Enhanced Mass-to-Light Ratios in UCDs through Tidal Interaction with the Centre of the Host Galaxy

0.79 MB·English

by  M. Fellhauer

Mon.Not.R.Astron.Soc.000,1–8(2005) Printed5February2008 (MNLATEXstylefilev2.2)
Enhanced Mass-to-Light Ratios in UCDs through Tidal Interaction
with the Centre of the Host Galaxy
M. Fellhauer1,2,3 ⋆ and P. Kroupa1,2 †
1ArgelanderInstituteforAstronomy,UniversityBonn,AufdemHu¨gel71,53121Bonn
6 2TheRhineStellar-DynamicalNetwork
0 3InstituteofAstronomy,UniversityofCambridge,MadingleyRoad,CambridgeCB30HA
0
2

n 5February2008
a
J

6 ABSTRACT
1 Arecentstudyofultra-compactdwarfgalaxies(UCDs)intheVirgoclusterrevealedthatsome
ofthemshowfaintenvelopesandhavemeasuredmass-to-lightratiosof5andlarger,which

1 cannotbeexplainedbysimplepopulationsynthesismodels.Itisbelievedthatthisprovesthat
v
someof the UCDsmustpossess a darkmatter haloandmay thereforebe strippednucleiof
0
dwarfellipticalsratherthanmergedstarclustercomplexes.
3
Using an efficient N-body method we investigate if a close passage of a UCD through
3
the centralregionof the host galaxyis able to enhancethe measured mass-to-lightratio by
1
0 tidal forces leaving the satellite slightly out of virial equilibrium and thereby leading to an
6 overestimationofitsvirialmass.
0 We find this to be possible and discuss the general problem of measuring dynamical
/ massesforobjectsthatareprobablyinteractingwiththeirhosts.
h
p Keywords: galaxies:dwarfs–galaxies:interactions–galaxies:kinematicsanddynamics–
-
o methods:N-bodysimulations
r
t
s
a
:
v 1 INTRODUCTION thatonlythe’naked’nucleusremains.(III)Theycouldbeamalga-
i matedyoungmassivestarclustersformedinastarclustercomplex
X Haseganetal. (2005) investigated ultra-compact dwarf galaxies
duringthestar-burstcausedbythetidalperturbationandpossible
r (UCDs) around M87, the central galaxy of the Virgo cluster. By
a disruptionofagas-richgalaxy(Fellhauer&Kroupa2002,2005).
measuring the surface brightness profiles and assessing the pro-
This scenario is well-established theoretically and was first pro-
jectedvelocitydispersionoftheobjectstheyconcludedthatsome
posedbyKroupa(1998).Itmusthavebeenprofusivelyactivedur-
UCDs of their sample have mass-to-light ratios of the order 5–
ingtheearlyhierarchicalstructureformationepochwhengas-rich
9. Furthermore, they find that some of the UCDs show faint en-
substructuresmergedtothepresent-daymajorgalaxies.
velopes.ThissupportsthenotionthattheseUCDsmaybestripped
Itisstillunder debate whether theUCDs,whichfillthegap
nucleiofdwarfellipticals.
betweenglobularclustersanddwarfgalaxies,followthefundamen-
UCDs were first discovered by Hilker (1998);
talplane(effectiveradius/velocitydispersion–totalluminosity)
Hilker,Infante&Richtler (1999) during a study of globular
relationforglobular clustersorfordwarf galaxies(Haseganetal.
clustersanddwarfgalaxiesaroundthecentralgalaxyintheFornax
2005;Evstigneeva,Gregg&Drinkwater2005).While,intheM –
cluster. These objects are compact with effective radii of about V
15–25 pc and a hundred to several hundred pc in extension, and σ0-plane(seee.g.Haseganetal.2005,theirFig.7),theyliecloser
theyaremassivewithmassesofafew106uptoafew107M⊙. totheglobularclusters,theirrelationseemstoratherfollowtheone
ofdwarfgalaxies.Furthermoretheyoccupy exactlythespacebe-
ThereareseveraltheoriesabouttheoriginofUCDs:(I)They
tweendwarfellipticalsandtheirnuclei.Thisseemstopointtofor-
couldbethemostluminousendofthedistributionfunctionofvery
mationtheory(II).Butthesurfacebrightnessprofilesofthebright
massive globular clusters (Hilkeretal. 1999; Mieskeetal. 2002;
UCDsinFornaxaremuchmoreextended(i.e.largereffectiveradii)
Dirschetal. 2003). (II) They could be the remnants of stripped
comparedwithnucleiofdEs(DeProprisetal.2005).
dwarf ellipticals (Bekki,Couch&Drinkwater 2001; Bekkietal.
