ApJ version - Astronomy

19 Pages·2006·1.66 MB·English

TheAstrophysicalJournalSupplementSeries,165:461–479,2006August A
#2006.TheAmericanAstronomicalSociety.Allrightsreserved.PrintedinU.S.A.
HIGH-RESOLUTION OPTICALVELOCITY FIELDS OF 11 LOW SURFACE BRIGHTNESS GALAXIES
Rachel Kuzio de Naray1 and Stacy S. McGaugh1
DepartmentofAstronomy,UniversityofMaryland,CollegePark,MD20742-2421;[email protected],[email protected]
W. J. G. de Blok1
ResearchSchoolofAstronomyandAstrophysics,MountStromloObservatory,CotterRoad,WestonCreek,ACT2611,Australia;
[email protected]
and
A. Bosma
ObservatoiredeMarseille,2PlaceLeVerrier,13248MarseilleCedex4,France;[email protected]
Received2005December13;accepted2006April24
ABSTRACT
Wepresenthigh-resolutiontwo-dimensionalvelocityfieldsfromintegralfieldspectroscopy,alongwithderived
rotationcurvesfor11lowsurfacebrightnessgalaxies.WefitNFWandpseudoisothermalhalomodelstothenewdata
combinedwithpreviouslong-slitandHidata.Inmostcases,wefindthepseudoisothermalhalotobetterrepresentthe
datathantheNFWhalo,astheNFWconcentrationsareoftenlowerthanexpectedfora(cid:1)CDMcosmology.Wealso
compareourresultstopreviousstudiesandfindthatincludingthenewtwo-dimensionalopticaldatadoesnotsig-
nificantlyalterthehaloparametersbutdoesdecreasetheuncertaintiesbyroughlyafactorof2.
Subject headingsg: dark matter— galaxies: fundamental parameters — galaxies: kinematics and dynamics
Online material: color figures
1. INTRODUCTION Blok & Bosma 2002 [hereafter BB02]; Marchesini et al. 2002;
Bolattoetal.2002;Blais-Ouelletteetal.2001;Coˆte´etal.2000).
Determiningthemassdensityprofilesofgalacticdarkmatter
Thesehaloshaveamassdensitythatremainsatanapproximately
haloshasbeenanexciting,yetcontentious,fieldforanumberof
constant value toward the center; thus, they are referred to as
yearsnow.Althoughitiswidelyagreedthatlowsurfacebright-
‘‘cored’’halos.UnliketheNFWprofile,however,thepseudo-
ness(LSB)galaxiesaredarkmatter–dominateddowntosmall
isothermalhalohasnocosmologicalmotivationortheoretical
radii (de Blok & McGaugh 1996, 1997; Pickering et al. 1997,
basis.
1999; Blais-Ouellette et al. 2001; Borriello & Salucci 2001;
Initsfavor,theCDMmodelhasbeensuccessfulonlargescales
Simonetal.2003;butseeFuchs2003)and,hence,areidealtest
inexplainingstructureformationintheearlyuniverse,aswellas
subjectsforstudyingthedarkmatterdistribution,aconsensuson
abundancesofgalaxyclusters(Tegmarketal. 2004).Itismore
the interpretation of their rotation curves has been difficult to
appealingtohaveahalomodelwithexplanationsrootedincos-
achieve.
mologythanamodelthatissimplyaconvenientfittothedata.Itis
Thedisagreementariseswhencomparingthedatatonumeri-
thereforenosurprisethatanumberofreasonshavebeengivenin
calsimulationsofcolddarkmatter(CDM).Themostcommon
anattempttosalvagetheappropriatenessoftheNFWprofileasa
description of CDM halo behavior is given by the analytic ap-
descriptionofgalacticdarkmatterhalos.
proximationofNavarroetal.(1996,1997)andisknownasthe
TheearliestobservationsthatindicatedcoresinLSBgalaxies
NFWprofile.ThecosmologicallymotivatedNFWhaloischar-
were two-dimensional 21 cm H i velocity fields (Moore 1994;
acterized by a mass density that rises very steeply toward the
Flores&Primack1994;deBloketal.1996[hereafterBMH96]).
center,apropertythatmakesthehalo‘‘cuspy.’’Cuspyhalosthat
Lowspatialresolution(i.e.,beamsmearing)wassuggestedtobe
risemoresteeplythantheNFWhalohavealsobeensuggested
asystematiceffectthatwoulderroneouslyindicatecores(vanden
(e.g.,Mooreetal.1999;Reedetal.2003;Navarroetal.2004;
Boschetal.2000;Swatersetal.2000).Thequestionofbeam
Diemand et al. 2005). Whether or not the dark matter halos of
smearingwasaddressedbylong-slitH(cid:1)observations,whichhad
LSBgalaxiescanbedescribedbycuspyNFW-likeprofileshas
anorder-of-magnitudeincreaseinspatialresolution(see,e.g.,
beenamatterofdebate.
