Bar pattern speeds in CALIFA galaxies: I. Fast bars across the Hubble sequence

1.4 MB·English

by  J. A. L. Aguerri

Astronomy&Astrophysicsmanuscriptno.23383˙ja (cid:13)c ESO2016
August11,2016
Bar pattern speeds in CALIFA galaxies
I. Fast bars across the Hubble sequence
J.A.L.Aguerri1,2,J.Me´ndez-Abreu1,2,J.Falco´n-Barroso1,2,A.Amorin3,J.Barrera-Ballesteros1,2,R.CidFernandes3,
R.Garc´ıa-Benito4,B.Garc´ıa-Lorenzo1,2,R.M.Gonza´lezDelgado4,B.Husemann5,V.Kalinova6,M.Lyubenova6,R.
A.Marino7,I.Ma´rquez4,D.Mast8,E.Pe´rez4,S.F.Sa´nchez4,9,G.vandeVen6,C.J.Walcher5,N.Backsmann5,C.
Cortijo-Ferrero4,J.Bland-Hawthorn10,A.delOlmo4,J.Iglesias-Pa´ramo4,9,I.Pe´rez11,12,P.Sa´nchez-Bla´zquez13,L.
Wisotzki5,andB.Ziegler14
5
1
0 1 InstitutodeAstrof´ısicadeCanarias.C/V´ıaLa´cteas/n,38200LaLaguna,Spain
2 2 DepartamentodeAstrofsica,UniversidaddeLaLaguna,38205LaLaguna,Tenerife,Spain
3 DepartamentodeFisica,UniversidadeFederaldeSantaCatarina.P.O.Box476,88040-900.Floriano´polis,SC,Brazil
n
4 InstitutodeAstrofsicadeAndaluca-CSIC,18008,Granada,Spain
a
5 Leibniz-InstitutfrAstrophysikPotsdam(AIP),AnderSternwarte16,D-14482Potsdam,Germany
J
6 Max-Planck-InstitutfrAstronomie,Konigstuhl17,69117Heidelberg,Germany
2 7 CEI Campus Moncloa, UCM-UPM, Departamento de Astrofsica y CC. de la Atmsfera, Facultad de CC. Fsicas, Universidad
2 ComplutensedeMadrid,Avda.Complutenses/n,28040Madrid,Spain
8 InstitutodeCosmologia, RelatividadeeAstrof´ısica ICRA,CentroBrasileirodePesquisasF´ısicas,RuaDr.XavierSigaud150,
]
CEP22290-180,RiodeJaneiro,RJ,Brazil
A
9 CentroAstrono´micoHispanoAleman,CalarAlto(CSIC-MPG),C/Jesu´sDurba´nRemo´n2-2.E-04004Almer´ıa,Spain
G 10 SydneyInstituteforAstronomy.SchoolofPhysicsA28.UniversityofSydney.NSW2006,Australia
. 11 Dpto.deFsicaTericaydelCosmos,UniversityofGranada,FacultaddeCiencias(EdificioMecenas),18071,Granada,Spain
h 12 InstitutoUniversitarioCarlosIdeFsicaTericayComputacional,FacultaddeCiencias,18071,Granada,Spain
p 13 DepartamentodeF´ısicaTeo´rica,UniversidadAutnomadeMadrid,Cantoblanco,E-28049Madrid,Spain
- 14 UniversityofVienna,Trkenschanzstrasse17,1180,Vienna,Austria
o
r
t Received;accepted
s
a
ABSTRACT
[

1 Context.Thebar patternspeed (Ωb)isdefined astherotational frequency of thebar,and it determinesthebar dynamics. Several
v methods have been proposed for measuring Ωb. The non-parametric method proposed by Tremaine & Weinberg (1984; TW) and
8 basedonstellarkinematicsisthemostaccurate.Thismethodhasbeenappliedsofarto17galaxies,mostofthemSB0andSBatypes.
9 Aims.WehaveappliedtheTWmethodtoanewsampleof15strongandbrightbarredgalaxies,spanningawiderangeofmorpho-
4 logicaltypesfromSB0toSBbc.Combiningouranalysiswithpreviousstudies,weinvestigate32barredgalaxieswiththeirpattern
5 speedmeasuredbytheTWmethod.TheresultingtotalsampleofbarredgalaxiesallowsustostudythedependenceofΩbongalaxy
0 properties,suchastheHubbletype.
. Methods.WemeasuredΩb usingtheTWmethodonthestellarvelocitymapsprovidedbytheintegral-fieldspectroscopydatafrom
1 theCALIFAsurvey.Integral-fielddatasolvetheproblemsthatlong-slitdatapresentwhenapplyingtheTWmethod,resultinginthe
0 determination of more accurate Ω . In addition, we have also derived the ratio R of thecorotation radius to the bar length of the
b
5 galaxies.Accordingtothisparameter,barscanbeclassifiedasfast(R<1.4)andslow(R¿1.4).
1 Results.Forallthegalaxies,Riscompatiblewithintheerrorswithfastbars.Wecannotruleout(at95%level)thefastbarsolution
v: foranygalaxy.WehavenotobservedanysignificanttrendbetweenRandthegalaxymorphologicaltype.
i Conclusions.OurresultsindicatethatindependentoftheHubbletype,barshavebeenformedandthenevolveasfastrotators.This
X observationalresultwillconstrainthescenariosofformationandevolutionofbarsproposedbynumericalsimulations.
r
Key words. Galaxies: kinematics and dynamics – Galaxies: structure – Galaxies: photometry – Galaxies: evolution – Galaxies:
a
formation
1. Introduction (see, e.g., Marinova&Jogee, 2007; Barazzaetal., 2008;
Aguerrietal., 2009). This fraction is even higher (about 60-
Bars are ellipsoidal-like structures present in the inner region 70%) when galaxies are observed through near-infrared fil-
ofmostdiscgalaxies.Thegalaxyclassificationintobarredand ters (see, e.g., Knapenetal., 2000; Eskridgeetal., 2000;
non-barredhasbeenmadesincethepioneeringHubblemorpho- Mene´ndez-Delmestreetal.,2007).Thebarfractiondependson
logical classification. Indeed, barred galaxies constitute one of differentgalaxyproperties,suchasHubbletype,mass,andenvi-
the branches of the so-called Hubble tuning-fork diagram (see ronment.Thereisadebateintheliteratureaboutthedependence
Hubble,1936). ofthebarfractionontheHubbletype(e.g.,Aguerrietal.,2009;
Butaetal., 2010; Barwayetal., 2011; Mastersetal., 2011;
About 40-50% of nearby disc galaxies observed in the
Marinovaetal., 2012). Several studies have recently demon-
optical wavelengths have been classified as barred systems
1
J.A.L.Aguerrietal.:PatternspeedinCALIFAbarredgalaxies
strated that total stellar mass is an important physical param- In general, S0 galaxies show weaker bars than late-type ones
eter that regulates bar formation (Me´ndez-Abreuetal., 2010; (see, e.g., Laurikainenetal., 2007; Aguerrietal., 2009;
Nair&Abraham, 2010; Shethetal., 2008). However, the en- Butaetal.,2010).
