The Tully-Fisher Relation in Cluster Cl0024+1654 at z=0.4

0.87 MB·English

by  Anne J. Metevier

APJACCEPTEDVERSIONJANUARY28,2006
PreprinttypesetusingLATEXstyleemulateapjv.6/22/04
THETULLY-FISHERRELATIONINCLUSTERCL0024+1654ATZ=0.412
ANNEJ.METEVIER3ANDDAVIDC.KOO
UniversityofCaliforniaObservatories/LickObservatoryandDepartmentofAstronomyandAstrophysics,UniversityofCalifornia,SantaCruz,CA95064
LUCSIMARD
HerzbergInstituteofAstrophysics,NationalResearchCouncilofCanada,Victoria,BCV9E2E7,Canada
AND
ANDREWC.PHILLIPS
UniversityofCaliforniaObservatories/LickObservatory,UniversityofCalifornia,SantaCruz,CA95064
6
ApJacceptedversionJanuary28,2006
0
0 ABSTRACT
2
Usingmoderate-resolutionKeckspectra, we haveexaminedthe velocityprofilesof 15membersof cluster

n Cl0024+1654atz=0.4.WFPC2imagesoftheclustermembershavebeenusedtodeterminestructuralparam-
a eters, includingdisksizes, orientations,andinclinations. We comparetwo methodsof opticalrotationcurve
J
analysis for kinematic measurements. Both methods take seeing, slit size and orientation, and instrumental

0 effectsintoaccountandyieldsimilarrotationvelocitymeasurements. Fourofthegalaxiesinoursampleex-
3 hibitunusualkinematicsignatures,suchasnon-circularmotions.OurkeyresultisthattheCl0024galaxiesare

marginallyunderluminous(0.50±0.23mag), giventheir rotationvelocities, as comparedto the localTully-
1
Fisher relation. In this analysis, we assume no slope evolution, and take into accountsystematic differences
v
betweenlocalanddistantvelocityandluminositymeasurements.Ourresultisparticularlystrikingconsidering
1
theCl0024membershaveverystrongemissionlines,andlocalgalaxieswithsimilarHαequivalentwidthstend
7
to be overluminouson the Tully-Fisherrelation. Cl0024 Tully-Fisher residualsappear to be correlatedmost
6
1 stronglywithgalaxyrotationvelocities,indicatingapossiblechangeintheslopeoftheTully-Fisherrelation.
0 However,wecautionthatthisresultmaybestronglyaffectedbymagnitudeselectionandbytheoriginalslope
6 assumed for the analysis. Cl0024 residuals also depend weakly on color, emission line strength and extent,
0 andphotometricasymmetry. InacomparisonofstellarandgasmotionsintwoCl0024members,wefindno
/ evidenceforcounter-rotatingstarsandgas,anexpectedsignatureofmergers.
h
p Subjectheadings:galaxies:clusters:individual(Cl0024+1654)—galaxies:evolution—galaxies:fundamen-
- talparameters—galaxies:kinematicsanddynamics
o
r
st 1. INTRODUCTION brighteningatz∼0.25- 0.6.Thesetwostudies,however,also
a hintthattheremaybeachangeinTFRslopewithredshift.
The Tully-Fisher relation (TFR, Tully & Fisher 1977) be-
:
v tween disk galaxy luminosities and rotational velocities is Recentstudiesusinglargersamplesoffieldgalaxies(≥60
i an essential diagnostic of galaxy evolution. By comparing compared to sample sizes of .20 in the studies mentioned
X
above)by Ziegler et al. (2002)and Böhm et al. (2004)have
galaxyevolutionmodelstoTFRobservationsatz∼0through
r provided further evidence for evolution in TFR slope, pos-
a z ∼ 1, it is possible to probe dark matter halo properties
sibly reconciling previous findings. More specifically, their
and galaxy star formation histories (e.g., Mo & Mao 2000;
work indicates that the mass-to-lightratios of the least mas-
Navarro&Steinmetz2000;Ferreras&Silk2001;Buchalter,
sivegalaxiesevolvemoststrongly.Theseauthorsattributethe
Jimenez&Kamionkowski2001a,2001b;Mo&Mao2004).
differing results of previous studies to selection effects and
Observations of the distant field galaxy TFR have clearly
small sample sizes. Their results are consistent with kine-
demonstrated luminosity evolution since z ∼ 1, but the
matic studies of blue compact galaxies at z≤1 (Koo et al.
amountof evolutionis contested. Forbeset al. (1996), Vogt
1995, 1997; Phillips et al. 1997; Guzmán et al. 1996, 1997,
et al. (1996, 1997) and Rigopoulou et al. (2002) find ≤1
1998). The latter studies demonstrate that distant compact
mag brightening between z ∼0 and z∼ 1, whereas Rix et
galaxies are overluminousas compared to the local TFR, in
al.(1997)findevidencefor1.5magbrighteningatz∼0.25.
manycasesanorderofmagnitudelessmassivethanexpected
Inagreementwith thelatter work, Simard&Pritchet(1998)
fortheirluminosities.
andMallén-Ornelasetal.(1999)findevidencefor1.5–2mag
While the work done to date is promising, there are still
1BasedonobservationsobtainedattheW.M.KeckObservatory,whichis waysin which distantTully-Fisherstudiescan be improved.
operatedjointlybytheCaliforniaInstituteofTechnologyandtheUniversity For instance, selection effects are thought to be responsible
ofCalifornia. for the differing results of some of the studies mentioned
2BasedinpartonobservationswiththeNASA/ESAHubbleSpaceTele-
above.However,whileeffectssuchasmagnitudeincomplete-
scope,obtainedattheSpaceTelescopeScienceInstitute,whichisoperated
ness have been exploredin local studies (e.g. Willick 1994,
bytheAssociation ofUniversities forResearch inAstronomy, Inc., under
NASAcontractNAS5-26555. Giovanellietal. 1997),little workhasyetbeen donetoward
3NSFAstronomyandAstrophysicsPostdoctoralFellow quantifyingandcorrectingforsucheffectsondistantsamples.
Electronicaddress:[email protected],[email protected]
Furthermore,thevelocitymeasurementtechniquesusedinlo-
Electronicaddress:[email protected]
Electronicaddress:[email protected] cal and distant Tully-Fisher studies are often very different
2 Metevieretal.
andmayaccountforsomeofthediscrepanciesbetweenpre- as to which processes are dominant. As a first step, we
viousresults.AuthorsofdistantTully-Fisherstudiesalsotend havechosentostudytheTFRinrichclusterCl0024+1654at
tocomparetheirsamplestotherelativelysmalllocalsample z=0.4,whereevolutionaryprocessesareverylikelytobeap-
of Pierce & Tully (1992) to draw evolutionary conclusions. parent. Ingeneral,morphological,luminosity,andcolorevo-
Whilethisisagoodstartingpoint,largerandbetter-calibrated lutionhavealreadybeenseeninclustergalaxiessincez≃0.5
localsamplesnowexistforcomparison(e.g.,Tully&Pierce (e.g., Dressler et al. 1997, Jrgensenet al. 1999, and Butcher
2000;Kannappan,Fabricant&Franx2002). & Oemler 1984, respectively). The redshift of this cluster
Wealsonotethatwhilesignificantrecentprogresshasbeen aloneplacesitatanepochwherewewouldexpecttoobserve
made investigatingthe evolutionof the Tully-Fisherrelation evolutionarysignatures. Cl0024was one of the two clusters
inthefield,TFRevolutionintheclusterenvironmentisonly originallystudiedbyButcher&Oemler(1978)andthushas
beginning to be explored. Many physical processes are ex- longbeenknowntohaveahighfractionofblue,presumably
pectedtoaffectgalaxiesinthisdenseenvironment,including star-formingmembers.Furthermore,evidencehasbeenfound
tidal encounters, interactions with the intracluster medium, for evolutionary processes such as mergers (Lavery, Pierce,
andgroupinfall.Alloftheseprocessesarepredictedtoaffect & McClure 1992)and recentsubcluster infall (Czoske et al.
cluster galaxydisks andgas, andin particulartheir mass-to- 2002).
