New Astronomy 22 (2013) 22–27

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New Astronomy

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Multivariate study of dynamically hot stellar systems: Clues to the originof ultra compact and ultra faint dwarfs

Tanuka Chattopadhyay ⇑, Pradip KarmakarDepartment of Applied Mathematics, Calcutta University, 92 A.P.C. Road, Calcutta 700 009, India

h i g h l i g h t s

" K means cluster analysis is performed for a large data set of hot stellar system." Four significant groups are found." Ultra compact dwarf galaxies are found in two groups." They share properties either with GCs or with nuclei of dE,N.

a r t i c l e i n f o

Article history:Received 23 August 2012Received in revised form 28 November 2012Accepted 6 December 2012Available online 25 December 2012Communicated by G.F. Gilmore

Keywords:Hot stellar systemsData analysisStatistical

1384-1076/$ - see front matter � 2012 Elsevier B.V. Ahttp://dx.doi.org/10.1016/j.newast.2012.12.002

⇑ Corresponding author.E-mail address: tanuka@iucaa.ernet.in (T. Chattop

a b s t r a c t

A multivariate classification has been performed for a large sample of dynamically hot stellar systemscomprising globular clusters to giant ellipticals, in quest of the formation theory of ultra compact dwarfgalaxies (UCDs). For this K means cluster analysis is carried out together with the optimum criterion(Sugar et al., 2003) with respect to three parameters, logarithm of stellar mass, logarithm of effectiveradius and stellar mass to light ratio. The present data set has been taken from Misgeld and Hilker(2011). We found five groups MK1–MK5. These are predominated by giant ellipticals (gEs), faint dwarfellipticals (dEs), globular clusters (GCs), massive compact objects (UCDs and nuclei of dE,Ns) and brightdwarf ellipticals respectively. Almost all UCDs are found either in MK3 or MK4. The fraction is roughly50%–50% between MK3 and MK4. Comparable fraction of UCDs share properties either with normalGCs or with nuclei of dE,N. This adds a quantitative constraint to the long discussed hypothesis that UCDsmay be formed either as massive globular clusters or have an origin similar to nuclei of dwarf galaxies.We finally find that for our clustering test in mass-size-stellar M/L ratios, ultra faint dwarf galaxies areattributed to globular cluster group (MK3) and not to the dwarf galaxy group (MK2). This highlights thatthere is no clear cut morphological distinction between extended star clusters and ultra faint dwarfs.These groups are highly consistent with the groups found in a previous classification for a smaller sampleand completely different set of parameters.

� 2012 Elsevier B.V. All rights reserved.

1. Introduction

Among various dynamically hot stellar systems the most enig-matic class of stellar systems is ultra compact dwarf galaxies(UCDs) since their discovery (Hilker et al., 1999; Drinkwateret al., 2000) in the Fornax cluster. These objects are intermediatebetween globular clusters (GCs) and dwarf ellipticals (dEs) as wellas compact ellipticals (cEs). The dynamical M/L ratios of theseUCDs are on the average about twice as large as those of Galacticglobular clusters at the same metallicity (Dabringhausen et al.,2008; Mieske, 2008; Forbes et al., 2008; Taylor et al., 2010). Thisindicates dark matter (Goerdt et al., 2008) or variation of initial

ll rights reserved.

adhyay).

mass function (IMF) (Dabringhausen et al., 2008; Mieske, 2008)in these small stellar systems.

There are various theories available in the literature for under-standing their physical properties. These are directly related to gal-axy interactions. For example, Fellhauer and Kroupa (2002)suggested that UCDs are the result of coalescence of many youngstar clusters under tidal influence of gas rich galaxy mergers whileothers (Bekki et al., 2001; Goerdt et al., 2008) have suggested thatthey are the remnant nuclei of dwarf galaxies which have lost theirstellar halos due to tidal field of cluster of galaxies. There are alsoother theories in which they are thought to be the luminous exten-sion of GCs (Mieske et al., 2002) or they are modelled to be origi-nated from primordial small scale over densities (Drinkwateret al., 2004). Several attempts have been made to unite old dynam-ically hot stellar systems from GCs, UCDs and dwarf spheroidals

