Missing dark matter in dwarf galaxies?

1.1 MB·

by  Kyle A. Oman

Mon.Not.R.Astron.Soc.000,000–000(0000) Printed7January2016 (MNLATEXstylefilev2.2)
Missing dark matter in dwarf galaxies?
Kyle A. Oman1,(cid:63), Julio F. Navarro1,2, Laura V. Sales3, Azadeh Fattahi1,
Carlos S. Frenk4, Till Sawala4,5, Matthieu Schaller4 and Simon D. M. White6
1DepartmentofPhysics&Astronomy,UniversityofVictoria,Victoria,BC,V8P5C2,Canada
2SeniorCIfARFellow
3DepartmentofPhysicsandAstronomy,UniversityofCaliforniaatRiverside,Riversida,CA,92521.
4InstituteforComputationalCosmology,DepartmentofPhysics,UniversityofDurham,SouthRoad,DurhamDH13LE,UnitedKingdom
6 5DepartmentofPhysics,UniversityofHelsinki,GustafHa¨llstro¨minkatu2a,FI-00014Helsinki,Finland
1 6MaxPlanckInstituteforAstrophysics,D-85748Garching,Germany
0
2
n 7January2016
a
J

6 ABSTRACT
WeusecosmologicalhydrodynamicalsimulationsoftheAPOSTLEprojecttoexamine

] the fraction of baryons in ΛCDM haloes that collect into galaxies. This ‘galaxy for-
A
mation efficiency’ correlates strongly and with little scatter with halo mass, dropping
G steadily towards dwarf galaxies. The baryonic mass of a galaxy may thus be used to
place a lower limit on total halo mass and, consequently, on its asymptotic maximum
.
h circular velocity. A number of dwarfs seem to violate this constraint, having baryonic
p
massesuptotentimeshigherthanexpectedfromtheirrotationspeeds,or,alternatively,
-
o rotating at only half the speed expected for their mass. Taking the data at face value,
r either these systems have formed galaxies with extraordinary efficiency – highly un-
t
s likelygiventheirshallowpotentialwells–ortheyinhabithaloeswithextremedeficits
a intheirdarkmattercontent.This‘missingdarkmatter’isreminiscentoftheinnermass
[ deficitsofgalaxieswithslowly-risingrotationcurves,butextendstoregionslargerthan

1 the luminous galaxies themselves, disfavouring explanations based on star formation-
v induced‘cores’inthedarkmatter.Analternativecouldbethatgalaxyinclinationerrors
6 havebeenunderestimated,andthatthesearejustsystemswhereinferredmassprofiles
2 have been compromised by systematic uncertainties in interpreting the velocity field.
0 Thisshouldbeinvestigatedfurther,sinceitmightprovideasimpleexplanationnotonly
1 for missing-dark-matter galaxies but also for other challenges to our understanding of
0 theinnerstructureofcolddarkmatterhaloes.
.
1
Keywords: darkmatter,galaxies:structure,galaxies:haloes
0
6
1
:
v
1 INTRODUCTION lockedupwithintheluminousregionsofgalaxies:currentes-
i
X timates of this quantity are in the range ∼ 6-10% (see, e.g.,
The baryon content of the Universe is one of the best known
r Madau&Dickinson2014).Galaxyformationhasthusbeena
a parameters of the present cosmological paradigm, and is well
veryinefficientprocess;mostoftheavailablebaryonshavebeen
constrained by a variety of independent observations, ranging
prevented (or preempted) from condensing into galaxies, pre-
fromthecosmicabundanceofthelightelements(e.g.,Steigman
sumablybycosmicreionizationandbythefeedbackeffectof
2007)tothefluctuationsinthecosmicmicrowavebackground
theenergeticoutputofevolvingstarsandactivegalacticnuclei.
radiation (e.g., Hu & Sugiyama 1995; Planck Collaboration
A simple quantitative estimate of the resulting galaxy
etal.2015).ItisnowwidelyacceptedthattheUniversehascriti-
formation efficiency – which we define hereafter as f =
caldensity(Ω=1)andthatmattermakesup∼31%ofthetotal eff
∼ M /(f M ),i.e.,theratiobetweenthebaryonicmassof
matter-energydensity(Ω ∼0.31),withbaryonscontributing bar bar 200
M agalaxy,M ,tothetheoreticalmaximumconsistentwiththe
onlyamodestfraction(f = Ω /Ω ∼ 0.17,PlanckCol- bar
bar b M virial1 massofitshosthalo(Whiteetal.1993)–maybeob-
laborationetal.2015).
tainedby‘abundancematching’modellingofthegalaxypopu-
Only a fraction of the Universe’s baryons are at present
1 We define the virial mass, M200, as that enclosed by a sphere of
(cid:63) [email protected] meandensity200timesthecriticaldensityoftheUniverse,ρcrit =
(cid:13)c 0000RAS
2 K.A.Omanetal.
lation. These models indicate that the mean galaxy formation photometryinmultiplepassbands,androtationcurvesthatpro-
efficiency should be low in haloes of all masses, peaking at vide estimates of the circular velocity well beyond the radius
∼ 18%ingalaxiesofstellarmassoforder3×1010M and that contains the majority of the stars in a galaxy. We there-
(cid:12)
decreasing steeply toward higher and lower masses (see, e.g., fore focus here on some of the best studied nearby galaxies,
Behroozietal.2013,andreferencestherein). includingthosefrom(i)theTHINGS(Walteretal.2008)and
TheMilkyWaysitsnearthepeakofthisrelationand,at LITTLETHINGS(Hunteretal.2012)surveys;(ii)sixdwarfs
f ∼0.2(forabaryonicmassoforder∼5×1010andavirial withexquisitemultiwavelengthdatafromAdamsetal.(2014),
eff
massof1.5×1012M ,Rix&Bovy2013;Wangetal.2015), as well as (iii) those included in the ‘baryonic Tully-Fisher’
(cid:12)
itisconsideredsomethingofanoutlierwheregalaxyformation compilationofMcGaugh(2012).The77selectedgalaxiesspan
hasproceededparticularlyefficiently.Galaxyformationisex- nearly four decades in baryonic mass, 107 < M /M <
bar (cid:12)
pected to be much less efficient in fainter systems due to the 1011,androughlyadecadeinmaximumrotationspeed,20 <
enhancedfeedbackeffectsonshallowerpotentialwells(Larson Vmax/kms−1<200.
rot
1974;White&Rees1978;Efstathiou1992;Bullocketal.2000; We address the theoretical modelling issues by using re-
Bensonetal.2002),droppingdowntoessentiallyzeroinhaloes sultsfromsomeofthelatestΛCDMcosmologicalhydrodynam-
withvirialmassesbelow∼109M (Sawalaetal.2014). icalsimulationsofgalaxyformation.Weuse,inparticular,re-
(cid:12)
The steady decline of f with decreasing halo mass is sults from the APOSTLE2 suite of simulations (Fattahi et al.
eff
now recognized as one of the basic ingredients of galaxy for- 2015), which uses the same code developed for the EAGLE
mation models in the ‘Lambda-Cold Dark Matter’ (ΛCDM) project(Schayeetal.2015;Crainetal.2015).Thiscode,based
paradigm, since it serves to reconcile the steeply-rising low- onP-GADGET3,adescendentoftheGADGET2code(Springel
mass end of the CDM halo mass function with the relatively 2005),hasbeenshowntoreproducethegalaxysizeandstellar
shallowfaint-endofthegalaxystellarmassfunction(White& massfunctionsinacosmologicalvolumeaswellastheabun-
Frenk1991).Assumingthatthescatterinthegalaxymass–halo danceandpropertiesofdwarfgalaxiesandsatellitesystemsin
mass relation remains relatively small at low mass, the bary- the Local Group (Sawala et al. 2015). These simulations thus
onicmassofagalaxythusimposesafairlystrictlowerlimiton providerealisticestimatesofthedependenceofgalaxyforma-
the massof the haloit inhabits and,given the self-similarna- tionefficiencyonhalomass,aswellasitsscatter.