lightratios,thusaffectingtheTFR. Thestructureofthispaperrunsasfollows: inthenextsec-
As a specific example, high-velocity tidal encounters be- tion, we discuss our observations of Cl0024+1654 and our
tweenclustergalaxiesandwith thegravitationalpotentialof sample selection for this study. Note that our sample of 15
theclusteritself(“harassment")havebeenmodeledbyMoore Cl0024 members is one of the largest samples of rotation
et al. (1996, 1998, 1999). These encountersare expectedto curvespresentedthusfarforgalaxieswithinasinglez>0.2
increasestarformationrateswhilestrippinggalaxiesofasig- cluster. We detail our basic spectral and image reductions,
nificantfraction of their mass (Fujita 1998), thus decreasing two methods of rotation curve analysis, and we discuss the
theirmass-to-lightratios. Gnedin(2003)predictsthatlower- differences between local and distant galaxy velocity mea-
density galaxies in clusters are more likely to be disrupted surementsin §3. In §4, we present the Cl0024 Tully-Fisher
andloseagreaterpercentageofmassintidalencountersthan relation, including a comparison to three local samples. In
largespirals. Themass-to-lightratiosoflow-andhigh-mass §5,wediscussevolutionaryindicationsfromcorrelationsbe-
galaxiesin clusters may therefore evolve differently. In dis- tweenTully-Fisherresidualsandothergalaxyproperties. We
tantgalaxyclusters,wehavetheopportunitytoobservesuch alsotakealookattheeffectofmagnitudeincompletenesson
evolutionaryprocessesinaction. DistantclusterTully-Fisher ouranalysis. We presentourconclusionsin §6. Throughout
studies will therefore allow us to test model predictionsand this paper we assume H =70 km s- 1 Mpc- 1, Ω =0.3 and
0 M
quantifyevolutionaryeffects. ΩΛ=0.7. Usingthiscosmology,onearcsecondcorresponds
Few studies of the Tully-Fisher relation in distant clusters to5.332kpc. WepresentallphotometryintheVegasystem.
currently exist. While studies of z∼0.1 clusters have been
conductedwith significant sample sizes (>50 galaxies; e.g., 2. OBSERVATIONSANDSAMPLESELECTION
Rubin et al. 1999, Dale & Uson 2003), kinematics of few
Spectra of all galaxies presented in this paper were taken
z>0.1 cluster disks have been measured. In a pioneering
as part of a larger spectral survey of Cl0024+1654 (Mete-
study, Vogt et al. (1993) measured the rotation velocities of
vier et al., in preparation). Survey observations were made
two cluster galaxies at z=0.20 and z=0.38. Franx (1993)
in September 1995, September 1997, and September 2001
alsodemonstratedrotationinan“E+A"galaxyinAbell665at
with the Low Resolution Imaging Spectrograph (LRIS, Oke
z=0.18. Allthreeobjectswerefoundtobe≤1magbrighter
etal. 1995)ontheKeck10-mTelescopes. AllCl0024spec-
thanlocaldiskgalaxies.
traweretakenthroughmulti-objectslitmaskswithslitwidths
More recently, Milvang-Jensen et al. (2003) analyzed the of 0.9- 1′′. A variety of gratings (400, 600, 900, and 1200
rotation curves of eight members of cluster MS1054-03 at
lines/mm)andsettingswereusedsuchthatdispersionsrange
z=0.83and foundthat theywere ∼1.5mag more luminous from0.65- 1.85Åpixel- 1 (correspondingto∼30-80kms- 1
thanlocalfieldgalaxies.Bamfordetal.(2005)haveexpanded
pixel- 1), and wavelength ranges cover at least Hα (9155Å,
this study with a larger sample size of 22 members of three
clusters at 0.3<z<0.9. They have found that the cluster observed)throughHβ (6780Å,observed)and in some cases
membersaresomewhat(∼0.5mag)moreluminousthanfield [OII] (5200Å, observed) at the cluster redshift. The spatial
galaxiesatthesameredshifts.Ontheotherhand,Ziegleretal. resolutionofallspectrainoursurveyis0.215′′pixel- 1. See-
(2003;seeJägeretal.2004fordetailsonanalysistechniques), ingrangedfrom∼0.65- 1′′ FWHM, andinstrumentalreso-
presented rotationcurvesof 13 membersof three clusters at lution ran from 1.0 to 2.9 Å FWHM (40 to 120 km s- 1). In
0.3<z<0.5andfoundnoevidenceforluminosityevolution manycases,slitswereapproximatelyalignedwithgalaxyma-
ofclustergalaxieswithrespecttothefield. Otherthanthese joraxes. Slitmisalignmentshavebeenexplicitlyincludedin
noteableexceptions,themajorityofkinematicstudiesindis- ourrotationcurveanalysis.
tantclustershavefocusedonthefundamentalplaneofearly- ArchivalHubbleSpaceTelescope(HST)imagesofCl0024
typegalaxies. Theseworksindicatethattheamountoflumi- weretakenwithWFPC2aspartoftwoprograms.Deepimag-
nosityevolutioninclusterearly-typesisconsistentwithpas- ingofasinglepointingatthecenteroftheclusterwastaken
siveevolutionouttoz=0.83(vanDokkum&Franx1996;van (proposal 5453, PI Turner) to study the mass of the cluster
Dokkumetal.1998;Kelsonetal.1997,2000a,b;Jrgensenet via strong lensing. Exposure times are 25.2 ksec and 19.8
al. 1999)andpossiblyoutto z=1.27(vanDokkum& Stan- ksec in B and I , respectively. More recently, shallower
450 814
ford2003). (4.0-4.4ksec)imagesoftheouterregionsoftheclusterhave
As described above, environmentally-dependent physical been taken in I (proposal8559, PI Ellis) for a weak lens-
814
processes are expected to affect cluster disks more strongly ing study. The latter program provides imaging of 39 non-
thanearly-types. Thedistantcluster TFRmayprovideclues contiguouspointingscoveringacircleofradius∼15arcmin,
TFRinCl0024atz=0.4 3
withafillingfactorofapproximately50%. telescopeelevationand azimuthaswere usedduringthe ob-
DiscrepanciesbetweentheresultsofTully-Fisherstudiesof jectexposuresinordertoreproduceandcombattheeffectsof
distantfieldgalaxieshavegenerallybeenattributedtodiffer- fringing.Theresultingcombinedflatswereusedtocorrectfor
ent sample selections. We have imposed very few selection pixel-to-pixelvariationsintwodimensions. Alongthelength
criteria here: we have restricted our Tully-Fisher sample to of the slit, the flats were also used to correct for instrumen-
emissionlineclustermemberswith0.37<z<0.41,andwe tal distortions and variationsin slit width. We then rectified
have required that the galaxies in this sample lie within the thespectrainthespatialdirectionandwavelengthcalibrated
HST-imaged region of the cluster. High-resolution WFPC2 against arc lamp exposures and known night sky lines. We
imagesareessentialtoourstructuralanalysisforgalaxydisk sky-subtracted the resulting spectra, then co-added multiple
sizes, inclinations, and position angles. In turn, these mea- exposures, accounting for sub-pixel offsets in the spatial di-
surements are crucial for kinematic analysis. We have also rection.Finally,wemaderedshiftmeasurementsusingcross-
requireddiskinclinationanglesrangebetween30◦<i<80◦. correlationsoftwaredevelopedbycoauthorA.C.Phillips.
These simple selection criteria narrowedthe originalsample We obtained pipeline-processed WFPC2 images from the
of 312totalobjectsin oursurveyto 44 clustermemberseli- Canadian Astronomy Data Centre archive service. Remain-
gibleforTully-Fisheranalysis. Note thatwe havenotinten- ingreductionconsistedofcosmicrayremovalandstructural
tionallyimposedselectionbasedoncolors,morphologies,or modelingofgalaxiesintheimages. Toremovecosmicrays,
emissionlinestrengths. wecombinedexposuresoftheclustercore,whichweretaken
Only15ofthe44objectsinourTully-Fisher-eligiblesam- withnooffsets. Exposuresoftheouterregionsofthecluster
ple have extended, high signal-to-noise emission lines such had subpixel offsets and were therefore individually treated
thatwe wereableto measurea reliableterminalrotationve- using the LACOSMIC routine (van Dokkum 2001). We fit
locity. Thislowsuccessrateimposesadditionalselectionon a two-dimensional deVaucouleurs bulge + exponential disk
top of the criteria described above. We explore these selec- modeltoeachgalaxyusingGIM2D(Simardetal.2002).This
tioneffectsfurtherinFigure1,wherewecomparetheRmag- analysisprovidedgalaxybulge-to-totalfluxratios(B/Ts)and
nitudes, B- R colors, morphologicaltypes (from Treu et al. disk inclinations, scale lengths, and position angles. These
2003),bulge-to-totalfluxratios(B/T),anddiskscalelengths measurementsarenotedinTable3.
ofgalaxiesintheTully-Fisherandlargerclustersamples. In
addition, in Figure 2, we present the distributions of emis- 3.2. RotationCurveAnalysis
sion line extents and projected cluster-centric distances for
Measuring the rotation velocities of distant galaxies from
the galaxies in the final Tully-Fisher sample (15 galaxies)
optical spectra is a challenging undertaking which requires
andtheTully-Fisher-eligiblesample(44galaxies). Emission
comparisonofemissionlinedatatoemissionlinemodels. In
lineextentsweremeasuredinthespatialdirectionalongeach
part this is because by z∼0.4, the size of a typical galaxy
galaxy’sspectrumfromthetoptothebottomofthegalaxy’s (∼1′′)isroughlyequivalenttothesizeoftheseeingdiskand
emission,assomegalaxiesdonotexhibitsymmetricemission
theslitwidth. Therefore,lightandvelocityinformationfrom
aboutthegalaxycentroid. Weestimatethattheerrorsonthe
asubstantialfractionofagalaxyaregatheredinitsspectrum.
extentmeasurementsareontheorderofonepixel(∼0.215′′).