vironment also plays a non-negligible role in their formation The bar pattern speed (Ω ) is a pure dynamical parameter
b
and evolution, as shown by Mendez-Abreu et al. (2012) when that fully determinesthe dynamicsof a barredgalaxy.It is de-
comparingthebarfractioninthreedifferentenvironments(field, fined as the rotational frequency of the bar. Theories of stellar
Virgo,andComaclusters).Theyshowthatthefractionofbarsin orbits have shown that Ω has a physical upper limit. Thus, a
b
the Virgo and Coma clusters are statistically differentfrom the barcannotextendbeyondthecorotationresonance(CR)radius
fieldone.Theyarguethatbrightdiscgalaxiesarestableenough (R ) of the galaxy. This corotation radius is the region of the
CR
againstinteractions,whereasforfaintergalaxies,interactionsin galaxywheretheangularspeedofthestarsofthediscincircu-
clusterenvironmentbecomestrongenoughtoheatupthediscs, lar motions equalsthe bar pattern speed. This limit is imposed
inhibitingbarformationandevendestroyingthediscs(seealso bythestabilityofthemainfamilyoforbitsformingthebar(the
Sa´nchez-Janssenetal.,2010). so-called x family; Contopoulos 1980) which are only stable
1
Bars are very prominent features in light. In contrast, they withinR .Orbitsintheouterregionofthedisc(R>R )can-
CR CR
represent a small fraction of the mass of the discs of galaxies. notsupportabarstructure(Contopoulos,1980;Athanassoula,
Hydrodynamical simulations of barred galaxies show that the 1992).
bar componentcontributes only about 10% to 20% of the disc Measuring the bar pattern speed is technically the most
potential (see Englandetal., 1990b; Laine&Heller, 1999; difficult amongst the observational parameters characterising
Lindbladetal., 1996a; Weineretal., 2001; Aguerrietal., bars,andseveralmethodshavebeendevelopedintheliterature
2001). Nevertheless, they produce important changes in the to determine it. Hydrodynamical simulations of individual
dynamics of the discs when they are present. In fact, simu- galaxies have been extensively used to determine Ω in barred
b
lations also show that bars are very efficient at redistributing galaxies. These methods start by computing the gravitational
angular momentum, energy, and mass on both luminous potentialof the galaxythat is used to producehydrodynamical
and dark matter galactic components (see Weinberg, 1985; galaxy models, with Ω as one of the free parameters of the
b
Debattista&Sellwood, 1998, 2000; Athanassoulaetal., models. Determination of the best value of Ω is done by
b
2003; Martinez-Valpuestaetal., 2006; Sellwood, 2006; matching the modelled and observed surface gas distribution
Sellwood&Debattista,2006;Villa-Vargasetal.,2009). and/or gas velocity field (see, e.g., Sanders&Tubbs, 1980;
Bars are fully characterized by three parameters: length, Hunteretal.,1988;Englandetal.,1990;Garcia-Burilloetal.,
strength,andpatternspeed.Bothlengthandstrengthcanbede- 1993; Sempereetal., 1995a; Lindbladetal., 1996a;
terminedusingopticaland/ornear-infraredimages.Incontrast, Lindblad&Kristen, 1996b; Laine&Heller, 1999;
thebarpatternspeedisadynamicalparameter,anditsdetermi- Weineretal., 2001; Aguerrietal., 2001; Pe´rezetal., 2004;
nationrequireskinematics. Rautiainenetal.,2008;Treuthardtetal.,2008).Othermethods
The length of the bars has been determined by optical vi- determinethepatternspeedbyidentifyingsomemorphological
sualinspectionKormendy (1979);Martin (1995),locatingthe galaxyfeatureswith Lindbladresonances.We can mentionthe
maximum of the isophotal ellipticity Wozniaketal. (1995); position of galaxy rings (see, e.g., Buta, 1986; Butaetal.,
Ma´rquezetal. (1999); Laineetal. (2002); Marinova&Jogee 1995; VegaBeltranetal., 1997; Mun˜oz-Tun˜o´netal., 2004;
(2007); Aguerrietal. (2009), or by structural decompositions Pe´rezetal., 2012); changes in the morphology or phase of
ofthegalaxysurfacebrightnessdistributionPrietoetal. (1997, spiralarmsnearRCR (Canzian, 1993; Canzian&Allen, 1997;
2001); Aguerrietal. (2001, 2003, 2005); Laurikainenetal. Puerari&Dottori, 1997; Aguerrietal., 1998; Buta&Zhang,
(2005, 2007); Gadotti (2008); Laurikainenetal. (2009); 2009); detecting the offset and shape of dust lanes (see, e.g.,
Weinzirletal. (2009); Gadotti (2011). All these studies vanAlbada&Sanders, 1982; Athanassoula, 1992); locating
have shown that a typical bar radius is 3-4 kpc (e.g., colour and star formation changes outside the bar region
Marinova&Jogee,2007;Aguerrietal.,2009).Thereisaclear (Cepa&Beckman,1990;Aguerrietal.,2000);orstudyingthe
dependencebetweenthebarlengthandothergalaxyparameters, morphologyof the residual gas velocity field after the rotation
such as disc scale length,galaxysize, galaxycolour,or promi- velocity subtraction (Sempereetal., 1995b; Fontetal., 2011,
nence of the bulge Aguerrietal. (2005); Marinova&Jogee 2014). Nevertheless, the most accurate method for measuring
(2007); Gadotti (2011); Hoyleetal. (2011). In addition, there thebarpatternspeedisthenon-parametricmethodproposedby
is a dependency of the bar length on the Hubble type. In Tremaine & Weinberg (1984; hereafter TW). The goal of this
particular, S0 galaxies show larger bars than late-type ones paper is to apply the TW method to a large sample of barred
(Elmegreen&Elmegreen, 1985; Aguerrietal., 2009; Erwin, galaxies.
2005;Mene´ndez-Delmestreetal.,2007,butseealsoMasterset Theorganizationofthe paperis as follows.The theoretical
al.2011). basisoftheTWmethodisshowninSect.2.Section3showsthe
The bar strength is a parameter that measures the descriptionofthe galaxysample.Section4 presentsthe photo-
non-axisymmetric forces produced by the bar potential metric parameters of the bars. The stellar velocity maps of the
in the disc of galaxies (see, e.g., Laurikainen&Salo, galaxies are shown in Sect. 5, and results are given in Sect. 6.
2002). The most popular methods for determining the ThediscussionandconclusionsareshowninSects.7and8,re-
bar strength are to measure the torques of the bar (e.g., spectively.Throughoutthis paper we have used the cosmology
Combes&Sanders,1981;Quillenetal.,1994;Buta&Block, H0 =70kmMpc−1s−1,Ωm =0.3,andΩλ =0.7.
