Top-heavy IMFs in ultra compact dwarf galaxies?

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by  Jörg Dabringhausen

**VolumeTitle**
ASPConferenceSeries,Vol.**VolumeNumber**
**Author**
(cid:13)c**CopyrightYear**AstronomicalSocietyofthePacific
Top-heavy IMFsinultra-compact dwarfgalaxies?
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1 J.Dabringhausen1,andP.Kroupa1
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2 1Argelander-Institut fu¨rAstrophysik, AufdemHu¨gel71,53121Bonn,Germany

n
a
Abstract. Ultra compact dwarf galaxies (UCDs) are dense stellar systems at the
J
borderbetweenmassivestar-clustersandsmallgalaxies. Theironaveragehighoptical
8 mass-to-light(M/L)ratiocannotbeexplainedbystellarpopulationswiththecanonical
1
stellarinitialmassfunction(IMF),whileitisdoubtfulthatnon-baryonicdarkmattercan

accumulateenoughonthescalesofUCDsforinfluencingtheirdynamicssignificantly.
]
O UCDs in the Virgogalaxycluster apparentlyalso have an over-abundanceof neutron
stars,stronglysuggestingatop-heavyIMF,whichwouldexplainbothfindings. Thisis
C
becauseatop-heavyIMFcanprovidetheunseenmassthroughanabundanceofstellar
.
h remnants. The suggested variation of the IMF can be understood if UCDs represent
p a case of rapid star-formation in an extremely dense environment. While top-heavy
- IMFs imply a much heavier mass-loss shortly after the formationof a stellar system,
o
thisprocessdoesnotnecessarilydissolvetheUCDs. Theirformationwithatop-heavy
r
t IMFwouldthereforenotcontradicttheirexistence.
s
a
[

1
v 1. Introduction
2
1 Ultra-compactdwarfgalaxies(UCDs)arestellarsystemswithV-bandluminositiesbe-
9
tween 106 and some 107 Solar luminosities, but half-light radii of only about 50 pc
3
. or less. Most confirmed UCDs are found in nearby galaxies with rich globular clus-
1
ter systems, such as NGC 5128 (Centaurus A), or nearby galaxy clusters, such as the
0
Fornaxcluster andtheVirgocluster. Evenwiththemostpowerfultelescopes available
2
1 at present, UCDs are barely resolved at those distances. Their true nature has there-
: fore only been revealed quite recently by estimating their distance from their redshift
v
i (Hilkeretal.1999;Drinkwateretal.2000). Beforethat, UCDswereeither interpreted
X
asbackground galaxiesorforegroundstars,becauseoftheirappearance asbrightpoint
r sources in most observations. Colours and in some cases also line indices suggest
a
intermediate- tohighagesforUCDs.
DuetothedistanceandthecompactnessofUCDs,itisdifficulttogetinformation
ontheirinternalstucture. TheobserveddensityprofilesofUCDscarryastrongimprint
ofthepoint-spreadfunctionandthespectrumofaUCDisobtainedinobservationsthat
coveragoodfractionofthewholeUCD.Estimatesoftheircentralvelocitydispersions,
theirglobalvelocitydispersions,theircoreradiiortheirhalf-lightradiithereforerequire
involved modelling oftheirdensity profiles,asdoneby,e.g. Hilkeretal.(2007).