The resulting rotation curve is far from the optimal narrow
InTables1and2,wequantifythemeanvalues,standarddevi-
slicedownthegalaxymajoraxisacquiredinlongslitstudies
ations,minimumandmaximumvaluesofthecomparedprop-
of nearby galaxies. Below we provide a more complete list
ertiesforthedifferentgalaxysamples.
of factors one must consider when converting raw emission
In general, we find that the galaxies in our Tully-Fisher
linemeasurementsintomaximumdiskrotationvelocitiesfor
samplearerelativelybrightandblueascomparedtotheother
distantgalaxies:
emission-line cluster members and the total cluster sample.
Furthermore,theytendtobelarge,late-type,disk-dominated
1. Spatialdistributionofobservablegalaxyemission
systems. GalaxiesinthefinalTully-FisherandTully-Fisher-
eligible samples are similarly distributed within the cluster. 2. Velocitydistributionofobservablegalaxyemission
However, galaxiesin the final sample have the largest emis-
sion line extents. We are therefore mindful of the fact that 3. Inclinationofthedisk
Cl0024 members with suppressed or centrally concentrated
4. Seeingblurringoftheobservedvelocitydistribution
star formation, perhaps due to physicalprocesses within the
cluster, are likely not included in our Tully-Fisher study. In
5. Instrumental blurring of observed emission due to in-
Table3,wegivebasicdataforthefinalsampleof15Cl0024
strumentoptics
memberswithreliablerotationcurvemeasurements.
3. DATAREDUCTIONANDANALYSIS 6. Slitwidthwithrespecttothesizeofthegalaxy
3.1. SpectralandImageReduction
7. Slit position angle with respect to the galaxy semi-
WereducedallLRISspectrausingPythonmodulesdevel- majoraxis
opedbyD.Kelson(seeKelsonetal.2000,Kelson2003). To
prepare the spectra for this reduction, we performed over- 8. Slitpositionwithrespecttothegalaxycenter
scan subtraction using standard IRAF procedures, and we
9. Anamorphicde-magnificationinthespectraldirection
cosmic ray reduced the frames with a task written by coau-
thor L. Simard. Using Python modules, each spectrum and
10. Pixelizationoftheobservedemissionline
domeflatwasrectifiedinthedispersiondirectiontoaccount
for “pincushion"-shaped distortion introduced by LRIS op- 11. Atmosphericdispersion
tics. Wethencombineddomeflatfields;domeflatsfromtwo
ofthethreerunsweretakenwiththesamegratinganglesand 12. Thicknessofthedisk
4 Metevieretal.
13. Presenceofbulge,bar,warps for factors 3 through 10. Through the implementation dis-
cussedin§3.2.3,atmosphericdispersion(factor11)canalso
Previousstudiesofdistantgalaxieshavemainlyusedoneof beaccountedfor. Wenotethatdiskthickness(factor12)has
two techniques for deriving velocities from rotation curves. not been incorporated in rotation curve analysis techniques
These two techniques are 1) comparison of velocity mea- presentedpreviouslyintheliterature,norisitconsideredhere.
surements from Gaussian fits to observed and model emis- Similarly,theeffectsofabulge,bar,andwarpshavenotbeen
sionlinesatseveralspatiallocations(Vogtetal.1996,1997; incorporated in distant galaxy rotation curve analysis. An-
Rigopoulou et al. 2002; Ziegler et al. 2002, 2003; Böhm et other improvement that could be made in the future is the
al.2004;Jägeretal.2004),and2)directcomparisonoftwo- direct use of color images to model emission line intensity
dimensionalinformationfromobservedand simulatedemis- distribution,ratherthantheassumptionofanexponentialdis-
sionlines(Simard&Pritchet1998,1999;Milvang-Jensenet tribution.
al. 2003; Bamford et al. 2005). We have implemented both
analysismethodsinourstudyofCl0024members;belowwe 3.2.1. GAUSS2D
refertoourversionofmethod1asGAUSS2Dandourimple- OurGAUSS2D velocityanalysisfollowsthe methodused
mentationofmethod2asGELFIT2D. byVogtetal.(1996,1997),Rigopoulouetal.(2002),Ziegler
Both of our analysis techniquesrely upon the same emis- etal.(2002,2003),Böhmetal.(2004),andJägeretal.(2004).
sionlinemodelingroutine. Theroutinewehaveadoptedas- We determined raw velocity measurements by fitting Gaus-
sumesaninfinitelythin,rounddiskgalaxywithnobulge,bar, sianprofilesto thestrongestobservedemissionlinesateach
orwarps. Thismodelgalaxyhasa truncatedexponentialin- rowalongthe slit. These fits providedGaussian amplitudes,
tensityprofileandasymmetric“stepfunction"(e.g.,Persic& centers, widths, and linear background measurements, with
Salucci 1991) or an arctangent (e.g., Willick 1999) velocity errors on each of the measurements. Fits were required to
distribution. We found that both velocity functions yielded meetcertaincriteriachosentothrowoutnoisepeaksormea-
similar rotation velocity measurements (generally within 10 surementswithunreliableS/N.Thesecriteriawere:Gaussian
kms- 1)foroursample. We thereforehavechosentousethe amplitude>10 counts, center >2σ in significance, and 1Å
arctangentfunctionforthispaper: < FWHM < 20Å. Gaussian centers were converted to ve-
2V r locitiesandwererequiredtodiffernomorethan100kms- 1
V(r)= arcarctan( ) (1) from one of the neighboringmeasurements. Generally, sev-
π r
to eralemissionlineswerefitforeachobject(doubleGaussians
whereVarc is the asymptotic rotation velocity, and rto is the werefitto[OII]),andtheresultingvelocityinformationwas
“turnover"radiuswhichdefinestheslopeoftheinnerveloc- converted to a single weighted mean and error at each row
itycurve. Wenotethatmoreelaborateempiricaldescriptions alongtheslit.
of galaxyvelocity distributionsmay better fit observedrota- To determine the rotation velocities of the galaxies in our
tioncurves(see,e.g.,Courteau’s1997studyofnearbygalax- sample,weappliedthesameGaussianfittingtoemissionlines
ies). Theyalsointroducenewparameterstobemodeledand modeledwithagridofV andr values.Gridswereinitially
arc to
thereforeweneglectthemhere. implementedwithV rangingbetween50and450kms- 1in
arc
Our emission line modeling routine first samples the as- 50km s- 1 increments, andwith r rangingbetween0.1 and
to
sumedintensityandvelocitydistributionsaccordingtoagrid 0.5′′ in 0.1′′ increments. We comparedobserved and model
sizespecifiedbytheuser. Inordertosampleatleast10times velocity distributions to create corresponding χ2 grids, then
acrosseachgalaxy,wegenerallysubsampledabovethereso- interpolated to determine the optimal V and r measure-
arc to
lutionofourmodeldataaccordingtothefollowingprescrip- ments (corresponding to the minimum χ2) with 68% confi-
tion,wherepixscaleisthespatialpixelscaleofourdata,rd is dence intervals. This process was then repeated with more
thediskscalelength,andiisthegalaxy’sinclination: refinedgridsforeachgalaxysuchthatV valuesweretested
arc
in increments of 10 km s- 1, and r in increments of 0.05′′.
pixscale∗5 to
subsamplingfactor= (2) Forsimplicity, we assumedmodelgalaxieswere centeredin
r ∗cos(i)
d theslitwhenusingthismethod.
The routine then convolvesthe modelgalaxy’slightand ve- Incomparisonwithpreviousimplementationsofthisanal-
locity profiles with a circular Gaussian seeing disk with a ysis method, our version incorporates some improvements.
givenFWHM.Theseeing-degradedmodelgalaxyismasked Theemissionlinemodelsweusefullytakeintoaccountfac-
withaslit,takingintoaccounttheslitwidthaswellasthepo- tors 3 – 7 and 9 – 10 above; it is unclear whether previous
sitionangledifferencebetweentheslitandgalaxymajoraxis. authorshaveconsideredanamorphicmagnification(9)orpix-
Thesubpixelpositionofthegalaxycenterwithrespecttothe elization (10) in their models. Furthermore, GAUSS2D al-
centeroftheslitcanalsobeaccountedfor(asinGELFIT2D, lows the option of simultaneously fitting multiple emission
§3.2.2)by varyingthe positionof the modelgalaxywith re- linesforagivengalaxy.Optimizationofthemeasuredveloc-
specttothemodelslitmask. Themodelgalaxyisthencom- ity and confidence intervals are determined using a χ2 grid.