tureofCDMhalostructure(Navarroetal.1997),onitsasymp- DarkmattercoresdonotdevelopindwarfsintheAPOS-
toticmaximumcircularvelocity.Thisbasicpredictioncouldin TLEsimulations,presumablyasaresultofchoicesmadewhen
principlebereadilyverifiedbyanalyzinggalaxieswherehigh- implementingsubgridphysicsinEAGLE(Schalleretal.2015;
qualityestimatesoftheirbaryonicmassesandrotationspeeds Oman et al. 2015). These choices are effective at preventing
areavailable. theartificialfragmentationofgaseousdisks,butalsolimitthe
Afewissuesmustbeconsidered,however,whenattempt- magnitudeoffluctuationsinthegravitationalpotentialthatre-
ing such a comparison. Observational estimates of baryonic sultfromtheassemblyanddispersalofdensestar-forminggas
massesincludethecontributionsofstarsandatomic/molecular clouds.Thelatter,accordingtorecentwork,areresponsiblefor
gas, and are subject to uncertainties in the mass-to-light ratio theformationofcoresinthedarkmatter(Pontzen&Governato
ofthestellarcomponent;intheconversionfromneutralhydro- 2014).WethereforesupplementourAPOSTLErunswithruns
gentototalgaseousmass;andinthedistancetoeachindividual fromtheliteraturewherebaryon-induced‘cores’havebeenre-
galaxy (well-studied dwarfs are usually too close for redshift- ported(Brooketal.2012;Chanetal.2015;Santos-Santosetal.
baseddistanceestimatestobeaccurate).Anotherproblemisthe 2016).
shortradialextentofrotationcurves,whichinmanycasesare LikeAPOSTLE,othersimulationshavealsoattemptedto
stillrisingattheoutermostpointand,therefore,donotconstrain reproduce the Local Group environment and kinematics, no-
themaximumcircularvelocityofthesystem.Finally,observa- tably those from the CLUES project (Gottloeber et al. 2010)
tionsmeasuregasvelocityfields,whichareusuallytranslated and from the ELVIS project (Garrison-Kimmel et al. 2014).
intoestimatesofcircularvelocitycurvestoprobetheunderly- Wedonotincludetheirresultshere,however,mainlybecause
inggravitationalpotential.Thistranslationincludescorrections (i) ELVIS consists of runs that follow solely the dark matter
forinclination,asymmetricdrift,non-axisymmetricandrandom component,andbecause(ii)thefeedbackalgorithmadoptedin
motions,andinstrumentallimitationswhichmustbecarefully CLUESistooweaktopreventexcessivestarformationinlow
takenintoaccount,especiallyindwarfgalaxies,manyofwhich mass haloes, leading to an unrealistic number of dwarfs (see,
arenotoriousfortheirirregularmorphology. e.g.,Ben´ıtez-Llambayetal.2013).
Thetheoreticalmodellingintroducesadditionaluncertain- We begin by describing the simulated (§2) and observed
ties.Alargescatteringalaxyformationefficiencyinlow-mass (§3)galaxysamples.Wethenanalyze(§4)thebaryoncontent
haloes is expected given the sharp decline in f required as andgalaxyformationefficiencyofAPOSTLEgalaxiesandes-
eff
haloesapproachthemassbelowwhichgalaxiesfailtoform.In tablishtheircorrelationswithhalomass/circularvelocity.These
addition,baryonsmayalterthestructureofthedarkhalo,creat- relationsarethencomparedwithourobservedgalaxysample,
ing‘cores’thatreducethecentraldensityanddepresssystem- an exercise that yields a number of outliers for which there
atically local estimates of the circular velocity (Navarro et al. are no counterparts in the simulations. Particularly interesting
1996a;Mashchenkoetal.2006;Pontzen&Governato2014). are outliers inferred to have exceptionally high galaxy forma-
Theobservationalissuesmaybeaddressedbyselectingfor
analysis a galaxy sample with well-calibrated distances, good
2 APOSTLEstandsfor‘AProjectOfSimulatingTheLocalEnviron-
ment’,asuiteof12volumesselectedfromalargecosmologicalbox
3H2/8πG.Virialquantitiesaredefinedatthatradius,andareidentified tomatchthemainpropertiesoftheLocalGroupofGalaxiesandits
bya‘200’subscript. immediatesurroundings.
(cid:13)c 0000RAS,MNRAS000,000–000
Missingdarkmatterindwarfgalaxies? 3
2.2 Thesimulatedgalaxysample
Table1.SummaryofthekeyparametersoftheAPOSTLEsimulations
usedinthiswork.Particlemassesvarybyuptoafactorof2between
GalaxiesareidentifiedinAPOSTLEusingtheSUBFINDalgo-
volumesatafixedresolution‘level’;themedianvaluesbelowarein-
rithm(Springeletal.2001;Dolagetal.2009).Particlesarefirst
dicative only (see Fattahi et al. 2015, for full details). Details of the
groupedintofriends-of-friends(FoF)haloesbylinkingtogether
WMAP7cosmologicalparametersusedinthesimulationsareavailable
darkmatterparticlesseparatedbylessthan0.2timesthemean
inKomatsuetal.(2011).
interparticlespacing(Davisetal.1985);gasandstarparticles
Particlemasses(M(cid:12)) Maxsoftening areassignedtothesameFoFhaloastheirnearestdarkmatter
Simulation DM Gas length(pc) particlewithinthelinkinglength.Substructuresarethensepa-
ratedalongsaddlepointsinthedensitydistribution;inthisstep,
AP-L3 7.3×106 1.5×106 711
dark matter, gas and star particles are treated as a single dis-
AP-L2 5.8×105 1.2×105 307
tributionofmass.Finally,particlesthatarenotgravitationally
AP-L1 3.6×104 7.4×103 134
boundtothesubstructuresareremoved.
We retain for analysis the main (central) galaxy of each
separate FoF halo; this excludes by construction satellites of
tionefficiency,or,alternatively,torotatefartooslowlyfortheir more massive systems and are best identified with ‘isolated’
baryonicmassbecausetheyareanomalouslydeficientindark fieldgalaxies.Foreachofthesegalaxieswemeasurethevirial
matter.Neitherpossibilityfindsanaturalexplanationincurrent massofitssurroundinghalo,M200,aswellasitsbaryonicmass,
simulationsofdwarfgalaxyformation.Wediscusstherelation Mbar,whichweidentifywiththetotalmassofbaryonswithin
betweenthese‘missingdarkmatter’systemsandthosewhere the galactic radius, rgal = 0.15r200. This definition includes
‘cores’ have been inferred from their inner rotation curves in the great majority of stars and cold gas within the halo virial
§4.4.Weconcludein§5withabriefsummaryanddiscussionof radius.
theimplicationsofthesepuzzlingsystemsforourunderstand- Weshallconsidertwocharacteristiccircularvelocitiesfor
ingofdwarfgalaxyformationinaΛCDMuniverse. each galaxy in our analysis: (i) the maximum circular veloc-
ity,V ,measuredwithinthevirialradius;and(ii)theveloc-
max
ity at the outskirts of the luminous galaxy, which we identify
withthecircularvelocityattwicethestellarhalf-massradius,
V (2rst). For simplicity, we estimate all circular velocities
circ h
2 THEAPOSTLEPROJECT using the total enclosed mass, assuming spherical symmetry;
i.e.,V2 (r)=GM(<r)/r.
circ
2.1 Thenumericalsimulations WeusethethreeAPOSTLEresolutionlevelstodetermine
which simulated galaxies are sufficiently resolved to measure
We select galaxies from the APOSTLE suite of zoom-in hy-
baryonicmassesandcircularvelocities.WeretainAP-L1galax-
drodynamicalsimulations.Thesefollowatotalof12volumes
ies with Vmax > 26 km s−1, AP-L2 galaxies with Vmax >
specificallyselectedfromacosmologicaldarkmatter-onlysim- circ circ
56kms−1 andAP-L3galaxieswithVmax > 120kms−1 in
ulation to contain two haloes with approximately the masses circ
oursample.Thesecutscorrespondtovirialmassesof>3×109,
anddynamicsoftheMilkyWayandM31,andnoothernearby ∼
3×1010 and 3×1011M , respectively, or a particle count
largestructures(fordetails,seeFattahietal.2015;Sawalaetal. (cid:12)
> 5×104.Allcircularvelocitiesusedinouranalysisarewell
2015). ∼
resolvedaccordingtothecriterionofPoweretal.(2003).
