Stellar Population and Kinematic Profiles in Spiral Bulges & Disks: Population Synthesis of Integrated Spectra

3.7 MB·English

by  Lauren A. MacArthur

Mon.Not.R.Astron.Soc.000,1–38(2008) Printed27January2009 (MNLATEXstylefilev2.2)
Stellar Population and Kinematic Profiles In Spiral Bulges & Disks:
Population Synthesis of Integrated Spectra
1⋆ 2 3
Lauren A. MacArthur , J. Jesu´s Gonza´lez †, and Ste´phane Courteau ‡
1DepartmentofAstrophysics,CaliforniaInstituteofTechnology,MS105-24,Pasadena,CA91125
2InstitutodeAstronomia,UniversidadNacionalAuto´nomadeMe´xico,ApdoPostal70-264,Cd.Universitaria,04510Me´xico
3DepartmentofPhysics,EngineeringPhysics&Astronomy,Queen’sUniversity,Kingston,ONK7L3N6,Canada
9
0
0
AcceptedJan16,2009
2

n
a ABSTRACT
J

7 We presentadetailedstudyofthestellarpopulations(SPs)andkinematicsofthebulge
2 andinnerdiskregionsofeightnearbyspiralgalaxies(Sa–Sd)basedondeepGemini/GMOS
data.Thelong-slitspectraextendto 1–2disk scale lengthswith S/N/A˚ >50.Severaldiffer-
]
O ent model fitting techniques involving absorption-line indices and full spectrum fitting are
exploredandfoundto weighage,metallicity,andabundanceratiosdifferently.We find that
C
SPs of spiral galaxiesare notwell matchedby single episodesof star formation;more rep-
h. resentative SPs must involve average SP values integrated over the star formation history
p (SFH) of the galaxy. Our “full population synthesis” method is an optimised linear combi-
- nation of model templates to the full spectrum with masking of regions poorly represented
o
by the models. Realistic determinations of the SP parameters and kinematics (rotation and
r
t velocitydispersion)alsorelyoncarefulattentiontodata/modelmatching(resolutionandflux
s
calibration). The population fits reveal a wide range of age and metallicity gradients (from
a
[ negativetopositive)inthebulge,allowingfordiverseformationmechanisms.Theobserved
positiveagegradientswithintheeffectiveradiusofsomelate-typebulgeshelpsreconcilethe
1
long-standingconundrumof the co-existenceof secular-likekinematics,lightprofileshape,
v and stellar bar with the “classical”-like old and α-enhanced SPs in the Milky Way bulge.
5
The disks, on the other hand, almost always show mildly decreasing to flat profiles in both
3
age andmetallicity,consistentwith inside-outformation.Ourspiral bulgesfollow the same
1
4 correlationsofincreasinglight-weightedageandmetallicitywithcentralvelocitydispersion
. as those of elliptical galaxies and early-type bulges found in other studies, but when SFHs
1
morecomplexandrealisticthanasingleburstareinvoked,thetrendwithageisshallowerand
0
thescattermuchreduced.Inamass-weightedcontext,however,allbulgesarepredominantly
9
composedofoldandmetal-richSPs.Whilesecularcontributionstotheevolutionofmanyof
0
ourbulgesisclearlyevident,withyoung(0.001–1Gyr)SPscontributingasmuchas90%of
:
v the optical(V-band)light, the bulgemass fractionfromyoungstars is small(.25%).This
i
X implies a bulge formation dominated by early processes that are common to all spheroids,
whethertheycurrentlyresideindisksornot.Whilemonolithiccollapsecannotberuledout
r
a insomecases,mergingmustbeinvokedtoexplaintheSPgradientsinmostbulges.Further
bulgegrowthviasecularprocessesor“rejuvenated”starformationgenerallycontributesmin-
imallytothestellarmassbudget,withtherelativesecularweightincreasingwithdecreasing
centralvelocitydispersion.
Keywords: galaxies:spiral—galaxies:evolution—galaxies:formation—galaxies:stellar
content—galaxies:bulges
1 INTRODUCTION
InthecontextofthecurrentlyfavoredcosmologicalΛ-ColdDark
Mattermodel(ΛCDM)ofourUniverse,theformationandevolu-
⋆ E-mail:[email protected]
† E-mail:[email protected] tionofgalaxiesremainsamajorunsolvedproblem.Inthismodel,
‡ E-mail:[email protected] structures form in a bottom-up, hierarchical, manner by which
(cid:13)c 2008RAS
2 L.A. MacArthuret al.
smallerfragmentsmergetogether toformmoremassivesystems. lar population (SSP), from which light-weighted SSP-equivalent
Whilethismodelhasbeenverysuccessfulatreproducingobserva- agesandmetallicitiescanbedrawnwiththehelpofspectralsyn-
tionsonlargescales,anumber ofissuesremaintoberesolvedat thesismodels(e.g.Vazdekis1999;Bruzual&Charlot2003,here-
thegalaxy-scaleregime(Mooreetal.1999;Navarro&Steinmetz afterBC03;Thomas,Maraston,&Bender2003; LeBorgneetal.
2000;Primack2007,andreferencestherein).Inparticular,thefor- 2004; Maraston 2005; Schiavon 2007). Elliptical galaxies (e.g.
mation of disk galaxies is not well represented in current imple- Trager,Faber,&Dressler2008)andglobularclusters(e.g.Cohen,
mentationsofsimulationsbasedonΛCDM(e.g.Belletal.2003; Blakeslee&Rhyzhov1998;Puziaetal.2005;Hernandez&Valls-
Kaufmann et al. 2007; Dutton et al. 2007). The discrepancies do Gabaud2008),areoftenassumedtoresultfromtheevolutionofa
not necessarily indicate a failure inthe ΛCDM model, but rather singleburstofstarformationandthuscanberepresentedbyaSSP
pointtophysicalregimesandprocessesthatareeithernotwellun- ofagivenageandZ.Thisassumption,however,breaksdownfor
derstood ordifficult toimplement inlargesimulations. Giventhe spiral galaxies that are believed to have been converting gas into
theoretical difficulties and limitations faced by current models, a stars at a relatively constant rate over most of their lifetime(e.g.
trueunderstandingofdiskgalaxiesmustincludeinformationfrom Kennicutt1983;James,Prescott,&Baldry2008).Sincethepres-
anobservationalperspective. enceof ayoung SPwilldominate theoptical light evenwhen its
All aspects of baryonic physics, from hydrodynamical pro- contribution to the mass is minimal, the light-weighted ages will
cessesinvolvinggas,throughstarformationandfeedbackfromsu- notberepresentativeoftheentirepopulation.Evenpureellipticals
pernovaeandAGN,canplayaroleintheformationandregulation showsignsof“frostings”ofyoungSPsandmaynotbewellrepre-
processes that shape galaxies, particularly where dynamically vi- sentedbyasingleSSP(Serra&Trager2007).