pressedinthespatialdirectionduetotheinstrumentanamor- We estimated further contributions to errors by varying the
phic factor and further convolved with a circular Gaussian followingfourparameters:diskinclinationandPAwereeach
representing blurring from instrumental optics. The result- variedby±10◦,theseeingFWHMby±0.2′′,andtheinstru-
inglightandvelocityprofilesare rebinnedandresampledto mentalprofileFWHMby±0.25pixels. Weaddedthelargest
create a model emission line matching the resolution of the rangeof errorsdeterminedby varyingthese four parameters
user’sdata. in quadrature with the formal fitting errors on our original
In short, while our emission line modeling routine makes measurements to derive a final set of errors on ourV and
arc
somesimplifyingassumptionsabouttheintensityandveloc- r measurements. We note that previousstudies (e.g., Vogt
to
itydistributionsofemissionwithinagalaxy(items1and2on 1996,1997)haveonlytakenintoaccounterrorsduetoestima-
our list of modeling considerationsabove), it fully accounts tionofthe inclinationandpositionangle, beyondthe formal
TFRinCl0024atz=0.4 5
fittingerrors. signal-to-noisedata.Theoptimizationalgorithmemployedin
GELFIT2Dhasalso beenusedinthegalaxystructuralmod-
3.2.2. GELFIT2D eling routine GIM2D; see Simard et al. (2002)for more de-
Our second rotation curve analysis method is very simi- tails. GELFIT2Doutputsalogfilespecifyingbest-fitparam-
lar to the ELFIT2D analysis described in detail by Simard eter values with errors as well as a thumbnail image of the
& Pritchet (1999) and used by Simard & Pritchet (1998), best-fit model emission line and a residual (data – best-fit
Milvang-Jensen et al. (2003), and Bamford et al. (2005). A model) image. Since GELFIT2D does not allow for simul-
Metropolisoptimizationwrapperwasappliedtoouremission taneousfittingofmultipleemissionlines,wefitseverallines
modeling routine in order to directly compare observed and separately for each galaxy, then took the weighted mean as
modeledemissionlines, varymodeledparametersanddeter- our final GELFIT2D velocity measurement. We determined
minebest-fitvalues. (Seebelowforamoredetaileddescrip- contributionsto the errorson ourV and r measurements
arc to
tionofthisoptimizationmethod.) by varying disk inclinations and PAs, as well as the seeing
Specifically, this routine takes the following inputs: 1) a andinstrumentalFWHMs,andaddingthelargestrangeofre-
two-dimensionalsky-andcontinuum-subtractedgalaxyemis- sulting errors in quadrature with the formal weighted errors
sionline“thumbnailimage";2)aninitialguessandrangeof from our original measurements, as described at the end of
possiblevaluesforeachmodeledparameter;3)alistoffixed §3.2.1.
parameter values. Fixed parameters include the type of ve- Ourimplementationof GELFIT2Dincorporatessome im-
locityfieldtobeusedintheemissionlinemodels(arctangent provementsover the similar ELFIT2D routine. Specifically,
orstepfunction),seeingFWHM,observedwavelengthofthe GELFIT2D accounts for considerations3 – 10 on our mod-
emission line, an optionalsecond observed wavelength (e.g. eling list, and provides some further flexibility in our as-
to be used in modeling the [O II] doublet), galaxy inclina- sumptionsregardingconsideration1byallowingforacentral
tion,positionanglebetweentheslitandgalaxymajoraxis,slit holeintheemissionintensitydistribution.GELFIT2D,unlike
width,dispersion,spatialpixelscale,instrumentalFWHM,a ELFIT2D,explicitlytakesintoaccountthepositionangleoff-
subsamplingfactortoaccountforpixelization,asigmavalue setbetweentheslitandgalaxymajoraxisaswellaspossible
describingthenoiseinthethumbnailimagebackground,and offsets of the slit center with respect to the galaxy centroid.
theCCDgain. However,wenotethatELFIT2Ddoeshavesomeadvantages
GELFIT2Dthenoptimizesthefollowingeightparameters: overGELFIT2D,themostnoteablebeingtheoptiontospec-
V ; r ; r , the emission line scale length; r , the in- ify an empirical seeing PSF and instrumental profile rather
arc to em hole
ner truncation radius (assuming a central hole in emission, thanassumingcircularGaussianprofiles.
e.g.dueto dustextinction);offsetsofthegalaxycenterwith
3.2.3. Comparisonofanalysismethods
respect to the input thumbnail image of emisson along and
acrosstheslit(canbesubpixel);andtheoffsetoftheslitwith Imagesandtwo-dimensionalemissionlines,aswellasout-
respecttothecenterofthethumbnailinthedispersiondirec- put from both of our rotation curve analysis techniques are
tion. Inthecaseof[OII]emission,thefluxratiobetweenthe showninFigure3.GAUSS2DandGELFIT2Dsharethesame
twolinesintheobserveddoubletisalsomodeled. emission line modeling routine and are therefore not com-
Tostartthe model,aninitialgridofparameterswithinthe pletely independent. However, they differ in two significant
user-specified range of possible values is first created. The ways:1)theroutinesusedifferentmethodsforcomparingob-
correspondingemission line models are comparedto the in- servedandmodelemissionlines,and2)theoptimizationrou-
put data image by calculation of the likelihood function for tinesusedtoconvergeonabest-fitmodelaredifferent. Both
each model. The mostlikely initial modelis then chosen as routines have advantages and disadvantages that may affect
a starting point for optimization. The Metropolis algorithm ourmeasurements,andwelistthemhere.
(Metropolis et al. 1953, Saha & Williams 1994) is used to OurGAUSS2Dfittingroutinehastwodistinctadvantages.
refine the best-fit parameter values. This algorithm gener- Forone,itdependslittleonanyassumptionaboutthespatial
ates random perturbationsabout the initial model parameter lightprofile of a galaxy in the determinationof the galaxy’s
values. The size of these perturbations is controlled by the rotation velocity. In this routine, velocity measurementsare
Metropolis“temperature":ifamodelishot,theperturbations madeseparatelyforeachspatialrow;thevelocityateachrow
arelarge;ifthemodeliscold,smallperturbationsaretried.At isdeterminedfromthecenterofaGaussianfittothegalaxy’s
eachiteration,thelikelihoodthatthenewsetofparameterval- emission along the dispersion direction. For the most part,
uesis correct,P , iscalculated. Thislikelihoodis compared therelativeamplitudesofthe Gaussian peaksin eachspatial
1
tothatofthepreviousiteration,P . Thenewtrialisadopted rowdonotaffecttherelativevelocitymeasurements. Dueto
0
ifP >P . IfontheotherhandP <P ,thenewtrialisstill seeing blurring and the small pixel scale of our data, emis-
1 0 1 0
adoptedP /P ofthetime. Thisallowsthealgorithmtowalk sionseeninadjacentspatialrowsisnotentirelyindependent,
1 0
itselfoutoflocalχ2 minima,aparticularlyimportantfeature though. Agalaxy’slightprofilecouldthereforehaveasmall
for low signal-to-noise data. Furthermore, the shallower the effectontheresultingvelocitymeasurements.
minimum,thehighertheprobabilitythatthemodelwillwalk A second advantage of this routine is that it concatenates
itselfout. velocitymeasurementsfromauser-specifiednumberofemis-
Convergenceisachievedwhenthedifferencebetweentwo sion lines for a given object before determining V . That
arc
likelihood values separated by 100 iterations is less than is, the emission lines can be fit together or separately. A
3σ of the likelihood value fluctuations. Once the Metropo- disadvantage of this method is that it assumes galaxy emis-
lis algorithm converges, GELFIT2D determines 68% con- sionprofilesareGaussianalongthedispersiondirection.This
fidence intervals by Monte-Carlo sampling the parameter doesnotnecessarilyreflectthetrueemissiondistributionand
space where the likelihood has been maximized. In other maybiasvelocitymeasurements,astheyarederivedfromthe
words, GELFIT2D does not assume that confidence inter- Gaussian-fitcentersoftheemission.Furthermore,thisroutine
valsareGaussian. Thisisagainimportantinthecaseoflow simplydoesnottakefulladvantageofthetwodimensionsof
6 Metevieretal.
informationavailablefromaspectrum. McClure(1992;hereafterLPM92)andlinewidthsweremea-
GELFIT2D is a much simpler fitting routine in that it di- suredbyKooetal.(1997).Thesearetheonlythreeobjectsin
rectly compares data to emission line models, without any oursamplethatoverlapwiththeLPM92andKooetal.stud-
intermediate (e.g., Gaussian fitting) steps. GELFIT2D fits ies. Oneoftheseobjects(TFR10)appearstocontainalarge,
a larger number of parameters than the GAUSS2D routine, knottyringofemission. LPM92describethisgalaxyashav-
providing additional measurements. These include the off- ing a “disturbed" morphology. This is the largest and most
set of a galaxy within a slit, the radius within which emis- rapidly rotating galaxyin our sample, and its velocity curve
sion is truncated at the center of a galaxy, the emission line appears to turn over at large radii. The morphological and
scalelength,andthefluxratioofthe[OII]doublet. Further- kinematic distortion in this galaxy indicate that it may have
more,GELFIT2Dhasamuchmoresophisticatedmethodfor undergonea recentinteraction. Kooet al. reporta linewidth
parameter optimization than GAUSS2D. While GELFIT2D σ=120kms- 1forthisobject,wherehereσreferstothestan-
only runs on one emission line at a time, a possible benefit darddeviationmeasuredbyfittingaGaussiantothespatially
isindependentmodelingofthepositionofthegalaxywithin collapsed (one-dimensional)emission. We measure a Gaus-
theslitatredandbluewavelengths,indirectlyallowingusto sian σ =115 km s- 1 for TFR 10 but findV =370 km s- 1.