T. Chattopadhyay, P. Karmakar / New Astronomy 22 (2013) 22–27 23

(dSphs) to giant ellipticals (gEs) (Zaritsky et al., 2006; Forbes et al.,2008; Dabringhausen et al., 2008; Misgeld and Hilker, 2011;Chattopadhyay et al., 2012; hereafter C12) to explore the originof UCDs. Most of the studies discussed above are based on twopoint correlations between different projections of the fundamen-tal plane (FP) of galaxies. But a full multivariate approach is bestsuited for uncovering the actual formation history of these poorlyunderstood objects. The present work is based on a large data setconsisting of gEs, dEs, Galactic and extragalactic GCs, nuclei ofdE,Ns, UCDs, dwarf globular transition objects (DGTOs), nuclearstar clusters (NuScs), bulges of Spiral galaxies (Sbul), dwarf galax-ies (dwarfs) and compact ellipticals (cEs) taken from Misgeld andHilker (2011). These objects are classified by multivariate statisti-cal method, K means cluster analysis, presented in Section 3. Thephysical properties of these groups are discussed in connectionto the origin of UCDs in Section 4. Final conclusions are drawn inSection 5.

0 2 4 6 8K

0.2

0.4

0.6

0.8

1.0

J K

Fig. 1. Jump curve for the present data set.

2. Data set

The present data set consists of 694 hot stellar objects coveringa wide range, starting from GCs, UCDs, DGTOs, Sbul, NuScs, dEs, nu-clei of dE,Ns to gEs taken from Misgeld and Hilker (2011) (hereafterMH11). From the original data set we have excluded GCs under ref-erence 14 of MH11 which were taken from Jordán et al. (2009) be-cause these GCs are candidate GCs and all are not confirmed GCs.Also the original data set contains 12,763 GCs of VCC out of13,456 objects i.e. 95% of the data set consists of only one particu-lar type of objects out of ten. In our treatment of multivariate datawe usually assume that the observations are taken from a homoge-neous population with a single mathematical form and a set ofparameters. Even if the distribution is not multivariate normal,we assume a smooth and unimodal distribution. But when the datadeviate from such assumption i.e. the data exhibit a nature of het-erogeneity due to the presence of different type of objects in goodproportion, the need for cluster analysis arrives. So if a large pop-ulation of the data set is occupied by one type of object, the basicneed of cluster analysis becomes irrelevant (Morrison, 1990) as alarge population of the data set will be homogeneous. Cluster anal-ysis will be successful if the underlying population can be consid-ered to be a mixture distribution caused by the presence ofdifferent type of objects in significant proportion. But later theanalysis is also carried out including these GCs to see the changein the results due to any change in the sub sampling. The parame-ters given in MH11 are logarithm of effective radius (logRe), loga-rithm of stellar mass (logMs), logarithm of mass surface densityaveraged over projected effective radius (logSe) and absolute mag-nitude in the V band (Mv ). However these are not all independentlymeasured quantities. Rather, some of them are strongly correlatede.g. stellar mass and absolute magnitude in V band. Also surfacedensity Se ¼ Ms=ð2pR2

e Þ (MH11) is calculated from two indepen-dent quantities Ms and Re. So we have considered logMs and logRe

among the four parameters above and computed stellar mass tolight ratio ðM=LV Þ by dividing Ms by luminosity in V band ðLV Þand LV is computed from MV , taking MV ;� ¼ 4:83. Finally threeparameters logMs; logRe and ðM=LV Þ have been considered for clus-ter analysis. Among the 694 objects of the present data set, 109 ob-jects are common to a comparatively smaller data set (389) of hotstellar objects considered in a previous work (C12). There we con-sidered a completely different set of parameters for classificationwhich were absolute magnitude in the K band (Mk), logarithm ofthe central velocity dispersion (logðr0Þ), logarithm of half light ra-dius (rh), virial mass to light ratio in K band (MVir=LK ), metallicity(½Fe=H�), visual mass to light ratio (Mv=L), Age etc. As the parameterAge, had large uncertainties it was not considered in the previous

classification but once the groups were identified it was used tostudy the properties of the groups. There we found six groups ofwhich two had three members each. So primarily four groups ofcomparable sizes were of interest. In the present work we haveused a much larger sample and a new set of parameters for classi-fication. But once the groups are identified, the values of all sevenparameters of the common objects are used for further study. Themotivation for the present study is to check the robustness of thegroups found in C12 and to explore any new origin for the forma-tion of UCDs in this connection. The present sample contains moredEs, nuclei of dE,Ns, cEs compared to previous sample and GCs ofLMC, SMC besides those of Milky Way with new objects like NuSc,Sbul etc.