A comprehensive list of globular clusters (GCs) and UCDs for which such mod-
ellinghasbeendone,leadingalsotoestimatesfortheirdynamical masses, M,isfound
in Mieskeetal. (2008). The half-light radii (r ) and dynamical mass-to-light (M/L)
h
ratiosoftheobjectsinthatlistareshowninFig.1. According tothisfigure,UCDsare
indistinguishablefromGCsataaluminosityof≈ 106L ,correspondingtoadynamical
⊙
1
2 Dabringhausen&Kroupa
100 10
GCs UCDs
GCs UCDs
o
adius ht rati
alf-light r 10 ass-to-lig
h m
1
1
0.1 1 10 100
0.1 1 10 100
dynamical mass [ 106 solar units ] dynamical mass [ 106 solar units ]
Figure1. Half-lightradiir (leftpanel)anddynamicalM/Lratios(rightpanel)of
h
GCsandUCDs,usingthecompilationofsuchobjectsbyMieskeetal.(2008). The
dashedverticallinesatadynamicalmass, M, of2×106M marka definitionthat
⊙
seperatesGCsfromUCDs,becauseobjectswithmasseshigherthan2×106M show
⊙
acleartendencytohigherr andM/Lratios,eventhoughGCsareindistinguishable
h
fromUCDsatM ≈2×106M . Notethatalsothetwo-bodyrelaxationtimesbecome
⊙
longerthanaHubbletimeM ≈2×106M ,i.e. GCsarerelaxedstellarsystemsand
⊙
UCDsarenot.
massof2×106 M (seealsoMieskeetal.2008). Thishasledsomeauthorstoconsider
⊙
UCDsas the most massive GCs(e.g. Mieskeetal. 2002) or to re-interpret ω Cen, the
most massive GC of the Milky Way, as a low-mass UCD. However, the average r )
h
andaverage dynamical(M/L)ratiosofobjectswith M ? 2×106 M increase system-
⊙
atically with M, whereas this is not the case for objects with M < 2 ×106 M . This
⊙
motivates to define the objects with M ≥ 2×106M as UCDs, in order to distinguish
⊙
themfrom’classical’ GCs.
TheoriginofUCDsisstilladebated issue. However,numerical experiments pre-
dictthattheyoungandmassivestar-cluster complexesobservedininteracting galaxies
evolveintoobjectsverymuchlikeaUCD.Thetimerequired forthisisonlyafew100
Myr (Kroupa 1998; Fellhauer&Kroupa 2002). Supporting evidence for this notion is
provided bythe discovery ofW3,anobject whichwasprobably created bythe forma-
tionofthemerger-remnant galaxyNGC7252andwhichisaUCDintermsofitsmass
anditshalf-light radius(Marastonetal.2004;Fellhauer&Kroupa2005).
2. TheM/LratiosofUCDs
Even if GCs and UCDshave the same origin, their differences in M and r imply that
h
they have evolved differently, which has implications on the difference of the average
M/L ratio between GCs and UCDs. The key to understanding this is that each stellar
system issubject totwokindsofevolution: Stellarevolution anddynamical evolution.
Stellar evolution implies that the brightest stars evolve first and thereby become dark
remnants, leading to an increase of the M/L ratio of a stellar system, unless they are
ejected. Dynamical evolution, on the other hand, tends to lower the M/L ratio of a
Top-heavyIMFsinUCDs 3
stellar system, as it leads to a preferential loss of low-mass stars, which have a high
M/L ratio (Baumgardt&Makino 2003). It is evident that the time-scale on which
stellar evolution changes the properties of a stellar system is independent of M and
r of the stellar system, but this is not the case for dynamical evolution. A measure
h
forwhether astellar system isaffected bydynamical evolution isitsmedian two-body
relaxation time,t ,whichcanbeestimatedusingequation (2-63)fromSpitzer(1987).
rh
Ift islongerthantheageofthesystem,itcanbeconsideredunaffectedbydynamical
rh
evolution.
Using their present-day parameters, it turns out that GCs usually have t very
rh
much below a Hubble time, whereas UCDs have t of the order of a Hubble time or
rh
longer (Dabringhausen etal. 2008). The M/L ratios of GCs are thereby determined
by an interplay of their stellar evolution as well as their dynamical evolution (see
Kruijssen&Mieske 2009). UCDs are, in comparison, rather simple systems, as the
evolution of their M/L ratio is essentially determined by stellar evolution. Therefore,
their M/L ratio has only increased after their star formation came to an end. Thus, as
the stellar populations of GCs and UCDs generally are of the same age (with the ex-
ception ofW3),theaverage M/LratioofUCDsbeinghigherthanthatofGCsappears
natural.