arc
accountfor atmospheric dispersion (factor 11). It should be Wediscusspossiblesourcesforthedifferencesbetweenthese
noted that GELFIT2D also has disadvantages, the main one measurementsbelow.
being the assumption of a symmetric exponential intensity Theremainingtwo“unusual"objects(TFR04andTFR08)
profile. This assumption can stronglyaffect resulting veloc- have odd morphologies poorly fit with our GIM2D bulge +
itymeasurements,particularlyforgalaxieswithasymmetries, diskmodeling. Bothobjectshavesuchsteeplyrisingrotation
spiralarms,and/orstar-forminghotspots. curves at their cores that a pure step function (r ≃0′′) ve-
to
Both routines take on average 15-20 minutes to run per locity distribution convolved with realistic seeing could not
galaxy. GAUSS2D requires real-time user input ofV and reproducetheobservedvelocitycurve. Therefore,ourveloc-
arc
r ranges and increments to be tested. GELFIT2D is com- ity measurements appear to be overestimated. This is most
to
pletelyautomated,butoptimizeseightparametersratherthan clearly apparent in output from GAUSS2D (see Figure 3).
two. Because GELFIT2D fits each emission line separately, Since the GELFIT2D velocity measurements closely match
this routine may take longer if a large number of lines are thosefromGAUSS2D,weassumetheyareoverestimatedas
fit. Run-times for both GAUSS2D and GELFIT2D are also well. AsinthecaseofTFR10,linewidthsmeasuredbyKoo
dependent upon the amount of subsampling desired: highly et al. (1997)are significantly smaller (40 and 50 km s- 1 for
inclinedgalaxieswilltakethelongesttorunbecausethesub- TFR04andTFR08,respectively)thanourV measurements
arc
samplingfactorwillbelargest. (120and135kms- 1).However,wemeasuresimilarGaussian
For ease of comparison,in Table 4 we againlist the mod- linewidths of 75 and 40 km s- 1 for the two objects, gener-
eling factors described in §3.2. We also describe how and allyinagreementwithKooetal. Bothoftheseobjectswere
whether we have taken them into account using GAUSS2D flaggedas probablemergers/interactinggalaxiesby LPM92;
and GELFIT2D. In Table 5, we list velocity measurements weconsiderthemtidallydistorted.
for our sample of 15 Cl0024 members determined via both Inthethreecaseswhereoursamplesoverlap(TFR04,TFR
routines. Ingeneral,wefindthatthetwomethodsyieldgrat- 08,andTFR10),ourV measurementsaremuchlargerthan
arc
ifyinglysimilar results, as can be seen in Figure 4. We note thevelocitywidthsmeasuredbyKooetal.(1997)fromspa-
thatin all cases, emission was measuredoutto radiibeyond tiallycollapsedemission.Thisisdueinparttoinherentdiffer-
2.2r , the radius at which local galaxy studies often deter- encesbetweenthemeasurementtechniques.Emissiontoward
d
mine rotation velocities (e.g., Courteau 1997). Objects with theouterregionsofagalaxy(wherevelocitiesareoftenhigh-
truncated emission were not eliminated directly because of est) is given more weight in rotation curve analysis than in
the small extentof their emission, but becausethe turnovers linewidthanalysis,wheretheemissionsignatureiscollapsed
intheirvelocitydistributionswerenotstrongenoughforusto intoonedimension.Furthermore,Kooetal.fitthelinewidths
measureV .Ofcourse,thelattercriteriondoesbiasoursam- of the three galaxies in question with Gaussians despite the
arc
pletowardgalaxieswithlargeemissionlineextents(seeFig- fact that the velocity profiles of these galaxies are complex,
ure 2). However, we note that some galaxieswith relatively exhibiting 2-3 local peaks. However, we again caution that
largeemissionlineextentsdidnotmakeitintoourfinalTully ourV measurementsmaybeoverestimatedforthesegalax-
arc
Fisher sample because the signal-to-noisein the outskirts of ies,asTFR10exhibitsaturnoveratlargeradiinotaccounted
theiremissionwastoolowforustoreliablymeasureV . for by our models, and TFR 04 and TFR 08 show possible
arc
non-circularmotions.
3.2.4. UnusualGalaxiesintheSample It is not surprising that a significant fraction of the galax-
Four of the objects in our sample yieldedparticularly odd iesinourCl0024Tully-Fishersample(27%)exhibitunusual
emissiondistributionsand/orpoorkinematicfits(seetheAp- kinematics. Norisitsurprisingthatthesegalaxieswererela-
pendix for more notes on individual objects). One object tivelypoorlyfitbyourrotationcurveanalysisroutines. Sim-
(TFR01)exhibitshigh-ionizationemissionlinescharacteris- ulations of the rotation curves of interacting galaxies (Bar-
ticofanAGN(e.g.,[NeV]λ3426)andhasameasured[OII] ton,Bromley,&Geller1999)predictcomplicatedbumpsand
flux ratio I(λ3729)/I(λ3726) = 0.4, indicating electron den- wiggles, and observations of close pairs in the nearby field
sities over1000cm- 3. This emission is particularlyconcen- (Bartonetal.2001)revealasignificantfraction(∼10%)with
tratedtowardthecenterofthegalaxy:wemeasureadiskscale centrally concentrated emission. In the nearby Virgo clus-
lengthof1.1′′andanemissionscalelengthofonly0.2′′. We ter, ∼50% of the 89 galaxies studied by Rubin, Waterman,
caution that the derivedrotation velocity may representmo- & Kenney(1999)exhibitkinematic disturbances. While the
tionofgasinthegalaxycoreonly. scales of many of these disturbances are too small for us
The other three objects are Butcher-Oemler “blue" galax- to observe at z=0.4, some general trends (such as velocity
ieswhosemorphologieswereexaminedbyLavery,Pierce,& turnoversat large radii) can be apparent (as in TFR 10). In
TFRinCl0024atz=0.4 7
their study of z∼0.4 cluster galaxies, Ziegler et al. (2003) outofourV measurements. Insteadweinclination-correct
arc
notethatfourofthe30diskgalaxiestheyobservedexhibited themeasurementsin laterstepsin orderto keeptheorderof
peculiarkinematicsandweredifficulttomodel,sotheywere our procedure consistent with the methods used in the local
notincludedintheauthors’Tully-Fisheranalysis. studies. Instep2,wehavecalibratedtheconversionbetween
Anomalous kinematic signatures have been found in dis- V andV byanalyzingdatainCourteau(1997),inwhich
arc pmm
tant field galaxy studies as well. Rix et al. (1997) identify V and V measurements were made for the same sam-
arc pmm
∼20%oftheirz∼0.25sampleaskinematicallyunusual,with ple of local galaxies. Using an iterative least-squares fit to
low[OII]fluxratios. Furthermore,Simard&Pritchet(1998) Courteau’sdata,wefind:
foundthat∼25%oftheirsampleshowedunusualkinematics,
generally with emission line scale lengths smaller than disk 2Varc=0.80(±0.02)Vpmm+23(±10)kms- 1 (3)
scalelengths.
In Table 7, we list our originalV measurements for each
arc
3.3. ComparingVelocityWidthMeasurements Cl0024clustermember,aswellasourderivedWRi andWVpmm
values. Wenotethatwehaveroundedallvelocitymeasure-
InthemajorityofliteratureonthedistantgalaxyTFR(in- ments to the nearest 5 km s- 1 to reflect the precision of our
cludingourownearlyanalysisoftheCl0024TFR,Metevier
data.
& Koo 2004),authorsdirectlycomparethe luminositiesand
velocities of galaxies in their distant samples to a locally-
3.4. GalaxyLuminosities
derivedTFRwithoutaddressingdifferencesinvelocitymea-
surement methods for distant and local galaxies. However, WemeasuredobservedtotalRmagnitudesand3′′diameter
systematic differences do exist between different measure- apertureB- RcolorsfromLRISimagingoftheCl0024field
ment methods. These have been discussed in several TFR (600sexposuresinbothBandR). Thisphotometrywasthen
studiesatz.0.25(e.g.,Courteau1997;Raychaudhuryetal. correctedforGalacticextinctionintwowaysinordertocom-
1997; Rix et al. 1997; Barton et al. 2001; Kannappan, Fab- pareourmeasurementsdirectlytothoseusedintheliterature.
ricant, & Franx2002). Inthissection, we describelocalve- One method was an application of the extinction correction
locitymeasurementmethodsandwedetailourprocedurefor givenbyBurstein&Heiles(1982,hereafterBH82),acorrec-
convertingourV measurementstovelocitywidthsthatcan tionof0.09maginRintheCl0024field,andacorrectionof
arc
bedirectlycomparedtolocally-derivedvalues. 0.15maginB. Theothermethodwasapplicationofthecor-
In §4, we compare the Tully-Fisher relation in Cl0024 rection from Schlegel, Finkbeiner, & Davis (1998, hereafter
to the TFR derived from three local galaxy samples: those SFD98),0.15maginR.
studied by Pierce & Tully (1992, hereafter PT92); Tully & The observed photometry was converted to restframe to-
Pierce(2000,hereafterTP00);andKannappan,Fabricant,& tal M magnitudesand aperture (U- B) colors by C. N. A.