2001;Laurikainenetal.,2007;Saloetal.,2010),barellipticity
Martinet&Friedli (1997); Aguerri (1999); Whyteetal.
2. TheoreticalbasisoftheTWmethod
(2002); Marinova&Jogee (2007); Aguerrietal. (2009),
or Fourier decomposition of the galaxy light Ohtaetal. We let(X,Y)beaCartesiancoordinatesystemintheskyplane
(1990); Marquezetal. (1996); Aguerrietal. (2000); andtaketheoriginatthecentreofthegalaxy,withX-axiscoin-
Athanassoula&Misiriotis (2002); Laurikainenetal. (2005). cidentwiththelineofnodes(LON),whichisdefinedasthein-
2
J.A.L.Aguerrietal.:PatternspeedinCALIFAbarredgalaxies
tersectionbetweentheskyplaneandtheplaneofthediscofthe 2.1.Fastandslowbars
galaxy.Assumingthatthediscofthegalaxyhasawell-defined
Barred galaxies are commonly classified according to the
patternspeedΩ andthatthesurfacebrightnessofthemeasured
b distance-independentratio R = R /a , where R and a are
tracersfollowthecontinuityequation,theTWmethodisbased CR b CR b
the corotation and bar radius, respectively. Theoretical works
ontheequation:
based on stellar orbits in barred potential predict that R =
Ω sini= −+∞∞h(Y) −+∞∞Σ(X,Y)VLOS(X,Y)dXdY ≡ hVi, (1) m1.2its±a0c.l2as(ssiefiecaAtitohnanoafssboaurlsai,nt1o9f9a2s)t.(T1h.0is<paRra<me1t.r4iz)aatinodnsploewr-
b R +∞hR(Y) +∞XΣ(X,Y)dXdY hXi ones (R > 1.4). Most observed bars have turned out to be fast
−∞ −∞
R R bars;nevertheless,therearefewbarsintheliteraturecompatible
where i is the galaxy inclination, V (X,Y) is the line of
LOS withbeingslowbars(seeRautiainenetal.,2008).
sight (LOS) velocity, Σ(X,Y) represents the surface brightness
Therearesomehintsinpreviousworksthatlate-typegalax-
of the galaxy, and h(Y) is a weight function. The numerator
ies could have higher mean values of R than early-type ones
ofthepreviousequationrepresentsthemeanvelocityweighted
(see Aguerrietal., 1998).Morerecentresultsbasedonhydro-
by the light of the galaxy (hVi). The denominator shows the
dynamicalmodelsandcomparingthemorphologyofrealgalax-
weightedmeanpositionofthetracers(hXi).We denotethenu-
ieswithmodelsshowthatwhileearly-typegalaxiesalwayshave
meratoranddenominatorofEq.(1)as”kinematic”and”photo-
fast bars, late-type galaxies host both slow and fast bars (see
metric” integrals, respectively. All previous parameters can be
Rautiainenetal., 2008). Nevertheless, this result has not been
measured from photometric or kinematic observations. Thus,
confirmed in a significant sample of galaxies of different mor-
i can be obtained from the ellipticity of the outermost galaxy
phologicaltypesby usingthe TWmethod.The sampleof late-
isophotes, Σ(X,Y) can be determined from optical photometry,
type galaxiesanalyzedso far by the TW is verysmall in order
and the velocity field of the galaxy (V (X,Y)) can be mea-
LOS toinfersomedependencebetweenR andtheHubbletype.The
sured from long-slit or integral-field spectroscopy. In practice,
aims here are to determine the pattern speed of a large sample
theintegralsfromEq.(1)arecalculatedalongseveraldirections
of galaxies throughout the Hubble sequence by using the TW
oriented parallel to the LON but offset by a distance Y . The
0 methodandtostudythedependenceofthepatternspeedofthe
slopeofthestraightlinedefinedbythehViversushXicomputed
barwiththeHubbletype.
pointsrepresentsΩ sini(seeTremaine&Weinberg,1984).In
b
the case of long-slit spectroscopy,the weight function is given
byh(Y)=δ(Y−Y ).Similarweightfunctionscanbedefinedfor 3. TheCALIFAsampleofbarredgalaxies
0
integral-fieldspectroscopy.Formally,integralsinEq.1areover
−∞ < X,Y < +∞.Nevertheless,theycanbelimitedto a finite The barred galaxies used in the presentstudy were taken from
the Calar Alto Legacy Integral Field Area (CALIFA) Survey
valueofX andY iftheaxisymmetricpartofthediscisreached
(Sa´nchezetal., 2012). CALIFA’s mother sample is formed by
(seeSect.6.1).
Stellar kinematics has been used to measure Ω using the 939 galaxies selected from the SDSS-DR7 photometric cata-
b
logue(Abazajianetal.,2009).Themainselectioncriteriawere
TW method for a large sample of early-type galaxies (e.g.,
angular isophotal diameter 45 < D < 80 arcsec and redshift
Kent,1987;Merrifield&Kuijken,1995;Gerssenetal.,1999; 25
range0.005 < z < 0.03.Thesecriteria ensurethatthe selected
Debattistaetal., 2002; Aguerrietal., 2003; Corsinietal.,
objects fit well into the field of view (FOV) of the instrument.
2003; Debattista&Williams, 2004; Corsinietal., 2007). In
This survey aims to obtain spatially resolved spectroscopic in-
contrast, few pattern speeds have been determined through
formation for a fraction of the mother-galaxy sample (≈ 600
this method for late-type galaxies (e.g., Gerssenetal., 2003;
galaxies),limited by available telescope time. For more details
Treuthardtetal.,2007).SeealsoCorsini(2011)forareviewof
aboutthepropertiesofthegalaxiesoftheCALIFAmothersam-
thebarpatternspeedmeasurementsusingtheTWmethod.The
ple,seeWalcheretal.(2014).Thisprojecthasbeenthebiggest
lackofmeasurementsofbarpatternspeedinlate-typegalaxies
by the TW method is basically due to the effects produced on effortwithintegralfieldspectroscopysofar.
thedeterminationofΩ bytheuncertaintiesin thepositionan- TheCALIFAobservationswerecarriedoutatthe3.5mtele-
b
gle(hereafterPA),i,and/ortheeffectofthepresenceofdustand scope of the Calar Alto observatory with the Potsdam Multi
Aperture Spectrograph (PMAS; Rothetal., 2005) in PPAK
starformationinlate-typediscs.Debattista(2003)demonstrates
mode.Thisinstrumentalmodeconsistsof382fibresof2.7arc-
that errors of a few degrees in determining the PA of galaxies
can significantly change the measured value of Ω using the sec diameter each. These fibres cover a FOV of 74′′ × 64′′.
b
A dithering scheme of three pointings were adopted to cover
TW method. For this reason galaxies with small errors in PA
and/or i should be selected. In addition, the measured value of the full FOV. This allows us to have a final resolution of 1
Ω can also be affected by dust and/or star formation in late- arcsec (see Sa´nchezetal., 2007; Pe´rez-Gallegoetal., 2010;
b
Rosales-Ortegaetal., 2010; Sa´nchezetal., 2012). Both the
type galaxies, since in these cases the light does not trace the
mass distribution of these galaxies. Nevertheless, these effects FOV and the spatial resolution of the observations make this
datasetidealforstudiesofextendeddiscgalaxiesproposedhere.
can be mitigated by computing the kinematic and photometric
Theobjectswereobservedusingtwodifferentsetups.First,
integrals of Eq. (1) using the mass distribution as weight (see
the gratingcalledV500showsa nominalresolutionofλ/∆λ =
Gerssen&Debattista,2007).