olent processes such asmajor mergersand rapid collapse arenot Greater potential for disentangling the SFH of spiral galax-
dominant.Forspiralgalaxies,theverypresenceofadiskcompo- iesexistsiftheycanbeassumedtohaveproceededsmoothlywith
nentimpliesthatnosuchmajoreventhasoccurredsincetheforma- time.ThisapproachwasfollowedbyMacArthuretal.(2004)us-
tionofthedynamicallyfragiledisk.Additionally,mostdiskgalax- ingbroad-bandopticalcoloursfor172low-inclinationdiskgalax-
ies harbor central bulge components whose prominence in terms ies. To the extent that the nearby spiral galaxies in this sample
oftotalmassorlightweightspansawiderangefromtrulybulge- share a similar underlying SFHand that no burst involving more
lesssystemstothebulge-dominatedearly-typeS0/Sa’s.Aquestion than 10% of the galaxy mass has occurred within the past 1–
thatnaturallyarisesisifthefinalsteptothedisk-less,i.e.pureel- 2Gyr∼,themethodprovidesreliablerelativeresults.Amongothers,
liptical, galaxies is a natural extension of bulge-to-total ratios in itwasfoundthattheSFHofspiralgalaxiesdependsstronglyonthe
systemsalongtheHubblesequence.Suchanextensionwouldim- galaxypotentialandhalospinparameter.
plythatthedominantbulgesofearly-typespiralshavefolloweda
Conclusionsbasedoncolourgradientsare,however,plagued
similarevolutionarypathtothoseofpureellipticalgalaxies.How-
byadegeneracybetweentheeffectsofage,Z,anddust,allleading
ever,comingfromtheoppositeend,aconnectionbetweenthetiny
to redder colours. Spectroscopic techniques, such as those based
bulgesof late-typespirals,through early-types, topure ellipticals
onabsorption-lineequivalentwidthsthatarelargelyimperviousto
may not seem as obvious, and allowance must still be made for
dusteffects(MacArthur2005),orfittingofthefullspectralenergy
thepurediskgalaxiesinanyscenario.Theemergingobservational
distribution(SED)whichcanincorporateadustcomponent,offer
picture of bulge formation currently implies similar evolutionary
amoredetailedanddiscriminatingview,especiallyinlightofthe
pathsforearly-typespiralsandpureellipticals,whilethelater-type
latestimplementationsofSPsynthesismodels(e.g.Vazdekis1999;
bulges exhibit much more diversity in their observed properties,
BC03;LeBorgneetal.2004).
consistent withhaving formed through a secular redistributionof
material from the disk (e.g. Kormendy & Kennicutt 2004). The Early-type spirals with their large bulge-to-disk ratio offer
nomenclaturepredominantintheliteraturetodistinguishbetween a significant observational advantage over late-types since their
formationscenariosforbulgesnamesthoseappearingverysimilar bulges, whichrisesignificantly aboveand below thedisk, can be
topureellipticalsystems(i.e.rapidand/orviolentformationwhich studiedspectroscopicallyintheedge-onperspectivefreefromdisk
includesboththemonolithiccollapseandmajormergingscenarios) contamination and extinction from dust. Late-type bulges, on the
as“classical bulges”andthoseformedsecularlyfromthediskas otherhand,aresmallandoftennothickerthanthegalaxydiskit-
“pseudobulges”.However,uncertaintiesinmakingaclear-cutdis- self,thusrequiringaface-onprojectionfortheirstudy.Whiledust
tinctionbetweenthesecasesstillremain,particularlyinregardsto andcontaminationfromtheinnerdiskwillstillthwartanypristine
thestellarpopulations(SPs)ofspiralbulges. observationofthebulge,theface-onorientationminimizesline-of-
Averyusefulprobeindiscerningbetweenformationscenarios sightintegrationsandkeepsthelightdistributionofthebulgeand
isadetailedbreakdownoftheage,metallicity(Z),andkinematic diskfreeofinclinationeffects.
properties of theSPscomprising bulges of all types. Information Spectroscopic studies of bulges spanning the full range of
about both light-andmass-weighted quantitiesisneeded toform Hubble types are few, and the results are often conflicting. The
a comprehensive picture of the star formation history (SFH)of a absorption-line studies of thecentral regions of Sa–Scspiralsof
given system. However, beyond our Local Group, we are limited Trageretal.(1999)andProctor&Sansom(2002,hereafterPS02)
toobservations of theintegratedlightalong agivenlineofsight. bothfindthatlate-typebulgescannotbereproducedusingprimor-
Of relevance is whether the integrated light at any location in a dialcollapsemodelsandinvokeextendedgasinfallontothecen-
galaxy can be deconvolved into the relative fractions of stars of tralbulgetoexplaintheobservations.Inasimilarstudy,Goudfrooij
agivenpopulation thatcontributetothetotallight.Thisquestion etal.(1999)concludetheopposite,theirfindingsbeingmorecom-
is especially acute for spiral galaxies that are known to harbor a patible with predictions of the ‘dissipative collapse’ model than
mixtureofyoungandoldstarsandcansufferfromtheextinction with those of the ‘secular evolution’ model for bulge formation.
effectsofdust. Theirsampleis,however,dominatedbyearly-typespiralsandthese
Observations of colour gradients and absorption line-indices conclusionsmaynotapplytothefullrangeofspiraltypes.Finally,
ingalaxiescanbothbeinterpretedasasingle-burst,single-Z stel- theanalysisofMoorthy&Holtzman(2006)oflinestrengthsinthe
(cid:13)c 2008RAS,MNRAS000,1–38
PopulationSynthesisof SpiralGalaxies 3
bulgesandinnerdisksof38spiralsalsofavoursascenariowhereby 3outlinesour techniqueforextractingSPparametersfrominte-
§
mergingisthedominantmechanismforbulgeformation. gratedspectraincludingdetailsofthefittingalgorithm,providing
Thomas&Davies(2006)reanalyzedthePS02dataandfound specificsabouttheweightingofindividualpixelsandourso-called
no difference between the SPsof spiral bulges and Es at a given “σ-clipping”procedureformaskingdeviantpixels,aswellasade-
centralvelocitydispersion,σ0,concludingthatprocessesinvolving scriptionofthemodelSPtemplatesusedinthefits.Ourresultsare
diskmaterialcannotberesponsiblefortherecentstarformationim- presentedin 4whichincludesthederivedSPparametersandtheir
§
pliedbytheyoungages.Inananalysisofstellarabsorptionlinegra- radial profiles, kinematic profiles (rotation velocity and velocity
dientsinthebulgesof32nearbyedge-onspirals(S0–Sc),Jablonka dispersion),aninvestigationofcorrelationsofcentralparameters,
etal. (2007) alsofindthat, whencompared at aatagiven veloc- and acomparison withprevious studies. Wediscuss in 5results
§
itydispersion,galaxybulgesresembleellipticalgalaxies.Recently, foreachindividualgalaxyinthecontextofbulgeformationscenar-
MacArthur et al. (2008) have extended these results to bulges at ios,and 6summarizesthesalientpointsfromtheentireanalysis.