B 0
Franx(2002,hereafterKFF02). BothPT92andTP00derive Willmer.Theprocedurefordoingthisisdescribedindetailin
velocity widths from 21cm observations. For each galaxy, Willmeretal.(2005)andbasicallyfollowsthesesteps:empir-
they measureW , the line width at 20% of the peak inten- icaltemplatespectrafromKinneyetal.(1996)areredshifted
20
sity. Fromthistheyderiveaninclination-corrected“rotation totheclusterz,andtheresultingSEDsareconvolvedwiththe
width”Wi by dividing by sin i and applying the turbulence knowntransmissioncurvesofourfilters,thencomparedwith
R
correctiongiveninTully&Fouqué(1985). the observed photometry. Restframe photometrywas calcu-
KFF02 measure “probable min-max” rotation velocities latedfromthebest-fittingtemplatespectrumforeachgalaxy.
fromopticalemissionlineobservations. The“probablemin- TheresultingrestframeM magnitudeswerethencorrected
B
max” velocity, V , is half the difference between (a) the forinternalextinctionusingtherelationsgivenineitherTully
pmm
velocitydeterminedtostatistically exceed90%oftheveloc- & Fouqué (1985, hereafter TF85) or in Tully et al. (1998,
itiesinthegalaxy’srotationcurveand(b)thevelocitydeter- hereafter T98), dependingon the literature we comparedto.
minedtostatisticallyexceedonly10%ofthevelocitiesinthe WenotethattheinternalextinctioncorrectionsgiveninTF85
rotationcurve. BothKFF02andRaychaudhuryetal. (1997) are inclination-dependent, whereas the corrections given in
demonstratethatV isarobustmeasurementofagalaxy’s T98 are depend both on a galaxy’s inclination and intrinsic
pmm
velocity, in part because it does not rely on a particular ro- luminosity(orrotationvelocity,Wi).
R
tation curve shape. However, this method is difficult to ap- In all, we derived four sets of restframe M magnitudes
B
plytodistantgalaxies,forwhichonemustmodelseeing,slit, for comparison to the literature. (1) Mdist magnitudes were
B
and instrumental effects and therefore make some assump- derivedusingSFD98 Galactic extinctioncorrectionsandthe
tionsabouttheshapeofagalaxy’sintrinsicvelocitydistribu- TF85 internal extinction corrections. This method follows
tion. that used in recent distant TFR studies such as Ziegler et
In order to directly compare to other local TFR studies, al. (2002,2003),Milvang-Jensenetal. (2003),andBöhm et
KFF02 convert their V measurements to velocity widths al. (2004). (2) MPT92 magnitudeswere derived using BH82
pmm B
equivalenttoW ,radiolinewidthsmeasuredat50%ofpeak Galacticextinctioncorrectionsandthe TF85internalextinc-
50
intensity. KFF02derivearelationshipbetweenV andW tioncorrections,forcomparisontoPierce&Tully(1992).(3)
pmm 50
by directly comparing optical and radio observations of the MTP00magnitudeswerederivedusingSFD98Galacticextinc-
B
galaxiesintheirsample.TheyalsofindthatW =W - 20km tion corrections and the T98 internal extinction corrections,
50 20
s- 1 (see also Haynesetal. 1999). KFF02adoptthe nomem- for comparison to Tully & Pierce (2000). (4) MKFF02 mag-
B
clatureW to describe their W -equivalent velocity mea- nitudeswerederivedusingBH82Galacticextinctioncorrec-
Vpmm 50
surementsderivedfromV . tions and the T98 internal extinction corrections, following
pmm
In Table 6, we list the simple steps we have taken to con- the method used by Kannappan, Fabricant, & Franx (2002).
vert our V measurements to velocity widths equivalent to Inthislattercase, wecalculatedWi tobeappliedintheT98
arc R
Wi andW forcomparisontoPT92,TP00,andKFF02.We internalextinctioncorrectionusingthemethodoutlinedinTa-
R Vpmm
note that in step 1, we have taken the inclination correction ble 6, but with steps 6 and 7 switched. In other words, the
8 Metevieretal.
turbulencecorrectionwasappliedtotherotationvelocitybe- offsetoftheCl0024relationfromPT92,wefindthatCl0024
fore the inclination correction in this case only. This same members are in this case only 0.16±0.23 mag brighter on
procedurewasadoptedbyKFF02. averagethanlocalgalaxies. Inotherwords,matchingourve-
Theinternalextinctioncorrectionswehavederivedforeach locity and luminositymeasurementtechniquesto those used
galaxyarenotedinTable8;absoluteM magnitudesandrest- byPT92haschangedourresultsby∼0.5mag.
B
frame (U- B) colors are in Table 7. Restframe colorshave We have also made “matched" comparisons to the more
0
been calculated using the BH82 Galactic extinction correc- recently-published local TF relations of TP00 and KFF02,
tions (see above) and T98 internalextinction correctionsfor showninFigure5(c)and5(d).TheTP00sampleislargerthan
comparisonto KFF02. Like KFF02, we use an extrapolated PT92, drawnfroma rangeofenvironments,andinternalex-
internalextinctioncorrectionfortheU band(see equation3 tinctioncorrectionshavebeenimprovedinthisstudy. KFF02
intheirpaper). isalsoanimprovementuponPT92.Theirsamplecomesfrom
the Nearby Field Galaxy Survey (NGFS, Jansen & Kannap-
4. THECL0024TULLY-FISHERRELATION pan2001),asampleoflocalgalaxieschosenwithoutprefer-
WepresenttheBbandTully-Fisherrelationforoursample ence for morphology, color, size, environment, or any other
of15Cl0024membersinFigure5. Ineachofthefourpanels galaxy property. Specifically, in Figure 5(d) we compare to
ofthisfigure,wemakeadifferentcomparisonoftheCl0024 the subsample of Sa-Sd galaxies in KFF02 with M <- 18
R
TFR to a local Tully-Fisherrelation. This was motivatedby and inclinations i>40◦. We note that we find a slight off-
thefollowing: insomeofthe veryfirststudiesofthe distant set(∼0.2mag)betweentheTP00andKFF02localrelations.
galaxyTFR, Vogt et al. (1996, 1997)comparedtheir results AsimilaroffsethasbeenfoundindependentlybyKannappan
to the local relation of PT92. Since then, larger local sam- (privatecommunication;seealsoKFF02),confirmingthatour
ples(suchasTP00andKFF02)havebeenbetteranalyzed,for velocityandluminositymeasurement“matching”isaccurate.
example with improved internal extinction corrections, and If we assume uniform shifts from the local TF relations
withsomewhatdifferentlocalTFRresults. However,theau- withnochangeinslopeordispersion,itisclearfromFigure
thorsof more recentstudies of the distant galaxyTFR (e.g., 5 thatthe Cl0024sample appearsmarginallyunderluminous
Milvang-Jensenet al. 2003, Ziegler et al. 2003, Böhm et al. ascomparedtobothTP00(<∆TF>=0.29±0.17mag)and
2004) have continued to compare to the local PT92 relation KFF02 (<∆TF> =0.50±0.23 mag; we note that the zero-
so that their results can be more directly juxtaposed against point errors on the reference TP00 and KFF02 Tully-Fisher
thoseofVogtetal. InFigure5,wecomparetoPT92forthe relationsare.0.1mag). Thisis somewhatsurprising,asal-
same reasons, but we also compare to the local relations of mostallotherdistantTFRstudieshavefoundthatbyz∼0.25,
TP00 and KFF02 in order to be more comprehensivein our galaxiesaresomewhatoverluminousascomparedtothelocal
analysis. TFR (see the introduction of this paper for a list of exam-
IneachpanelofFigure5,theinverseTully-Fisherrelation ples). However,ourresultsareconsistentwithPT92who,as
(velocityasafunctionofluminosity)isshown:inmagnitude- notedabove,foundthatlocalclustergalaxiesare∼0.25mag
limitedsamples,fittingtheinverserelationhelpstoavoidbi- lessluminousintheBbandthantheirlocalfieldcounterparts.
asesduetoasymmetricfaint-endscatterinluminosities(e.g., Furthermore, Kannappan et al. (2003) found a slight under-
Schechter 1980). In Figure 5(a), we present a “raw" com- luminositywhentheyre-analyzedthedistantfieldsampleof
parisonbetweenthe Cl0024TFR andthe PT92 relation. By Vogtet al. (1997). Specifically, Kannappanet al. foundthat
thiswemeanthatwedirectlycompareourV -Mdist relation this<z>∼0.5sampleis.0.5magunderluminousascom-
arc B
totheirWi-MPT92 relationwithoutaccountingfordifferences paredtogalaxiesintheNGFSwithsimilarrotationvelocities
R B
in velocitymeasurementtechniquesor for differencesin ex- andsimilarlylargeemissionlineequivalentwidths. Kannap-
tinctioncorrectionsusedtocalculaterestframeBmagnitudes. panetal.suggestthatthismaybeduetoadecreaseinstellar
This is the type of comparison commonly made in distant massfractionwithlookbacktime.Ourresultsnotonlyhintat
galaxy TFR studies in order to deduce luminosity evolution suchanunderluminosity,butalsohighlighttheimportanceof
results. the choice of comparisonsample for studies of Tully-Fisher
Because our sample spans a limited range in luminosi- evolution, and of “matching" measurements in the resulting
ties, we examine the Cl0024 TFR in Figure 5(a) assuming comparison.
the slope determined by PT92. Using the biweight method As in distant field galaxy TFR studies, there has thus far
(Beers, Flynn, & Gebhardt 1990), we determine an offset been some evidence for brighter cluster galaxies, relative to
fromthePT92fieldrelationof<∆TF>=- 0.69±0.24mag. a given rotation velocity, in the past. Milvang-Jensen et al.