In recent years, an extension of the TW method explained 850at5000Åandcoversfrom3745to7300Å.Thesecondsetup
above has been applied to galaxies that show multiple pat- wasdoneusingtheV1200gratingwithbetterspectralresolution
tern speeds (see Maciejewski, 2006; Corsinietal., 2007; λ/∆λ=1650at4500Å.Thisgratingcoversfrom3400to4750
Meidtetal., 2009). The TW method was also applied to gas Å.Inthepresentworkweusedtheobservationsthroughoutthe
tracers, such as CO (Zimmeretal., 2004; Rand&Wallin, V1200grating.Itwasselectedinordertohavereliablevelocity
2004) or Hα (Hernandezetal., 2005; Emsellemetal., dispersioncurvesofthegalaxiesneededforcomputingR (see
CR
2006; Fathietal., 2007; Chemin&Hernandez, 2009; Sect.5.2).Thegalaxysampleofthepresentpaperwasselected
Gabbasovetal.,2009;Fathietal.,2009). amongthe200thatwerefirstobservedandreducedobjectswith
3
J.A.L.Aguerrietal.:PatternspeedinCALIFAbarredgalaxies
theV1200grating.Formoredetailsabouttheobservationstrat-
egyandthedatareductionprocess,seeSa´nchezetal.(2012)and
Husemannetal.(2013).
The CALIFA mother-sample photometric properties were
obtained from SDSS-DR7. In addition, the galaxies of the
CALIFAmothersampleweremorphologicallyclassifiedbyus-
ingthei-bandSDSSimagesbyagroupoffivepeoplefromthe
CALIFA team (see Walcheretal., 2014). The total number of
galaxiesshowingstrongbars(SB)ontheCALIFAsampleturned
outtobe156.Only41ofthemhavealreadybeenobservedwith
theV1200grating.Nevertheless,theTWmethodcannotbeap-
pliedtoallgalaxies.Galaxyinclination,positionangle,andbar
orientationshould be consideredfor its application. In particu-
lar,lowandhighinclinedgalaxiesandthosewithbarsnearthe
galaxy’s major or minor axis should be not taken into account
becausetheTWisnotapplicabletotheseobjects.Therefore,we
excludedfromour analysisall barsthat show PA less than 10◦
withrespecttothemajororminoraxisofthegalaxiesandeither Fig.1. Normalizeddistributionofmorphologicaltypes(a),red-
those face-on (b/a > 0.86) or edge-on (b/a < 0.34) galaxies. shift (b), absolute r-band magnitudes(c), and bar radius (d) of
This restriction reduces the total number of barred galaxies to theCALIFA’smother-samplebarredgalaxies(fullblacklinehis-
20.Inaddition,fivemoregalaxieswereexcludedforotherrea- tograms) and the barred galaxies selected in the present paper
sons,suchasthelargenumberoffieldstars,thenon-flatrotation (dashedblue-linehistograms).
curveatlargeradius,or/andtheinsufficientqualityofthestellar
velocitymaps.
Thefinalselectedsampleofbarredgalaxiescontainsobjects tural components of galaxies (see, e.g., Wozniaketal., 1995;
that cover the morphological types: 1 SB0, 2 SB0/a, 1 SBa, 1 Aguerrietal., 2000b). The galaxy inclination makes the
SBab,6SBb,and4SBbc.SimilartotheCALIFAmothersam- isophotes of the galaxies appear as ellipses in the plane of the
ple,ourgalaxysampleisdominatedbyspirals(SBb-SBbc).This sky.Wefittedtheisophotesofourgalaxiesbyellipsesusingthe
isappropriateforfillingthe gapofpatternspeedsmeasuredby ELLIPSEroutinefromtheIRAFpackage(Jedrzejewski,1987).
theTWmethodinlate-typegalaxies. The ellipticity and PA isophotal radial profiles obtained from
Figure 1 shows the comparison of the distribution of mor- thesefitsareshowninFig.3.
phologicaltypes,redshift,absoluter-bandmagnitudes,andbar The ellipticity radial profile of an unbarred spiral galaxy
radiusbetweenthebarredgalaxiesintheCALIFAmothersam- growsfromalmostzerovaluesatthe centreofthe objectupto
ple and the selected barred galaxies of the present work. Our aconstantvalueatlargeradii,whichcorrespondstothegalaxy
sample is a small subsample of the total bar population of inclination. The PA isophotal radial profile also reaches a con-
the CALIFA mother sample. Nevertheless, the Kolmogorov- stant value at large radii, which corresponds to the orientation
Smirnov test indicates that our subsample does not have a sta- of the LON of the galaxy. This behaviour can be observed in
tistically differentdistributionofmorphologicaltypes,redshift, the ellipticity and PA isophotalradial profiles shown in Fig. 3.
andabsolutemagnitudesfromthetotalsampleofbarredgalax- We thereforecomputed the i and PA of our barred galaxiesby
ies. The actual sample loss bars have radii larger than 10 kpc. averagingtheirouterisophotes.TheresultsaregiveninTable1.
Thelackoflargebarsisdueto:i)galaxyinclination,ii)barori-
entation,and/oriii)noobservationsusingtheV1200grating.We
nevercut the bar sample accordingto bar size. It is also worth 4.2.Determinationofthebarradius
noticing that the galaxies presentedhere are all brightgalaxies
Thedeterminationofthebarradiusisnotaneasytask.Several
(M >−19.0).Inthisrangeofmagnitudes,CALIFAisrepresen-
r methodshavebeenproposedintheliteratureduringthepastfew
tative of the local Universe. No dwarf galaxieshave been con-
decades.We used threeofthe mostpopularmethods(a ,a ,
sidered in the present work. The r−band SDSS images of the b,1 b,2
anda )forestimatingthebarradius(a )ofourgalaxies.
finalsampleareshowninFig.2andthemainparametersofthe b,3 b
Twoofthebarradiusmeasurements(a anda )wereob-
galaxiesaregiveninTable1. b,1 b,2
tainedbyusingtheinformationoftheellipticityandPAisopho-
In summary, the sample presented in this work overcomes
talradialprofilesandthedifferentmethodsproposedin the lit-
twomajorproblemsofothersamplespresentedintheliterature.