§
intermediateredshifts(0.1<z<1)findingthatthemassassembly Finally, we provide several appendical sections: A presents the
§
historyofbulges, inferredviatheFundamental Plane,isindistin- observed radially resolved spectra for our galaxies. B discusses
§
guishablefromthatofpurespheroidalgalaxies(E/S0s)atagiven derivations of SP parameters for our spiral galaxies based on the
mass. Lick-indexsystemandoffullspectrumfittingofsingleSSPs.All
Asignificantoutlierfromthistrend,however,isthebulgeof techniquesarecomparedandcontrastedin C.
§
our own Milky Way (MW). Detailed photometric (Zoccali et al.
2003)andspectroscopic(Rich&Origlia2005;Zoccalietal.2006)
studiesofabundanceratiosofindividualMWbulgestarsrevealold
andα-enhancedSPsthatmusthaveformedlongagoandonshort 2 DATA
timescales,andnoevidenceisfoundforthepresenceofayounger
Thelong-slitspectroscopicdataforthisstudywerecollectedusing
SP.ThisobservationisdifficulttoreconcilewiththeMW’ssmall
theGeminiMulti-ObjectSpectrograph(GMOS;Hooketal.2004)
σ0 and the presence of a stellar bar (e.g. Lo´pez-Corredoira et al. onthe8-mGeminiNorthtelescopeatMaunaKeainHawaii.The
2007). AsThomas&Daviespoint out,theMWstudiessamplea
GMOSdetectorconsistsofthree2048 4608CCDswith13.5µm
largerphysicalradiusthanthoseofexternalgalaxiessothisconun- pixelsprovidingaspatialresolutionof×0.072′′/pixandadispersion
drum could be resolved if there is a positive age gradient in the of0.45A˚/pixwiththeB600 G5303grating.Theinternalstability
bulge.
oftheslitmaskrequirestwoequallyspacedbridgesbetweentheslit
Adding further complexity to the picture, in a study of
edgeswhichliealongthespatialdirection.Thespacingsbetween
absorption-linemapsof24early-typespirals,Peletieretal.(2007) the3CCDdetectorsmanifestassmall( 17A˚)gapsinwavelength.
findthatwhileinclinedsamples,whichsamplethedisk-freeouter ∼
The high sensitivity of the B600 G5303 grating in the blue
bulge regions, reveal uniformly old SPs, randomly oriented sam-
matches well our simultaneous spectral coverage of 4050–
ples,spanningthesamerangeinHubbletype,showawiderange 6750A˚.Thisrangeincludesmostofthemajoratomicand∼molecu-
in SP parameters. This discrepancy, along with their observation
larfeaturestodisentangleageandmetallicityeffectsinintegrated
of central dips in the velocity dispersion profiles of half of their
galaxy spectra (Worthey1994). Theslit fieldof view (FOV) was
bulges, indicative of the presence of a colder central component, 5′(length) 2′′ (width)forallofourobservations.Thechoiceof
canbereconciledinapicturewhereby thecentersof mostearly- ×
slit-widthwasprescribedbytheneedtomaximizesignal-to-noise
type spirals contain multiple kinematic components: an old and
(S/N)intheouterdiskwhilemaintainingadequatespectralresolu-
slowly rotating elliptical-like component, and one or more disk- tionthroughout.The2′′slitandB600gratinggiveatop-hat10.81A˚
like,rotationallysupported,componentswhicharetypicallyyoung,
fullwidthathalfmaximum(FWHM)resolutionandaGaussianin-
butcanbeold.Thesumofallcentralcomponentsmakeupthepho- strumentalresolutionof0.8 0.02A˚ (asmeasuredfromthewidth
tometricallydefinedbulge,andthedifferentcomponentscontribute ±
ofthenarrowestskyemissionlines).
differentlytotheintegratedlightdependingontheviewingangle.
Their conclusion of a rejuvenation of the central region through
dynamical disk-like processes, however, isdifficult to understand
2.1 GalaxySample
inthecontextoftheaboveresultsinthatthe“rejuvenated”low-σ
ellipticalsdonothavediskcomponents. Ideally, we desire a large and homogeneous sample of nearby
Attheheartoftheseconflictsisthefactthatextantstudiesof spiralgalaxiesspanningthefullHubblesequencetostudyspectro-
localbulgesarelimitedinonewayoranother(samplesize,range scopically the SPsof spiral bulges and disks. The sample should
inHubbletype,dataofinsufficientdepthand/orspatialresolution alsoinclude barred and non-barred spiralsinorder totest for the
forstudiesofgradientsandassessmentofdiskcontamination,etc.). expected mixing effects by a bar. The size of the current sample
Ouraimistoremedythissituationwithasystematicandhomoge- wasacompromisebetweenareasonabletelescopetimerequestfor
neousstudyoftheSPsandkinematicsofbulgesforthefullrange apilotstudyandtheneedtomeasuresystematicvariationswithin
ofHubbletypes.Afirst,andimportant,stepistoestablishareliable thatsample.Wehavethusnarrowedinonthefollowingcriteria:
procedureforextractingaproperrepresentationoftheSPcontent HubbletypeSa–Sd(withemphasisonlatertypes)
•
thatdoesnotsufferfromthedegeneraciesandlimitationsdiscussed Mixofbarred/unbarredsystemsandSBprofiletypes
above.Inthispaper,wepresentapilotsampleoflong-slitoptical •Face-on(inclination.35◦)
•
spectroscopy of eight nearby, low-inclination, spiral galaxies ob- Blue Galactic extinction A =4 E(B V)60.5mag
B
• × −
served with Gemini/GMOS with which we develop such a tech- (Schlegeletal.1998)
niqueandattempttoaddresstheformationofspiralbulgesthrough Bluemajoraxis.2 slitlength(.10′.5),butlargeenoughto
astudyoftheirradialprofilesinSPsandkinematics. r•esolvebulgeandinner×disk(&2′′).
Theorganizationofthepaperisasfollows.In 2wedetailthe
§
sampleselection,observationalstrategy,andreductionprocedures. The galaxy sample and catalog information from theNASA
(cid:13)c 2008RAS,MNRAS000,1–38
4 L.A. MacArthuret al.
Table1.GalaxySample:cataloginformation.