Thevalueofthisoffsetremainsconsistenttowithin∼0.1mag (2003) studied 19 field spirals at 0.15<z<0.90 and eight
whetherweusethetotalCl0024TFRsampleoronlytheob- members of cluster MS1054-03 at z = 0.83. By making a
jectswith“normal"kinematics. WenotethatPT92measured “raw"comparisonoftheir fieldsample to thelocalPT92re-
aBbandzeropointoffsetbetweenlocalclusterandfieldsam- lation, they determined a relation between galaxy redshifts
ples,indicatingthatlocalclustergalaxiesare∼0.25magless and their offsets from the local TFR: ∆TF ≈ - 1.6z, assum-
luminousinthisbandthangalaxiesinthenearbyfield. This ing H =75 km s- 1 Mpc- 1 and q =0.05. Convertingto our
0 0
would make our Cl0024 sample 0.94 mag brighter than the cosmology, they predict ∆TF =- 0.93 mag at z=0.4. Our
PT92localclustersample. “raw" Cl0024 TFR, with ∆TF =- 0.69 mag, is slightly less
However,thisresultmaybemisleading. Ifweconvertour luminousthantheirprediction.
V measurementsforCl0024memberstoWi (see§3.3)and However, Milvang-Jensen et al. showed that their cluster
arc R
deriverestframeM usingthesameGalacticandinternalex- sampleissomewhat(∼0.5–1.0mag)brighterthantheirfield
B
tinctioncorrectionsasthoseusedbyPT92(see§3.4),wecan sampleatthe sameredshift. Theysuggestthatthisluminos-
makea“matched",ratherthan“raw",comparisonofthedis- ity enhancementmay reflect increased star formationin spi-
tant cluster TFR to the local relation. This “matched” com- rals falling into cluster MS1054 for the first time. More re-
parison is shown in Figure 5(b). Recalculating the biweight cently, Bamford et al. (2005)have expandedthis study with
TFRinCl0024atz=0.4 9
largerfield(58galaxies)andcluster(22galaxies)samplesand 5.1. TFResidualsandOtherFundamentalGalaxyProperties
have derivedsimilar results. These results appear to contra-
Severalauthors(e.g., Verheijen2001) have searched for a
dictours,aswellasthoseofZiegleretal.(2003),whostudied
“thirdparameter"totheTully-Fisherrelationforspiralgalax-
theTFRfor13clustergalaxiesatz∼0.5andfoundnosignif-
ies, analogous to the dependence of velocity dispersion and
icantluminosityevolution. This mayreflect truedifferences
surface brightness on galaxy size for early-types (known as
betweenthespiralpopulationsofdifferentclustersand/ordif-
thefundamentalplane, Djorgovski&Davis1987). Untilre-
ferencesbetweenoursampleselectiontechniques. Inthefu-
cently, no strong evidence has been given for a relationship
ture, we intend to explore this apparent discrepancy with a betweenTully-Fisherresiduals(∆TF)andothergalaxyprop-
largersample of severalhundredspirals spanninga rangeof
erties.However,intheirstudyofnearbyfieldgalaxies,KFF02
environmentsintheGOODSfieldsandExtendedGrothStrip. haveshownthat∆TFandgalaxycolorsarecorrelated,reflect-
SpectroscopyinthesefieldsisunderwayaspartoftheDEEP2
ing an influence from galaxy star formation histories. This
Survey(Davisetal.2003)andtheTeamKeckTreasuryRed-
finding is supported by a similar trend found in the nearby
shiftSurvey(Wirthetal.2004).
UrsaMajorclusterbyVerheijen(2001).Althoughthenumber
ofgalaxiesinoursampleisrelativelysmall,weattempthere
5. DISCUSSIONOFTULLY-FISHERRESIDUALS to look for correlations between Tully-Fisher residuals and
otherfundamentalgalaxypropertiesin Cl0024, in the hopes
FromFigure5,onecanseethattheobservedscatterinthe
that they may provide clues about evolutionaryprocesses in
Cl0024 TFR spans the 3σ confidence intervals of the PT92
thecluster.
andTP00localrelations. Furthermore,scatterintheCl0024
Inthefollowinganalysis,wedefine∆TFasthedifference
TFR is comparable to that found by KFF02, whose sample
betweenagalaxy’sobservedluminosityanditspredictedlu-
is unusual in that it has not been “pruned” to include only
minosity, derived from a comparison of its rotation velocity
normalspirals. Increasedscatter in the Tully-Fisherrelation
totheCl0024TFR(characterizedbyasimple0.50magoffset
has been linked on the observational side to galaxy-galaxy
fromtheKFF02relation):
interactions (Barton et al. 2001). On the theoretical side, it
hasbeenlinkedto theratioof darkto luminousmasswithin ∆TF(mag)=MKFF02- {- 19.83- 10.09[log(W )- 2.5]+0.50}
B Vpmm
galaxies of different luminosities (Salucci, Frenk, & Persic (4)
1993). Using the biweight technique and comparing to the We have determined errors on these TF residuals by adding
KFF02relation, we findσTF =1.00magin theCl0024TFR ourphotometryerrors(0.15mag)inquadraturewith ourve-
(objectswith“normal"kinematicsonly,σTF increasesabitto locity measurement errors, converted to magnitudes. Our
1.14magif we includethefullsample). Thisis comparable ∆TFmeasurementsarelistedinTable9.
to but slightly larger than the 0.82 mag dispersion found by WediscussTFresidualsintermsofmagnitudesinthispa-
KFF02. After accounting for photometry errors (0.15 mag) perin orderto compareto local Tully-Fisherresidualanaly-
and errors on our velocity measurements (corresponding to sis (e.g., KFF02). However, we note that this can be prob-
0.42mag),wedeterminetheintrinsicCl0024σTF=0.90mag. lematic for distant Tully-Fisher studies, including our own,
Thisissomewhatlargerthantheintrinsicscatter(σTF =0.57 whichhavesignificantluminosityselectioneffects. Infuture
mag)measuredbyKFF02 in theB band, andismuchlarger studies,abettertreatmentofthedatawillbetodiscussveloc-
thanthetotalscatter,includingmeasurementerrors,reported ity residualsfromthe Tully-Fisherrelationfor distantgalax-
by PT92 (σTF =0.41 mag) and by TP00 (σTF =0.38 mag). ies. Therefore,inTable9wealsolisttheCl0024memberTF
Below,weanalyzethisscatter,or“residuals”fromtheCl0024 residualsasvelocities,determinedbycomparingthegalaxies’
Tully-Fisherrelation,inmoredetail. luminositiestotheCl0024TFR:
Beforepresentingthisanalysis,wenotethatauthorsoflo-
cal Tully-Fisher studies (e.g., Courteau 1997, Willick 1999) ∆TF(kms- 1)=WVpmm- 10{[MBKFF02+19.83- 0.50]/- 10.09+2.5} (5)
havefoundthatusingV insteadofV reducesscatterinthe
2.2 arc Again,weaddourphotometryerrors(convertedtovelocities)
TFR. Here, V is the rotation velocity measured at 2.15r ,
2.2 d andvelocityerrorsinquadraturetodeterminetheerrorsonthe
where rd is the disk scale length; the radius 2.15rd corre- residuals. Wealsoroundthevelocityresidualstothenearest
spondstothepointatwhichtherotationamplitudeofapure 5kms- 1toreflecttheprecisionofourdata.
exponentialdiskreachesitsmaximum(e.g.,Freeman1970).