APOSTLE uses the same code and physics as the ‘Ref’
EAGLEsimulationsdescribedbySchayeetal.(2015).EAGLE
usesthepressure-entropyformulationofsmoothedparticlehy-
drodynamics(Hopkins2013)andtheANARCHYcollectionof
numerical methods (Dalla Vecchia et al., in preparation; for a 3 THEOBSERVEDGALAXYSAMPLE
brief description see Schaye et al. 2015). It includes subgrid
Ourobservedgalaxysamplehasbeendrawnfromseveralhet-
modelsforradiativecooling(Wiersmaetal.2009a),starforma-
erogeneoussources,placinganemphasisongalaxieswithgood
tion(Schaye2004;Schaye&DallaVecchia2008),stellarand
estimates of their baryonic masses and high-quality rotation
chemical enrichment (Wiersma et al. 2009b), energetic stellar
curvesderivedfrom2Dvelocityfields.Thisisasubsetofthe
feedback(DallaVecchia&Schaye2012),andcosmicreioniza-
full compilation of rotation curves presented in Oman et al.
tion(Haardt&Madau2001;Wiersmaetal.2009b),andiscal-
(2015),andcontainsgalaxiestakenfromthesourceslistedbe-
ibrated to reproduce the galaxy stellar mass function and size
low.Wetakebaryonicmassesdirectlyfromthelistedsources3,
distributionforgalaxiesofM >108M (Crainetal.2015).
∗ (cid:12) andadopttheirpublishedcircularvelocityestimates,whichare
The APOSTLE volumes are simulated at three different
basedonfoldedrotationcurvescorrectedforinclination,asym-
resolution levels which we denote AP-L1, AP-L2 and AP-L3
metricdrift,andinstrumentaleffects.Nofurtherprocessingof
inorderofdecreasingresolution.Eachresolutionlevelissep-
thesedatahasbeenattempted.Thepropertiesofgalaxiesinour
arated by a factor of ∼ 10 in particle mass and a factor of
compilationthathaverotationcurvesextendingtoatleasttwice
∼ 2 in force resolution. All 12 volumes have been simulated
theirstellarhalfmassradius(see§4.3)aresummarizedinTa-
at AP-L2 and AP-L3 resolution levels, but only volumes 1
ble2.Below,webrieflydiscusseachofthesedatasets.
and4havebeensimulatedatAP-L1resolution.APOSTLEas-
sumesWMAP7(Komatsuetal.2011)cosmologicalparameters:
Ω = 0.2727,Ω = 0.728,Ω = 0.04557,h = 0.702and
m Λ b
σ8 = 0.807.Table1summarizestheparticlemassesandsoft- 3 WehaveadoptedMgas/MHI =1.4toaccountforthegasmassin
eninglengthsofeachresolutionlevel. Heliumandheavyelements.
(cid:13)c 0000RAS,MNRAS000,000–000
4 K.A.Omanetal.
3.1 THINGSandLITTLETHINGS 11
10
Rotation curves for 44 galaxies in the THINGS and LITTLE AP-L1
THINGSsurveyswerepublishedbydeBloketal.(2008),Oh AAPP--LL23 NNGGCC 33169281
eratnagl.e(2o0f1m1)asasneds,Owhitehtaml.ax(2im01u5m).Tcihrceuselagravlaexloiecsitisepsanbeatwweidene 1010 AOPbOseSrTvLaEt ioVnmcisrac xVmroatx UGCLL S6SB9BN 8F GF35C566 898-21-53NGC 2403 NGC 4736
LSB F5L6S3B- VF5268-V1
∼ 20and∼ 400kms−1.ThesurveysobtainedHIdatacubes
usingtheNRAOVeryLargeArraywithangularresolutionsof ]fl UGUGC C6L S84B14IC8 9F 92I5C5N7 712G4-2CV3 153U58G5C N11G7CN0 G57C9 479793
M UGC 9211NGC 1560UNGGCC 32751512
12(THINGS)and6(LITTLETHINGS)arcsec,makingthem [ 109 DDO 50 NGC 2UL3SG6BC6 D 8500505UU-LG2SGCBC 8 NF545G796C2051 -9V529
saovmaileabolfe.thTehemroosttatfiionnelcyusrvpeastiawlleyrerecsoonlsvterudcHtedIfrrootmatitohnecvuerlvoecs- Mbar UGNCGACH 9o12 N5IG69C 3741DDO L1US5UDGB4GDC DCO D85 D 4D587ND15O75DG1O0- D512C 56O 328 1407N9GC N29G7CN6 G2UC9G1 5C52 202459 NGC 3738
ityfieldsusingatilted-ringmodel(Rogstadetal.1974;Kam- DDO 43 DDO 46
phuis et al. 2015), corrected for inclination, and asymmetric 108 IC 1613 P5D1D6KO5LK S959B38K DK2DU594D1G86O2 CW2 - 1L257LS212MHB64a 2DDro5D 02O09 -1333KKHHa r1o1D 3D6O 101
drift when necessary. A few galaxies are analyzed in multiple DDO 183DDO 181 MU81G Cd w6D 1BD45O 70
LSB F564-V3
publications;inthesecasesweuseonlythemostrecentanal- UGCC a8m21 B5 UCGVLnCSI Bd8 w8D3A5364-8
ysis. HI masses are derived from the THINGS and LITTLE 7 DDO 216 IC 10UGC 8508
10
THINGSdatabyWalteretal.(2008)andOhetal.(2015),re-
20 30 40 70 100 200
spectively.
V [km s 1]
Stellar masses are estimated by fitting stellar population circ −
spectral energy density models to Spitzer IRAC 3.6µm ob-
servations(Hunter&Elmegreen2006).Weusethediskscale Figure1.Baryonicmassesofsimulatedgalaxies,Mbar,asafunction
lengthsreportedinHunteretal.(2012)toestimaterhstforLIT- oftheirmaximumcircularvelocityintheAPOSTLEsimulations(red
TLETHINGSgalaxies–foranexponentialprofilethehalfmass symbols).Galaxymassesaremeasuredwithinthegalacticradius,de-
radiusisrelatedtothescalelength,rd,asrhst ≈ 1.68rd.For finedasrgal = 0.15r200.Thethickredsolidlineshowsafittothe
theTHINGSsample,noscalelengthsarereported,butthecon- velocitydependenceofthemedianMbarinthesimulations.Observed
tribution of stars to the circular velocity is shown as a func- galaxieslabelledbytheirnameareshownwithopensquaresanduse
themaximummeasuredrotationspeedofeachgalaxyandtheirbary-
tionofradius.Wethereforeassumeanexponentialdiskprofile
onicmasses,takenfromtheliterature(see§3fordetailsonthesample).
andestimateascalelengthfromthepositionofthepeakofthe
Squares containing dots correspond to galaxies with rotation curves
contributionofthestellarcomponentofeachgalaxy(Binney&
extending out to at least twice the stellar half-mass radius (see §4.3
Tremaine2008,§2.6.1b).
andFig.4).Squareswithcrosseshighlightthegalaxieswhoserotation
curvesareshowninFig.3.
3.2 Adamsetal.(2014)
Adams et al. (2014) present a sample of 7 rotation curves of duplicateentry(UGC4115a.k.a.LSBD631-7).Themajorityof
galaxies with maximum circular velocities of ∼ 100 km s−1. theremaininggalaxiesdonothavehighqualityrotationcurve
ThevelocityfieldsweremeasuredwiththeVIRUS-Wintegral measurements that are readily available, so we only use these
field spectrograph on the 2.7-m Harlan J. Smith Telescope at datainour‘baryonicTully-Fisher’andfeff analysisbelow.
McDonaldObservatorywithanangularresolutionof3.1arcsec.
Theauthorsanalyzeseparatelyabsorptionlines,tracingthestel-
larvelocityfield,andHβ,OIII4959A˚ andOIII5007A˚ emis- 4 RELATIONBETWEENGALAXYBARYONICMASS
sion, tracing the gas velocity field. Using a tilted-ring model,
ANDDARKHALOMASS
two independent rotation curves, one for each velocity field,
wereconstructedforeachgalaxy.Inmostcasesthetwocurves 4.1 ThefaintendofthebaryonicTully-Fisherrelation
areingoodagreement.Weusethegasemissionbasedcurves
Fordarkmatter-dominatedgalaxies,themostreliablemeasure
inouranalysis,andnotethatusingthestellarabsorptionbased
ofvirialmassistheirmaximumrotationvelocity.Wetherefore
curves would not change anything substantial in our analysis.
beginouranalysisbypresenting,inFig.1,thebaryonicmass
Weusethediskscalelengthsreportedbytheauthorstoestimate
ofAPOSTLEgalaxies(smallredsymbols)asafunctionofthe
rhst,andtheHImassestheyquotefromPatureletal.(2003).We maximum circular velocity, Vmax, measured within the virial
usethestellarmassestheyderivebymodellingthegasrotation circ
radius.ThisfigurecombinesresultsfromthethreeAPOSTLE
curves,whicharebetterconstrainedthanthosederivedbymod-
resolutionlevels,usingonlythosegalaxieswhoserelevantprop-
ellingthestellarrotationcurves(see,e.g.,theirfig.13).
ertiesarewellresolved(see§2).