2003; DeProprisetal. 2005). In this ’threshing’ scenario a nu- Onthe other hand, Marastonetal.(2004) found aninterme-
cleated dwarf elliptical looses its envelope and most of its dark diate age object (W3, age 300–500 Myr) in the merger remnant
matter content due to tidal interaction with the host galaxy, such galaxy NGC 7252. The mass (M = 8·107 M⊙), size (reff =
17.5 pc, and velocity dispersion of 45 kms−1) strongly suggest
thisobjecttobeaUCDratherthanaglobularcluster.Theageof
⋆ [email protected] this object, which corresponds to the time elapsed since the ma-
† [email protected] jorinteraction,unambiguouslyshowsthatthisobjectcannotbea
2 M. Fellhauerand P.Kroupa
Table1.Tableofourinitial modelparameters. Thecolumnsdenotetheinitial massofour
model (Mpl = Mini), the scale length (Plummer radius, Rpl; analytical & measured as
describedinSect.3),thecharacteristiccrossingtime(Tcr),thecentralprojected(line-of-sight)
velocitydispersion(σ0,p;analytical&measuredasdescribedinSect.3),andthescalingfactor
(A)tocomputethevirialmass(seeEq.11).
Mass[M⊙] Rpl[pc] measured Tcr[Myr] σ0,p[kms−1] measured A
107 25 23.7 3.69 15.92 16.20 1608
107 50 46.6 10.43 11.25 11.71 1565
107 100 94.6 29.50 7.96 8.43 1487
107 250 221.0 116.61 5.03 6.30 1140
108 25 25.2 1.17 50.33 50.2 1573
108 50 47.4 3.30 35.59 36.8 1558
108 100 92.8 9.33 25.16 26.9 1489
108 250 213.0 36.88 15.92 19.91 1184
strippednucleusofadwarfelliptical.Adwarfellipticalcannotbe mericalsimulationsweintendtofindoutwhichsetsoforbitsallow
stripped in a time interval of only 500 Myr. Fellhauer&Kroupa anenhancedmass-to-lightratio,i.e.howclosetheUCDhastoap-
(2005) showed that W3 could be the merger object of a massive proachtothecentreofitshostgalaxy,forwhichwechoosethepa-
starclustercomplexwhichwasformedduringtheinteraction.The rametersofM87toaccountfortheUCDswithhighmass-to-light
subsequentmergingofstarclustersformsanobjectwithproperties ratiosfoundaroundthecentralgalaxyofVirgo.
similartothoseofW3.Theevolutionofthesimulatedsupercluster
showsthatittransformsintoaUCDsuchasthosefoundinFornax
(Hilkeretal.1999;Phillippsetal.2001),Abell1689(Mieskeetal.
2004), and Virgo (Haseganetal. 2005; Evstigneevaetal. 2005).
2 SETUP
Moreover,Fellhauer&Kroupa(2005)showedthat,duetoitshigh
mass, the object was able to retain an envelope of bound stars Wemodeltheparentgalaxyasananalyticalpotential becauseon
which initially were expelled from the individual clusters during onesinglepassagedynamical frictionforadwarfgalaxyofmass
themergerprocess.Thus,anenvelopearoundaUCDisnotaproof M 6 108 M⊙ affectstheorbittoatmost2–3percent,estimated
ofitscosmological originasadwarfelliptical.Stillthepuzzleof usingChandrasekhar’sformula(Chandrasekhar1943)asdescribed
high mass-to-light ratiosof some of the UCDsin Virgoremains. inPortegiesZwart&McMillan(2002).Wealsolookforonlyone
Thesemass-to-lightratios(5–9)arefoundfortheUCDslyingclos- centralpassagebecauseunboundstarsdispersealongtheorbitand
esttothehostgalaxy.Thissuggeststhatdeviationsfromvirialequi- arelostatsubsequentpassages.Someofthemmightstillbearound
libriummayplayarole. theobjectafterthesecondorthirdcentralpassagebutdefinitelynot
fordozensoforbits.