As UCDs are thus nearly unaffected by dynamical evolution, their present-day
stellar population should be determined by their IMF and their star formation history.
A good initial assumption for the IMF of UCDs is the canonical IMF, since this IMF
is found to be consistent with all currently resolved stellar populations (Kroupa 2001,
2008). However, the observed dynamical M/L ratios of a clear majority of UCDs ex-
ceed the predictions for a single-age, single-metallicity stellar population (SSP) with
the canonical IMF (see e.g Dabringhausen etal. 2008 or Mieskeetal. 2008). This is
eventhecaseifthestellarpopulations ofallUCDsareassumedtobe13GyroldSSPs,
i.e. if all stars in UCDswere nearly as old as the Universe. Note that for a given IMF
andmetallicity,nostellarpopulationcanhaveahigher M/Lratiothanthisoldestpossi-
blestellarpopulation. AlsonotethatUCDsmayconsistofmultiplestellarpopulations,
as is the case with ω Cen, and that the sub-populations in them may have different
metallicities, aswellasdifferent ages. However, themetallicity ofaUCDisestimated
fromitsintegratedlight,leadingtosomevaluethatshouldberepresentativeforallstars
intheUCD.
3. Top-heavyIMFsinUCDs?
3.1. Evidenceforatop-heavyIMFinUCDsfromtheir M/Lratios
Thesurprisinglyhigh M/L-ratioofUCDsimpliessomeunseenmassinthem. Thiscan-
not be the non-baryonic dark matter that is often invoked to explain, e.g., the rotation
curvesofspiralgalaxiesorthe M/L-ratioofgalaxyclusters. Thisisbecause structures
ofcolddarkmatterhavebeen showntoobeyauniversal density profile (Navarroetal.
1997; Bullocketal. 2001). This density profile implies that only a very small amount
ofcolddarkmattergatherswithinthequitecompact UCDsandtheir M/L-ratiossould
thereforebeindistinguishable fromtheonesofpurestellarpopulations (Murray2009).
Theinternal accelerations ofUCDsare also abovethe transition between pure Newto-
niandynamicsandMOND,whichisamodificationoftheclassicaltheoryofgravitation
4 Dabringhausen&Kroupa
4 2.4 _
α (M)
3.5 2.2 3
F
s IM 3 ope 2
s sl 1.8
ma 2.5 canonical IMF MF
gh- 2 s I 1.6
hi as 1.4
e of 1.15 gh-m 1.2
op hi 1
sl 0.5
0.8
0
0.5 1 1.5 2 2.5 2 10 100
6
observed over canonical M/L ratio dynamical mass [ 10 solar units ]
Figure2. Thehigh-massIMFslopesofUCDs(cf. Eq.1), assuggestedbytheir
M/L ratio as a functionof their observedovertheir predictedM/L ratio, assuming
the canonical IMF (left panel), and as a function of their dynamical mass (right
panel). Forthecurveintheleftpanel,itisassumedthat20percentoftheNSsare
retained,whichseemstobeareasonableassumption(seeSection3.1). Theaverage
valuefortheM/L ratioofUCDs overthe predictionforthe canonicalIMF(dotted
verticalline)withits 1-σvariance(shadedarea)suggeststhattheIMFinUCDs is
considerably top-heavy, even though the assumtion that they all are 13 Gyr old is
veryconservative.
inthelimitofweakgravitational fields(Milgrom 1983). Thus,alsoMONDcannotex-
plainthe M/L-ratiosofUCDs.