Names Hubble Diam RA DEC V M A
helio B B
NGC/IC UGC Type a(′)×b(′) (J2000) (kms−1) (mag) (mag)
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
N0173 U369 SA(rs)c 3.2 ×2.6 00h37m12s.47 +01◦56′32′.′1 4366 13.70 0.110
N0628 U1149 SA(s)c 10.5 ×9.5 01h36m41s.77 +15◦47′00′.′5 657 9.95 0.301
N1015 U2124 SB(r)a 2.6 ×2.6 02h38m11s.56 −01◦19′07′.′3 2629 12.98 0.139
N7490 U12379 Sbc 2.8 ×2.6 23h07m25s.17 +32◦22′30′.′2 6213 13.05 0.362
N7495 U12391 SAB(s)c 1.8 ×1.7 23h08m57s.18 +12◦02′52′.′9 4887 13.73 0.371
N7610 U12511 Scd 2.5 ×1.9 23h19m41s.37 +10◦11′06′.′0 3554 13.44 0.171
N7741 U12754 SB(s)cd 4.4 ×3.0 23h43m54s.37 +26◦04′32′.′2 751 11.84 0.323
I0239 U2080 SAB(rs)cd 4.6 ×4.2 02h36m27s.88 +38◦58′11′.′7 903 11.80 0.307
Notes—Cols.(1)&(2):NGC/IC,andUGCGalaxyIDs.Nameshighlightedinboldarethoseusedsubsequentlytorefertotheparticulargalaxy.Col.(3):
HubbleType(fromNED).Cols.(4&5):Major(a)andminor(b)axisdiameters(inarcmin).Cols.(6&7):GalaxyRAandDEC(J2000).Col.(8):Heliocentric
radialvelocity.Col.(9):TotalB-bandmagnitude(Vega)fromNED.Col.(10):B-bandgalacticextinctionfromSchlegel,Finkbeiner,&Davis(1998).
ExtragalacticDatabase(NED)1areshowninTable1.Opticalimag-
Table 2. Bulge and Disk Photometric
ing for all eight galaxies was collected using the Large Format ScaleParameters
Cameraonthe200-inchHaletelescopeatthePalomarObservatory
inDecember2006.ObservationswereobtainedintheBVRIBessel Name re Se´rsic rd
filtersforallgalaxiesexceptN0173,forwhichonlyB&Vwereob- NGC (′′) n (′′)
tained (due to bad weather). Surface brightness profiles were ex- (1) (2) (3) (4)
tractedfromtheseimagesandbulgeanddiskphotometricparame-
N0173 3.8 1.5 21.9
terswerederivedfrombulge-to-disk(B/D)decompositionsintoan
N0628 10.5 1.1 68.2
exponential diskplusageneralizedpower-law(Se´rsic)profilefor U2124 5.7 1.5 12.2
thebulge,aslistedinTable2.Wereferthereader toMacArthur, N7490 4.5 1.6 21.4
Courteau, & Holtzman (2003, hereafter Mac03) for details about N7495 3.6 2.3 17.2
profileextractionandB/Ddecompositions.Notethatherewerefer N7610 1.7 0.8 17.6
to the disk scale length as r and the bulge effective (half-light) N7741 6.7 1.0 42.3
d
radius as r for aprofile characterized by the Se´rsicnshape pa- I0239 8.2 0.9 43.8
e
rameter. Notes—Photometricbulgeanddiskscaleparameters
Asistypicalforlate-typebulges(e.g.deJong1996;Graham basedonopticalimaging(eitherRorI-band,but
V forN0173)fromthePalomar200-inchtelescope.
2001; Mac03), most of our decompositions reveal bulge profile
Errorsonthediskscalelengthsare.10%and.20%
shapesclosetoexponential,whichtranslatestoaSe´rsicindexn=1. forbulgeparameters.SeeMac03fordetailsofour
Mostnotably,thebulgeofN7495wasbestfitwithn=2.3.Bulges B/Ddecompositionscheme.Col.(1):GalaxyID.Cols.
(2–4):B/Ddecompositionvaluesforbulgeeffective
withn&2aretypicallyfoundinearlier-typebulgesthoughttobe
radius(re),Se´rsicn,anddiskscalelength(rd).
more akin to elliptical galaxies (e.g. Fisher & Drory 2008). This
suggestsperhapsthattheHubbletypeofthisgalaxyisearlierthan 2.3 IntegrationTimesandObservingStrategy
Sc.Infact,asnotedinNED,theoriginalUGCcataloguedoesrefer
tothisasan“earlyspiral”(Nilson1973). Ontheother hand, our Theon-targetintegrationsweredividedintoseparateexposuresto
onlySabulge,U2124,isbestfitwithn=1.5whichislowforan filter out cosmic rays and confirm weak features. On-target In-
early-typebulge.However,thestrongbarinthisgalaxyrendersthe tegration times were 3 15 min for MB<10.5, 3 18 min for
× ×
decompositionlesscertain. 10.5<MB<12, and 4 18 min for MB>12, for total integra-
×
tionsof45–72minpergalaxy.Anestimateoftheskybackground
wasmeasuredfromtheslitedgesforgalaxieswithmajoraxisdi-
ameters<4′.Forgalaxieswiderthantheslit,wedividedourexpo-
2.2 StandardStarSample
suresintosky/galaxy/skysequenceswithintegrationtimesforsky
WeobservedsevenLick/IDSstandardstars(Wortheyetal.1994) (off-target) pointings of 1/5 of the on-target integrations2. See
∼
with the same observational set-up as the main targets for flux Fig.1fortheobservational set-upforeachgalaxy.Skypositions,
calibration of the galaxy spectra. These included dwarfs and whennecessary,areshownbytheyellowslits.Skyexposureswere
giants with a range of physical parameters relevant for star- binnedtoachievethesameS/Nasthegalaxy.
forming galaxies (spectral type: A1–F5; effective temperature:
T 4700–9000K,surfacegravity:log(g)=2.4–4.3;andmetal-
eff∼ 2.4 DataReduction
licity: [Fe/H]= 0.45–0.07). Flux calibration was achieved by
−
comparison of our standard star observations withflux calibrated Therelevant measurements for thisstudy donot requireabsolute
spectra of stars in common with the ELODIE archive (Moultaka spectrophotometric calibration of the data. However, they do re-
etal.2004;seehttp://atlas.obs-hp.fr/elodie).
2 Inhindsight,skyintegrationtimesof1/3–1/2oftheon-targettimeswould
have been preferred. The short sky exposures prevented a deeper explo-
1 http://nedwww.ipac.caltech.edu/ rationofthelow-SBdiskregions.