Thereasoningisthatdwarfgalaxiesareonradialratherthan
Asamodelfortheanalyticalpotentialwechoosetheparam-
circularorbits,iftheUCDsformedasstar-clustercomplexesduring
eters for M87, the central galaxy in the Virgo cluster, consisting
themergingofmajorgas-richsubstructures.Thisallowsthesatel-
ofaNFW-profileforthedarkhalo,aHernquistprofile(H)forthe
litestopassclosetothegalacticcentre.Tidalforcesinthecentral
visiblematter(stars)andacentralsuper-massiveblackhole(BH)
regionofthehostgalaxyareratherstrong.Hence,thedwarfobject
(McLaughlin 1999; Vesperinietal. 2003; DiMatteoetal. 2003).
loosesstarsandsubsequentlydepartsfromvirialequilibrium.Some
Thedensityprofileofthehostgalaxyis
oftheloststars(starswhicharenolongerboundtotheobject)do
notimmediatelyleavetheobjectoritsvicinitybutdisperseslowly
ρtot(r) = ρNFW(r)+ρH(r)
alongtheorbit.Thus,aline-of-sightvelocitydispersionmeasure-
ment may be contaminated by these unbound stars which inflate = ρ0,NFWrs,NFW + MHrs,H , (1)
thevelocitydispersion.Furthermore,thegravitationalshockofthe r 1+ r 2 2πr(rs,H+r)3
central passage leads to an expansion of the dwarf galaxy which (cid:16) rs,NFW(cid:17)
islaterreversedagain.Butstillthisexpansion throughtidalheat- withthefollowingparameters,
ingmayresultinameasurableincreaseofthecoreradiusoncethe
dwarfobjectisagainoutsidethehostgalaxy.Bothoftheseeffects ρ0,NFW = 3.17·10−4M⊙/pc3, (2)
mayleadtoanoverestimationofthemeasureddynamicalmassre- rs,NFW = 560kpc, (3)
sultinginahighermass-to-lightratio.Theseeffectsarenotnewto MH = 8.1·1011M⊙, (4)
theastronomicalcommunityandarestudiedintensivelybyvarious
rs,H = 5.1kpc, (5)
authors (e.g. (Kroupa 1997) for dwarf spheroidals, (Mayeretal.
2001,2002)fordwarfdiscsanddwarfspheroidalsor(Bekkietal. MBH = 3·109M⊙. (6)
2003)fordwarfellipticals).Withthispaperwewanttoextendthese
Theaboveparametersdenotefromtoptobottomthecharacteristic
studiesontomassive(comparedtoglobularclusters)andcompact
densityandthescale-lengthoftheNFW-profile,thetotalmassand
(comparedtootherdwarfgalaxies)objectslikeUCDs.
thescale-lengthoftheHernquist-profileandfinallythemassofthe
It isdefinitely clear that these effects must be very strong if centralsuper-massiveblackhole.
anobjectcomesclosetothegalacticcentre.Butontheotherhand WemodeltheUCDasaPlummer-sphere(Plummer1911)in
theseveryclosepassagesmaybehighlyunlikely.Bymeansofnu- the numerical realisation described by Aarseth,Henon&Wielen
EnhancedM/L-ratiosinUCDs 3
3 RESULTS
Table2.Listofminimumdistancesandthecorrespondingtangential ve-
locitiesatthestartofthesimulation.
Wecarriedoutaparametersurveyof76simulationscoveringdif-
ferent dwarf galaxy objects and different orbits. The parameter
Dmin[pc] vtan[kms−1] rangeisshowninTables1and2.Foreachparametersetonesim-
0 0.0 ulationovertwocentralpassagesiscarriedout.Forthedetermina-
50 6.0 tionofourresultswelookatthesatellitewhenitreachesapogalac-
100 10.9 ticonagainafterthefirstcentralpassage.