Excluding those possiblities leads totheassumption ofanIMFthat isnot univer-
sal, but varying, as an explanation for the high M/L ratios of UCDs. This notion of a
varying IMFdoes notneccesarily contradict theresults byKroupa (2001), asthese re-
sultswereobtainedconsideringresolvedstellarpopulationsintheMilkyWay;i.e. from
stellarpopulationsinourimmediateneighbourhood. UCDs,however,mayhaveformed
inmuchstronger starbursts thantheones thathave occured intheLocalGroup. These
extremeinitialconditions wouldthenbewhatdistinguishes UCDsfromtheopenclus-
tersandGCsintheMilkyWay. Ithasindeedbeenshownthatextremelyhighdensities
wouldleadtostellarcollisions, whichwouldaltertheIMF(Bonnell&Bate2002).
AvaryingIMFcanbeformulated as
ξ(m ) = kkm−αi, (1)
∗ i ∗
with
m
∗
α = 1.3, 0.1 ≤ < 0.5,
1
M
⊙
m
∗
α = 2.3, 0.5 ≤ < 1,
2
M
⊙
m
α ∈ R, 1 ≤ ∗ ≤ 150,
3
M
⊙
where m is the initial stellar mass, the factors k ensure that the IMF is continuous
∗ i
wherethepowerchangesandkisanormalisationconstant(Kroupa2008). ξ(m )equals
∗
Top-heavyIMFsinUCDs 5
2.4
nt ] 2.2
e e
r c 10 op 2
XB [ pe s IMF sl 11..68
M as
L m
with 1 gh- 1.4
s hi 1.2
C encounter rate
G
GCs with LMXB 1
0.01 0.1 1 10 100 2 4 6 10 20 40 60
dynamical mass [ 106 solar units ] dynamical mass [ 106 solar units ]
Figure3. Comparisonoftheencounterratetothe fractionofGCs andUCDs in
the Virgo galaxy cluster containing an LMXB (left panel) and the high-mass IMF
slopethatcanexplaintheabundanceofLMXBsinUCDs(rightpanel). Thex-axes
in both panelshave been re-scaled, so that they show the average dynamicalmass
correspondingto a certain luminosity instead of the luminosity itself. This allows
easy comparisonsbetween this figure and Figs. 1 and 2. The solid line in the left
panelshowstheencounterrateundertheassumptionthattheIMFinGCsandUCDs
is canonical. By assuming that the IMF in GCs is canonical, but given by Eq. 1
inUCDs, theencounterrateinUCDscanbychangedintotheoneindicatedbythe
dashedline. Thisrequiresacertaindependencyofthehigh-massIMFslopeonthe
massoftheUCDs. Thisfunctionisshownintherightpanel.Itisremarkablysimilar
to the one shown in the right panel of Fig. 2, even though it was derived entirely
differently.
0 if m < 0.1M or m > 150M , where 150M arguably is the upper mass-limit
∗ ⊙ ∗ ⊙ ⊙
for stars (e.g. Weidner&Kroupa 2004; Oey&Clarke 2005). Eq. 1 is the canonical
IMF for α = 2.3. For α < 2.3, the IMF is top-heavy, implying more intermediate-
3 3
mass stars and in particular more high-mass stars. In old stellar populations like the
UCDs,these stars have evolved into whitedwarfs andneutron stars (NSs)andthereby
contribute to the mass of the total stellar population but hardly to its luminosity. We
note that the IMF-variation proposed here is not the only one that can explain high
M/Lratios. AlternativescenarioshavebeendiscussedbyMieske&Kroupa(2008)and
Murray (2009). However, the advantage of the top-heavy IMF used here is that it can
explainseveralproperties ofUCDsatthesametime.