Baryonic mass clearly correlates strongly and with little
3.3 McGaugh(2012) scatterwithVcmiracxinsimulatedgalaxies;indeed,thedispersion
about the fit4 shown by the thick solid line is only 0.33 dex
Weusethecompilationof47galaxiesofMcGaugh(2012)to in mass, or 0.08 dex in velocity. This ‘baryonic Tully-Fisher’
supplementourowncompilation.Itprovidesself-consistentes- (BTF)relationis,onaverage,inremarkableagreementwiththat
timates of the height of the flat portion of the rotation curve oftheobservedgalaxysample(openblacksquares),forwhich
(whichweconsiderequivalenttoVmaxinournotation),stellar
rot
masses,andgasmasses.ThegasmassesassumeM /M =
gas HI
1.33;weincreasethegasmassesby∼5%forconsistencywith 4 ThefunctionalformofthefitshowninFig.1isMbar/M(cid:12)=5.00×
the rest of our compilation. We remove 7 galaxies already in- 108ν3.08exp(−ν−2.43),whereν isthemaximumcircularvelocity
cluded in our compilation from the THINGS survey and one expressedinunitsof46.99kms−1.
(cid:13)c 0000RAS,MNRAS000,000–000
Missingdarkmatterindwarfgalaxies? 5
Table2.Summaryofpropertiesforgalaxieswithrotationcurvesextendingtoatleast2rhst,orderedbyVrot(2rhst),i.e.left-to-rightinFig.4.Columns:
(1)galaxynameusedbyreferencein(2);(2)rotationcurvesource;(3)distanceasgivenbyreferencein(2);(4)inclinationasgivenbyreferencein(2);
(5)stellarhalfmassradiusestimatedasdescribedin§3;(6)maximummeasuredrotationvelocity;(7)measuredrotationvelocityattwicethestellar
halfmassradius;(8)stellarmassasgivenbyreferencein(2);(9)baryonicmassassumingstellarmassin(7)andMgas/MHI = 1.4;(10)galaxy
formationefficiencyasshowninFig.2.
Galaxy Ref. D i rhst Vrmotax Vrot(2rhst) M∗ Mbar feff
[Mpc] [◦] [kpc] [kms−1] [kms−1] [M(cid:12)] [M(cid:12)]
IC1613 Ohetal.(2015) 0.7 48 0.97 21.1 19.3 2.88×107 8.77×107 36.4%
NGC1569 Ohetal.(2015) 3.4 69 0.64 39.3 23.0 3.63×108 5.67×108 34.2%
CVnIdwA Ohetal.(2015) 3.6 66 0.96 26.4 24.1 4.90×106 3.37×107 7.0%
DDO43 Ohetal.(2015) 7.8 41 0.69 38.3 25.6 0.00×100 2.34×108 15.3%
UGC8508 Ohetal.(2015) 2.6 82 0.45 46.1 26.0 7.76×106 1.98×107 0.7%
DDO50 Ohetal.(2015) 3.4 50 1.85 38.8 29.0 1.07×108 1.43×109 88.9%
Haro29 Ohetal.(2015) 5.9 61 0.49 43.5 33.1 1.45×107 1.08×108 4.7%
DDO70 Ohetal.(2015) 1.3 50 0.81 43.9 33.7 1.95×107 5.75×107 2.4%
LSBF564-V3 Ohetal.(2015) 8.7 56 0.89 39.2 33.8 0.00×100 4.37×107 2.6%
WLM Ohetal.(2015) 1.0 74 0.96 38.5 34.3 1.62×107 9.57×107 6.1%
DDO154 Ohetal.(2015) 3.7 68 0.99 51.1 35.9 8.32×106 3.63×108 9.6%
DDO126 Ohetal.(2015) 4.9 65 1.46 38.7 38.7 1.62×107 1.78×108 11.2%
Haro36 Ohetal.(2015) 9.3 70 1.16 58.2 39.5 0.00×100 1.12×108 2.0%
DDO87 Ohetal.(2015) 7.7 56 2.20 56.6 44.4 3.24×107 3.21×108 6.2%
NGC2366 Ohetal.(2015) 3.4 63 2.28 59.8 55.5 6.92×107 1.14×109 18.6%
DDO47 Ohetal.(2015) 5.2 46 2.30 64.7 60.1 0.00×100 4.68×108 6.0%
DDO52 Ohetal.(2015) 10.3 43 2.18 61.7 60.5 5.37×107 3.85×108 5.7%
DDO168 Ohetal.(2015) 4.3 46 1.38 61.9 60.5 5.89×107 3.16×108 4.6%
NGC5204 Adamsetal.(2014) 3.2 47 0.79 89.4 76.2 2.51×108 5.33×108 2.5%
IC2574 Ohetal.(2011) 4.0 55 5.23 80.0 78.2 1.02×109 2.84×109 18.7%
NGC2552 Adamsetal.(2014) 11.4 53 3.23 96.1 95.7 1.26×109 2.17×109 8.1%
UGC11707 Adamsetal.(2014) 15.0 73 3.69 103.7 96.7 1.20×109 3.20×109 9.3%
NGC7793 deBloketal.(2008) 3.9 50 2.65 117.9 114.1 2.75×109 3.98×109 7.8%
NGC2403 deBloketal.(2008) 3.2 63 2.40 143.9 122.7 5.13×109 8.76×109 9.2%
NGC3621 deBloketal.(2008) 6.6 65 3.83 159.2 139.6 1.58×1010 2.58×1010 19.9%
NGC4736 deBloketal.(2008) 4.7 41 2.62 198.3 153.1 2.00×1010 2.05×1010 8.0%
NGC3198 deBloketal.(2008) 13.8 72 5.60 158.7 153.4 2.51×1010 3.92×1010 30.5%
NGC6946 deBloketal.(2008) 5.9 33 5.34 224.3 195.3 6.31×1010 6.89×1010 18.2%
weadoptthemaximumspeedreachedbytherotation5curveof Fig. 1. Although theexistence of such outliers has inthe past
agalaxy,Vmax. beenregardedwithskepticismandascribedtoinferiordata,the
rot
Theagreementisencouraging,especiallysincetheAPOS- situation has now changed, and a number of authors have ar-
TLE simulations use the same calibration as the EAGLE gued that the scatter in the BTF relation genuinely increases
project,whichwascalibratedtoreproducetheobservednum- towardfainterobjects(see,e.g.,Gehaetal.2006;Trachternach
berandsizeofgalaxiesofstellarmasslargerthan∼108M as etal.2009).Thescatterintheinclination-correctedvelocities
(cid:12)
afunctionofstellarmass.Fig.1thusshowsthatΛCDMsimula- ofobservedgalaxiesshowninFig.1increasesfrom∼0.08dex
tionsthatmatchthoseconstraintsalsoreproduceboththezero- to ∼ 0.17 dex above/below a baryonic mass of 2×109M .