McGaughetal.2001[hereafterMRB01];BMR01);cuspsdid
NFW halos can be fitted to the observations, but the fits are
not appear when the resolution was increased, showing that
usually of lower quality than fits with pseudoisothermal halos.
beam smearing had been of only minor importance in the H i
Moreover,theimpliedcosmologicalparametersareinconsistent
observations. Possible systematic errors in the long-slit spec-
withthestandard(cid:1)CDMpicture.Inparticular,theobservedcon-
troscopy (e.g., Simon et al. 2003;Rhee etal.2004;Spekkens
centrationsoftheNFWhalosaretoolow(McGaughetal.2003;
etal.2005)havesincebecomethefocusofattention,withslit
Swaters et al. 2003b). Much better fits to LSB observations are
misplacement (Swaters et al. 2003a) and noncircular motions
foundwhenusingthepseudoisothermalhalomodel(Simonetal.
amongthetopconcerns.Iftheslitmissesthedynamicalcenter
2005;deBloketal.2001a,2001b[hereafterBMR01],2003;de
ofthegalaxyoriftherearenoncircularmotionsfrom,forinstance,
abar,thecircularvelocitymaybeunderestimatedandleadtothe
1 Visiting Astronomer, Kitt Peak National Observatory, National Optical
falseinferenceofacoredhalo.DeBloketal.(2003)conducted
AstronomyObservatory,whichisoperatedbytheAssociationofUniversitiesfor
extensivemodelinginwhichtherotationcurvesofbothcuspyand
ResearchinAstronomy(AURA),Inc.,undercooperativeagreementwiththe
NationalScienceFoundation. coredhalosweresubjectedtovariouseffectsandconcludedthat
461
462 KUZIO DE NARAY ETAL. Vol. 165
no systematic effect will entirely mask the presence of a cuspy Our sample of 28 observed galaxies is both weather- and
haloforrealisticobservingconditions.Swatersetal.(2003a)per- signal-limited.Poorweatherpreventedusfromobservingmore
formedasimilarexercisewithsimilarresultsbutarguedthatit ofthe‘‘clean’’sample.Oursampleissignal-limitedinthatnotall
mightstillbepossibletoretaincuspyhalos. ofthegalaxieshaveenoughH(cid:1)emissiontoconstructusefulve-
Clearly, there are a number of issues that new observations locityfields.Whilepreexistinglong-slitobservationscanbeused
must simultaneously address. The data must be both high- asaguide,thereisnowayofknowinghowmuchH(cid:1)emission
resolution and two-dimensional in nature. Observations must willbedetectedbytheintegratedfieldunit(IFU)untiltheexper-
haveresolutionP1kpc,asthatisthecriticallengthscaleatwhich imentisdone.Oursampleisintentionallyfocusedonthemost
thedistinctionbetweencuspsandcorescanbedetermined(de darkmatter–dominatedobjects.Thesetendtobeverylowsur-
Blok2004).Anynoncircularmotionsshouldbereadilyidenti- facebrightnessdwarfsthatarehardtoobserve.
fiableinatwo-dimensionalvelocityfield.Inaddition,slitplace- Thegalaxieswereobservedduringthenightsof2004April12–
mentisnotaconcernoftwo-dimensionalvelocityfields.This 15,2004November14–19,and2005September1–7.Observa-
observationalapproachhasalsobeenappliedbysuchgroupsas tionsweremadeusing the DensePakIFUonthe 3.5 m WIYN2
Simonetal.(2003,2005). telescope at the Kitt Peak National Observatory (KPNO).
In this paper, we present the rotation curves derived from DensePakiscomprisedof300diameterfibersarrangedina4300;
high-resolution two-dimensional velocity fields of a sample of 2800rectangle.Wemeasuredthefiberseparationtobe3B84.The
LSB galaxies. In x 2, we discuss the sample and observations; separationwasdeterminedbycenteringabrightstarinafiberand
datareductionisdiscussedinx3.Theresultsfortheindividual repeatedlyshiftingbetweenfibersandacrossthearray.Thereare
galaxiesarepresentedinx4.Inx5,wediscusshalofitstothe 85workingfibersinthisarrangement;anadditionalfourskyfibers
minimum-diskcaseofthenewdatacombinedwithpreviouslong- arearrangedoutsidethemainbundle.Weusedthe860linesmm(cid:2)1
slitandHirotationcurvesandcompareourresultstothoseof grating in second order, centered near H(cid:1), giving a 58 km s(cid:2)1
previous studies. Noncircular motions are also briefly dis- velocityresolution.Thedistancestothegalaxiesinthesample
cussed.Ourconclusionsandgoalsforfutureworkarestatedin aresuchthata300 fiberprovidessubkiloparsecresolution.
x6. Becausethegalaxiesweretoofainttobevisibleontheguide
camera,wecenteredtheDensePakarrayonanearbystarandthen
2. SAMPLE AND OBSERVATIONS
offsettotheopticalcenterofthegalaxy.Subsequentpointingson
Ourprimarytargetswerethegalaxiesinthe‘‘clean’’sampleof thegalaxyweremadebyshiftingthearraybysmallamountsfrom
de Blok et al. (2003). In brief, galaxies in the ‘‘clean’’sample itscurrentposition.Foranumberofgalaxies,thesemoveswere
have inclinations between 30(cid:1) and 85(cid:1), are likely to meet the thefineshiftsrequiredtoobservethespacesbetweenthefibers.