erature (see Ma´rquezetal., 1999; Athanassoula&Misiriotis,
First,integral-fieldobservationssuchasthosepresentedhereget
2002;Michel-Dansac&Wozniak, 2006;Aguerrietal., 2009).
rid of many of the problems of long-slit observations. Second,
These methodsare based on the peculiar features producedby
oursampleisdominatedbylate-typegalaxies,themissingpiece
the shape and orientation of the stellar orbits of barred galax-
ofinformationintheTWstudiesofbarpatternspeeds.
ies(Contopoulos,1980;Athanassoula,1992).Inparticular,the
galaxyisophotesarealmostcircularatthegalaxycentre,because
4. Photometricparametersofthebarredgalaxies ofeitherseeingeffectsorthe presenceofa sphericalbulge.As
wegetawayfromthecentre,thereisageneralincreaseintheel-
4.1.Inclinationsandpositionangles
lipticityuptoalocalmaximum,andthenitsuddenlydecreases
Analysis of the galaxy isophotes provides the inclinations1, towardsaminimumatthelocationwheretheisophotesbecome
PA, and other important information about the different struc-
axis of the disc, and q represents its intrinsic thickness. In this paper
1 The inclination (i) of a disc is given by b/a = (q2 +(1−q)2 × wehaveassumedthethindiscapproximation(q = 0).Thus,wehave
cos2(i))1/2,whereb/aistheratiobetweentheobservedminorandmajor computedtheinclinationofthegalaxiesbycos(i)=b/a
4
J.A.L.Aguerrietal.:PatternspeedinCALIFAbarredgalaxies
Table1.MainparametersoftheCALIFAbarredgalaxysample
Galaxy RA(J2000) DEC(J2000) Morph.Type i PA R m
e r
(hh:mm:ss) (o:′:′′) (degrees) (degrees) (arcsec) (mag)
NGC0036 00:11:22.3 06:23:22 SBb 57.2±3.7 23.4±1.3 14.9 12.7
NGC1645 04:44:06.4 -05:27:56 SB0a 64.5±0.6 84.7±0.4 9.2 12.7
NGC3300 10:36:38.4 14:10:16 SB0a 57.2±0.7 172.0±0.3 12.0 12.3
NGC5205 13:30:03.6 62:30:42 SBbc 50.0±0.7 170.1±1.6 15.9 12.5
NGC5378 13:56:51.0 37:47:50 SBb 37.8±3.1 86.5±5.4 19.9 12.5
NGC5406 14:00:20.1 38:54:56 SBb 44.9±0.4 111.8±0.8 18.1 12.2
NGC5947 15:30:36.6 42:43:02 SBbc 44.6±1.4 72.5±3.1 12.4 13.4
NGC6497 17:51:18.0 59:28:15 SBab 60.9±0.7 112.0±0.4 10.7 13.0
NGC6941 20:36:23.5 -04:37:07 SBb 42.3±0.8 127.5±2.7 14.3 13.1
NGC6945 20:39:00.6 -04:58:21 SB0 51.3±2.3 126.1±1.3 9.3 12.4
NGC7321 22:36:28.0 21:37:19 SBbc 48.3±0.5 13.4±1.3 12.0 12.9
NGC7563 23:15:55.9 13:11:46 SBa 55.8±2.4 149.8±1.3 8.1 12.4
NGC7591 23:18:16.3 06:35:09 SBbc 57.6±0.5 144.0±2.0 12.0 12.6
UGC03253 05:19:41.9 84:03:09 SBb 56.8±1.6 92.0±1.7 11.8 13.2
UGC12185 22:47:25.0 31:22:25 SBb 64.0±0.6 161.0±1.0 8.8 13.5
– Note: Columns are: (1) NGC name of the galaxy; (2) galaxy right ascension, (3) galaxy declination, (4) morphological type, (5) galaxy
inclinationmeasuredfromisophotalellipticityprofilesoni-bandSDSSimages,(6)galaxyPAmeasuredfromisophotalPAradialprofileson
i-bandSDSSimages,(7)effectiveradiusinr-bandfromSDSS-DR9,(8)modelr-bandmagnitudefromSDSS-DR9
axisymmetric (disc region) in the face-on case. Typical mea- Athanassoula&Misiriotis, 2002). The values of a for our
b,3
surements of the bar radius using the ellipticity profile involve sampleareshowninTable2.
measuringthepositionofthismaximumandminimum.Infact, Aguerrietal. (2009)demonstratedthatthe bestmethodfor
they represent two extreme cases (Michel-Dansac&Wozniak, determining the bar radius depends on the shape of the sur-
2006), and therefore they can be understood as the lower and face brightness profile of the bar (see their fig. 4). This bar
upperlimitstothebarradiusmeasurement.Weadoptedthepo- type is only available after accurate multi-component surface-
sition of the local maximum of the isophotal ellipticity of our brightness decomposition of photometrical images. They also
galaxiesas one measurementof the bar radiusof our galaxies. demonstratedthata <a <a independentofthebartype.
b,1 b,2 b,3
Table 2 showsthe valuesof the barradiusforourgalaxiesa In addition,the real bar radiusis always between a and a .
b,1 b,1 b,3
determinedbythismethod. For these reasons, we considera as the mean of a ,a , and
b b,1 b,2
a . Moreover,theupperandloweruncertaintiesofthe barra-
The secondestimate ofthe barradius(ab,2) takesthe infor- b,3
mationprovidedbytheisophotalradialPAprofilesintoaccount. dius are the differences between ab and ab,1,ab,2, and ab,3, re-
The PA radial profile is also characteristic of barred galaxies, spectively.
since itisconstantin thebarregionandthenchangesto fitthe
outerdiscorientation(e.g.,Wozniaketal.,1995;Aguerrietal.,
5. Stellarvelocitymaps
2000b).Atypicalbarlengthismeasuredattheradiuswherethe
positionanglechangesby∆PA with respecttothe valuecorre- The stellar kinematics of the galaxies was measured from the
spondingtothemaximumellipticity.Usually∆PA=5◦ isagood spectral datacubes observed with the V1200 grating. The full
valueforthebarradius(seee.g.,Aguerrietal.,2009).Thevalue descriptionoftheprocedurewillbeexplainedinFalcon-Barroso
ofthebarradiusobtainedwiththismethodcouldbecorrelated etal.(inprep.).Forthesakeofclarity,webrieflysummarisethe
to ab,1. This is due to the behaviours inside the bar region of processhere.