3. Method

By K means clustering technique, K homogeneous groups of ob-jects are found with respect to a specified set of parameters oncethe number of groups i.e. value of K is assumed. For the presentstudy we have used K means partitioning algorithm due to Mac-Queen (1967) and MINITAB package. The details of the methodhave been discussed in lterature (Chattopadhyay and Chattopad-hyay, 2007; Chattopadhyay et al., 2007; Chattopadhyay et al.,2009; Chattopadhyay et al., 2010; Chattopadhyay et al., 2012). Thisalgorithm selects K groups or clusters so that each object mustbelong to any group and each group must contain at least one ob-ject. With this algorithm first the structures of sub populationsare determined for K = 2,3,4 etc. Then using the method ofSugar et al. (2003) optimum value of K is found. The method isas follows. We computed the values of a distance measure dk ¼ð1=pÞminxE½ðxk � ckÞ0ðxk � ckÞ� which is defined as the distance ofthe xk vector from the center ck. The cluster centres ck’s have beenchosen on the basis of group average method. This makes the pro-cess almost robust (Milligan, 1980). Let d̂k is the estimate of dk.Then d̂k versus K gives the distortion curve. Then the jump at K isdefined as Jk ¼ ðd̂k

�p=2 � ^dk�1�p=2Þ where p is the number of param-

eters in the parameter set considered for the cluster analysis (herep = 3). Plotting Jk versus K gives the jump curve (Fig. 1). It is clearfrom Fig. 1 that there is a sharp peak at K = 5. So the optimum valueof K is taken as 5, with respect to the present sample and presentset of parameters.

4. Results and discussions

For the present set of parameters viz. logMs; logRe;M=LV , fivegroups MK1–MK5 are found. The groups are dominated by gEs,

Table 1Average properties of the five groups MK1–MK5 with standard errors.

Parameters MK1 MK2 MK3 MK4 MK5

Members 141 151 218 68 114Common objects with C12 52 0 35 16 6Predominance gEs Faint dEs GCs MCOs Bright dEsGroups of C12 FK1 ⁄ FK6 FK3 FK5Mv (mag) �21.08 ± 0.14 �11.85 ± 0.10 �8.21 ± 0.14 �11.50 ± 0.17 �16.54 ± 0.13logRe(pc) 3.49 ± 0.04 2.73 ± 0.02 0.74 ± 0.03 1.00 ± 0.07 2.94 ± 0.03logSe(M�pc�2) 3.20 ± 0.04 0.75 ± 0.05 2.99 ± 0.10 4.32 ± 0.11 2.35 ± 0.07logMsðM�Þ 10.98 ± 0.07 7.01 ± 0.04 5.26 ± 0.06 7.12 ± 0.07 9.02 ± 0.05M=Lv ðM�=L�Þ 4.21 ± 0.07 2.19 ± 0.02 1.57 ± 0.05 4.05 ± 0.16 3.04 ± 0.06Mk(mag) �24.59 ± 0.13 ⁄ �10.73 ± 0.29 �14.34 ± 0.20 �19.68 ± 0.25lh;kðmagarcsec�2Þ 18.07 ± 0.11 ⁄ 15.28 ± 0.26 14.402 ± 0.37 19.01 ± 0.24

logr0ðkms�1Þ 2.33 ± 0.02 ⁄ 0.91 ± 0.06 1.51 ± 0.03 1.53 ± 0.04

MVir=LkðM�=L�Þ 3.03 ± 0.28 ⁄ 1.29 ± 0.11 2.77 ± 0.44 1.81 ± 0.52½Fe=H�(dex) 0.019 ± 0.02 ⁄ �1.35 ± 0.090 �0.72 ± 0.11 �0.51 ± 0.08Age(Gyr) 5.81 ± 0.30 ⁄ 11.58 ± 0.36 13.26 ± 0.34 2.60 ± 0.75

Table 2Type of objects in each group.

Groups MK1 MK2 MK3 MK4 MK5

Member 141 152 218 69 114gEs 123 1 0 0 28dEs 0 134 0 2 75UCDs 0 3 18 35 0DGTOs 0 1 1 0 3nuclei of dE,Ns 0 1 22 21 1GCs 0 0 152 2 0NuScs 0 1 14 6 1Sbuls 15 0 0 0 2dwarfs 0 11 11 2 0cEs 3 0 0 1 4

Table 3Average properties of the four groups M1–M4 with standard errors.