minimum-diskassumption,havelong-slitrotationcurvesthatare Theseinterstitialpointingseffectivelyincreasedtheresolutionto
wellresolvedintheinner1kpc,havesmallerrorbars,andlack (cid:3)200.Thefiberbundleorientationontheskyandthetotalnumber
largeasymmetries.Theminimum-diskassumptionisconsidered ofpointings pergalaxy were tailored to each galaxy so that the
applicable to those galaxies that require substantial amounts of criticalcentralregionswerecoveredbytheDensePakfibers.Each
darkmatteratsmallradiieveninthemaximum-diskmodel.We exposurewas1800s,andtwoexposuresweretakenateachpoint-
then expanded our sample to include other LSB galaxies that ing.ACuArlampwasobservedbeforeandaftereachpointingto
nearly made the ‘‘clean’’ cut. We also searched for low-mass providewavelengthcalibration.
dwarfgalaxiestofillouttherangeofrightascensionavailable
atthetelescope,givingpreferencetothosetargetswithdiffuse 3. DATA REDUCTION
H(cid:1)emissiondetectedbylong-slitobservations.
TheobservationswerereducedinIRAF3usingtheHYDRA
We observed eight ‘‘clean’’ galaxies: UGC 4325, DDO 64,
package.Thedatawerebias-subtractedandflattened.TheIRAF
NGC 4395, F583-4, F583-1, DDO 185, DDO 189, and NGC
taskdohydrawasusedtoextractthespectra.Awavelengthso-
4455.Thesegalaxieswereselectedfromthe‘‘clean’’samplebe-
lutioncreatedfromtheobservationsoftheCuArlampwasapplied
causethewell-resolvedlong-slitH(cid:1)observations(BB02;BMR01)
tothespectra.Thetwoexposuresperpointingwerecombinedto
showthatthereisdiffuseH(cid:1)emissionfordetectabilityintwo-
increasethesignal-to-noiseratioandtoremovecosmicrays.Sky
dimensionalvelocityfieldsandthatthegalaxieslackindicators
subtractionwasnotperformed,becausetheDensePakskyfibers
ofsignificantnoncircularmotions(e.g.,strongbarsorgrossasym-
oftenfellinsidethegalaxiesratherthanontheskyandwerethere-
metries).Whilenotacriterionconsideredintheselectionprocess,
forecontaminatedbygalacticemission.Wemadeuseofthenight-
itturnsoutthatthelong-slitobservationsofthesegalaxiesimply
sky emission lines by using them as the reference wavelengths
thatthe galaxieseitherhaveunreasonablylowNFW concentra-
(Osterbrocketal.1996)bywhichthevelocitiesofthegalactic
tionsordonothavecuspsatall.Thesekindsofgalaxiespose
emissionlinesweremeasured.WealsotriedusingtheCuArcal-
thebiggestproblemforCDMand,assuch,provideimportant
ibration to measure the velocities, but the night-sky lines gave
testcases.
cleanerresults.Velocitieswere measured by fittingGaussians to
WeobservedfourgalaxiesfromMRB01(F563-V2,F563-1,
boththeskylinesandthefourgalacticemissionlinesofinterest:
F568-3,andUGC5750)thatalmostmadethe‘‘clean’’sample.
H(cid:1),[Nii]k6584,[Sii]k6717,and[Sii]k6731.Theaverageerror
Theyshowdiffuse H(cid:1)emissionbuteitherdidnothavethere-
on individual emission-line velocities due to centroiding accu-
quirednumberofindependentpointsintheinner1kpcofthe
racywasroughly1.5kms(cid:2)1.Weusedthearithmeticmeanofthe
long-slitrotationcurveorhadaninclinationoutsidethe‘‘clean’’
range.
Finally, we observed 16 galaxies from the Nearby Galaxies
Catalogue (Tully 1988). Selection criteria for these galaxies 2 Based on observations obtained at the WIYN Observatory. The WIYN
included positions satisfying 18hP(cid:1)P08h and þ10(cid:1)P(cid:2)P ObservatoryisajointfacilityoftheUniversityofWisconsin–Madison,Indiana
þ50(cid:1),inclinationsbetween30(cid:1) and85(cid:1),heliocentricvelocities University,YaleUniversity,andtheNationalOpticalAstronomyObservatory.
3 IRAFisdistributedbytheNationalOpticalAstronomyObservatory,which
P2500kms(cid:2)1,andanestimatedVflat(approximatedbyVCat(cid:3) isoperatedbytheAssociationofUniversitiesforResearchinAstronomy(AURA),
0:5W20sin(cid:2)1i)betweenroughly50and100kms(cid:2)1. Inc.,underagreementwiththeNationalScienceFoundation.
No. 2, 2006 LSB OPTICALVELOCITY FIELDS AND ROTATION CURVES 463
TABLE1
PropertiesofObservedGalaxies
R.A. Decl. (cid:4)(R) Distance i V R V P.A.