(cid:13)c 2008RAS,MNRAS000,1–38
PopulationSynthesisof SpiralGalaxies 5
Figure1.Observationalset-upfortheeightgalaxiesinoursample.ThebackgroundimagesarefromtheCanadianAstronomyDataCentre’sDigitizedSky
Server(CADC;http://cadcwww.dao.nrc.ca/).Thebluelinerepresentstheslit,thered(dashed)boxandlongarmrepresenttheFOVoftheGMOSwavefront
sensorcamera,withtheboxattheendofthearmcenteredontheguidestar.Thepanelsforlargegalaxies(NGC628,NGC7741,andIC239)alsoshow,as
yellowlines,theskyoffsetpositions.TheFOVfortheCADCpicturesdifferinallthepanelsbuttheslitlengthiseverywherethesame(5′).
quire extreme care in removing instrumental effects in order to 3.1 FullPopulationSynthesis
achieveaccuraterelativecalibrationalongboththedispersionand
Populationsynthesisisatechnique appliedtotheintegratedlight
spatial directions. Proper subtraction of the sky and instrumental
ofcomposite systemstodeterminethefractionof light(or mass)
and far-field scattered light is also crucial. Finally, accurate flux
contributedbyeachofthemainstellargroupscomprisingthesys-
calibrationisrequiredforthegalaxyobservations,particularlyfor
tem.Usingalinearcombinationofstellarormodeltemplatesthat
long-baselinemeasurementssuchasthoseofmolecularindicesand
cover the optical spectral range, the temperature mix of a galax-
fullspectrumfitting.Wewenttogreatlengthstoassurethehighest
ian(composite)systemcanbedeterminedandusedtoexploreits
possiblequalityinourfinaldataproducts.Intheinterestofspace,
evolutionaryhistoryandtopredictthefluxofthesystematother
thedetaileddatareductionprocedureswillbedescribedinaforth-
wavelengths as a test of the synthesis (Jacoby, Hunter, & Chris-
comingpaper.
tian1984;Pickels1985;Heavensetal.2000;CidFernandes2007;
Tojeiroetal.2007).
The“fullpopulationsynthesis”techniquedevelopedherecon-
3 EXTRACTINGSTELLARPOPULATION
sistsofdeconvolvinganobservedgalaxyspectrumintobasiccom-
PARAMETERSFROMSPECTRA
ponentsrepresentingtherelativecontributionsofabasissetoftem-
Many different techniques can be used to characterize the stellar plate spectra. It is important for the method of decomposition to
populationparametersofanintegrated(optical)spectrum.Wehave allowforconstraintstobeplacedonthecomputedparametersfor
exploredseveraloftheseindetail.Appendix Bpresentsouranal- which we turn to the method of boundconstrainedoptimization
§
ysesbasedontheLicksystemofabsorption-lineindicesandthat (Byrdetal.1995;Zhu,Byrd,&Nocedal1994,1997).Theproblem
offullspectrumsingleSSPfits.BothmethodsproduceSPparam- canbesummarizedassolvingfor
etersbased on SSPsand arethus extremely sensitive to themost
recentepisodeofSF,evenwhenitscontributiontotheSPinterms minf(x)
, (1)
ofmassisinsignificant.Theline-indextechniqueisalsoverysen- subjecttol6x6u
sitivetoanyongoingSFastheemission-linesfromHIIregionsfill
in the underlying absorption features, thus thwarting reliable age where f(x) is the merit function which depends non-linearly, in
estimates.WeconcludeinAppendix CthattheSPsofourspiral general,onthefitparametersx ,andl andu arelowerandupper
j j j
§
galaxiesarenotwellrepresentedbySSPsandanaccuraterepresen- boundsrespectivelyoneachparameterx .Additionally,thegradi-
j
tationmustrepresenttrueaveragevaluesoftheSPparameters,i.e. entgofthemeritfunctionf withrespecttothefitparametersmust
integratedovertheSFHofthegalaxy.Inthefollowingsectionswe beavailable.Thealgorithmperformstheminimizationiteratively
describeourdevisedmethodforachievingthisgoal,whichreferto where, at each iteration, the current fit parameters are varied by
as“fullpopulationsynthesis”. amountsdeterminedbythecurrentpartialderivativesofthemerit
(cid:13)c 2008RAS,MNRAS000,1–38
6 L.A. MacArthuret al.
function.Tostarttheiterationaninitialconfigurationmustbesup- chosen for “moderate” accuracy. Similarly,pgtol isatolerance
plied. levelforterminationofaniterationif
Ideally, thelocus of themerit function’s minimum will bea
max(projg , i=1..n)6pgtol
singlepointinthevectorspacedefinedbythebasislibraryoftem- | i|
platespectra.Thenecessaryconditionsforthisidealcaseare:(1) whereproj g istheith component oftheprojectedgradient. For
i
thebasissetiscompleteandnon-redundantand(2)thereisnonoise thecurrentapplicationpgtolwassetto10−5.Theiterationter-
inthedata.Inthissituationthesolutionwillbeindependentofthe minatedaccordingtothelattercriterionforalltestsandrunsofthe
initialconfiguration.However,inanyrealsynthesiswearelimited program.
byobservationaluncertainties,resolution,physicaldifferencesbe- Themeritfunctiontobeminimizedisdefinedas
tweentheobservedspectrumandmodeltemplates(e.g.abundance 1
N 2
ratios,dust,emissionlinesfromH IIregions,anynon-stellarcon- Merit= 1 R2 , (2)
tributionfromAGN,etc.)andpossibledegeneraciesinthelibrary N M i
itself.Hence,thelocusoftheminimummeritfunctionwillbeafi- − Xi=1 !
nitevolumeinthebasisspace.Theultimatesuccessofapopulation where
synthesisisthereforelimitedbytheobservational accuracyofthe
R =w (G S ). (3)
i i i i
spectraandthematchbetweendataandtemplatelibrary. −
Intheaboveexpressions,N isthenumberofdatapointsincluded
in the fit, M is the number of templates in the library, G is the
i
3.2 TheProgram observedgalaxyfluxatwavelengthλi,wi istheweightoftheith
pixel(see 3.3),andS isthemodeledgalaxyfluxatλ givenby
i i
Theproblemofboundconstrainedoptimizationarisesinnumerous §
M
scientificandtechnicalapplicationsandhasbeenanactiveareaof
S = x F , (4)
research in the field of numerical analysis. As a result, there are i j ji
now a number of robust optimization routines available; XRQP Xj=1
(Bartholomew-Biggs 1979) and LANCELOT (Conn, Gould, & where F denotes the fluxat theith wavelength of thejth tem-
ji
Toint1992),tonameafew.Theprogramofchoiceforthepresent plate,andx istherelativecontributionofthejth templatetothe
j
problemisthatofZhuetal.(1994;1997)calledL-BFGS-B3.This synthesizedspectrum.
isaFORTRAN77code thatsolveslargenon-linear optimization In order to prevent negative stellar contributions, as a non-
problemswithsimplebounds. Ithasbeenwelltestedandisideal physicalartifactofthedecomposition,thespectralcoefficientsare
forthecurrentproblem.AfulldescriptionoftheL-BFGS-Balgo- subjecttoalowerboundonthefitparameterssuchthat
rithmisbeyondthescopeofthispaper,buttheinterestedreaderis
referredtoByrdetal.(1995)andZhuetal.(1994;1997). xj >0.