150 15.9
250 25.4
500 48.1 3.1 Theanalyticalmethod
1000 89.3
1500 126.0 Thesurface density profileof the satelliteis fittedby aPlummer
2000 158.9 profileoftheform
r2 −2
Σ(r) = Σ0(cid:18)1+ R2 (cid:19) , (8)
pl
byapplyinganon-linearleast-squaresMarquardt-Levenbergalgo-
rithm.Fromthisprocedure wetakethefittedPlummerradiusfor
ourdeterminationofthevirialmass.ItcanbeshownthatthePlum-
(1974),
mer radius exactly coincides with the half-light (projected half-
ρpl(r) = 43πMRp3l (cid:18)1+ Rr22 (cid:19)−5/2, (7) massF)urardthiuersmoofraePwluemdmeteerrmspihneeret.he line-of-sight velocity disper-
pl pl sionprofile.Incaseswhereitispossible,i.e.theprofileisnottoo
contaminated by unbound stars, weagain fitthe Plummer profile
withvarying scale-lengths, Rpl,andinitialmasses,Mpl,because fortheline-of-sightvelocitydispersion,
DeProprisetal.(2005)foundaPlummer-profiletofitfouroutof
fiveUCDsintheFornaxclusterquitewell.Furthermore,thePlum- r2 −1/4
mer model is analytically simple and the Plummer radius is not σp(r) = σ0,p(cid:18)1+ R2 (cid:19) . (9)
pl
onlythescale-lengthofthemodelbutalsoitshalf-lightradius(the
projectedradiusfromwithinwhichhalfofthelightoftheobjectis Theprojectedvelocitydispersion,aswellasthesurfaceden-
emitted). sity,ismeasuredalongallthreeCartesiancoordinatesinlogarith-
micallyspaced,concentricringscentredontheobject.Forthemea-
The masses of UCDs range between several million M⊙ up
toseveraltensofmillions.Sowechooseforourmodels107 and surementallstarswithinacertaindistanceRmax infrontandbe-
108M⊙asinitialmasses(Mpl =Mini).Wevarytheinitialscale- hindthecentreoftheobjectaretakenintoaccount.Theprocedure
isdone along all threeCartesian axes and wetake the arithmetic
lengthofourmodelstobeRpl =25,50,100and250pctodeter-
mean value (i.e. a mean profile), because we do not know which
minetheinfluenceoftheconcentrationoftheobjects.Thecut-off
orientationourobjectshavewithrespecttotheobserver.Therefore
radius(Rlim;theradiuswherewetruncatethePlummerdistribu-
effects may be very strong measuring along the trajectory of the
tionof our object) of allour modelswas kept constant at 500 pc
object but almost not visible in the perpendicular direction. Any
which is larger than the initial tidal radius. A detailed list of our
randomdirectionislikelytoyieldanintermediateresult.
modelparameterscanbefoundinTable1.ThePlummerspheres
are modelled using 106 particles. The object is set-up and inte- ForthesurfacedensitywealwaysfitaPlummerprofileevenif
theobjectiscompletelydestroyedanddoesnotfollowaPlummer
gratedinisolationuntilequilibrium,asmeasuredbytheconstancy
distributionatall.Butinmostofourmodelstheremainingobjectis
ofthe90%Lagrangianradius,isreached(Kroupa1997).
stillfairlywellrepresentedbyaPlummerprofileevenifitisonthe
TheUCDmodelisthenplacedatadistanceof10kpctothe
waytocompletedestruction.Incaseswherewearenotabletofit
centreofthehostgalaxywithnoradialvelocity.Thismeansthatthe
thevelocitydispersionprofilewithaPlummerprofile(seee.g.first
effectofthecentralpassageisthemostharmfulpossiblebecause
panel of Fig. 3) we take an average of all measured line-of-sight
it isthe slowest possible. Thefaster the passage would be (ifthe
velocitydispersionvalueswithintheinnermost10pcinprojected
satellitewastostartfurtherout)thelesstidalinfluencethecentral
radiustodeterminethecentralline-of-sightvelocitydispersion.
passagewouldhave.NoUCDisfoundcloserthan10kpcfromthe
We now determine the virial mass taking the formula from
centreofitshostandthereforeitactsasaminimumapogalacticon,
Haseganetal. (2005) which is based on the theoretical work of
whichhasthestrongesttidaleffectpossible.Tovarytheminimum
King(1966),
distance (perigalacticon) we give our models different tangential
velocitieswhicharelistedinTab.2.Weassumetheproblemtobe 9 ν
sphericallysymmetric,soweareabletoplacethetrajectoryofour Mvir = 2πG αp Rcσ02,p, (10)
model inthe x-y-planeof our simulation area without restricting
theproblem. whereRcisthecoreradiusandσ0,pisthecentralvalueofthepro-
jectedvelocitydispersion.Theparametersν,α,andparedepen-
We use the particle-mesh code SUPERBOX to carry out the
dent onthekindof Kingmodel one wantstofit.Becauseweare
simulations. SUPERBOXhashigh-resolutionsub-gridswhichstay
using Plummer spheres we accumulate these parameters together
focusedonthecoreofthedwarfobjectwhileitismovingthrough
withtheconstantsintoonesingleparameterA,whichwedetermine
the host galaxy. The resolution of the innermost grid contain-
fortheisolatedPlummerspherebeforewestartthesimulation,
ing the core is 3 pc. For a detailed description of the code see
Fellhaueretal.(2000). Mvir = ARplσ02,p, (11)
4 M. Fellhauerand P.Kroupa
Figure1.Theratiobetweenvirialandboundmass(Mvir/Mb)forourob- Figure2.Parameterspaceofoursimulations;PlottedarethePlummerra-
jects,measuredatt = 60Myr,thepointwheretheobjectisagainmost diusofourmodels,Rpl,againsttheclosestdistancetothecentreofthehost
distanttothecentreofthehostgalaxy,againsttheclosestdistancefromthe galaxy,Dmin.CapitalD(online:red)denotesthesatellitegetscompletely
centreofthehost(Dmin).Firstpanel:Objectswithinitialmassof107M⊙. dissolvedduringthefirstpassage.Smalld(online:magenta)denotessatel-
Secondpanel:Objectswithinitialmassof108M⊙.Tri-pointedstars(on- liteswhichdonotsurvivethenextcentralpassage.Smallsdenotessatellites
line: black) denote objects with initial Plummer radii of Rpl = 25 pc, whichsurviveandformboundobjectsevenafterthenextcentralpassage.
