Oii]λλ3726,3729,[Oiii]λλ4959,5007,H Balmer’sseries, general, comes from the low resolution of the data, because in
and[Sii]λλ6717,6731. manycasessomefilterscanbeaffectedbymorethanoneemis-
Thanks to the design of MUFFIT, we can also provide sionline,suchasHαand[Nii].Still,aspresentedinSect.5.2,
a list of typical AGN emission lines to reduce their effects thistechniqueopensnewpathsforfutureworkonemission-line
on the fittings, but broad AGN lines may affect two or more galaxieswithmulti-filterdata.
A14,page9of31
A&A582,A14(2015)
3.2.4. StellarpopulationparametersoftheSSPmixture
21.0
21.5 The stellar-population parameters of the mixture of SSPs are
B 22.0 estimated from the parameters of each component in the mix-
A
m 22.5 ture. This can be donein differentways, which mainly depend
23.0 of the weightsassignedto the parametersof the differentcom-
23.5 z =0.818 ponents. The most common definitions, provided by MUFFIT
phot
duals 00..02 awnedigehmtepdl.oTyehdeilnatttehrispproavpiedre,sarmeoluremrienaolsisittyic-winefiogrhmteadtioanndsimncaessi-t
si −0.2 accountsforthetotalmassofstarsineachpopulation,henceas-
e
R 500 1000 1500 2000 signinglargerweightstothemoreabundantordominantstellar
λeff[nm] populations. However, these populationsmay have very differ-
entluminosities.In this sense, luminosity-weightedparameters
21.0 zphot=0.258 aremorerepresentativeofthepopulationsthatdominatetheob-
served spectrum, since the galaxy SEDs are predominantlyled
21.5
B bythebrighterpopulations,eveniftheyarenotdominantinrel-
A
m 22.0 ativemass.
Best-fittingmodel
Throughout this work, the luminosity-weighted and mass-
22.5 Emissionlines weighted stellar population parameters of a mixture of n SSPs
ALHAMBRAgalaxy (forthisworkn = 2), p and p ,respectively,aredefinedfrom
als 0.2 thestellarpopulationpaLrameterMsofeachithcomponent(p;age,
sidu −00..20 metallicity,extinction,IMFslope,or[α/Fe])as i
e
R
500 1000 1500 2000 (cid:21)n
λeff[nm] αi×Li×pi
p = i=1 , (16)
Fig.5. Spectral fitting examples for galaxies from the ALHAMBRA L (cid:21)n
α ×L
survey using MUFFIT and the MIUSCAT SSP models. The galaxy i i
i=1
photo-spectraandtheirerrorsaregiveninred,whereasthebest-fitting (cid:21)n
gmaoladxeylsfaorrewghivicehnnionebmluies.sioTnhelintoepsapraendeelteccotrerdes.pTohnedsbottotoamqpuaiensecleinl-t p = (cid:6)n M(cid:12),ip = i=1αi×κi,SSP× pi, (17)
ltuhsretreabteasndthseaffcaesceteodfbaysetmari-sfsoiromnilningegsa,lianxyyelfloorww.ThhicehdMashUeFdFbIlTacdkeltiencetss M i=1 M(cid:12),T i (cid:21)n αi×κi,SSP
indicatethewavelengthsforHβ,Hα,and[Sii].Photometricredshifts i=1
aregivenintheinsetsinthefigure. whereα istherelativeflux-contributionoftheSSPmodelinthe
i
ithcomponent,κi,SSP therelativestellarmasscorrectionforthe
3.2.3. Stellarmasses ith component in the SSP mixture, and Li the luminosity of
the SSP modelin the observedspectral range.Both definitions
As we explainin Sect. 3.2.1,boththe normalizationterm ε in- agreewhentheparametervalueisthesameineachcomponent.
troduced in the χ2 minimization equation and the intrinsic lu-
minositiesofthetwobest-fittedSSPsaredirectlyrelatedtothe
3.2.5. Determiningthespaceofbestsolutions
totalstellarmassofthegalaxy.SSPmodelsareusuallynormal-
ized to an initial stellar mass of 1 M(cid:7), but this decreases with Becauseof thewellknowndegeneraciesamongstellar popula-
time, therebyaccountingfor the evolutionof the most massive tion parameters, it is essential to perform a reliable analysis of
stars.Thiseffectisproperlytakenintoaccountfordetermining thepossiblesolutions(asmixturesoftwoSSPs)foreachgalaxy
thefinalgalaxymassbyapplyingacorrectiontermtoeachSSP, accordingtotheuncertaintiesofthedata.Forthisreason,rather
κ ,whichisusuallyprovidedbythemodels. than providingonly the best-fitting solution for each galaxy (it
SSP
Whentakingtheaboveconsiderationsintoaccount,thetotal iswellknownthatthemostlikelyparametersarenotalwaysthe
stellarmass, M(cid:12),T,ofamixtureofnSSPs(forthisworkn = 2) best-fitting model parameters), our code accounts for the pho-
canbeexpressedas tometric errors of the multi-filter galaxy data to provide a set
ofthebest-fittingsolutions,therebyprovidingasetofprobable
(cid:6)n (cid:6)n
M(cid:12),T = M(cid:12),i =10−0.4εm ×4πdL2× κi,SSPαi vualalutieosnopfarreadmsehtiefrtss,(satgeellsa,rmmeatasslleisc,iteiexst,inacntdionIMs,Fasn)dfostreellaacrhpoobp--
i=1 i=1 ject.Thesevaluescanultimatelybeaveragedaccordingtotheir
(cid:6)n
weights and frequencies to derive the average final parameters
=εf ×4πdL2 × κi,SSP αi, (15) assigned to each galaxyand their errors. In this section we ex-
i=1 plain the processes and the applied criterion used to carry out
whereM(cid:12),iisthestellarmassofeachpopulationinthemixture, thisanalysis.
ε is the normalization term defined in Eq. (12), d the lumi- The determination of the best solution space is based on a
m L
nositydistancein cm units(seeHogg1999),κi,SSP the relative MonteCarlomethodthat,usingthepropersignal-to-noiseratio
stellar mass correction for the ith component in the SSP mix- ofeachfilter,seekstofindwhichparametervaluesarecompati-
ture,andα therelativefluxcontributionoftheSSPmodelinthe blewithinthephotometricerrorsofthedata.Sincephotometric
i
ith component(see Eqs. (13) and (14)).Throughoutthis work, uncertaintiesusuallyfollowanormaldistribution(orGaussian),
thederivedstellarmassesarequotedincludingstellarremnants we assume an independentGaussian distribution in each filter,
throughκi,SSP,butfora moregeneralcase,thisparametermay centred on the band flux/magnitude, with a standard deviation
notincluderemnants. equalto itsphotometricerror.Itis worthnotingthateach filter
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