Parameters M1 M2 M3 M4

Members 189 233 9859 3175Predominance gEs dEs GCs GCsComparable

groups ofTable 1

MK1 MK2 + MK5 MK3 MK4

Mv (mag) �20.17 ± 0.16 �13.06 ± 0.14 �7.63 ± 0.01 �7.39 ± 0.02logRe(pc) 3.36 ± 0.02 2.71 ± 0.03 0.45 ± 0.002 0.41 ± 0.003logSe(M�pc�2) 3.209 ± 0.04 1.31 ± 0.07 3.65 ± 0.006 3.93 ± 0.01logMsðM�Þ 10.60 ± 0.07 7.53 ± 0.06 5.36 ± 0.005 5.55 ± 0.07085M=Lv ðM�=L�Þ 4.04 ± 0.06 2.44 ± 0.04 2.43 ± 0.004 4.65 ± 0.01

Table 4Type of objects in groups M1–M4.

Groups M1 M2 M3 M4

Member 189 233 9859 3175gEs 146 5 0 0dEs 17 194 0 0UCDs 0 9 26 21DGTOs 2 2 1 0nuclei of dE,Ns 0 9 29 7GCs 0 0 9775 3139NuScs 0 2 17 3Sbuls 17 0 0 0dwarfs 0 11 11 2cEs 6 1 0 1

24 T. Chattopadhyay, P. Karmakar / New Astronomy 22 (2013) 22–27

faint dEs, GCs, massive compact objects (MCOs) and bright dEs (viz.Table 1). For these groups the values of other parameters(MK ; logr0;Mvir=LK , [Fe/H], Age) have been included for the 109common objects discussed above. The average properties of allthese five parameters have been computed together with 4 param-eters of MH11 and ðM=LV Þ. These are listed in Table 1. The type ofobjects in each group are shown in Table 2. It is clear from the aver-age properties of Table 1 (present work) and Table 3 of C12 thatMK1, MK3–MK5 can be associated with FK1, FK6, FK3 and FK5 ofC12 respectively, though the number of common objects are verysmall compared to the number of total objects for both the datasets. Surprisingly MK2 having no common objects with the dataset of C12 forms a separate group of objects. In the previous workwe have found 4 groups and here we have found one more groupwhich has no common objects with the previous data set and theremaining groups are similar in nature in terms of their averageproperties especially size and composition when compared thetwo classification schemes. The analysis is also performed includ-ing GCs from Jordán et al. (2009) to see the changes, if any, occurin the results. In the latter one the majority of objects are GCs fromVirgo cluster (not all confirmed) of galaxies. For this data set wehave found 4 groups M1–M4 (Fig. 3). The average properties andtype of objects are listed in Tables 3 and 4 respectively. It is clearfrom the tables that M1 and M3 can be associated with MK1 andMK3 in terms of objects as well as average properties. M2 is thecombination of MK2 and MK5 i.e. all dEs have been classified intoone group. It is clear from Fig. 3 that M2 contains besides brighterdEs a few number of UCDs (9), DGTOs (2) and nuclei of dE,Ns (9)which clearly occupy separate region in the diagram unlike previ-ous clustering. Also GCs of VCC which belong to M3 and M4 havebeen overlapped to a large extent. They are also overlapped in

logSe—logRe plane but in logðM=LV Þ ¼ logMs plane they are com-pletely separated only along ðM=LV Þ parameter (Fig. 4). Objects ofM4 have higher ðM=LV Þ ratio compared to those of M3. For M3GCs the ðM=LV Þ ratio is 2.47 ± 0.004 which is comparable toðM=LV Þ ratio of MK3 GCs (viz 1.5 ± 0.07). For M4 GCs ðM=LV Þ ratiois very high (viz 4.65 ± 0.014). MK4 has only two GCs with higherðM=LV Þ ratio. Though M4 contains majority of GCs it is comparablewith MK4 having similar values of mass to light ratios. Overall weconclude that the resulting clustering appears more finely griddedwhen. various sub samples are of comparable size than with pre-dominance of one particular species. In case of strong underlyingheterogeneity even with such bias the over all grouping is not af-fected to a great extent like the present situation. Finally we cansay that the existence of these 4/5 groups are more or less robustin nature in spite of variability both in the data sets as well as in

-25 -20 -15 -10 -5MV

0

1

2

3

4

logR

e

MK1 : red circleMK2 : blue starMK3 : black squaresMK4 : green plusMK5 : magneta triangle

Fig. 2. logRe versus Mv diagram for the groups found for the present data set.