the ellipticity, and PA profiles are similar among galaxies. The In the first step, the spaxels of the datacube were Voronoi-
valuesofab,2forourgalaxiescanbeseeninTable2. binned to achieve a limiting signal-to-noise ratio S/N > 20
Fourierdecompositionhasbeenusedextensivelyincharac- (see Cappellari&Copin, 2003), while spectra with S/N < 3
terisingstructures,likebars,whichrepresentsabisymmetricde- were not considered. The values of the LOS velocity and ve-
parturefromaxisymmetry.WeusedthemethodbasedonFourier locitydispersionwereobtainedbyfittingthebinnedspectraus-
decompositionofthelightdistributionofthegalaxiesproposed ingthepenalisedpixel-fittingmethod(pPXF)fromCappellari&
byAguerrietal.(2000).Followingthismethod,thebarradiusis Emsellem(2004).Thefittakesthecontinuumandthegalaxyab-
determinedbytheratiosoftheintensitiesinthebarandinter-bar sorptionfeaturespresentedinthewavelengthrangeofthespec-
regions.Theazimuthalsurfacebrightnessprofilesofthedepro- tra into account. Emission lines were masked where present in
jected galaxies were decomposed in a Fourier series. The bar the spectra of the galaxies. A non-negativelinear combination
intensity, I ,isdefinedas I = I +I +I +I (whereI ,I ,I of a subset of 328 stellar templates from the Indo-US library
b b 0 2 4 6 0 2 4
and I arethem = 0,2,4,and6termsoftheFourierdecompo- (Valdesetal., 2004) were used for the fit of the spectra. This
6
sition,respectively).Similarly,the inter-barintensityis defined subsetwascarefullyselectedintheparameterspacedefinedby
asI = I −I +I −I .Thebarregionisdefinedastheregion thestellarproperties:T ,log(g),and[Fe/H].Errorsinbothve-
ib 0 2 4 6 eff
where I /I > 0.5× [max(I /I ) −min(I /I )]+ min(I /I ). locities andvelocitydispersionwere obtainedvia Monte Carlo
b ib b ib b ib b ib
The bar radius (a ) is identified as the outer radius at which simulations.
b,3
I /I >0.5×[max(I /I )−min(I /I )]+min(I /I ).Numerical The stellar velocity maps of the galaxies considered in the
b ib b ib b ib b ib
simulationshaveshownthatthismethoddeterminesthebarra- present paper are shown in Fig 4. In these maps, the systemic
dius within 8% accuracy except for very thin bars (see, e.g., velocityofthegalaxieswascomputedastheaveragevelocityof
5
J.A.L.Aguerrietal.:PatternspeedinCALIFAbarredgalaxies
Table2.Barde-projectedradiusmeasurementsfortheCALIFA This wavelength window was used because no prominent
barredgalaxysample emissionlinesareobservedinthisrange.Itisalsoimportantto
noticethatthelightdistributiondoesnotalwaystracethemass
Galaxy a a a a distribution of the galaxies. This is especially true in late-type
b,1 b,2 b,3 b
(arcsec) (arcsec) (arcsec) (arcsec) galaxieswherestarformationiscommon.Togetridofthis,we
(1) (2) (3) (4) (5) alsocomputedthemass-weightedmeanpositionofstarsbyus-
NGC0036 20.8 24.7 15.1 20.2+5.1 ing the profiles extracted along the pseudo-slitpositions in the
−4.5
NGC1645 13.6 17.3 17.0 16.0+2.4 massmapsofthegalaxiesprovidedbyGonza´lezDelgadoetal.
−1.3
NGC3300 13.4 17.6 17.4 16.1−+12..57 (2013) and Pe´rez et al. (2013). Thus, for each galaxy we have
NGC5205 14.9 18.3 19.8 17.7+2.8
−2.1 two values of the photometric integrals of the TW: the mass-
NGC5378 25.3 34.4 23.4 27.7+4.3
−6.7 andlight-weightedphotometricintegrals.
NGC5406 20.0 23.2 20.0 21.1+1.1
−2.1 Twodifferentapproacheswereusedtomeasuretheweighted
NGC5947 9.6 12.5 10.7 10.9+1.3
−1.6 LOSstellarvelocity(hVi)foreachpseudo-slitposition.Thefirst
NGC6497 12.6 15.6 16.0 14.7+2.1
NGC6941 14.6 18.0 15.0 15.9+−11..33 approachwasbycomputingtheintegralsinthenumeratorofEq.
NGC6945 13.8 16.4 19.2 16.5+−22..71 (1)usingpseudoslitsplaceddirectlyinthevelocitymapsofthe
NGC7321 10.4 14.1 11.7 12.1+−12..77 galaxies.Thesecondapproachconsistsinaweightedsumofthe
−2.0
NGC7563 22.8 30.9 22.7 25.5+2.8 rawspectrafromthedatacubealongthepseudoslits.Thisresults
−5.4
NGC7591 11.0 15.0 14.5 13.5+2.5 in a new,single spectrumfor each pseudo slit, which was then
−1.5
UGC03253 14.5 18.0 14.9 15.8+1.3 analysed using the pPXF method as explained in the previous
−2.2
UGC12185 12.0 24.3 24.5 20.3+8.3 section.Thus,hViistheradialvelocityobtainedfromthefitto
−4.2
this single spectrum. In the two previous approaches, hVi was
Notes. Col. (1) Galaxy name. Col. (2): bar radius measured from the
obtained by also using light and mass as weights. In all cases,
maxima of the ellipticity radial profile. Col. (3): bar radius measured
MonteCarlo(MC)simulationswereusedtocomputetheerrors
whenthePAinthebarregionchangesmorethan5◦.Col.(4):barra-
ofhVi.
diusmeasuredfromtheFourierbar/interbarintensities.Col.(5):mean
ofthethreebar-lengthestimations.Errorscorrespondtothemaximum Formally, all the TW integrals shown in Eq. (1) are over
differencesbetweenthemeanandthethreemeasurements. −∞ < X < ∞. But, theycan be limited to −Xmax < X < Xmax
if X reaches the axisymmetric part of the disc. We used the
max
maximumvalueofX allowedbyourvelocitymaps.Inmost
max
thestarsinthecentral5′′apertureandsubtractedfromtheveloc- ofthecases,thisvaluewas X = 20−30arcsec(seeFig.4).
max
itymaps.Thestellarvelocityobtainedforourgalaxieswasused ForourgalaxieswehaveameanvalueofX /h =1.6,where
max disc
for computing the kinematic integrals of the TW method (see h is the exponentialscale length of the disc of the galaxies.
disc
Eq. 1). Figure 5 shows stellar-streaming mean velocities with Thediscscalelengthwasdeterminedbyfittingtheoutermostre-
Vsys subtracted,whichwereobtainedalongthegalaxy’sphoto- gions(outsideofthebarregion)ofther-bandisophotalsurface-
metricmajoraxis. brightness profiles of the galaxies by an exponential law (see
Freeman,1970).