0 hel max max
Galaxy (J2000.0) (J2000.0) (magarcsec(cid:2)2) (Mpc) (deg) (kms(cid:2)1) (kpc) (kms(cid:2)1) (deg) References
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11)
UGC4325........................ 081920.5 +500035 21.6 10.1 41 514 2.3 86 52 1
F563-V2........................... 085303.7 +182609 21.2a 61 29 4316 6.7 104 328 2
F563-1.............................. 085506.9 +194458 22.6 45 25 3482 5.6 146 341 2
DDO64b.......................... 095022.4 +312916 ... 6.1 60 520 2.1 51 97 1
F568-3.............................. 102720.3 +221422 22.2a 77 40 5905 8.4 114 169 2
UGC5750........................ 103545.1 +205924 22.6 56 64 4160 8.5 61 167 1
NGC4395c...................... 122548.9 +333248 22.2 3.5 46 310 0.8 33 327 1
F583-4.............................. 155212.7 +184706 22.9a 49 55 3620 7.5 75 115 2
F583-1.............................. 155727.5 +203958 23.2a 32 63 2256 4.9 83 355 2
UGC477.......................... 004613.1 +192924 ... 35 82 2635 10 112 347 3
UGC1281........................ 014932.0 +323523 22.7d 5.5 85 145 1.9 38 218 3
Notes.—Unitsofrightascensionarehours,minutes,andseconds,andunitsofdeclinationaredegrees,arcminutes,andarcseconds.Col.(1):Galaxyname.Col.(2):
Rightascension.Col.(3):Declination.Col.(4):CentralsurfacebrightnessinR-band.Col.(5):Distance.Col.(6):Inclination.Col.(7):Heliocentricsystemicvelocity.
Col.(8):MaximumradiusoftheDensePakrotationcurve.Col.(9):MaximumvelocityoftheDensePakrotationcurve.Col.(10):Positionangleofmajoraxis;seex4
fordetails.Col.(11):Referencesforsurfacebrightness,distance,andinclination.
a ConvertedfromBbandassumingB(cid:2)R¼0:9.
b DDO64=UGC5272.
c NGC4395=UGC7524.
d TakenfromBB02.
References.—(1)BB02;(2)BMR01;(3)Tully1988.
measuredemission-linevelocitiesineachfiberasthefibervelocity. Theobservedvelocityatpositionx,y,V(x,y),isafunctionof
Themaximumdifferencebetweenthemeasuredvelocitiesandthe thesystemicvelocity(V ),therotationvelocity(V ),thein-
sys rot
mean was taken to be the error on the fiber velocity. Many of clination(i),thepositionofthecenterofrotation(x ,y ),and
0 0
theseerrorswerelessthan5kms(cid:2)1,althoughafewwereashigh thepositionangle(PA)ofthemajoraxis.Thepositionangleis
as(cid:3)20kms(cid:2)1.IfonlyH(cid:1)wasobservedinafiber,theobserved defined as the angle between north and the receding side of
H(cid:1)velocitywastakenasthefibervelocityandtheerrorwasset themajoraxis,measuredfromnorththrougheast.Eachpointis
to10kms(cid:2)1. weightedbytheinversesquareoftheerroronthefibervelocity
Theobservedvelocityfieldsweremadebycombiningthein- timescos((cid:3)),theangleawayfromthemajoraxis.
dividual DensePak pointings using the input shifts at the tele- TheDensePakdatacoverthecentersofthegalaxies.Wefind
scope.Toconfirmtheaccuracyoftheoffsets,anH(cid:1)fluximage these tobeintheregime ofsolid-bodyrotation. Consequently,
ofthegalaxyconstructedfromtheDensePakobservationswas neitherthecenternortheinclinationcouldbedeterminedbythe
compared to an actual H(cid:1) image. Relative positions between observations. The center was therefore fixed to the position of
featuresinthegalaxy(i.e.,brightHiiregions)inthetwoimages theopticalcenter,andtheinclinationwasfixedtopublishedval-
weremeasuredandcompared.Thefluxesinanyoverlappingfi- ues(BMR01;BB02;Tully1988).Thesystemicvelocitieswere
bers were also compared. The accuracy ofthe fiber positions is determinedbyROTCUR.WealsousedROTCURtodetermine
(cid:3)0B6, and we found the telescope to be capable of accurately the position angle of the major axis, using published long-slit
shiftingfromthenearbybrightoffsetstars(typically10–20shifts), valuesastheinitialguess.Ifthepositionanglecouldnotbewell
aswellasthesmallerdistances((cid:3)0B7shifts)requiredtoobserve constrainedbyROTCUR,thenitwasfixedtothelong-slitvalue.
thespacesbetweentheDensePakfibers.Thetelescopepointingis Thelong-slitpositionanglesaregenerallyfromeithertheHive-
robustandrepeatable. locityfieldorthesurfacephotometry,or,insomecases,arethe
We used the NEMO (Teuben 1995) program ROTCUR positionanglesindicatedinacatalogsuchastheUGC(Nilson
(Begeman 1989) to derive rotation curves from our two- 1973).Onlytwogalaxies,UGC477andUGC1281,hadposi-
dimensionaldata.ROTCUR treatstheobserved velocityfield tionangleswellconstrainedbyROTCUR.
asanensembleoftiltedringsandthenfitsforthecenter,sys- Ring radii were set to the effective fiber resolution for each
temicvelocity,inclination,positionangle,androtationvelocity galaxy.Theresultingrotationcurvewasinspectedforringswith
in each ring. Specifically, ROTCUR does a nonlinear least- considerablyhigherorlowervelocitiesthanneighboringrings.