M1: red circleM2: blue starM3: black squareM4: green plus

-25 -20 -15 -10 -5MV

0

1

2

3

4

logR

e

Fig. 3. logRe versus Mv diagram for the groups M1–M4. About 10,000 GCs fromJordán et al. (2009) are added, to illustrate how clustering results vary whenrelative sample sizes are varied.

2 4 6 8 10 12

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

log(

M/L

V)

logM s

Fig. 4. logðM=LV Þ—logMs diagram for objects in groups M1–M4.The colors andsymbols are same as that of Fig. 3.

12 14 16 18 20μ h,k

-3

-2

-1

logr

h - 2

log

σ0

black line : logrh - 2 log σ 0 = -4.55 +0.205 μ h,k

red line : logrh - 2 log σ 0 = - 7.3 +0.384 μ h,k

Fig. 5. Fundamental plane diagram for the common objects in groups MK1, MK2–MK5. Colors and symbols are same as in Fig. 2.

-2 0 2 4K1

0.0

0.2

0.4

0.6

0.8

1.0

K3

Fig. 6. k3—k1 diagram for the common objects in groups MK1, MK3–MK5. Colorsand symbols are same as in Fig. 2.

T. Chattopadhyay, P. Karmakar / New Astronomy 22 (2013) 22–27 25

the parameters. For both sets, UFDs are associated to the star clus-ter regime. When including the Jordan GCs, massive UCDs are as-signed more preferentially to dwarfs than to star clusters. This isalso clear from the several two point scatter diagrams. For examplein logRe versus Mv diagram (Fig. 2) the objects of the groups MK1,MK3–MK4 occupy similar regions of logrh—MK of C12 (viz. Fig. 4 ofC12) for the groups FK1, FK6, FK3 and FK5 respectively while MK2occupies a different region. Secondly the common objects of MK3–MK5 and those of MK1 lie along two FP (Fig. 5) which arelogrh � 2logr0 ¼ �4:55þ 0:205lh;K and logrh � 2logr0 ¼ �7:3þ0:384lh;K respectively. These two planes correspond torh / r2

0I�0:513e and rh / r2

0I�0:960e , where Ie is the effective luminosity

density. These relations are close to Virial theorem rh / r20I�1

e

ðM=LV Þ�1. The different slopes (0.513 and 0.960) might be referredas the tilt in the Fundamental Plane whose cause is still under de-bate (Fraix-Burnet et al., 2010; Fraix-Burnet et al., 2012). The devi-ation from the I�1

e is very likely due to varying effect of dark matter(varying M=LV ) ratio in case of MK3–MK5 objects. Crossing timescales are in the millions not billions of years such that one expectsmost/all these objects are in Virial equilibrium. The shift in zeropoints of the regression lines for MK3–MK5 and MK1 objects is

due to 10 times larger M=LV ratios for gEs (Dabringhausen et al.,2008).

The k parameters (Bender et al., 1992)(viz. k1; k2; k3) for thecommon objects taken from C12 show (Fig. 6) that the objects of

2 4 6 8 10 12

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

logMs

log(

M/L

v)

MK1:red circleMK2: blue starMK3:black squaresMK3 LMC GCs: black squares with crossMK3 SMC GCs: black squares with plusMK4: green plusMK5: magneta triangle

Fig. 7. logðM=LV Þ—logMs diagram for the objects in groups MK1–MK5. Colors and symbols are same as in Fig. 2. Objects towards very low stellar M/L are young star clusters inLMC (square cross) and SMC (square plus).

0 1 2 3 4

-2

0

2

4

6

logS

e

logRe

Fig. 8. logSe—logRe diagram for the objects in groups MK1–MK5. Colors and symbolsare same as in Fig. 2. Square crosses are for Ultra faint dEs in MK3.