(cid:12)
point and velocity scaling of the BTF relation without further This is much greater than the circular velocity scatter of sim-
calibration. ulated galaxies, which is 0.04 dex and 0.05 dex, respectively,
Onedifference,however,seemsclear:thescatterintheob- above/belowthesamebaryonicmass.
servedBTFrelationseemstoincreasetowardlessmassiveob-
jects,exceedingtherathernarrowdispersionaboutthemedian
trend of the APOSTLE galaxies (see Papastergis & Shankar
4.2 Galaxyformationefficiency
2015,forasimilarconclusion).Weshalldiscussthefaintend
of the simulated BTF relation in a companion paper (Sales et Examples of BTF outliers – two of the galaxies highlighted
al., in preparation), and focus here on the origin and cosmo- with crosses in Figs. 1, 2 and 4 – are provided by DDO 50
logicalsignificanceoftheoutlierstotheBTFrelationseenin (M =1.43×109M ,Vmax =38.8kms−1)andIC1613
bar (cid:12) rot
(M = 8.77×108M ,Vmax = 19.3kms−1),twonearby
bar (cid:12) rot
dwarfgalaxiesthathavebeencomprehensivelystudiedaspart
oftheLITTLETHINGSsurvey.Thesearesystemswhosebary-
5 Onatechnicalnote,forobservedgalaxiesweactuallyusethemax-
onicmassesaremuchhigherthanexpectedfortheirvelocities
imumcircularvelocityestimatedfrom2Dvelocityfieldsasprovided
or,equivalently,whosemeasuredvelocitiesaremuchlowerthan
bytheauthors,whichtypicallycorrectrotationspeedsforinclination,
asymmetricdrift,andinstrumentaleffects.Wedistinguishthesefrom expectedfortheirmass.
circularvelocitiesofsimulatedgalaxies,whichareestimateddirectly ThismaybeseeninFig.2,whereweshowfeff asafunc-
fromtheenclosedmassprofile,V2 (r)=GM(<r)/r. tion of Vmax for APOSTLE galaxies. As expected from the
circ circ
(cid:13)c 0000RAS,MNRAS000,000–000
6 K.A.Omanetal.
e.g.,thediscussionin§4.1.2ofCrainetal.2015).AllAPOS-
100% TLE dwarfs are dark matter dominated; heavily concentrated,
DDO 50 high-surface brightness dwarfs are absent from the simulated
sample.
eff 10%DDUOG C2C 1a8I6Cm2 11 B5613DDUOCGV L1nCS8I Bd38 w8DD3A5D36OP45 D-118D86KO15LK S959B3U8K GDNK2DDUC594GDA1DG86CHO2 OC W92o -1 1 L225 N745LIS2123MG6HB649Ca 2DDr 3o5D7 02O4091 D-13D3O3 L1US5UDGNB4GDCG DCO DC85U D 4 D5872GNULD15O753SDCGG1O0- 6B D512CC 96 56O D U23828 51GU10401G05C7NN095U CGU6GL-LG2 SS8CG4CCBB14 CIN2C1 8 98 NFF9G5 5942I557G6CC795N7660C2 071522G1 4--299UCVVN315G 12G5359CU5C 8G 32L57CU5S1 5BGN112 1GCFL7L C5SNL60S6B SG957BN3 B8C9F G- F35V 4F7C5695276 86998-8231--53VN1GC 2NN4GG0CC3 33169281NGC 4736 DidnoDesOscaOn5totu0ettrlasineeinerdsmfICwetffoe1l6thlo1ewa3lpb,a,aordsrvieenlmoctwehoeeritermtdmhiaifacifinskcsluyesslotalsdtioeddeesnlxgipnianlelaaitxinhni.eeTsFshiiwmgei.itunh2lca,srtmeiloaiaknsleesl
f MU81G Cd w6 1B45 UGC 2259 efficiencies.Indeed,wefindnosimulatedgalaxywheretheeffi-
LSB F564-VD3DO 70 NGC 5204
KKHHa r1o1 36 ciencyexceeds27%overthewholehalomassrangespannedby
DDO 46
1% IC 10 DDO 101 thesimulations.DDO50,ontheotherhand,issomassivethat
UGC 8508 AP-L1NGC 3738 over90%ofitsavailablebaryonsmusthavebeenabletocool
AP-L2 and assemble at the centre of the galaxy. This corresponds to
AP-L3
APOSTLE Vmciracx roughly25timestheaverageefficiencyexpectedforitscircular
0.1% Observations Vmroatx velocity. The discrepancy is even more dramatic for IC 1613,
20 30 40 70 100 200 whoseestimatedefficiencyis∼ 40%–thesimulationaverage
V [km s 1] foritsvelocityismuchlessthan1%.
circ − Galaxies like DDO 50 and IC 1613 are therefore gen-
uinelypuzzlingsystemsforwhichwefindnocounterpartsinthe
Figure 2. Galaxy formation efficiency, feff = Mbar/(fbarM200), APOSTLEsimulations,andwhosesurprisinglyhighgalaxyfor-
asafunctionofmaximumcircularvelocity.SymbolsareasinFig.1; mationefficiencieswouldbedifficulttoexplaininanyΛCDM-
smallredsymbolscorrespondtoAPOSTLEsimulatedgalaxies(pale motivatedmodelofgalaxyformation.Itseemsthereforelegiti-
symbolshaveMbar <107M(cid:12)andsodonotappearinFig.1);open matetosearchforalternativeexplanations.
squaresareobservedgalaxies.Forthelatterweplotthemaximumob-
servedrotationvelocity,andestimatefeffusingthebest-fittingrelation
betweenvirialmassandmaximumcircularvelocityderivedfromthe
simulations:M200/M(cid:12) =1.074×105(Vmax/kms−1)3.115.Note 4.3 Theeffectsofbaryon-induceddarkmatter‘cores’
thatfeffinasimulatedgalaxyneverexceeds30%,butthatanumberof
outlierswithanomalouslyhighgalaxyformationefficienciesareseen Onepossibilityisthatthemaximummeasuredrotationveloc-
intheobservedsample. itysomehowunderestimatestheasymptoticcircularvelocityof
itssurroundinghalo.Thiswouldbethecase,forexample,for
agalaxywitharotationcurvethatrisesouttoitslastmeasured
discussion in §1, feff peaks at ∼ 15% for circular velocities point,butitdoesnotapplytoeitheroneofthetwooutliershigh-
comparabletotheMilkyWay(∼200kms−1)butdeclinespre- lightedabove:therotationcurvesofbothDDO50andIC1613
cipitously6 toward lower masses, dipping to less than 1% for showclearsignsofhavingreachedtheirmaximumvalues(see
haloesbelow30kms−1.IftherotationvelocitiesofDDO50 toppanelsofFig.3).ThatofDDO50isaparticularlygoodex-
and IC 1613 trace reliably the maximum circular velocity of ample,risingquicklytoreachitspeakandstayingflatbetween
theirdarkmatterhaloesthentheseoutlierswouldcorrespondto 2and10kpc.
systemswherethegalaxyformationefficiency,feff,isextraor- Another possibility is that baryons might have carved a
dinarilyhigh. ‘core’inthedarkmatter,thusreducingitscentraldensityand,
Thosetwogalaxiesarenottheonlyoutliersfromthetrend consequently, the circular velocity in the central regions. This
predictedbythenumericalsimulations.Therearealsosystems createsan‘innerdeficit’ofdarkmattercomparedwith‘cuspy’
thatfallwellbelowthesolidredcurveinFig.2andcorrespond CDM haloes, which are well approximated by the NFW pro-
tosystemswithunexpectedlyhighrotationvelocitiesfortheir file (Navarro et al. 1996b, 1997). The characteristic signature
mass. There are two broad scenarios that could explain these ofthiseffectisarotationcurvethatrisesmoregraduallynear
outliers.Theymaybesystemswithunusuallylowgalaxyfor- thecentrethanthesharpriseexpectedforanNFWprofile.We
mation efficiency, perhaps as a result of heating by ionizing examine this possibility in Fig. 4, where we show again the
backgroundradiation,ofparticularlyeffectivestellarfeedback ‘baryonic Tully-Fisher’ relation but using, for both simulated
following a strong past starburst, or of environmental effects and observed galaxies, the circular velocity at the outskirts of
such as cosmic web stripping (Ben´ıtez-Llambay et al. 2013). theluminousgalaxy–i.e.,attwicethestellarhalf-massradius,
They may also be galaxies where the baryonic component is V (2rst)–ratherthanitsmaximumattainedvalue.
rot h
heavilyconcentratedanddominatesthepotentialinthecentral This choice is useful for two reasons. One is that
regions,raisingthelocalcircularvelocityabovethehaloasymp- V (2rst)ismuchclosertothemaximumvelocitiesactually
rot h
totic value. The latter scenario does not arise in APOSTLE, measuredinobservedgalaxiesthantheVmaxofthehalo,which
circ
sincetheequationofstatechosenforthestar-forminggasim- isoftenreachedatradiimuchlargerthantheradialextentofthe
posesaminimumsizeforthestellarcomponentofdwarfs(see, luminous galaxies. The second reason is that velocities mea-
suredasfarfromthecentreas∼ 2rst shouldalsobelargely
h
unaffectedbythepresenceofapossiblebaryon-induced‘core’.