The pattern speed of the galaxies was determined by the
6. Results
slopeofthestraightlinefittedtothehVivshXipoints.Theun-
certainties in Ω were obtained by using MC simulations tak-
6.1.Thebarpatternspeed b
ingtheuncertaintiesinthePAofthegalaxiesintoaccount.The
Thebarpatternspeedofthegalaxieswasmeasuredbyapplying PA uncertaintieswere distributed accordingto Gaussian distri-
theTWmethodasdescribedinEq.(1).Thismethodrequiresde- butions. We have four different determinations of the pattern
termining the mean weighted position (hXi) and velocity (hVi) speed(Ω toΩ )ofthegalaxiesdependingonboththeweight
b,1 b,4
of stars in several slits oriented along and offset with respect used for computing the TW integrals and the method used for
totheLONofthegalaxies.Werefertotheseslitsdefinedinthe the kinematic integrals. The TW kinematic integrals were ob-
integral-fielddatacubesaspseudoslits.Dependingonthebarra- tainedbycomputingtheintegralsshowninthenumeratorofEq.
diusanditsorientationwiththeLON,wehaveusedthreeorfive (1), using the velocities provided by the galaxy velocity maps
pseudoslitsof1arcsecwidtheachandaminimumseparationof along pseudo-slit positions for Ω (light-weighted) and Ω
b,1 b,3
2arcsecbetweenthemtoavoidrepeatedinformation.Lightand (mass-weighted). The sum of the spectra from the galaxy dat-
masswereusedastwodifferentweightsforcomputinghXiand acube along the pseudo-slit position was used for computing
hViforeachpseudoslit. thekinematicintegralsinΩ (light-weighted)andΩ (mass-
b,2 b,4
The high S/N ratio of the broad-band photometric images weighted).Figure6showsthehVivshXilinefitsforthesample
has led in the past to their being broadly used for computing galaxies. The linear fits shown in Fig. 6 do not take the uncer-
the photometricintegrals of the TW method. Nevertheless, the tainties of the photometrical integrals into account. The errors
trace of different stellar populations between the photometric ofthephotometricintegralsareinallcasessmallerthan0.1ex-
andspectroscopicdata,causedbydifferentwavelengthcoverage cept for one pseudo slit in the case NGC0036, which is 0.14.
andproblemswiththepositioningofthepseudoslitsinthepho- Table3showsthevaluesofΩ fortheCALIFAbarredgalaxies
b
tometricimages, canaffectthe computationofthe photometric presentedhere.
integrals. These problemscan be solved by using integral-field Figure7showsthecomparisonofthevaluesofΩ siniob-
b
data.Inparticular,wecomputedthemeanpositionofstarsalong tainedbydifferentmethods.Ingeneral,nosystematicand/orsig-
thepseudoslitsbyusingthesurfacebrightnessdistributionob- nificant differences in the value of Ω sini can be seen. Only
b
taineddirectlyfromtheCALIFAdatacubesofthegalaxies.The three galaxies (NGC5406, NGC5947, and NGC6497) present
surface brightness map of each galaxy was obtained by sum- some value of Ω that does not agree, within the errors, with
b
ming up all the flux from each spectrum of the datacube in a theothers.Itisnotcleartouswhichisthemainreasonforthis
wavelengthwindowof150Åwidth,andcentredat4575Å. difference,sincethesegalaxiesdonotpresentirregularfeatures
6
J.A.L.Aguerrietal.:PatternspeedinCALIFAbarredgalaxies
Fig.2.SDSSr-bandimagesoftheCALIFAbarredgalaxiespresentedinthisstudy.Inallimages,northisupandeastisleft.Thefull
anddashedlinesrepresenttheconsideredslitsformeasuringthekinematicandphotometricintegrals.Thefulllinealsorepresents
thelineofnodesofthegalaxy.
intheirrotationvelocitymaps(seeFig.4)and/orvelocitycurves somemodellingtorecovertherotationcurvefromtheobserved
(see Fig. 5). In addition,theyare galaxiesofdifferentmorpho- stellarstreamingvelocities.
logicaltypes,whichseemstoindicatethatthesedifferencesare
notrelatedtodifferentamountsofdust,gas,orstarformationin
their discs. These differencescould simply reflect the observa-
The corotation radius is derived from the circular velocity
tionaluncertaintiesinthedeterminationofΩ .
b of the galaxy.To obtain the circular velocity (V ) from the ob-
c
servedstellarstreamingvelocity(V ),theasymmetricdriftcor-
∗
6.2.DeterminationofR=R /a rectionisneeded.Oneoftheaimsofthepresentworkhasbeen
CR b
to compareourpatternspeedsforSBb andSBbc galaxieswith
The dimensionlessquantityR = R /a is definedas the ratio those from early-type systems from the literature.To keep the
CR b
between the corotation radius (R ) of the galaxy and the bar homogeneityinthiscomparison,wefollowedthesameapprox-
CR
radius (a ). Unlike the bar pattern speed, measure R requires imationfortheasymmetricdriftcorrectionasinpreviousworks
b
7
J.A.L.Aguerrietal.:PatternspeedinCALIFAbarredgalaxies
Fig.3.IsophotalellipticityandPAradialprofilesfromellipse-fittingofthebarredgalaxiesofthesample.Thehorizontallinesshow
themeasuredellipticityandPAcorrespondingtothedisc.
Table3.PatternspeedandcorotationradiusoftheCALIFAbarredgalaxies
Galaxy Ω R Ω R Ω R Ω R
b,1 CR,1 b,2 CR,2 b,3 CR,3 b,4 CR,4
(kms−1arcsec−1) (arcsec) (kms−1arcsec−1) (arcsec) (kms−1arcsec−1) (arcsec) (kms−1arcsec−1) (arcsec)
NGC0036 13.2±3.7 16.9+6.6 17.4±5.2 12.6+5.4 19.3±4.3 14.2+3.2 19.5±4.3 11.1+3.9
−4.8 −3.9 −2.6 −3.0
NGC1645 -10.9±11.6 18.915.5 -22.4±9.4 12.16.7 -13.7±12.4 19.111.5 -20.2±11.7 13.110.0
7.6 3.8 5.3 4.8
NGC3300 -9.8±3.1 23.2+8.9 -9.0±2.4 24.58.2
−5.9 6.1
NGC5205 17.1±4.3 10.2+3.2 15.1±2.8 11.33.0 11.5±2.8 11.28.4 13.8±1.7 12.32.7
2.4 2.5 4.7 2.4
NGC5378 -11.2±6.1 16.3+13.0 -9.8±4.5 18.0+12.0 -9.3±4.5 17.5+15.0 -9.0±3.9 19.7+12.4
−6.6 −7.3 −8.7 −7.8
NGC5406 16.3±9.3 15.5+12.0 22.8±8.0 11.0+4.8 7.2±5.6 14.7+36.3 9.1±3.8 27.4+14.7
−5.3 −3.0 8.7 −8.3
NGC5947 -16.4±7.3 11.6+8.3 -31.7±4.2 5.8+2.4 -18.5±4.9 10.7+4.4 -16.4±5.6 11.2+6.8
−4.8 −2.3 −3.6 −4.8
NGC6497 -32.4±5.5 7.4+2.6 -42.7±7.4 5.5+2.1 -21.4±3.6 8.7+6.3 -26.6±2.7 8.8+3.0
−2.0 −1.6 −4.1 −2.4
NGC6941 12.8±10.4 14.6+14.4 18.4±9.5 10.7+7.4 9.4±9.3 14.1+19.9 21.9±6.2 9.2+3.1
−5.8 3.7 −6.8 −2.2
NGC6945 -10.3±3.6 20.2+8.9 -15.5±2.1 13.0+2.9 -9.7±2.4 20.3+7.2 -13.6±1.6 14.7+3.0
−5.7 −2.5 −5.4 −2.6
NGC7321 -16.7±3.8 15.6+5.7 -21.6±6.5 11.8+5.4 -18.7±4.0 14.6+3.9 -16.7±4.3 15.3+6.2
−4.4 −4.0 −3.3 −4.9
NGC7563 7.6±3.3 33.2+18.4 4.5±2.7 45.4+19.6 8.0±3.0 32.2+13.5 3.9±2.1 51.3+16.0
−10.2 −15.8 −8.4 −17.1
NGC7591 -9.8±4.6 18.5+10.7 -13.9±5.0 13.2+6.6 -10.5±3.5 18.3+7.0 -7.7±4.4 20.6+10.6
−6.2 −4.3 −4.9 −7.4
UGC03253 -10.5±3.1 18.0+6.6 -15.5±3.1 11.9+3.2 -12.8±2.4 16.2+2.3 -12.6±2.3 14.6+3.8
−4.5 −2.7 −2.0 −3.2
UGC12185 13.3±1.7 16.7+8.6 10.0±2.0 21.612.3 12.8±1.6 16.6+9.2 11.6±1.7 18.4+10.1
−6.4 9.1 −6.9 −7.6
– Note:NGC3300hasnovaluesofΩ andΩ becausethemassdistributionofthisgalaxyisnotavailable.