26 T. Chattopadhyay, P. Karmakar / New Astronomy 22 (2013) 22–27

the four groups (MK1, MK3–MK5) occupy different regions ink3—k1 plane which is the edge on view of the FP and the regionsfor the four groups are similar for the groups of C12(viz.Fig. 6 ofC12). To find the position of MK2 corresponding to remaininggroups we have also drawn logðM=LV Þ � logMs diagram which issimilar to k3—k1 (Bender et al., 1992) except here the virial masseshave been replaced by corresponding stellar masses (Fig. 7). Herealso the positions of the five groups are more or less different.

Both the groups MK3 and MK4 contain UCDs and nuclei ofdE,Ns. In addition MK3 contains low metallicity globular clusters(GCs) of LMC, SMC and MW. In MK3, for nuclei of dE,Ns, UCDsand GCs, Se / 1

R1:47e; Se / 1

R1:94e; Se / 1

R2:57e

i.e. the relations are similarfor UCDs and GCs (i.e. steeper) rather than for nuclei of dE,Ns(rather flatter). In MK4, for nuclei of dE,Ns and UCDs the corre-sponding variations are same (viz. Se / 1

R1:2e

). The above featuresindicate that UCDs in MK3 might constitute the high mass tail ofGCs (Mieske et al., 2002) whereas UCDs of MK4 could be formedby mass threshing from nuclei of dE,Ns due to some tidal forces(Goerdt et al., 2008; Bekki et al., 2001).

The above conjectures are also supported by the ðM=LV Þ ratiosfor the UCDs in those groups (viz. 1.788 ± 0.103 in MK3 and4.095 ± 0.24 in MK4). From Table 1 it is clear that objects of MK4have brighter surface brightness than objects in MK3 for same

logRe i.e. objects in MK4 are more massive than those in MK3(MV ¼ �11:5 in MK4, MV ¼ �8:21 in MK3) So from the similaritiesin ðSe;ReÞ variation, high mass to light ratios, brighter surfacebrightness profiles, brighter luminosity and compactness at sameradius it might be speculated that objects in MK4 have strippedtheir envelopes in tidal environment. The GCs in MK3 are massiveGCs (�104M�—105M�) of LMC, SMC and MW. Also the metallicityof the objects in MK4 is higher compared with those in MK3. SoMK3 GCs are low metallicity GCs i.e. they are mainly halo GCs.

In MK2 and MK5 both have dEs and a very few UCDs andDGTOs. For dEs in MK2, Se / 1

R0:9e

and for those in MK5, Se / 1R1:4

e. So

stellar density increases more rapidly for dEs in MK5 than inMK2. This is evident from the average values of logSe in MK5 andMK2 (viz. logSe � 2:35 in MK5; logSe � 0:75 in MK2 respectively).On the other hand DGTOs and UCDs in MK5 and MK2 are differentin all respects. For example DGTOs in MK5 are brighter i.e. moremassive having higher values of mass to light ratios and surfacedensities than UCDs in MK2.

Again it is interesting to note that ultra faint dwarfs (UFDs)(Mv > �8) (viz. Fig. 8) are found along with GCs in MK3 and notin the faint dwarf group MK2. So judging from the three parame-ters mass, size, stellar M=LV , the UFDs could readily be classifiedas extended star clusters rather than small dwarf galaxies. Ofcourse the internal velocity dispersions of the UFDs are quite ele-vated implying lots of dark matter, which is a separate issue.Yet also star clusters in dissolution would be expected to showseemingly elevated dynamical M/L. Detailed simulation of this fea-ture will be interesting to see.

5. Conclusions

In the present work a larger sample of hot stellar objects areclassified with respect to a completely new set of parameters un-like the previous one (C12) but similar groups are found whichestablishes the robustness of the classification. Secondly severalformation channels of UCDs emerge. One is for UCDs in MK3.Low metallicity and less massive UCDs having lower mass to lightratios share the common properties with low metallicity GCs in thehalos of galaxies. On the contrary high metallicity and massiveUCDs having higher mass to light ratios in group MK4 share theirproperties with those of nuclei of dE,Ns. Ultra faint dwarf galaxiescan be classified as extended star clusters rather than dwarfgalaxies.

T. Chattopadhyay, P. Karmakar / New Astronomy 22 (2013) 22–27 27

Acknowledgements

T. C. thanks DST, India for supporting her a Major ResearchGrant. Authors are very much grateful to referee for very importantand useful suggestions in improving the quality of the work to agreat extent.

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