Given Eq. 1, it is possible to translate some observed M/L ratio divided by the
M/L-ratio predicted by a SSP-model into some value of α that corresponds to this
3
ratiobyprovidingtheappropriate amountofdarkmatterinformofWDsandNSs(see
left panel of Fig. 2). Note that the fraction of NSs that actually remain bound to the
UCDis an important issue when calculating α . Given the large peculiar velocities of
3
many pulsars (Lyne&Lorimer 1994), which are thought to be NSs, a lot of NSsmay
escape from the UCDs. On the other hand, it is observationally confirmed that GCs
andespeciallyUCDsdohaveapopulationNSs(visibleaslow-massX-raybinaries,cf.
Section3.2).
6 Dabringhausen&Kroupa
Theright panelofFig.1showsthatthere isarelation between the M/LofUCDs
andtheirdynamicalmass. Combiningthisinformationwiththeα impliedbyacertain
3
M/Lratio (left panel of Fig. 2) leads to arelation between the average α of UCDsas
3
a function of their mass (see Dabringhausen etal. 2009 for details). This relation, as
showninfig.5inDabringhausen etal.(2009),isplottedintherightpanelofFig.2.
3.2. Evidenceforatop-heavyIMFinUCDsfromtheirlow-massX-raybinaries
If UCDs have indeed formed with the IMF formulated in Eq. 1 and the IMF is top-
heavy (i.e. α < 2.3), they should have a large population of NSs. Thus, compared to
3
thecasewiththecanonicalIMF,UCDswouldalsohaveahighernumberofclosebinary
systems ofalow-massstar andaNS.Insuch systems, theNScan accrete matterfrom
its companion star and thereby become a bright X-ray source; a so-called low-mass
X-ray binary (LMXB). The NSs in LMXBs thereby become observable, even though
theyremaininvisible intheoptical.
Observationsshowthatthedenseststellarsystemsalsohavethehighestlikelihood
to harbour a bright LMXB. This suggests that they are formed by three-body encoun-
ters;especiallyencountersbetweenastarandabinary. Thisisbecausetheseencounters
tighten binary systems if the binary entering the interaction was already tight (Heggie
1975). Itthusappears thatstellardynamics isthemostimportant andperhaps eventhe
onlyimportantfactorfortheformationofLMXBs(Verbunt2003;Sivakoffetal.2007;
Peacocketal.2010).
ThenumberofencountersrelevantforthecreationofLMXBs,i.e. encountersthat
involve starsandNSs,canbewrittenas
n n r3
Γ ∝ ns s c, (2)
σ
wheren isthenumberdensityofNSs,n isthenumberdensityofotherstars,r isthe
ns s c
coreradiusandσisthevelocitydispersion (Verbunt2003). Ratherthanmeasuring the
volumeofthestellarsystem byr3,weuser3. Thisisaquantity thatisavailable forall
c h
GCs and UCDs plotted in Fig. 1 and arguably only changes the proportionality factor
inEq.2.
Interesting for the purpose here is to find the average encounter rate of GCs and
UCDs as a function of their luminosity, Γ(L). This quantity can be compared to the
fraction of GCs and UCDs in certain luminosity-bins that actually have an LMXB, P,
whichisanestimatorfortheprobability tofindanLMXBinasystemintheaccording
luminosity range(andacorresponding massrange). Observational dataonwhichfrac-
tion of GCs and UCDs in the Virgo-galaxy cluster have a bright LMXB can be found
inSivakoffetal.(2007). IfthestellarmassfunctioninGCsisthesameasinUCDs,the
shape of Γ only depends on how the average r of GCs and UCDs changes with their
h
luminosity, which is a function that can be derived using the data plotted in Fig. 1. A
non-changing stellar mass function for all GCs does indeed suggest that the observed
riseofPmatchestheincreaseofΓexpectedforthem. However, PstillrisesforUCDs,
whereasthecalculatedΓdropssteeplyiftheyallhadthesamestellarmassfunction(cf.
leftpanelofFig.3).