crosses(online:red)haveRpl = 50pc,five-pointedstars(online:green) CapitalEmarkssimulationswheretheM/M-ratioisenhancedifthecentral
haveRpl=100pc,andsix-pointedstars(online:blue)Rpl=250pc. valuesaredirectlymeasured.Smallemarkssimulationswhichonlyshow
enhancedM/M-ratiosiftheobservationalmethodisapplied(seemaintext
forexplanation). Surviving satellites withenhanced M/M-ratios areplot-
wherethevaluesofthescalingfactor AcanbefoundinTable1. tedgreenonline.Finally,nmarkssimulationswhichshownoenhancement
As one can see these values are lower for higher masses and in- measuredwitheithermethod(online:blue).Firstpanelisforobjectswith
creaseforlargerscale-lengths.NeverthelessweusethesameAde- initialmassof107M⊙,secondpanelfor108M⊙.
terminedfortheisolatedmodelforallfinalmodelsstemmingfrom
thisinitialmodel,evenifthemass-lossissignificant.Thismaylead
toaslightunderestimationofthefinalvirialmass. mostbacktovirialequilibriumagainiftheyarenotonthewayto
OntheotherhandSUPERBOXcalculatesthenumberofbound completedissolution.
particles(energybelowzero)ateachtime-step.Thereforeweknow Theresultsshowclearlythatonlyobjectswhicharenotcom-
therealboundmassMb. pactand/orhavealowmasscanbeinfluencedenoughbyonecen-
With these two masses we can determine a virial-mass-to- tralpassagetoenhancetheM/Mtoaccountforthehighmass-to-
bound-massratio(Mvir/MborshortM/M)whichcanthenbemul- lightratiosfoundinUCDs.Butthesesatelliteswillalsonotsurvive
tiplied by a ’normal’ mass-to-light ratio for a population of stars thenextcentralpassageorhavenotsurvivedthefirstoneatall.
withthedeterminedageandmetallicityandwithoutdarkmatterto The best representation of real UCDs is the model with an
obtainthedynamicallymeasuredM/L-ratio. initialmassof107M⊙andaninitialPlummerradiusof25pc.The
ThisM/M-ratio isplotted inFig. 1, when thesatelliteshave resultsforthismodelareshownastri-pointedstarsinthefirstpanel
reachedtheirapogalacticaagain.Atthispointthesatellitesareal- ofFig.1andthelowestlineinthefirstpanelofFig.2.Theresults
EnhancedM/L-ratiosinUCDs 5
Figure3.Line-of-sightvelocitydispersionprofilesandtheGaussianfitvalues forthreeofoursatellites. Three-,four-andfivepointedstarsdenotethe
line-of-sightvelocitydispersionvaluesmeasuredinconcentricringsaroundthesatellitealongthex-,yandz-axis,respectively.Filledsquares(online:red)
arethemeanvaluesofalldirections.Opensymbols(online:magenta)ontherightdenotethecentralline-of-sightvelocitydispersionvaluesderivedwiththe
observationalmethod(seeFig.5).Firstpanel:Thisobjectgetscompletelydissolvedandshowsanenhancementofthevelocitydispersionineithermethod.
ButthisdestroyedsatellitecannotaccountfortheUCDsinVirgo(seeFig.4).Secondpanel:Objectwhichshowsanenhancementonlyifthecentralvelocity
dispersionisderivedwiththeobservational method.Theopensymbolsdenotingtheobservationalvaluesinthex-andy-directionareclearlyabovethe
’real’centralvalue.Third:Simulationofaverymassivesatellitewhichshowsnoclearenhancementinbothmethods.