squaresfittothefollowingequation: These highly deviant points in the rotation curve were investi-
gated and were usually attributable to a single fiber in the ring
V(x; y)¼V þV cos(cid:3)sini; ð1Þ havinganextremevelocity.Theseextremefiberswereremoved,
sys rot
and the rotation curve was recalculated. Finally, we added in
where quadraturetotheerrorbarsonthefinalrotationcurvetheveloc-
ityerrorfromcentroidingaccuracy,correctedforinclination.We
cos(cid:3)¼ (cid:2)(x(cid:2)x0)sin(PA)þ(y(cid:2)y0)cos(PA) ð2Þ didnotimposeaminimumerrorontherotationcurvepoints,as
r wasthecaseinsomepreviousworks(e.g.,5kms(cid:2)1inSwaters
etal.2003aand4kms(cid:2)1inBMR01).Thenatureoftheerrors
and
ontherotationcurvepointsfromthevelocityfieldsisdifferent
fromthatoftheerrorsonlong-slitrotationcurves.Inthelong-slit
r2 ¼(x(cid:2)x0)2þ(y(cid:2)y0)2=cos2 i: ð3Þ case,theerrorisonasinglevelocitymeasurementandgivesthe
464 KUZIO DE NARAY ETAL. Vol. 165
Fig.1.—ResultsforUGC4325.Topleft:PositionofDensePakarrayontheH(cid:1)imageofthegalaxy.Thisisanexampleofwhereinterstitialpointingshavebeen
madetofillinthegapsbetweenthefibers.Topright:ObservedDensePakvelocityfield.Emptyfibersarethosewithoutdetections.Bottomleft:DensePakrotation
curve.Bottomright:DensePakrotationcurveplottedwiththerawlong-slitH(cid:1)rotationcurveofBB02andtheHirotationcurveofSwaters(1999).TheHidata
wereexcludedfromthehalofits.[SeetheelectroniceditionoftheSupplementforacolorversionofthisfigure.]
accuracywithwhichaGaussiancouldbefittedtoanemission- rotation curves when available. Properties of the galaxies for
line profile, or the error is given by the consistency of the ob- whichrotationcurvesarederivedarelistedinTable1;therewere
servedemissionlines(H(cid:1),[Nii]k6584,[Sii]k6717,and[Sii] 17observedgalaxiesforwhichmeaningfulvelocityfieldscould
k6731). The error does not contain information about the un- not be constructed.4 As a result of remarkably poor weather, a
certainty in the rotation velocity. Errors can become arbitrarily numberofgalaxieshavelopsidedDensePakcoverage.
smallinhighsignal-to-noiseratiodata,andthisiswhyminimum UGC 4325.—This galaxy is large on the sky, and four
errorswereimposed.Intwo-dimensionaldata,therotationveloc- DensePak pointings were made on the approaching side. The
ityisobtainedfromatilted-ringfit.Theerrorindicatessomething positionsareshownontheH(cid:1)imagefromvanZee(2000).The
aboutthespreadofthevelocitiesinaring.Inthiscase,asmaller fibervelocitiesweretheaverageoftheH(cid:1)and[Sii]k6717lines.
error indicates that the gas in the ring has smaller noncircular H(cid:1)isprevalentandwasdetectedinalmosteveryfiber.Theposi-
motions. tionanglewasfixedattheaverageofthepositionanglesofprevi-
ouslong-slitobservations(BB02;Swatersetal.2003a).Thereis
4. RESULTS FOR INDIVIDUAL GALAXIES
In this section, we presentthe DensePakfiberpositions, ob-
4 CamB,F750-4,KK98251,UGC891,UGC1501/NGC784,UGC2455/
served velocity fields, and rotation curves in Figures 1–11. A
NGC1156,UGC2864,UGC4543,UGC4787,UGC5414/NGC3104,UGC
descriptionisgivenforeachgalaxy,andwecomparetherotation
7603/NGC4455,UGC8837/DDO185,UGC9211/DDO189,UGC11583,
curvestopreviousrawlong-slitH(cid:1)rotationcurves,aswellasHi UGC12344,UGC12713,andUGC12791.
No. 2, 2006 LSB OPTICALVELOCITY FIELDS AND ROTATION CURVES 465
Fig.2.—ResultsforF563-V2.Topleft:PositionofDensePakarrayonanH(cid:1)imageofthegalaxy.Topright:ObservedDensePakvelocityfield.Emptyfibersare
thosewithoutdetections.Bottomleft:DensePakrotationcurve.Bottomright:DensePakrotationcurveplottedwiththeHirotationcurveofBMH96.Triangles
representtheHipointsusedinthehalofits.[SeetheelectroniceditionoftheSupplementforacolorversionofthisfigure.]
excellentagreementbetweentheDensePakrotationcurveandthe [Sii]k6717,and[Sii]k6731lines.Thefiberswereoffsettoward
long-slitH(cid:1)rotationcurveofBB02.Verysimilarresultshavealso therecedingsideofthegalaxy,andtherewasverylittleemission
beenobtainedwithSparsePak(R.A.Swaters2005,privatecom- inthefibersontheapproachingside.Thepositionanglewasfixed
munication).TheHidata(Swaters1999)lieabovetheopticaldata tothevalueinMRB01andBB02.Whencomparedtothelong-slit
attheinnerradii.ThissuggeststhattheHidatahavebeenover- H(cid:1)rotationcurvesofBMR01andBB02,thereisgoodagreement
correctedforbeamsmearing(BB02).TheouterHipointsareabit upto1500.Beyondthat,however,thelong-slitcurvesandtheHi
lowerthantheopticaldatabutarewithin1(cid:5).Thedeclineinthero- curve (BMH96) turn over and flatten out, while the DensePak
tationcurveattheouterradiimaybearealfeature(Bosma2004). curvecontinuestorise.AdditionalDensePakcoveragewouldbe
F563-V2.—There was one pointing for this galaxy. The usefulindeterminingwheretheDensePakcurveturnsover.