This leads to the alternative assumption that the mass function of UCDs does
change with their luminosity. An IMF that becomes increasingly top-heavy with the
luminosity of UCDs implies that n in Eq. 2 changes with luminosity. Consequently,
s
Top-heavyIMFsinUCDs 7
also σ increases, because more NSsimply a higher total mass. Assuming the popula-
tionofNSsandotherstarsinGCsisgivenaccording tothecanonicalIMFandthatthe
IMF in UCDs is given by Eq. 1, Γ in UCDs can be calculated such that it is not only
proportional to PinGCs,butalsoinUCDs. Thisimpliesthatthatthehigh-mass slope
oftheIMFchanges withtheirluminosity (mass), asshownintheright panelofFig.3.
Comparing the right panel of Fig. 3 with the right panel of Fig. 2 shows a qualitative
agreement of how the high-mass IMF slope of UCDs would have to change in order
to explain their M/L ratios and how it would have to change in order to explain the
abundance ofLMXBsinthem(Dabringhausen &Kroupa,inpreparation).
4. ImplicationsfortheinitalconditionsinUCDs
Thedynamicalevolutionofyoungstellarsystemsisstronglyinfluencedbyrapidmass-
loss, especially if their IMF is top-heavy. This is because of the strong radiation of
massivestars, whichcanquicklyremovealltheinterstellar mediumthatisnotusedup
instarformation. MassivestarsevolvingtoSNcaninprinciplereplenishtheinterstellar
medium, but provide at thesame timeso much energy that also this gas ismore likely
to leave the stellar system, even if it is as massive a UCD. Stellar evolution can thus
lead to further mass-loss that becomes more rapid and more severe with the the top-
heaviness of the IMF. This mass-loss would lead to a strong expansion or even to a
dissolutionofthestellarsystem. TheextremeIMFssuggestedforUCDsinSections3.1
and 3.2 therefore imply that UCDs must have been extremely compact if they are to
surviveuntiltoday withtheobserved densities (Dabringhausen etal.2010). Assuming
that their stellar populations formed on a time-scale of a few Myr (as implied by the
formation scenario suggested in Section 1), the more massive UCDs may have had
initialmassesofsome108 M whilehavinginitialhalf-light radiiofonlyafewparsec.
⊙
A top-heavy IMF would then imply a population of the order of 106 O-stars with a
total luminosity of the order of 1011L . If this is the case, UCDs should be bright
⊙
point-likesources,identifiablebyaspectrumthatisconsistentwithastellarpopulation
(Pflamm-Altenburg, Dabringhausen &Kroupa,inpreparation).
Thehighinitialdensityimpliedbytheinitialmassandinitialradiuscouldexplain
why the IMF was top-heavy in the first place. At such densities, collisions between
proto-stars become common, which may cause a deviation from the canonical IMF
(Bonnell&Bate2002).
5. Conclusion
The observed dynamical M/Lratios of UCDsand the number of LMXBsin them can
beusedtoconstrain their IMF.Theirhigh M/Lratios areastrong argument foranon-
canonicalIMFinUCDs,buttheM/Lratiosaloneleaveanumberofpossibilitiesonhow
theIMFcouldvarywiththemassoftheUCDs. However,UCDsapparentlyalsohavea
richer population ofNSsthan GCs. Thiscannot beexplained bysimplyassuming that
moreNSsremainboundtoUCDs,whileGCsandUCDsbothformedwiththecanonical
IMF,because in this case the M/Lratios of UCDsshould not tend to exceed thevalue
predicted for a canonical IMF. Thus the number of LMXBs in UCDs and the M/L
ratios ofUCDsincombination imply thattheIMFofUCDswastop-heavy, especially
for very high-mass stars. This implies that UCDs would have formed compact and
8 Dabringhausen&Kroupa
with very high densities. Note that the number of LMXBs also give a constraint on
thelow-massIMFinUCDs,becauselow-massstarshavetoberatherfrequent aswell.
Otherwise, LMXBsinUCDswouldberareforalackoflow-masscompanions forthe
NSs(cf. Eq2).
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