Figure4.ContourplotsofthethreemodelsofFig.3intheorbitalplane(x-y-plane).Thecentreofthehostgalaxyisat0–0kpc.Theorbitoftheobject
isplottedasthethick(online:green)line.Contourshavemagnitudospacing(assumedM/L = 1.0M⊙/L⊙)andtheoutermostcontourcorrespondsto
28magarcsec−2(thetwobrightestcontoursineachpanelareplottedredonline).Almostfilledblackareasdonotdenotehighsurfacebrightnessbutareas
withveryfaintcontributions (atthegivenresolution thebrightness fluctuates frompixeltopixelatthelowestlevel). Firstpanel: Thisobject isclearly
dissolved;itshowsnocoreanymoreandisoutofvirialequilibrium.Second:Survivingobjectwhichshowsfainttidaltailsalongtheorbitwhichenhance
themeasuredvelocitydispersion.Third:Thisobjectshowsonlyafewstarswhichareunboundandspread(blackareas).Thesmallfractionofthesestars
arenotabletoenhancethevelocitydispersion.
show clearly that either the satellite gets completely dissolved if terminethevelocitydispersionofamarginallyresolvedobjectisto
Dminiscloserthan50–100pcorshowsnodeviationinM/Matall placeaslitontheobjectandobtainaspectrum.Fromthisspectral
(Fig.2). informationone chooses oneor twospectral linesandfitsatem-
In Fig. 2 we distinguish the models according to their sur- platespectrumconvolvedwiththeinstrumentalline-widthfunction
vival of the passage and if they show enhanced M/M-ratios. The andaGaussianvelocitydistribution.ThisGaussianvelocitydistri-
panelsshowclearlythatonlydissolvedoralmostdissolvedobjects butionmeasurestheline-of-sightvelocitydispersionofthewhole
showenhanced M/M-ratios.Allsurvivingobjectsshownodevia- object.Basedonassumedtheoreticalmodelsthisvalueisthencor-
tionfromvirialequilibrium. rectedtothecentralline-of-sightvelocitydispersion.Inthecaseof
the simple Plummer model one has to multiply the result for the
wholeobjectbyafactorof1.25.Thus,thecentralvelocitydisper-
3.2 The’observational’method sionis
The results in Sect. 3.1 are based on the exact knowledge of the
theoretical central line-of-sight velocity dispersion. Observers on σpl = 3πGMpl, (12)
theotherhanddonothavethisinformation.Theusualwaytode- 0,p r 64Rpl
6 M. Fellhauerand P.Kroupa
Figure5.SamesimulationsasinFig.3.Theplotsshowthevelocitydistributionsalongthex-axis.Histogram(online:black)arethedata-points.Solidline
(online:red)isthesingleGaussianfit,dottedlines(online:green)arethethreeGaussianstocorrectforfastandslowunboundparticlesinfrontandbehind
theobjectandthedashedline(online:magenta)isthesumofthesethreeGaussians,whichisanexcellentreproductionofthedataandisbarelyvisible
bybeingmaskedbythedata.ThethreeGaussiansalwaysfitthedatabest.WhileinthefirstpaneltheobjectisalmostdissolvedandtheGaussiansofthe
unboundparticlesarestrongerthantheboundone(resultinginaM/M-ratioof20inxand5iny-direction),thesecondpanelshowsaboundobjectwith
enhancedM/M-ratioduetothesmallcontributionoftheunboundparticles(M/M-ratiois2.5and2.2).Inthelastpanelthecontributionoftheunbound
particlesistoolowtoenhancetheM/M-ratio(M/M=1.2inbothdirectionsandwithintheuncertaintiesofthemeasurement).
while the projected velocity dispersion integrated over the whole
Table3.Centralvelocity dispersionalongthex-axisderivedbydifferent
Plummersphereis methods. Shown are the values of the same three simulations plotted in
∞ Figs. 3 to 5 now labelled ’dissolved’, ’enhanced’ and ’massive’, respec-
1
σpl = 2πr′Σ(r′)σ (r′)dr′, tively.Therowsshowthedifferentvaluesofthecentralvelocitydispersion.
obs,p Mpl Z0 p Firstrowisthedirectmeasurementofthecentral dispersion,’single’de-
notesthecentraldispersionderivedfromthefitofasingleGaussiantothe
= 3πGMpl, (13) dataand’triple(c)’denotesthevalueofafitusingthreeGaussianswhere
r 100Rpl thecentralone(c)isusedtocomputethevelocitydispersionofthebound
sothat object.
σpl
0,p = 1.25. (14) [km/s] dissolved enhanced massive
σpl
obs,p trueactual 10.6±3.1 9.49±0.05 35.7±0.2
σpl denotesthecentralline-of-sightvelocitydispersionandσpl single 44.6±0.3 15.90±0.30 38.4±0.1
th0e,pweighted line-of-sight velocity dispersion integrated oveorbtsh,pe triple(c) 13.3±0.1 12.35±0.04 35.3±0.3
wholeobject.