AdriverprogrampopsynthwaswrittenwhichcallstheL-
BFGS-Broutine.popsynthperformsthefollowingsteps:
3.3 Weighting
(i) Setupinputvaluesforcalltosetulb,thecallingstatement Thenatureofourfittingalgorithmisparticularlyusefulformask-
ofL-BFGS-B ingoutundesirableregionsinthespectrum.Thefollowingpatholo-
(ii) Setupinitialvaluesforfitparametersxj gies,whichdifferforeachgalaxydue,inmostpart,tovelocitydif-
(iii) Readinthegalaxyspectraandassociatedvariancevectors, ferences, are examples of regions that one may want to omit: (i)
andthetemplatelibrary gapsinwavelengthcoverageduetothespacingbetweenthethree
(iv) Compute the merit function and its gradient for the given GMOSCCDs,(ii)strongandvariablenightsky-lineregions,and
setoffitparameters (iii)emissionlineregions(duetoHIIregionsand/orplanetaryneb-
(v) Callthesetulbsubroutinewiththenewmeritfunctionand ulae).Asafirstguess,allof(i),(ii),&(iii)aremaskedfortheinitial
gradientvalues fitofeachspectrum.Subsequently,weallowforallpointstoenter
(vi) Testforconvergence,ifnotrepeat(iv)–(vi) backintothefit(subjecttotheconstraintsdefinedbelow)exceptfor
(vii) Outputstellarfractionstodatafiles. thegapregions,inwhichnorealdataexist,thusarealwaysfixed
tozeroweight.
Zhuetal.(1997)provideacompletedescriptionoftheinputparam-
eters,butabriefintroductionisrelevanthereinordertounderstand
theconvergencecriteriaofthealgorithm. 3.3.1 σClipping
The input variable factr is a double precision number
which defines atolerance level inatermination test for the algo- Wedefineamaskvalue,mi,foreachdatumsuchthat
rithm.Theiterationwillstopwhen 1, includeincurrentfit
m =
i 0, removefromcurrentfit
fk−fk+1 6factr epsmch, n
max(fk , fk+1 , 1) ∗ andtheweight,wi,as,
| | | |
where epsmch is the machine precision which is automatically w =m 1 , (5)
generated by theL-BFGS-Bcode (equal to2.22 10−16 onthe i i σi2
Linuxmachineusedforthisproject.)Avalueoffa×ctr=107was whereσ istheerroronG .
i i
Inageneralweightedfit,verydissimilarweightscanbedis-
tributedamongthedatapoints.Asaresult,thenumber ofdatum,
3 Canbedownloadedfromhttp://www.ece.northwestern.edu/∼nocedal/lbfgsb.htmNl ,doesnot alwaysrelatedirectlytotheactualinformationfeed-
asofwriting. ing the fit. Instead, an effective number of points, Neff, can be
(cid:13)c 2008RAS,MNRAS000,1–38
PopulationSynthesisof SpiralGalaxies 7
estimatedby the sumof theweights divided by themean weight whichusethespectrallibrarySTELIBofLeBorgneetal.(2003),
(Gonza´lez 1993) (note that in the following, all sums run from forarangeofmodelSSPsandallowingforawavelengthdependent
i=1..N,whereN isthetotalnumberofdatapoints): (velocity-like,i.e.constantwith∆λ/λ)terminadditiontoaterm
thatisconstantwithwavelength.Ouranalysisiscarriedoutusing
w w ( w )2
N = i = i = i . (6) anupgradedversionoftheMovelalgorithmdescribedinGonza´lez
eff Phwii ( wiP∗wi)/ wi P wi2 (1993).Inbrief,Movelderivesvelocityshift,velocitydispersion,
Next we define the effective number of templates entering andγ (ameasureoftherelativelinestrengths,withγ=1indicat-
P P P
each fit,M . Thisisrequired asit ispossible for asignificant ingaperfectmatch)throughaFouriertransformprocedure.Inve-
eff
fractionofthetotalnumberoftemplatesconsideredtoendupwith locity space, the observed galaxy spectrum can be characterized
zerocontributiontothefit.M isdefinedasfollows(heresums bythespectrumofitspopulationconvolvedwiththeinstrumental
eff
runfromj=1..M,whereM isthetotalnumberoftemplatescon- response function and a broadening function which characterizes
sidered): the distribution of stellar radial velocities along the line of sight
(LOSVD).The“population”isrepresentedbyatemplate(observed
M = Fj = ( Fj)2 = 1 , (7) or model) of higher resolution than the galaxy spectrum. Movel
eff FPj2/ Fj PFj2 Fj2 derivesthebroadening functionthat best matchesthetemplateto
where FjPis the fPractional coPntribution oPf SSP model Mj (thus thegalaxyspectrum.Totheninfertheabsoluterotationandveloc-
F =1bydefinition). itydispersionparametersoftheobservedspectrum,onemustknow
j
The expected variance (of the mean) based on the measure- veryaccuratelythecharacterizationofthetemplateused.
mPenterrorsis For the purpose of characterizing the BC03 resolution (both
globally and as a function of wavelength), we use as a template
N
σ2 = eff , (8) spectrumthevery high-resolution (effectivelyinfinitefor thisap-
exp w
i plication)solarspectrumofWallace,Hinkle,&Livingston(1998)
andthetypicalvariancefromthefitis, alongwiththeBC03model SSPs,whichareeacheffectivelydif-
P
σ2 == Neff (wi∆2i) , (9) fSeTreEnLtIcBo.aTdhdeitsioonlasrt(einmprelalatetivaendwmeiogdhetlSanSdPssatarrespurosecdes)seodftshtarorsugihn
fit Neff −Meff (cid:20)P wi (cid:21) Movelin200A˚ wavelengthintervalscenteredaround26spectral
where∆i Gi Si. P features,from3575A˚ upto7400A˚ definedby21Lick-likeindices
Finall≡y,t|hefi−tχ2|istheratioofthemeantypicalandexpected plustheHαandCaIIH&Klines,and3moresomewhatadhocre-
variances, gionsshortwardofCaIIH&KandlongwardofHαtocoverthefull
opticalrange.SpectralfeaturesinanygivenSSPthatarenotwell
χ2 =σ2 /σ2 . (10)
fit exp characterized bythesolar template areweightedout accordingly.
Ateachiteration,thequantitiesinEqs.4–9arecomputedand Wethen fitthetrendof resolution vs. λfor alargerange of SSP
theindividualmasks,m ,areassignedaccordingtothecriterion, templates using three different constraints; (i) fitting for constant
i
termswithbothλandvelocitywithbothtermsasfreeparameters,
1, if ∆ <N σ
m = i σ fit (ii)fixingFWHM=3A˚ andfittingforavelocityterm,and(iii)forc-
i 0, otherwise
ingonlyalinearFWHMcomponent.Thisprocedurerevealedthat
n
OnthefirstiterationwesetNσ=5,thesecond hasNσ=3.2,and theresolutiontrendoftheBC03modelsismuchbetterrepresented
twofinaliterationshaveNσ=2.8.Werefertothisiterativemasking by a FWHM constant with λ plus a velocity term (constant with
schemeas“σ-clipping”. ∆λ/λ).