b,3 b,4
(seeDebattistaetal.,2002;Aguerrietal.,2003;Corsinietal., haveusedthevaluesgivenbyGerssen&Shapiro(2012)forthe
2003).Thus,theasymmetricdriftequationbecomes differentmorphologicaltypesofgalaxies.Inparticular,wehave
usedα = 0.85±0.15forSB0-SB0/a,α = 0.86±0.24forSBa-
σ2 1 2 SBab,andα=0.62±0.2forSBb-SBbc.Inaddition,R andR
V2 =V2+ obs 2R + −1 (2) d σ
c ∗ sin2i(1+2α2cot2i)" Rd Rσ! # are thescale lengthsofthe surfacebrightnessandvelocitydis-
persionprofiles,assuminganexponentiallawforthedisc(e.g.,
whereR,V , andσ are thedistancetothegalaxycentre, Freeman,1970).
∗ obs
the LOS velocity, and velocity dispersion along the major axis
of the galaxy, respectively. Parameter α is defined as the ratio This correction was applied to the velocity data along the
between the perpendicularand radial disc velocity dispersions. major axis of the galaxy discs and beyond to the bar region.
The value of α can vary from early- to late-type galaxies. We The value of V for the galaxies was obtained by averag-
c,flat
8
J.A.L.Aguerrietal.:PatternspeedinCALIFAbarredgalaxies
Fig.4. Binned versionof the stellar velocitymapsof the barredgalaxiesin our sample. The orientationof the mapsis as in Fig.
2.Bluecoloursrepresentapproachingvelocities,whileredonesshowrecedingvelocities.Thefullanddashedlinesrepresentthe
consideredslitsformeasuringthekinematicandphotometricintegrals.Thefulllinealsorepresentthelineofnodesofthegalaxy.
ingV outsideofthe barregion.TheTully-Fisherrelation(TF; ies (see Theureauetal., 1998). In all cases, this HI rota-
c
Tully&Fisher,1977)showsthatthereisacorrelationbetween tion velocity agrees within the errors with our values of
thecircularvelocityofthegalaxiesatlargeradiiandtheirabso- V . For these five galaxies, the ratios between the maxi-
c,flat
lute magnitudes.We located our galaxiesin the TF relation by mum circular HI rotation velocity (V ) and our V are
c,HI c,flat
using the V obtained from the asymmetric drift correction. V /V = 1.12,1.14,0.99,0.88, and 1.05 for NGC0036,
c,flat c,HI c,flat
Figure 8 shows the TF relation for our galaxies and other spi- NGC6941, NGC7321, NGC7563, and UGC03253. This indi-
ralgalaxiesobtainedfromtheliterature(seeReyesetal.,2011). cates a maximun uncertainty of 14% in our flat rotation deter-
WenoticethatourgalaxiesarelocatedwithinthenoiseoftheTF minations.
relation. This indicates that the V we obtainedis consistent
c,flat The value of the corotation radius is then given by R =
CR
withwhatisproposedbytheTFrelationforspiralgalaxies.
V /Ω . This assumes that the rotation curve of the galaxies
c,flat b
In addition, we found in the literature the maximum cir- is flat. ThevaluesofR forourgalaxiesare givenin Table 3.
CR
cular velocity measured from HI data for five of our galax- We finally measure R as R /a . The valuesof R are given in
CR b
9
J.A.L.Aguerrietal.:PatternspeedinCALIFAbarredgalaxies
Fig.5.LOS-streamingvelocitiesofthegalaxiesalongtheirmajoraxis.
Table4.ErrorsinTables3and4werecomputedbyMonte-Carlo intoaccount.Wecannotruleoutafastbarinanyofourgalaxies
simulations. (at95%probability).
We have also determined the mean value of R for the total
sample of 32 galaxieswith Ω determined by the TW method.
b
6.3.Fastorslowbars
Taking our four different measurements of R into account, we
obtained< R >= 1.2+0.7, < R >= 1.0+0.7, < R >= 1.2+0.7,
The galaxy sample presented in this work complemented by 1 −0.5 2 −0.4 3 −0.4
thoseavailableintheliterature(seeTable1fromCorsini2011) and < R4 >= 1.1+−00..74. Table 4 shows that some of our values
makeatotalof32galaxieswithbarpatternspeedmeasuredby of R have large errors. We selected a subsample of galaxies
theTWmethod.Thisrepresentsanappropriatesampleforinfer- withsmalluncertaintiesinR.Inparticular,weconsideredthose
ringstrongobservationalconstraintsonthevalueofRinbright galaxiesfromtheliteratureandfromourmeasurementswithun-
barred galaxies. Table 4 shows that all bars have values of R, certaintiessmallerthan30%indeterminingR.Forthissubsam-
withintheerrors,compatiblewithbeingfastbars(R< 1.4).We ple of galaxies, we have < R1 >= 1.0+−00..33, < R2 >= 0.9+−00..32,
computedthe probabilityof havingR > 1.4 in the whole sam- < R >= 1.0+0.3, and < R >= 0.9+0.3. In all cases, the mean
3 −0.2 4 −0.2
plebyusingMonteCarlosimulationsthattakethequotederrors valuesindicatethatbarsfinishnearcorotationinagreementwith
10