AsonecanseeinFig.3itcanbeacrucialpointhowstrongly
ameasurementoftheline-of-sightvelocitydispersioniscontami- thelinebecausewedonotaccountforthechangeoftheconstant
natedbyunboundstars.Theobservationalvaluescanhighlyover- Awhichshouldincreaseforlowermasses.Butinanyrandomori-
estimatetherealcentralvalue.Unboundstarshaveadifferentve- entationoftheobjectwithrespecttotheobservertheeffectofthe
locitydistributionthantheboundones.Theyareeithertravellingin enhancedM/M-ratioshouldatleastbepartlyvisible.
frontorbehindtheobject(seenalongthetrajectory;thisisshownin Summing up our results we state the following: Satellites
Fig.4)andarefasterorslower.Butthevelocitydistributionofthese whichareout of virialequilibrium, i.e.inthestateofdissolution
starswhicharestilllocatedinthevicinityof theobject andstem show enhanced virial masses and therefore the real mass content
fromonecentralpassage,peakoneithersideoftheGaussiandistri- isoverestimated. Figure 6 shows in the first panel the M/M-ratio
butionoftheboundstars,leadingtoaneffectivebroadeningofthe plotted against the ratio of final to initial bound mass of the ob-
measured velocitydistribution.FittingjustasingleGaussianwill ject. The dividing dashed line separates objects which have lost
thereforeleadtoanenhancedmeasuredvelocitydispersionandan morethan50percentoftheirmassduringthecentralpassageand
overestimationofthecentralvelocitydispersionvalueofthesatel- arealreadydissolvedorarenotlikelytosurvivethenextpassage,
lite.ThisisdemonstratedinFig.5wherethevelocitydistribution from objects which are stable for several more passages through
ofallstarsisshowntogetherwiththebestfittingsingleGaussian the centre. While on the left side the derived M/M-ratios (using
andthefittingcurveofatripleGaussianwhichtakestheunbound the observational method) can climb up to very high values, the
starsintoaccount.Themeasuredvaluesforthecentralline-of-sight stableobjectsshowonlyslightenhancementsoftheratioifatall.
velocitydispersionareshowninTable3. But in the second panel one already sees that even if the object
Clearlythiseffectisstrongestintheplaneoftheorbitandis itself is in virial equilibrium (Mvir/Mb ≈ 1.0) there are satel-
not visible perpendicular to it. This can be seen in Fig. 3 where liteswhichshowabroadeningofthevelocitydistributionleading
thesymbolforthez−axis-valueinallthreepanelsshowsthesame toanenhancedmass-ratioifmeasuredtheobservationalway.The
value as the direct measurement. Actually for strongly disturbed thirdpanelfinallyshowsanenlargementofthisareaandonefinds
systems(i.e.highmass-loss)thevaluesinthez-directionarebelow M/M-ratiosoverestimatedbyuptoafactoroffive.Survivingob-
EnhancedM/L-ratiosinUCDs 7
Figure6.Summaryoftheresultsderivedusingtheobservationalmethod(Sect.3.2).Mobsdenotesthevirialmassderivedbytheobservationalmethod,
i.e.fittingasingleGaussiantothevelocitydistribution,Mbdenotestherealboundmassoftheobject,MiniistheinitialboundmassandMviristhevirial
massderivedbytheanalyticalmethod(Sect.3.1).Measurementsalongthex-axisarethree-pointedstars(online:red),alongthey-axisarecrosses(online:
green)andz-axismeasurementsarerepresentedbyfive-pointedstars(online:blue).SimulationswithinitialparameterssimilartotheUCDsinVirgoare
representedbyfilledsymbols.Firstpanelshowsthederivedmass-ratioasafunctionofthefinal/initialbound-mass-ratio.Satelliteswithfinalmasseslarger
than50percentoftheinitialmass(rightofthedashedline)aredeemedstableagainstimmediatetidaldestruction.Objectsleftofthedividinglineareout
ofequilibriumandthereforehavetoshowenhancedM/M-ratios.Buttherearealsodatapointswhicharelargerthanoneontherightofthedividingline.