6 TheEAGLEhydrodynamicsmodelusedinAPOSTLEdoesnotin-
Thisisbecause,atleastforthecoreformationmechanismdis-
cludeacoldgasphaseandthereforedoesnotmodelmolecularhydrogen
cussedbyPontzen&Governato(2014),theeffectsofbaryons
cooling.Thisartificiallysuppressesstarformationinsmallhaloesbe-
forecosmicreionization,sosomeofthedwarfsinoursimulationshave onthedarkmattermassprofileislargelylimitedtotheregions
unrealisticallylowstellarmasses–thedeclineinfeff maybeslightly ofagalaxywherestarsform.
lessabruptthanourresultssuggest. WeshowthisexplicitlyinFig.4,wheretheconnectedsym-
(cid:13)c 0000RAS,MNRAS000,000–000
Missingdarkmatterindwarfgalaxies? 7
r/rst
h
0 1 2 3 4 5 0.0 0.5 1.0 1.5 2.0 2.5 3.0
18.00 60
M /M =1.43 109 M /M =8.77 107
70 f ba=r89%fl × 50 f ba=r36%fl ×
eff eff
60 Kirby et al. (2014)
40
50
40 30
30
20
0.8
20
10
10 DDO 50 IC 1613
0 0
0 2 4 6 8 10 0.0 0.5 1.0 1.5 2.0 2.5
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0.0 0.5 1.0 1.5 2.0 2.5
80 100
M /M =1.14 109 M /M =2.84 109
07.60 f ba=r19%fl × f ba=r19%fl ×
eff 80 eff
] 60
1
−
s 50 60
m
40
k
[ 30 40
c
r
ci 20
V 20
0.4
10 NGC 2366 IC 2574
0 0
0 1 2 3 4 5 6 7 8 0 2 4 6 8 10 12 14
0 2 4 6 8 10 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
60 70
M /M =1.08 108 M /M =3.21 108
50 f ba=r5%fl × 60 f ba=r6%fl ×
eff eff
0.2 50
40
40
30
30
20
20
10
10
Haro 29 DDO 87
0.00 0
00.0 1 20.2 3 4 0.54 0 01.6 2 3 40.85 6 7 18.0
r [kpc]
Figure3.Examplesofgalaxieswithrotationcurvesthatextendbeyondtwicethestellarhalf-massradius,rst.Thesesixgalaxiesaremarkedwitha
h
crossinFigs.1–4.Ineachpanelthehorizontalaxisshowstheradiusinunitsofkpc(bottomaxisscale)andstellarhalf-massradius,rst(topaxisscale).
h
Thingreylinesshow,forreference,theΛCDM(NFW)circularvelocityprofilesofhaloesthatmatchtheobservedmaximumrotationspeedofeach
galaxy.Thedarkandlightred-shadedareasindicatetheinterquartileandfullrange,respectively,ofVcircprofilesofthe12simulatedgalaxieswhose
baryonicmassesmostcloselymatchthatofthegalaxyshownineachpanel.Wehighlighttheregionthatcontainsmostofthestarsineachgalaxy
(i.e.,r < 2rst)withadarkertint.Outsidethisradius,baryonsarenotexpectedtobeabletomodifythedarkmatterprofile.Thetoptwogalaxies
h
areexamplesofoutliersinthevelocity-massrelation:thesegalaxiesareanomalouslydeficientindarkmatter(giventheirbaryonicmass).Thebottom
fourgalaxieshave‘normal’galaxyformationefficiencyparametersbutdifferintheirinnercircularvelocityprofiles.Thoseintheleftcolumnhave
rotationcurveshapeslargelyconsistentwithΛCDMhaloesofmatchingmaximumvelocity.Thoseontherightshowtheinnerdeficitofdarkmatterat
thestellarhalf-massradiusthatisusuallyassociatedwitha‘core’.ForIC1613(topright),anindependentestimateofthemassintheinner1.4kpcby
Kirbyetal.(2014)isshownwithanopenbluesymbol.
(cid:13)c 0000RAS,MNRAS000,000–000
8 K.A.Omanetal.
11 These two systems are clearly missing dark matter from the
10
entire body of the galaxy if their galaxy formation efficiency
AP-L1 NGC 6946
AP-L2 is comparable to that in simulations. The differences are not
NGC 3198
AP-L3
APOSTLE Vcirc(2rhst) NGC N36G2C1 4736 subtle. For DDO 50, the comparison implies a total deficit of
1010 APOSTLE Vmciracx roughly∼8×109M(cid:12)fromtheinner10kpc,almostanorder
Brook et al. (2012) NGC 2403
Chan et al. (2015) ofmagnitudegreaterthanthebaryonicmassofthegalaxyitself.
]fl SOabnsteorsv-aStaionntoss et al. (2016) IC 2574UGC 1170N7GC 7793 ThecaseofDDO50andIC1613alsoillustratesthatun-
M NGC 2552 usuallyhighgalaxyformationefficienciesdonotoccursolely
9 DDO 50
[ 10 NGC 2366 ingalaxieswithslowly-risingrotationcurves,wherethepres-
r
ba NGC 1569 DDO 47NGC 5204 enceofa‘core’inthecentraldarkmatterdistributionmightbe
M DDO 154 DDO 87 DDDDOO 1 6582 suspected.Thismaybeseenbyconsideringthethingreylines
DDO 43
8 DDO 126 inFig.3,whichindicatetheexpectedmassprofilesofΛCDM
10 IC 1613 Haro W29LMHaro 36 haloes (i.e., NFW profiles with average concentration for that
LSB FD5D6O4 -7V03 Vmciracx cosmology,see,e.g.,Ludlowetal.2014)chosentomatchthe
CVnIdwA
observedmaximumrotationvelocity.IC1613showsclearlythe
UGC 8508
107 inner mass deficit ascribed to a core: at r = rhst ∼ 1 kpc,
20 30 40 70 100 200 the predicted circular velocity exceeds the measured value by
V (2rst) [km s 1] nearlyafactorof2.Ontheotherhand,DDO50showsnoevi-
circ h −
denceforaprominentcore;itsrotationcurverisessharplyand
flattensoutjustasexpectedforaΛCDMhalo.
Figure4.AsFig.1,butforthecircularvelocity,Vcirc(2rhst),estimated TheotherfourgalaxiesshowninFig.3providefurtherex-
attwicethestellarhalf-massradius.Themagentasmallfilledsymbols
amplesofthedisconnectbetweeninnercoresandgalaxyforma-
andthickdashedlinecorrespondtoAPOSTLEsimulatedgalaxies.The
tionefficiency.Thesegalaxieshavebeenchosentospanawide
thickredsolidlineindicates,asinFig.1,theresultsforthemaximum
rangeinf ,decreasingfromtoptobottom.Thoseontheright
circularvelocity,andisincludedforreferenceonly.Opensquarescor- eff
haverotationcurveswithclearsignsofaninnercore,whereas
respondtoallgalaxiesinourobservedsamplewheretherotationcurve
extendsatleastasfaras2rst.Thelargerbluesolidsymbols(connected thoseontheleftarereasonablywellfitbycuspyNFWprofiles
h
byathinline)areindividualsimulatedgalaxieswheretheformationof (thingreylines)overtheirfullradialextent.Therotationcurves
a‘core’inthecentraldarkmatterdistributionhasbeenreported. ofallgalaxiesinoursamplewheretherotationcurveextendsto
atleast2rstareshownintheAppendix.
h
The anomalies in the galaxy formation efficiency high-
bolsindicateresultsfor22simulatedgalaxieswhereabaryon-
lightedabovethusseemtooccurregardlessoftheinferredpres-
inducedcoreinthedarkmatterhasbeenreportedinthelitera-
enceofacore.InthecontextofΛCDMthisimpliesthatamech-
ture(thesehavebeenselectedfromBrooketal.2012;Santos-
anismthatallowsthegalaxyformationefficiencyindwarfsto
Santosetal.2016;Chanetal.2015).Themagentasymbolsin
varywildlyatfixedhalomassisneededinordertounderstand
thesamefigureshowtheresultsforAPOSTLEgalaxies,which
theseobservations.Italsoimpliesthatitisunlikelythatthese
shownoevidenceforacore(Schalleretal.2015;Omanetal.
twopuzzlescanbeexplainedawaybyasinglemechanism,such
2015). As may be seen from the slight shift between the con-
asbaryon-inducedcoresinthecentralstructureofdarkhaloes.
nectedlineandthemagentadashedline,coresinduceaslight
Resolvingthesepuzzleswouldthusseemtorequiretheinclu-
reductioninthecircularvelocityat2rst,butthechangesdonot
h sionofsomeadditionalphysicsstillmissingfromsimulations
exceed20%relativetoAPOSTLE,evenforthemostextreme
ofdwarfgalaxyformationinΛCDM.
examples. Galaxies like DDO 50 or IC 1613 are still extreme
outliersthatremainunaccountedfor,eveninsimulationswith
cores. 4.5 Alternativeexplanations?