DensePak fibers are shown on the H(cid:1) image from McGaugh DDO64.—Therewerethreepointingsforthecenterandap-
etal.(1995).ThefibervelocitiesweretheaverageoftheH(cid:1), proachingsideofthisgalaxy.TheDensePakfiberpositionsare
[Sii]k6717,and[Sii]k6731lines.ThereislittleH(cid:1)emission, shownonaDigitizedSkySurvey5image.Fibervelocitieswere
andonlyroughlyhalfofthefibershaveanH(cid:1)detection.Thepo- the average of the H(cid:1) and [S ii] k6717 lines. The amount of
sitionanglewasfixedtothevalueusedinSwatersetal.(2003a).
TheDensePakrotationcurvegenerallyagreeswiththeHirotation
curveofBMH96. 5 TheDigitizedSkySurveyswereproducedattheSpaceTelescopeScience
InstituteunderNASAgrantNAGW-2166.Theimagesofthesesurveysarebased
F563-1.—There was one pointing for this galaxy. The fiber
onphotographicdataobtainedusingtheOschinSchmidtTelescopeonPalomar
positionsareshownonanH(cid:1)image(W.J.G.deBlok2005,un-
MountainandtheUKSchmidtTelescope.Theplateswereprocessedintothe
publisheddata).ThefibervelocitiesweretheaverageoftheH(cid:1), presentcompresseddigitalformwiththepermissionoftheseinstitutions.
466 KUZIO DE NARAY ETAL. Vol. 165
Fig.3.—ResultsforF563-1.Topleft:PositionofDensePakarrayonanH(cid:1)imageofthegalaxy.Topright:ObservedDensePakvelocityfield.Emptyfibersare
thosewithoutdetections.Bottomleft:DensePakrotationcurve.Thelastfourpointsareomittedfromthehalofits.Bottomright:DensePakrotationcurveplottedwith
therawlong-slitH(cid:1)rotationcurvesofBB02andBMR01andtheHirotationcurveofBMH96.ThetrianglerepresentstheHipointusedinthehalofits.[Seethe
electroniceditionoftheSupplementforacolorversionofthisfigure.]
emissioninthisgalaxyisveryhigh,andnearlyallfibersdetected UGC5750.—Therewasonepointingforthisgalaxy.Thefi-
emission.ThepositionanglewasfixedtotheBB02value.The berpositionsareshownonanH(cid:1)image(W.J.G.deBlok2005,
DensePakpointsriseandfallinapatternsimilartothelong-slit unpublished data). The average of the H(cid:1), [N ii] k6584, [S ii]
data(BB02).Thestructureintherotationcurveappearstobereal. k6717,and[Sii]k6731lineswastakenasthefibervelocity.H(cid:1)
Thattheinnertwopointsfallbelowthelong-slitdatamaysuggest emissionwassparseinthisgalaxy,andonlyroughlyhalfofthe
the presence of noncircular motions in the inner regions. The fibershadadetection.Thepositionanglewasfixedtothevalue
Hidata(Stil1999)lieslightlybelow,butwithintheerrorsof, listed inMRB01andBB02. Thereisgoodagreement with the
theopticaldata.Itshouldbenoted,however,thatoverthera- long-slitH(cid:1)rotationcurvesofbothBB02andBMR01.
dialrangeplottedinFigure4thereareonlytwoHipoints. NGC 4395.—There were five pointings for this galaxy, and
F568-3.—There was one pointing for this galaxy, and the thepositionsoftheDensePakfibersareshownonanR-bandim-
fiber positions are shown on an H(cid:1) image (W. J. G. de Blok age(W.J.G.deBlok2005,unpublisheddata).TheH(cid:1)lineover-
2005,unpublisheddata).Thefibervelocitiesweretheaverageof lappedslightlywithaskyline.Thiswasnotaseriousproblemfor
theH(cid:1)andthe[Nii]k6584lines.H(cid:1)emissionwasdetectedin thisgalaxy,becausetheemissionlines(particularlytheH(cid:1)line)
roughly 60% of the fibers. The position angle was fixed to the wereverystrong.TheH(cid:1)linewasmeasuredinafiberifthe[Nii]
MRB01andSwatersetal.(2003a)long-slitvalue.TheDensePak k6584,[Sii]k6717,and[Sii]k6731lineswerevisibleandstrong
rotationcurveisconsistentwiththelong-slitH(cid:1)curveofBMR01 and if the H(cid:1) line was stronger than the neighboring sky lines.
andtheHicurveofBMH96. Withthesecriteria,H(cid:1)wasdetectedinnearlyallthefibers.The
No. 2, 2006 LSB OPTICALVELOCITY FIELDS AND ROTATION CURVES 467
Fig.4.—ResultsforDDO64.Topleft:PositionofDensePakarrayonaDigitizedSkySurveyimageofthegalaxy.Topright:ObservedDensePakvelocityfield.