SecondpanelshowsthesameresultsbutnowtheobservationalM/M-ratioisplottedagainsttheanalyticalratio.Alldata-pointsexceptthemeasurements
perpendiculartotheorbitareabovethe’analytical’method(dashedlineshowsthelinewherethevaluesoftheobservationalmethodareequaltothedirect
method).z−valuesarebelowthedashedlinebecausewedonotcorrecttheconstantAforobjectswithhighmass-loss.Aclumpofdata-pointsisvisible
aroundMvir/Mb=1whichpointstooverestimatedmasses.Thethirdpanelfinallyisamagnificationofthisregion.Oneclearlyseesthattheobservational
methodcanleadtooverestimatesofthetruemassbyafactorofuptofive.Horizontallineshowsaratioof1withdashedlinesdenotinganerrorrangeof
20percent.
jectswhichshowanenhancementintheirM/M-ratio,ifmeasured wefoldourdistributionwiththeline-widthoftheobservationsof
withthisobservational method,arealreadymarkedinFig.2with theVirgo-UCDsandaddnoisetomimicthesameS/N-ratioasin
a small ’e’. As one can see there is a range of critical distances the observations. There is no deviation from Gaussiantity visible
(D > 100 pc and D < 1 kpc) to the centre of the host galaxy anymore.
whereanUCDliketheonesfoundinVirgocouldshowanoveres-
timatedmass-to-lightratio.
4 DISCUSSION&CONCLUSION
Wehaveshownwithourmodelsthatdwarfsatellitesaroundagiant
3.3 Observability
ellipticalgalaxylikeM87canhaveanenhancedmass-to-lightratio
In the previous section we claimed that with the ’observational’ duetoclosepassagestothecentreofthehostgalaxy.Whilevery
method themass-to-light ratiosofUCDscould beoverestimated, closepassagesleadtothedestructionofthesatellitethereareorbits
becausethevelocitydistributionisnotGaussiananymorebut’con- which allow for enough ’damage’ to the satellite to enhance the
taminated’byunbound starsaroundtheobject.Inthissectionwe mass-ratio(measuredthesamewayanobserverwoulddo)without
show thatthereisalmostnochanceforanobserver todetectthis completelydestroyingtheobject.
’non-Gaussianity’ofthevelocitydistribution. Theamountofdestructionislargerifthesatelliteislessmas-
When measuring a spectrum of a distant object, observers siveandlessconcentrated.Butthelossofabout20percentofthe
havetodealwithtwomajorshortcomings.Firstthereistheintrin- initial mass is enough to have the object surviving several more
sicline-widthproducedmainlybytheinstrument.State-of-the-art closepassages andtomimicanenhanced mass-to-lightratio.For
instrumentslikeUVESorFlamescanreducethisline-widthdown modelscomparabletotheUCDsinVirgoandFornaxtherangeof
toabout2kms−1.ButtheobservationsoftheUCDsinVirgowere possibleminimumdistancesduringcentralpassagesisabout100to
madewithaninstrumentalline-widthofabout25kms−1. 1000pc.Allpassagesclosertothecentreleadtocompletedestruc-
Thesecondeffectanobserverhastotakeintoaccountisnoise tionandallpassagesfurtherawayshownomeasurableeffectatall,
inthespectrum. except for a mass-loss of the order of a few per cent. We there-
TakingthevelocitydistributionfromtheenhancedM/M-ratio foreconcludethattheenhancedM/L-ratiosmeasuredfortheVirgo
simulationwefolditwithaGaussianofthewidthσitomimicthe UCDsbyHaseganetal.(2005)maynotbeduetodarkmatter.
instrumentalline-widthanddetermineatwhichline-widththe’fea- Amoregeneralresultofourstudyisthediscrepancybetween
tures’ofourdistributionarewashedout.Thishappensataninstru- the derived virial masses if one has access to the correct proper-
mentalline-widthofσi = 7.5kms−1 (asshowninFig.7).Then tiesofthesatellitescomparedtothevirialmassesderivedtheway
wetakethebeststate-of-the-artline-widthofσi = 2kms−1 and anobserverwouldmeasure.Whileverymassiveobjectswhichare
addrandomwhitenoisetothedistributionuntilagainthe’features’ almostunaffectedbytidalforcesshowthesameresultswithinthe
arealmostinvisibleagain.Thishappensalreadyatasignal-to-noise uncertaintiesonehastobecarefulifobjectsarelessmassiveand
ratioof20(seeFig.7lowerleftpanel).InthefinalpanelofFig.7 aresurroundedbyacloudoftidallystrippedstars.Thesestarsare
8 M. Fellhauerand P.Kroupa
measuringvelocitydispersionsoffaintanddistantobjects.
Acknowledgements:
MF thankfully announces financial support through DFG-grant
KR1635/5-1andPPARC.WealsowanttothankM.HilkerandT.
Richtlerforusefulcommentsregardinghowtomimicobservations.
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