Beforeentertainingmorefar-fetchedexplanationsofthepuzzles
4.4 Missingdarkmatter discussed above, we explore a few more prosaic possibilities.
Theseincludethepossibilitythat(i)erroneousgalaxydistances
Rather than being anomalously baryon rich, galaxies like
haveledtosubstantialoverestimationoftheirbaryonicmasses
DDO50,IC1613,NGC1569,andDDO43(theleftmostout-
(whichscalewiththeassumeddistancesquared);(ii)thatsome
liersinFig.4)couldbeconsideredasanomalouslylowintheir
ofthedarkmatterhasbeentidallystrippedbyinteractionwith
dark matter content. These galaxies would then have low cir-
amoremassiveneighbour;and(iii)thattheinclinationofthe
cular velocities because they would be ‘missing dark matter’,
galaxieshasbeenoverestimated,leadingtosubstantialunderes-
aresultreminiscentoftheinnerdeficitofcolddarkmatterthat
timationoftheirtruerotationspeeds.
characterizesdwarfswherea‘core’hasbeeninferredfromtheir
A full analysis of these possible explanations for the full
inner rotation curves (for a full discussion, see Oman et al.
observedsampleisbeyondthescopeofthispaper,butwehave
2015).Fromthisperspective,galaxieslikethefouraforemen-
checkedwhethersuchconcernsapplytoDDO50andIC1613,
tioned outliers would be simply systems where the dark mass
twoclearoutliersfromtherelationsdiscussedabove.
deficitisnotrestrictedtotheinnerregionsbutratherappliesto
thewholeradialextentoftheluminousgalaxy,andbeyond.
This is illustrated in the top two panels of Fig. 3, where
4.5.1 Distances
wecomparetherotationcurvesofDDO50andIC1613with
the circular velocity profiles of APOSTLE galaxies of match- Thedistancestobothgalaxiesseemquitesecure:bothhavedis-
ingM ,whichareshownbracketedbytheredshadedareas. tancesmeasuredwithmultipleprecisedistanceestimators.The
bar
(cid:13)c 0000RAS,MNRAS000,000–000
Missingdarkmatterindwarfgalaxies? 9
apparentluminosityofCepheidsinDDO50yieldsadistance sincerotationspeedandinclinationaremathematicallydegen-
estimate of 3.05±0.21 Mpc (Hoessel et al. 1998), and Hub- erateparametersintilted-ringanalysisoflinearlyrisingrotation
ble Space Telescope (HST) photometry gives a tip of the red curves(see,e.g.,Kamphuisetal.2015),suchasthatofthein-
giant branch (TRGB) distance estimate of 3.38 ± 0.05 Mpc nerregionsofIC1613.Thisdegeneracycannotbebrokenusing
(Dalcanton et al. 2009). IC 1613 has similarly high-quality kinematicalinformationalone,whichledOhetal.(2015)tofix
data, with HST-based Cepheid and TRGB distance estimates theinclinationat∼ 35◦ (seetheirfig.A.56)inordertoderive
of 0.77±0.04 and 0.71±0.06 Mpc, respectively (Ferrarese therotationcurve.Wenotethataninclinationof∼ 22◦ would
etal.2000).Thesedistancesareingoodagreementwiththose beneededtobringIC1613withinthescatterofoursimulated
assumedbyOhetal.(2015,3.4MpcforDDO50and0.7Mpc BTFrelationbyraisingitsrotationvelocityfrom∼20to∼30
forIC1613).Theerrorsinthedistancesrequiredtoreconcile km/s.TheV-bandshapeofIC1613yields,however,anincli-
thebaryonicmassesofthesegalaxieswithourBTFrelationare nationestimateof37◦.9(Hunteretal.2012).Interestingly,an
extreme.Forinstance,toreducetheinferredmassofDDO50 independentestimateofthecircularvelocityat∼1.4kpcmay
bytheorderofmagnitudeneededtomakeitplausiblyconsistent beobtainedusingthevelocitydispersionandhalf-lightradiusof
withourpredictionwouldimplyadistanceofonly1.1Mpc. thegalaxy(Kirbyetal.2014):thisgives18.7+1.7kms−1,con-
−1.6
sistentwiththemaximumvelocityinferredfromHI(seeopen
bluesymbolinthetop-rightpanelofFig.3).Thisisstillsignif-
4.5.2 Stripping icantlyshortofwhatisneededtobringthisgalaxyintoagree-
mentwithoursimulationpredictions.
ItalsoseemsimprobablethateitherDDO50orIC1613have
The preceding discussion, albeit somewhat inconclusive
undergone any substantial dark matter stripping due to an in-
for DDO 50 and IC 1613, illustrates that inclination error es-
teractionwithamassiveneighbour.Accordingtothecatalogue
timates,aswellasdegeneraciesinthealgorithmsusedtomap
of nearby galaxies compiled by Tully et al. (2009), the near-
thecircularvelocityofagalaxyfrom2Dvelocityfields,should
estbrightergalaxytoDDO50isNGC2403ataseparationof
becarefullyreviewedandcriticallyexamined.Onefinalexam-
373kpc.IC1613issimilarlyisolated,withnogalaxiesbrighter
plemakesthispointquiteclear:NGC3738isalsoanextreme
thanitselfcloserthanM33ataseparationof449kpc.
BTFoutlier7,butontheoppositesideoftherelationshownin
Fig.1.Thisisacasewheretherotationspeedistwiceashighas
expectedforitsbaryonicmassanditcouldevenbehigher,since
4.5.3 Inclinationeffects
itsrotationcurveappearstostillberisingattheoutermostmea-
Oftheeffectsconsideredinthissection,theestimatesofthein- suredpoint.Takenatfacevalue,thiswouldimplyanextremely
clinationsofDDO50andIC1613areperhapstheleastsecure, low galaxy formation efficiency (f ∼ 1%, see Fig. 2), per-
eff
althoughtheerrorsnecessarytobringthegalaxiesintoagree- haps signalling unusually efficient feedback or environmental
mentwithourpredictedefficienciesarenotsmall. effects.Oraninclinationerror.NGC3738isanearlyface-on
The mean inclination of DDO 50 (also known as Holm- galaxy(i∼22◦.6,seeOhetal.2015),whereinclinationcorrec-
berg II) derived by the tilted-ring analysis of Oh et al. (2015) tionsareextreme:shoulditstrueinclinationbe∼ 20◦ higher,
is49◦.7±6◦.0,arelativelyhighvalueconsistentwiththatin- thisgalaxywouldbewellwithinthescatterofoursimulation
ferredbyBureau&Carignan(2002)fromindependent,lower- predictions.
resolutiondata,andwiththe∼ 47◦ inclinationestimatedfrom Ifinclinationerrorscontributesubstantiallytothescatterat
theshapeofthegalaxyintheV-band(Hunteretal.2012).The thefaint-endoftheBTFrelation,theycouldpotentiallyexplain
true inclination would need to be of order 20◦ to match our the large dispersion in dwarf galaxy rotation speeds at fixed
simulationresults,implyingacorrectionoforder∼30◦,much baryonic mass, reconciling observations with ΛCDM predic-
largerthanthequoteduncertainty.Suchalowinclination(and tions.Wehastentoaddthatwehavenotdemonstratedthistobe
hence much larger rotation velocities) has been argued for by thecase.Wemerelywishtonotethatthisdoesnotseemimplau-
Gentileetal.(2012,seealsoSa´nchez-Salcedoetal.2014)after siblegiventheverylargestructuralandkinematicirregularities
reanalyzingthedataforDDO50presentedbyOhetal.(2011). seeninmanydwarfgalaxies,andthusmeritsthoroughinvesti-
TheGentileetal.analysisfocusesonthelowellipticityofthe gationbeforedecidingthat”missingdarkmattergalaxies”in-
outerregionsoftheHIdisk,andwasmotivatedbyanattemptto validateourstandardstructureformationparadigm.Morespec-
reconcileDDO50withthepredictionsofModifiedNewtonian ulatively,onealsowonderswhetherasimilarkindofunrecog-
Dynamics(MOND). nized(orunderestimated)systematiceffectmightnotbeatthe
More recent evaluation of the same data by Oh et al. rootofthegreatdiversityintheshapeofDM-dominateddwarf
(2015),however,appearstoconfirmtheoriginalinclinationes- galaxyrotationcurveshighlightedbyOmanetal.(2015).This
timate, although some oddities remain. These are clearly il- wouldofferasimplesolutiontoanumberofvexingproblems
lustrated by the ‘disk-halo decomposition’ analysis shown in that have so far defied explanation within the current ΛCDM
fig.A.15ofthelatterreference.Note,forexample,thedecreas- paradigm.
ingimportanceofthedarkmatterwithincreasingradius,are-
sult that runs counter the established trend for most galaxies.