Forourdata,thetypicalnumberofdatapointsforeachspec- Toinvestigatethecause of thisdiscrepancy, wedownloaded
trumisintherange N=1280–1340; after the“σ-clipping” itera- theSTELIBlibrary4andexaminedtheindividualspectra.Firstwe
tionsdescribedabove,thetypicaleffectivenumberofpointsinthe notedthatthestartingλanddispersionarenotall3200&1A˚ as
finalfitspanstherangeNeff=850–1250. Inthisanalysisweuse stated in the documentation on their website. The reason is that
M=70modeltemplates(see 3.4)andtypicalvaluesforMeffare the2003v3.2librarystarshadtheirradialvelocitiesremoved,but
§
intherange2–6. the spectra were not rebinned to the λ0=3200 & disp=1A˚. A
lookintotheheadersrevealedaspreadinthestartingwavelength
ofRMS =1.09A˚ andindispersionofRMS =0.00033A˚.As
3.4 StellarPopulationTemplates λ0 disp
thesetwodifferencesintherelativewavelengthcalibrationarecor-
Thestellarpopulationtemplatesusedthroughout thisanalysisare related and, if fixed values are assumed when coadding the indi-
from the models of BC03 which provide spectra of simple stel- vidual stars, the combined effect will degrade the effective reso-
lar populations (SSPs), single-Z/single-bursts of star formation. lution of the model SSPs. In measuring the resolution as a func-
Thesecover thewavelength range3200–9500A˚,alargerangeof tionofwavelengthfor12individualsolar-typestarsintheSTELIB
ages(0.0001–20Gyr),andmetallicities(Z=0.0001–0.05)atare- library we found, not surprisingly, that the individual stars are
portedresolutionof 3A˚ FWHM.Weuseherethemodelswith consistentwithapureconstantresolution(novelocity-likebroad-
∼
theChabrier(2003)initialmassfunction(IMF). ening at all) and we measured the best constant FWHM to be
3.08A˚( 0.03). We thus concluded that the above-mentioned λ0
±
&dispersionmismatchwasnottakenintoaccountwhenthestars
3.4.1 TemplateCharacterization
werecoadded tocreatetheBC03modelSSPs,thusresultingina
Giventheimportanceofknowingthepreciseresolutionofthetem- velocity-likebroadeninginadditiontotheconstantresolutionterm.
platesforcomparisonwithgalaxydataandformeasuringthesmall
velocity dispersions of spiral galaxies (see 4.4), we undertook a
§
deep investigation into the true resolution of the BC03 models, 4 http://www.ast.obs-mip.fr/users/leborgne/stelib/index.html
(cid:13)c 2008RAS,MNRAS000,1–38
8 L.A. MacArthuret al.
We also found a spread in the velocities of the 12 stars (whose models which is the least well modeled and exhibits anomalous
measured relative velocities were removed in STELIB) with an SSPspectra).Thisprovidesatotalbasissetof70SSPspectra,all
RMS=11.4kms−1,whichwillalsocontributetothevelocity-like showninFig.26.
broadeningoftheSSPs. Weare interested in both the light- and mass-weighted con-
Theaboveprocedureleadstothefollowingconclusionsabout tributions of each SSP to the integrated galaxian light. All SSPs
thetrueeffectiveresolutionoftheBC03SSPs:(i)Theactualspec- in our library have been normalized to their V-band flux, so the
tral resolution of the models is worse than 3.0A˚ (significantly V-bandlight-weightforSSP iscomputedas(heresumsrunfrom
j
larger than for individual stars in STELIB); (ii) The best con- j=1..M,whereM=70isthetotalnumberofSSPtemplatescon-
stant (no velocity broadening) FWHM is 3.40A˚( 0.04); (iii) If sidered):
the 3.08A˚ resolution derived for individual stars i±s assumed, the
SSPmodels(co-addedSTELIBstars)needasignificantadditional lj =xj/ xj, (11)
velocitybroadening(35.8 3.6kms−1),butthefitisnotasgood j
X
as when assuming a const±ant 3.4A˚ resolution. After exploring andthemass-weightas
∼
thefitresultsunder alltheabove assumptions, theadopted (best)
values for the FWHMresolution and velocity broadening for the mj =xj (M/LV)j/ (xj (M/LV)j), (12)
∗ ∗
BC03modelsarefoundtobe: j
X
FWHMBC03 =3.375A˚ & σBC03 =11.40 kms−1. where(M/LV)j istheV-bandmass-to-lightratioofthejthSSP.
Thustheaveragelight-weightedquantitiesarecomputedas:
Theseresultscanbeunderstoodasthecombination(convolution)
of:(i)the3.08A˚ FWHMresolutionofeachindividualstar,plus(ii) A = l A and Z = l Z , (13)
l j j l j j
the11.40kms−1radialvelocityRMSerrorinSTELIB,and(iii)an h i ∗ h i ∗
j j
additional 1.38A˚ residual FWHMdegradation in themodels due X X
andthemass-weightedas:
totheerrorsintheassumed initialwavelengthand dispersionsin
STELIBinthecoadditionofBC03.
A = m A and Z = m Z . (14)
m j j m j j
Finally, we used the same solar template to map the h i ∗ h i ∗
j j
wavelength-scale of STELIB. The systematic deviations are no X X
larger than ∆λ= 0.5 to +0.5A˚ across the observed wavelength Finally,wealsocomputethestellarV-bandM/Lratioofthecom-
−
range, yet are relevant enough for a fair comparison with high- positesystemasM/LV = j(lj∗(M/LV)j).
quality modern data. These true systematic trends in resolution AnumberofcaveatsexistwhenapplyingmodelSSPstothe
and wavelength scale of the BC03/STELIB spectra are in excel- integratedlightofastarforPminggalaxy.First,themodelsarebased
lentagreementwiththosefoundinthesimilaranalysisbyKoleva onempiricallibrariesofstarswhicharenecessarilylimitedtothe
etal.(2008). rangeofTeff,[Fe/H],log(g),and[α/Fe]ofstarswithinthesolar
Inourfullpopulationsynthesisfitting,alloftheaboveisac- neighborhood. Stellar populations in other regions in our Galaxy
countedfor.Inparticular,wefirstdistortourobservedgalaxywave- andinexternalgalaxieswillnotbeconfinedtothisparameterspace
lengthscaletomatchthatofSTELIB.Wethenaccountforresolu- andthusnotbefaithfullyrepresented. However,extrapolationsin
tioneffectsbyconvolvingallmodelandgalaxyspectra(atallradii) the(Teff,[Fe/H],log(g))-spacewithinthemodelsdoprovideex-
to the same resolution: top-hat=10.81A˚, σ=168kms−1. These tensivecoverage, withtheextremes(lowTeff,small[Fe/H])be-
account fortheslit-widthandapproximatelyhighestvelocitydis- ingtheleastwellmodeled.Additionally,theBC03modelsdonot
persion in our galaxy sample (measured on thefirst iteration and includetheeffectsofnon-solarabundanceratiosandafullassess-
limitedtothecentral,highS/Nregions),respectively.Thisdisper- ment of potential biasesawaitstheupcoming implementations of
sionissufficientlygreaterthanthatofthenativeBC03modelssuch stellarpopulation modelswhich include abundance patternvaria-
that any residual variations, e.g. due to different combinations of tions.Second,themodelsdonotaccountforemissionfromplan-
starsindifferentSSPs,willbesmoothedout.Wediscussin 4.4our etarynebulaeandH IIregionswhichcanbedominantinactively
§
accounting for the BC03 effective resolution for kinematic mea- starforminggalaxiessuchasthelate-typespiralsinoursample.In-
surements, which are iteratively derived from the full spatial and deed,manyofourgalaxyspectrashowstrongemissionlines(e.g.