Theemptyfibersarethosewithoutdetections.Bottomleft:DensePakrotationcurve.Bottomright:DensePakrotationcurveplottedwiththerawlong-slitH(cid:1)rotation
curveofBB02andtheHirotationcurveofStil(1999).ThetrianglerepresentstheHipointusedinthehalofits.[SeetheelectroniceditionoftheSupplementfora
colorversionofthisfigure.]
fibervelocitiesweretheaverageoftheH(cid:1)and[Sii]k6717lines. beam smearing in the H i data turned out to be important
ThepositionangleofBB02wasusedastheDensePakposition (BMR01).
angle.TheDensePakrotationcurveisconsistentwiththelong-slit F583-1.—Thereisonepointingforthisgalaxy.TheDensePak
H(cid:1)curveofBB02,aswellastheHicurve(Swaters1999)atthe fibersareshownontheR-bandimageofthegalaxyfromBMH96.
innermost radii.Atthe outerradii,the Hicurve fallsbelowthe ThefibervelocitiesaretheaveragesoftheH(cid:1),[Sii]k6717,and
opticaldataataboutthe2(cid:5)level. [Sii]k6731lines,andmoreoftheapproachingsideofthegalaxy
F583-4.—Thereweretwopointingsforthisgalaxy:acentral isseenthan thereceding side.TheMRB01positionangle was
pointingandaninterstitialpointing;thefiberpositionsareshown taken as the DensePak position angle. The DensePak rotation
onthe R-band image fromBMH96. Thefibervelocitiesare the curveisconsistentwithboththelong-slitH(cid:1)rotationcurveof
averagesoftheH(cid:1),[Sii]k6717,and[Sii]k6731lines,andthe BMR01andtheHirotationcurveofBMH96.
approachingsideofthegalaxyhasslightlybettercoveragethan UGC477.—Therewerethreeinterstitialpointingsalongthe
the receding side. The position angle was fixed to the value in lengthofthisgalaxy,andspatialcoverageofthegalaxywasop-
MRB01.TheDensePakrotationcurveisgenerallyconsistentwith timal.TheDensePakfibersareshownontheR-bandimageob-
the long-slit H(cid:1) rotation curve of BMR01. Both optical rota- tained at the KPNO 2 m telescope. Fiber velocities were the
tioncurvesareoffsettonoticeablyhighervelocitiesthantheHi averageoftheH(cid:1),[Nii]k6584,[Sii]k6717,and[Sii]k6731
rotationcurveofBMH96.Thisisoneofthefewgalaxieswhere lines.Theamountofemissionwasveryhighinthisgalaxy,and
468 KUZIO DE NARAY ETAL. Vol. 165
Fig.5.—ResultsforF568-3.Topleft:PositionofDensePakarrayonanH(cid:1)imageofthegalaxy.Topright:ObservedDensePakvelocityfield.Theemptyfibers
arethosewithoutdetections.Bottomleft:DensePakrotationcurve.Bottomright:DensePakrotationcurveplottedwiththerawlong-slitH(cid:1)rotationcurveof BMR01
andtheHirotationcurveofBMH96.TrianglesrepresenttheHipointsusedinthehalofits.[SeetheelectroniceditionoftheSupplementforacolorversionofthis
figure.]
almosteveryfiberhadadetection.Thepositionanglewaswell theDensePakfibersaresymmetric.UGC1281isunlikelytobe
constrainedbythedata. soopticallythickthattheobservationsarehamperedbyobscu-
UGC 1281.—There were five interstitial pointings for this ration(deNarayetal.2004).Ourinstrumentalresolution,how-
galaxy.Theamountofemissionwassparse,asfewerthan50% ever, is probably not high enough to resolve any skewing that
ofthefibershadadetection.TheDensePakfibersareshownon maybepresent.Wepresenttheminimum-diskcaseanalysisfor
the R-band image obtained at the KPNO 2 m telescope. Fiber thisgalaxyinx5.2butexcludeitfromfurthermodeling.
velocities were the average of the H(cid:1), [S ii] k6717, and [S ii] Obtaininghigh-qualityvelocityfieldsisnottrivial.LSBgal-
k6731lines.Thepositionanglewaswellconstrainedbythedata, axiesaredifficulttoobserve.TheH(cid:1)emissionisfaint.Inaddi-
andtheDensePakrotationcurveisconsistentwiththelong-slit tion,the emissionmay notbespreadout enoughtobedetected
H(cid:1)rotationcurveofBB02.UGC1281isanearlyedge-ongal- acrosstheentireDensePakfiberarray.Althoughwetriedtoselect
axy.Athighinclination,line-of-sightintegrationeffectsbecome galaxieswithpromisingH(cid:1)emission,theremaining17galaxies
important and may cause an intrinsically steeply rising rota- of our sample6 were observed, but unfortunately the detections
tioncurvetoappearslowlyrising.Theshapeoftheemission-line werenotgoodenoughtoconstructmeaningfulvelocityfields.
profilescanbeusedtoconstraintheshapeoftherotationcurve. For the 11 galaxies for which we have constructed velocity
Ifinstrumentalresolutionishighenoughandthereisnoline-of- fields,thereisgoodoverallagreementbetweenthenewDensePak
sightobscuration,thensymmetriclineprofilesindicateasolid- rotationcurvesandthepreviousdatasets.Inallcases,thedataare
bodyrotationcurveandskewedlineprofilesindicateacurved,
NFW-likerotationcurve(Kregeletal.2004).Thelineprofilesin 6 Foralistofthesegalaxies,seefootnote4inx4.