Indeed, at the outermost radius, where dark matter is usually
mostprominent,thegascontributionaccountsalmostfullyfor
theobservedvelocityandthedarkmattercontributionisnegli-
gible.Theseunusualpropertiescastdoubtsontherobustnessof
thederivedcircularvelocities. 7 NGC3738isthefarthestrightoutlierinFig.1,atMbar = 5.9×
Themeantilted-ringinclinationofIC1613of48◦quoted 108M(cid:12),Vrmotax ∼133kms−1.ItisnotincludedinTable2because
intable1ofOhetal.(2015)couldalsobecontested,especially oftheshortradialextentofitsavailablerotationcurve.
(cid:13)c 0000RAS,MNRAS000,000–000
10 K.A.Omanetal.
5 SUMMARYANDCONCLUSIONS datasuggestthattheirdarkmattercontentandradialdistribu-
tionvaryseeminglyatrandomfromgalaxytogalaxytoanex-
Wehaveanalyzedthebaryonicmassesandcircularvelocitiesof
tent well in excess of theoretical predictions. This schism be-
asampleofgalaxieswithexcellentphotometricdataandhigh-
tweenbaryonsanddarkmatteronthescaleofdwarfsisquite
qualityHIobservationsandcomparedthemwiththeresultsof
unexpectedinΛCDM,especiallygiventhestrongsimilarityex-
recentΛCDMcosmologicalhydrodynamicalsimulationsfrom
pectedinthestructureofcolddarkmatterhaloesandthefact
theAPOSTLEproject.Thesimulationsusedthesamecodede-
thatmostdwarfsarestronglydarkmatterdominated.Nogalaxy
veloped for the EAGLE project, where the subgrid feedback
formationsimulationhasyetbeenabletoreproducethestrong
physicsmoduleshavebeencalibratedtomatchthegalaxystellar
diversityinthestructuralpropertiesofdwarfswhileatthesame
massfunctionandstellarsizes.Thecorrelationbetweenmaxi-
timematchingtheircosmicabundanceasafunctionofmassas
mumcircularvelocityandbaryonicmass(the‘baryonicTully-
wellastheirstellarandgaseouscontent.
Fisher’,orBTFrelation)ofsimulatedgalaxiesreproduceswell
The severity of the problem, together with the apparent
thezero-pointandvelocityscalingofobservedgalaxiesinthe
failureof‘baryonphysics’tosolveitbegsfortheconsideration
range(30,200)kms−1.ThisimpliesthatΛCDMgalaxiesof
of various alternatives, of which we cite two. One is that the
therightsizeandmasscanmatchnaturallythemaintrendsof
diversityreflectssomeintrinsicparticle-physicspropertyofthe
theBTFrelationwithoutfurthertuning.
dark matter. This is the case of ‘self-interacting’ dark matter,
A corollary of this result is that the ‘efficiency of galaxy
where, it has been argued, sizeable dispersion in the inner re-
formation’,definedasthefractionofbaryonswithinthevirial
gionsofdarkmatterhaloesofgivenmassmayresultfromscat-
radius that can cool and condense at the centre of a halo to
terintheirassemblyhistory(see,e.g.,Kaplinghatetal.2015,
formagalaxy,isasmoothfunctionofhalomassthatdecreases
andreferencestherein).Nodetailedsimulationsofthisprocess
steeplytowardlow-masshaloes.Suchpredicteddecreaseisnot
are available yet on dwarf galaxy scales, but it is certainly a
apparentintheobservedrelation,wherethescatterappearsto
possibilitythatneedstobedevelopedfurther.
increase at the low-mass end without a significant drop in the
A second alternative concerns systematic uncertainties
mean efficiency. Indeed, a number of outliers from the simu-
and/or degeneracies in the data modeling. As we discuss in
lated relation are clearly present below 40–50 km s−1 which
§4.5.3, some of the worst BTF outliers are galaxies where
donotappeartobetheresultofinferiordata,butratherobjects
there are reasonable grounds for disputing the inclination es-
whosebaryoniccontentandcircularvelocityprofilesaregen-
timatesthatresultfromapplicationofthe‘tilted-ring’model.If
uinelydistinctfromthesimulationpredictions.
suchdatamodelingissueswerewidespread,especiallyindwarf
Particularlypuzzlingaresystemswhosebaryonicmasses galaxies,thenitmighthelptoexplainthelargeand,apparently,
are much higher than expected from their circular velocities. random variations in the inferred mass profiles of dwarfs. An
Takenatfacevalue,thesegalaxiesareeithersiteswheregalaxy overhaulofthedataanalysistechniques,especiallyifvalidated
formation has proceeded with extraordinarily high efficiency throughapplicationtothevelocityfieldsofsimulatedgalaxies,
(up to nearly 100%), or where the estimated circular veloci- wouldbewelcome.Althoughitremainstobeseenwhetherthe
tiesunderestimatesubstantiallythecharacteristicvelocityofthe ‘missing dark matter’ problem points to ‘missing physics’ or
surroundinghalo.Noknownmechanisminthesimulationscan ‘modelmisses’,wearehopefulthatthepuzzleitraiseswillbe
accountforsuchhighgalaxyformationefficiencies,sowepre- profitablyusedtohelpguidefuturedevelopmentsinourunder-
fertocharacterizethediscrepancyasadeficitofmass(‘missing standingofdwarfgalaxyformation.
dark matter’) in the inner regions of the haloes that surround
thesedwarfgalaxies.
The problem outlined above has implications for other
small scale problems in cosmology. ‘Missing dark matter’ is
reminiscentoftheinnermassdeficitthatcharacterizes‘cored’
ACKNOWLEDGEMENTS
galaxies with slowly-rising rotation curves, but applies to the
wholeluminousgalaxyandbeyondratherthanjusttoitsinner We thank S.-H. Oh, E. de Blok, C. Brook and J. Adams for
regions. This implies that it cannot be explained by ‘baryon- datacontributions.ThisworkwassupportedbytheScienceand
induced’ cores in the dark matter: we show this explicitly Technology Facilities Council (grant number ST/F001166/1).
bycomparingtheaforementionedoutlierswithsimulationsof CSF acknowledges ERC Advanced Grant 267291 ‘COSMI-
galaxieswithcores.Noneofthosesimulationsareabletoex- WAY’ and JFN a Leverhulme Visiting Professor grant held
plainthispuzzle. at the Institute for Computational Cosmology, Durham Uni-
More intriguingly, evidence for a ‘core’ inferred from versity. This work used the DiRAC Data Centric system at
slowly-rising rotation curves does not seem to correlate with Durham University, operated by the Institute for Computa-
evidencefor‘missingdarkmatter’inferredfromanomalously- tional Cosmology on behalf of the STFC DiRAC HPC Fa-
high galaxy formation efficiencies: galaxies with and without cility (www.dirac.ac.uk). This equipment was funded by BIS
obviouscoresexhibitmissingdarkmatter,andviceversa.Miss- National E-infrastructure capital grant ST/K00042X/1, STFC
ing dark matter is also directly related to the ‘too-big-to-fail capital grant ST/H008519/1, and STFC DiRAC Operations
problem’(Boylan-Kolchinetal.2012;Garrison-Kimmeletal. grant ST/K003267/1 and Durham University. DiRAC is part
2014;Papastergisetal.2015),sincebothhighlightthefactthat oftheNationalE-Infrastructure.Thisresearchhasmadeuseof
somegalaxiesseemtoinhabithaloesfarlessmassivethanex- NASA’sAstrophysicsDataSystem.Thisresearchhasmadeuse
pected. oftheNASA/IPACExtragalacticDatabase(NED)whichisop-
Thepuzzleswedescribeaboveareanothermanifestation eratedbytheJetPropulsionLaboratory,CaliforniaInstituteof
ofthesurprisingdiversityinthemassprofilesofdwarfgalax- Technology,undercontractwiththeNationalAeronauticsand
ieshighlightedbyOmanetal.(2015).Takenatfacevalue,the SpaceAdministration.
(cid:13)c 0000RAS,MNRAS000,000–000