spectralresolutiondata. Hβ,[OIII]λλ5007,4959,Hα,[NII],[SII],etc.;seeFig.A1).We
successfullycircumventthisissuewithouriterativemaskingpro-
ceduredescribedin 3.3.1.Third,andagainparticularlyimportant
§
3.4.2 SSPTemplateLibrary in star forming systems, the optical stellar light will likely suffer
from the extinction and reddening effects of dust. While there is
Wearelimitedheretoatemplatelibrarythatcomprisesadiscrete
no straightforward way to account for dust effects on integrated
samplingofSSPagesandmetallicities.Ultimately,wewouldlike
spectra,weattempttodetermineifaparticularspectrumisaffected
ourlibrarytobeacompleteandnon-redundant basisset,butthis
by extinction by comparing dust-free fits with those incorporat-
wouldrequireanexactmatchbetweenmodelsanddatathatisnot
ingamodelfordustextinction.Weadoptthetwo-componentdust
realizedinpractice.Throughaseriesoftestsandcarefulexamina-
modelofCharlot&Fall(2000,hereafterCF00).TheCF00model
tionoftheindividualSSPspectra,weconvergedonaselectionof
accounts for the finite lifetime ( 107yr) of stellar birth clouds
SSPsat14ages,roughlylogarithmicallyspaced5,and5metallic- ∼
ities(excluding only thelowest metallicityprovided intheBC03
findthe “best behaved” age (i.e. bluer for younger ages). The0.006Gyr
SSPshadthemostreasonablespectra.
5 The spacing in not exactly logarithmic, particularly at ages of about 6 Notethatwearenotconcernedherewithmodelagepredictionsthatare
0.004GyratthelowestZs,wherewenotedanomalousSSPspectrainthe olderthantheageoftheUniverse.Modelagesarenotpreciselycalibrated
BC03models.Thespectraaroundthisagewereinspectedindividually to and,assuch,weareconcernedprimarilywithrelativetrends.
(cid:13)c 2008RAS,MNRAS000,1–38
PopulationSynthesisof SpiralGalaxies 9
Figure2.Spectraofthe70SSPtemplatesusedinthepopulationsynthesisfits.Metallicityincreasesfromlefttoright.Differentageshavedifferentcolours
andarelabeledinleftmostpanel.AllspectraarenormalizedtotheirV-bandflux.
throughtheparameterµ,whichrepresentsthefractionoftotaldust 4 RESULTS
absorptioncontributedbydiffuseinterstellarmedium(cirrus)dust.
4.1 FullPopulationSynthesisFits
The wavelength dependence of the effective absorption curve is
λ−0.7,sothe“effective”extinctioninagivenband,τˆλ,isgiven We here present example fits from the code and procedure de-
∝
by, scribedin 3.1.Fig.3showsthecentral,r=0′′,spectrumfitforall
§
eightgalaxies.Ineachplot,blackandredlinesarerespectivelythe
dataandsynthesisfits.Thegrayshadingindicatesregionsmasked
inthefitsasdeterminedbyour “σ-clipping”proceduredescribed
τˆ (λ/5500 A˚)−0.7 for t6107 yr, in 3.3.1.Shownatlowerrightoneachpanelaretheaveragelight-
τˆλ = µτˆVV(λ/5500 A˚)−0.7 for t>107 yr, (15) we§ightedage, A l,andmetallicity, Z l,effectiveτˆV,andχ2of
(cid:26) h i h i
thefit.Thebottompanelsshowthepercentdata modelresiduals.
−
Inallcases,thefullsynthesisfitsrepresent thegalaxyspectrare-
markablywell.Ourσ-clippingprocedureclearlydoesagoodjob
wheretistheageofanysinglestellargeneration. atmaskingoutregionswhereemissionlinesarepresent.
ForeachSSPspectruminourlibrary,wecreateextinctedver- Closerexaminationofthedata modelresidualsforallofthe
−
sionswithafixedµ=0.3(theaveragevalueforstarforminggalax- spectra that show little or no evidence for current SF reveal the
ies) and varying τˆ in steps of 0.5. For reference, in this model, sameoverallrollingshape,withthemostsignificantfeatureoccur-
V
τˆ =2 isequivalent to acolour excess E(B V) 0.1 for aso- ringaroundλ 5150–5450,aregionrichwithFeandMgabsorp-
V
− ∼ ∼
lar metallicity template (see Fig. 1 in MacArthur 2005). We per- tionlines.Whilethismaybeduetoafluxcalibrationproblem, it
formthefullsynthesisfirstonthedust-freeSSPs.Theresultsare couldalsobeanindicationofnon-solar abundanceratiosthatare
recorded and the Merit function (Eq. 2) tabulated. The fits are nottakenintoaccountintheBC03models.Asimilarpatternwas
then performed on the extincted SSPs, starting with τˆ =0.5. If observedinthefitresidualsofSDSSgalaxyspectrainthestudies
V
the Merit function has decreased from the previous fit, the next ofPanteretal.(2007)andCidFernandes(2007).Thefactthatthese
extinction level is fit, until a minimum in the Merit function is independentdatasetsshowthesamefeatureseffectivelyrulesout
reached. Whilethe reddening effects of dust add an extra degen- afluxcalibration problem. Panteret al. (2007) suggest that these
eracytothefits,wealwaysreachaconvergence(minimumMerit features may be due to an error in the balance of K–M giants in
intheAge/Z/dust-space). theBC03models,whereasCidFernandes(2007)attributesthemto
(cid:13)c 2008RAS,MNRAS000,1–38
10 L.A. MacArthuretal.
Figure3.Centralobservedspectra(black)andfullpopulationsynthesisfit(red)foralleightgalaxies.Grayshadingindicates regionsmaskedinthefitas
determinedbyouriterative“σ-clipping”procedure(see§3.3.1)aswellastheCCDgapregions(greenverticaldash-dottedlines)whicharealwaysmasked.
Shownatlowerrightoneachpanelaretheaverage light-weighted age,hAil ,andmetallicity, hZil ,effective τˆV,andχ2 ofthefit.Thebottom panels
showthepercentdata−modelresiduals.Inthebottompanels,dashedverticallinesindicatevariablesky-lines(whichcanbedifficulttoaccountforduring
sky-subtraction),anddottedverticallinesindicateemissionlinesprevalentinstarforming(HII)regions.
(cid:13)c 2008RAS,MNRAS000,1–38