Asatest,wehaveredeterminedtheCl0024TFRbycalculat- 5.1.1. Luminosity
ingV for the cluster members, entering the measured val-
2.2 In Figure 6 (top panels), we compare TF residuals (∆TF)
ues ofV , r , and 2.15r for each galaxy into equation(1)
arc to d
to the fundamentalparametersof the TFR itself: luminosity
of this paper (see §3.2 for the equation and Tables 3 and 5
(MKFF02) and velocity(logW ). As can be seen in Figure
for the measurements). Furthermore, we have redetermined 6(aB), there is no dependenceVpomfm∆TF on luminosity: using
radio-equivalent velocity widths based on the V measure-
2.2 the Spearman rank test on the “normal” sample, we find a
ments, replacing step 2 of Table 6 with a similar calibration
77%probabilitythatthecorrelationbetween∆TFandMKFF02
derived from the min-max velocities, arctangent velocities, B
occurredbychance. Aformallinefittothissampleyieldsa
andturnoverradiipresentedinCourteau(1997),andthedisk
slopeof- 0.42±0.27,indicatingthatthedataareinconsistent
scalelengthsgiveninCourteau(1996).WefindthatusingV
2.2 withthenullhypothesis(zeroslope,ornocorrelation)atonly
doesreducethetotalscatterintheCl0024TFR,measuredas
the1.6σlevel.WeshadetheleftsideofFigure6(a)toindicate
a simple offset from the KFF02 relation, to 0.42 mag; this
our selection bias against galaxies with M >- 19.5. Only
is comparable to our measurement errors alone. However, B
one galaxy fainter than this limit (TFR 08) has made it into
the choice of V or V does not qualitatively change the
arc 2.2 oursampleduetoitsverystrongemission.
results of our Tully-Fisher analysis or our analysis of Tully-
FisherresidualsinCl0024. Therefore,we continuewithour
5.1.2. Velocity
TFresidualanalysisbasedonV measurements.
arc
10 Metevieretal.
Ontheotherhand,inFigure6(b),TFresidualsforoursam- lower” measuredTully-Fisher slopes with increasing disper-
pleappeartobecorrelatedwithrotationvelocity(thechance sion. (We note that “shallower”Tully-Fisherslopes actually
probabilityof the correlation is six in 10,000), such that the appearsteeperinourdiagrams,aswehaveplottedtheinverse
most slowly rotating systems are most overluminous. Fur- Tully-Fisherrelationin Figures5 and 7.) This slope change
thermore, our formalfit to the “normal” sample is inconsis- isinthesamedirectionasthatindicatedbyourowndataand
tent with the null hypothesis at the 9σ level. This may in- measured in other distant Tully-Fisher studies (e.g., Ziegler
dicateslopeevolutionoftheTFRandbeevidenceformass- etal. 2002,Böhmetal.2004). Anapparentslopechangein
segregated luminosity evolution, a possible outcome of ha- thisdirectionduetomagnitudeincompletenesshasalsobeen
rassment(e.g.,Gnedin2003). Indeed,ifwedonotassumea foundinthelocalstudiesofWillick(1994)andGiovanelliet
localTully-FisherslopeinCl0024,wefindthataninversefit al.(1997).Inourcase,theselectionbiasresultsinanincreas-
to the“normal”sampleshownin Figure5(d)yieldsa Tully- ingly prominent and steep correlation between velocity and
Fisher slope of- 7.04±0.30as opposedto the KFF02 slope ∆TFwithincreasingdispersion.FromFigure7andTable10,
of- 10.09±0.39.Evidenceforaslopechangeinthesamedi- weseethatanyTully-Fisherslopeevolutioninferredparticu-
rectionhasalsobeenobservedinthefield(Simard&Pritchet larlyfromourlow-luminosityCl0024datapointsisstrongly
1998,Mallen-Ornelasetal. 1999,Ziegleret al. 2002,Böhm affected by magnitude incompleteness in combination with
etal.2004),sothismaynotbespecifictotheclusterenviron- measurementerrorsandtheintrinsicdispersionofthegalax-
ment. ies’properties.However,iftherewerenoslopeevolution,we
Our sample is small and incomplete at low luminosities, wouldexpecttoseeaturn-offto∆TF=0atthehigh-velocity
soweexplorehowmagnitudeselectionaffectsmeasurements endinthelog(velocity)-∆TFdiagram(seeFigure7b).Wedo
of slope evolutionbeforeplacing greatweighton our result. notseethisintheCl0024sample(Figure6b).
While incompletenesseffects on Tully-Fisher measurements Itispossiblethatanincorrectmeasurementoftheslopeof
havebeenstudiedingreatdetailatlowredshifts(e.g.,Willick theTully-Fisherrelationwouldcauseusnottoseeaturn-off
1994, Giovanelli et al. 1997), these effects are significant to∆TF=0atthehigh-velocityendoftheFigure6(b). This
yetrelativelyunexploredin distantTully-Fisherstudies. We wouldbethecaseparticularlyifwemeasureda“steeper”,or
have shaded Figure 6(b) to demonstrate how luminosity in- more strongly negative, slope than that which characterized
completeness at M >- 19.5 affects the distribution of data the true distribution of our sample. However, as explained
B
points in this diagram. It is possible that the correlationbe- above,itismuchmorelikelythatwewouldmeasureanoverly
tweenvelocityand∆TFwefindmaybeartificiallytightbe- “shallow”slope,givenourmagnitudeincompleteness. Inthe
cause we cannot observe galaxies to the lower left in this bottom panels of Figure 7, we demonstrate the effect of a
plot.WeinvestigatethisfurtherinFigure7,wherewedemon- “shallow” slope measurement on the log(velocity)-∆TF re-
stratehowmagnitudeselectionaffectsTully-Fishermeasure- lation. InFigure7(c),weplotthelog(velocity)-∆TFrelation
mentsofthreerandomlygeneratedgalaxypopulations:alow- for the high-dispersion sample of generated data, as this is
dispersion sample (black points), a medium-dispersionsam- the sample for which it is most difficult to measure a Tully-
ple (dark grey points), and a high-dispersion sample (light Fisherslope.Here,asinFigure7(b),wehavederived∆TFby
greypoints). We haveperturbedthevelocitiesandluminosi- comparingthegeneratedgalaxymagnitudestotheirexpected
ties of the galaxies in each of these samples around the B- magnitudes,giventheirvelocitiesandtheknowninputTully-
bandTFRmeasuredinKFF02,increasingtheperturbationsas Fisher relation. In Figure 7(d), we again plot log(velocity)
thegalaxies’luminositiesandvelocitiesdecreasetoreflectthe versus∆TF, but this time we have calculated ∆TF by com-
fact that we typically incur larger measurementerrorsat the paring generated galaxy magnitudes to those expected from
low-luminosityendoftheTully-Fisherrelation.Thenumbers the measured Tully-Fisher relation (see Table 10), assuming
ofgalaxieswe havegeneratedin each luminositybinfollow the input relation was unknown. As can be seen in this di-
theshapeoftheg-bandluminosityfunctiongiveninBlanton agram, an underestimated (or less strongly negative) Tully-
etal.(2001),with0.45subtractedfromtheg-bandmagnitude, Fisherslopestillresultsinaturn-off,orhereaturn-up,atthe
asthisisthetypicalg-BcolorofanSab galaxy(Fukugitaet high-velocityend of the log(velocity)-∆TFrelation. Again,
al.1995). wedonotseethisintheCl0024sample(seeFigure6b),and
In Figure 7(a), we show the Tully-Fisher relation for the we therefore conclude that the Tully-Fisher slope evolution
three samples we have generated. This panel is shaded weseeintheclustermaybereal.
to demonstrate a selection bias against galaxies with M > Wewouldneedalargergalaxysampletodiscernmorecon-
B
- 19.5,asseenintheCl0024sample. Foragivenlowveloc- clusivelywhetherornottheslopeoftheTully-Fisherrelation
ity, one can see that only the highest-luminosity data points isevolving.Furthermore,quantifyingtheeffectofmagnitude
make it into the unshaded region of the diagram. In Figure selectiononourmeasurementofTully-Fisherslopeevolution
7(b), we present the corresponding log(velocity)-∆TF rela- requiresMonte-Carlosimulationswith knowledgeof galaxy
tion,alsoshadedtoreflectourmagnitudeselectionbias. The number counts built in. That work is beyond the scope of
low-velocity, high-luminosity galaxies show up as a tail to- thispaper. Wecautionherethattheapparentslopeevolution
ward the upper left of the unshaded region of the diagram. foundby otherauthors(e.g., Böhm et al. 2004)may also be
Thistailisparticularlyprominentforthehigh-dispersionsam- affectedbymagnitudeincompleteness.Itisalsopossiblethat
ple, and could lead one to measure Tully-Fisher slope evo- theirresultsaredrivenbylow-luminositygalaxieswithtrun-
lution despite the fact that no slope change was input into catedrotationcurvesor otherkinematic anomaliesthathave
the sample. This is clear in Table 10, where we list the the resultedin underestimatedrotation velocities(Kannappan&
input Tully-Fisher and log(velocity)-∆TF relations, as well Barton 2004). This does not appear to be the case for our
asthemeasuredTully-Fisherandlog(velocity)-∆TFrelations sample (see §5.1.6), as Cl0024 members with the smallest
forthe galaxieswithM ≤- 19.5ineachofthethreegener- emission line extents are generally the most underluminous.
B
atedsamples. Again,thispointstowardthefactthattheTully-Fisherslope
Themagnitudeselectionbiasresultsinincreasingly“shal- evolutionweseeinCl0024maybereal. Futurestudieswith