No. 2, 2006 LSB OPTICALVELOCITY FIELDS AND ROTATION CURVES 469
Fig.6.—ResultsforUGC5750.Topleft:PositionofDensePakarrayonanH(cid:1)imageofthegalaxy.Topright:ObservedDensePakvelocityfield.Emptyfibers
arethosewithoutdetections.Bottomleft:DensePakrotationcurve.Bottomright:DensePakrotationcurveplottedwiththerawlong-slitH(cid:1)rotationcurvesofBB02
andBMR01.[SeetheelectroniceditionoftheSupplementforacolorversionofthisfigure.]
broadlyconsistentwithpreviouslong-slitrotationcurves.Inonly siontotheminimum-diskcaseinwhichweignorethecontribu-
twocases,F563-1andF583-4,dotheseindependentdataseemto tionofthestarsandgasandattributeallrotationtodarkmatter.
differ,andthenonlyoveraverylimitedrangeinradius.Incases Thisputsanupperlimitontheslopeand/orconcentrationofthe
whereHidataareavailable,fiveareingoodoverallagreement.In halodensityprofile.Moredetailedanalysis,includingmassmod-
twocases,DDO64andF583-4,theHidataaresomewhatlower eling,willbepresentedinafuturepaper.
thantheopticaldata.Inonecase,UGC4325,theHidataaretoo
high.Itistemptingtoblamethesecasesonbeamsmearingor,in 5.1. Halo Models
the case of UGC 4325, overcorrection for beam smearing, al-
thoughotherfactors,suchastheintrinsicHidistribution,arealso Twoofthemostprominentcompetingdarkmatterhaloden-
sityprofilesarethepseudoisothermalhaloandtheNFWprofile.
relevant.Onthewhole,weareencouragedbytheextenttowhich
Weprovideabriefdescriptionofeachbelow.
various independent datasetsagree,given the difficult observa-
tionalchallengeposedbyLSBgalaxies.
5.1.1. PseudoisothermalHalo
5. PRELIMINARYANALYSIS AND DISCUSSION Thedensityprofileofthepseudoisothermalhalois
Inthissection,wewishtogiveanimpressionofhowwellthe
dataaredescribedbyvarioushalomodels.Welimitthisdiscus- (cid:6)iso(R)¼(cid:6)0½1þ(R=Rc)2(cid:4)(cid:2)1; ð4Þ
470 KUZIO DE NARAY ETAL. Vol. 165
Fig.7.—ResultsforNGC4395.Topleft:PositionofDensePakarrayonanR-bandimageofthegalaxy.Topright:ObservedDensePakvelocityfield.Empty
fibersarethosewithoutdetections.Bottomleft:DensePakrotationcurve.Bottomright:DensePakrotationcurveplottedwiththerawlong-slitH(cid:1)rotationcurveof
BB02andtheHirotationcurveofSwaters(1999).TheHipointsusedinthehalofitsextendbeyondtheradialrangeofthisplot.[Seetheelectroniceditionofthe
Supplementforacolorversionofthisfigure.]
with(cid:6) beingthecentraldensityofthehaloandR representing galaxyclustersasfortheCDMhaloofasinglegalaxy.TheNFW
0 c
thecoreradiusofthehalo.Therotationcurvecorrespondingto massdensitydistributionisdescribedas
thisdensityprofileis
(cid:6)
(cid:6) (R)¼ i ; ð6Þ
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi NFW (R=R )(1þR=R )2
(cid:2) (cid:3) (cid:4)(cid:5) s s
R R
V(R)¼ 4(cid:7)G(cid:6) R2 1(cid:2) c arctan : ð5Þ
0 c R R inwhich(cid:6) isrelatedtothedensityoftheuniverseatthetimeof
c i
halocollapseandR isthecharacteristicradiusofthehalo.The
s
NFWrotationcurveisgivenby
This form has traditionally been used in rotation curve fitting
becauseitworkswell.Byconstructionitproducesflatrotation sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ln(1þcx)(cid:2)cx=(1þcx)
curves at large radii. This halo form is empirically motivated, V(R)¼V ; ð7Þ
predating those stemming from simulations. 200 x½ln(1þc)(cid:2)c=(1þc)(cid:4)
5.1.2.NFW Profile
withx¼R/R .Therotationcurveisparameterizedbyaradius
200
NumericalsimulationsproducetheNFWprofileanditsvar- R andaconcentrationparameterc¼R /R,bothofwhichare
200 200 s
iants.ItpredictsthesamefunctionalbehaviorforCDMhalosof directlyrelatedtoR and(cid:6).HereR istheradiusatwhichthe
s i 200