aa r X i v : . [ a s t r o - ph ] F e b THE FLATTENING OF GLOBULAR CLUSTERS
Sidney van den Bergh
Dominion Astrophysical Observatory, Herzberg Institute of Astrophysics, National Research Council ofCanada, 5071 West Saanich Road, Victoria, BC, V9E 2E7, Canada [email protected]
ABSTRACT
In the three nearest luminous galaxies, the Milky Way System, the Andromeda Galaxy andNGC 5128 the brightest globular clusters are rounder than the faintest ones. On the other hand(contrary to some previous results) the flattening of individual LMC clusters is found to be in-dependent of their luminosities. This suggests the possibility that the relationship between theflattening and luminosity of clusters might depend on host galaxy luminosity. No significantdifferences are found between the intrinsic flattening distributions of Galactic old halo, Galac-tic young halo and Galactic bulge/disk clusters. Such a dependence might perhaps have beenexpected if tidal forces (which are largest at small Galactocentric distances) removed angularmomentum from globular clusters. The preliminary conclusion by Norris that clusters with bluehorizontal branches are more flattened than red HB clusters is not confirmed by the larger database that is now available. In other words there is no evidence for the puzzling claimed correlationbetween the flattening and the horizontal branch morphology of Galactic globular clusters.
Subject headings: (Galaxy:) globular clusters: generalgalaxies: star clusters
1. INTRODUCTION ∼ harris/mwgc.dat] and by Mackey & van den Bergh (2005). The obser-vations by Harris et al. (2006) also provide information on the flatteening of globular clusters in the nearbygiant elliptical galaxy NGC 5128. Finally old and new data on the ellipticity of clusters in the MagellanicClouds are combined to re-investigate the dependence of cluster ellipticity on the luminosities and ages ofclusters in the LMC and SMC. This study is facilitated by the fact that the metallicity (and hence thendust content) of the Magellanic Clouds is low, so that the effects of asymmetric foreground absorption canbe neglected.A theoretical discussion of the interpretation of flattening distributions of globular clusters, togetherwith references to the literature on this subject, has been published by Akiyama (1991). He found that 2 –gravothermal contraction makes the inner regions of clusters rounder as they evolve. Furthermore, the outerregions of clusters are expected to become rounder with age due to the stripping of stars by external tidalfields. On the other hand, tidal fields might also be able to stretch clusters and make them more elongated.Finally Goodwin (1997) has pointed out that strong tidal fields might rapidly destroy velocity anisotropiesin initially tri-axial rotating globular clusters. Mergers might produce highly flattened clusters. However,the absence of binary Galactic globular clusters, and the paucity of young binary clusters like h and χ Persei,suggests that this process may not have been an important factor in shaping Galactic star clusters. In thisconnection it is of interest to note that the clusters NGC 6388 and NGC 6441, which might be regarded aspossible merger suspects because they are composed of stellar populations with slightly different ages (Piotto2008), are observed to be almost circular in outline with axial ratios of 0.99 and 0.98, respectively.
2. Flattening and globular cluster luminosity2.1. Flattening of Galactic globular clusters
Following Hubble (1936) the flattening of globular clusters will be defined as ǫ = (a-b)/a , where a and b are the major and minor axes of the cluster. Mackey and van den Bergh list values of ǫ for 94 globular clusters.The flattening values of Galactic globular clusters were derived by White & Shawl (1987) from images inblue light using the Palomar and SRC Sky Surveys. A weakness of this database is that the derived clusterflattening values do not all refer to a standard isophote such as the cluster half-light radius. Mackey and vanden Bergh (2005) list values of ǫ for a total of 94 Galactic globular clusters. Two of these objects, ω Centauri= NGC 5139 and M54 = NGC 6715 are widely regarded as being the stripped cores of now defunct dwarfspheroidals and will therefore be omitted from the present study. Data on the ellipticity of all remainingGalactic globular clusters for which this information is available are plotted in Figure 1. This figure clearlyshows that the faintest Galactic globular clusters are also the flattest ones. Furthermore the data in thefigure strongly hint at the possibility that the most strongly reddened Galactic globular clusters (whichare plotted in red) may appear more flattened than the less reddened Galactic globular clusters (plotted inblue). In the the present analysis are all clusters with A v > A v = 3.1 E(B-V) assumed] have beenexcluded because their apparent flattening might have been affected by patchy foreground absorption. Themost blatant example of this effect is provided by M19 (= NGC 6273), which has A v = 1.27 mag and is theflattest ( ǫ = 0.27) known Galactic globular cluster. It suffers heavy absorption along its eastern edge (vanden Bergh 1982a). M19 is also observed to exhibit strong differential internal reddening (Harris, Racine &deRoux 1976), but according to unpublished observations by Rosino, quoted by Coutts Clement & SawyerHogg (1978), it shows little flattening at infrared wavelengths. A Kolmogorov-Smirnov test shows a 91%probability that Galactic globular clusters with A v > A v < A v < ǫ values, are collected in Table 1. The data in this table, which are plotted in Figure 2, showthat intrinsically faint Galactic globular clusters with M v > -7.0 are flatter than more luminous ones having M v < -7.0. A Kolmogorov-Smirnov test shows that there is only a 3% probability that the luminous andthe faint cluster samples were drawn from the same parent population. This conclusion strengthens and 3 –confirms a similar result by Davoust & Prugniel (1990) who, however, neglected to take into account theeffects of absorption on the apparent flattening of globular clusters. The data in Table 1 show that the flattening of globular clusters in M31 (Barmby et al. 2007) alsodepends on luminosity. Adopting ( m − M ) o = -24.4 and A v = 3.1 E(B-V) one finds that (for objects with A v < M v > -8.0 are more flattened than are the more luminous ones with M v < -8.0. A K-S test shows that there is only a 1.5% probability that the faint and the luminous M31clusters were drawn from the same parent distributions of flattening values. The M31 globular cluster systemtherefore resembles the one surrounding the Milky Way, in which the intrinsically most luminous clustersare also found to be the roundest. A similar result (see Table 1) is also found in the giant elliptical galaxy NGC 5128. Using ǫ measurementsfrom Harris et al. (2006) and M v values given in van den Bergh (2007) one finds that the clusters with Mv > -7.0 are flatter than those with M v < -8.0. [None of these clusters is heavily reddened, so that the observedflattening values will not be greatly affected by patchy foreground absorption.] A Kolmogorov-Smirnov testshows that there is only a 0.1% chance that the flattening distributions of the bright and faint samples ofclusters in NGC 5128 were drawn from the same parent distribution. It is particularly noteworthy that all13 clusters in NGC 5128 with ǫ > M v = -7.5. An obvious caveat about the presentdiscussion of the flattenings of globular clusters in NGC 5128 is that the globulars with M v > -7.0 arevery faint (V ∼ ǫ values may be subject to quite large random errors.Taken at face value the present results for the Galaxy, M31 and NGC 5128 suggest that the faintest globularclusters associated with giant galaxies are intrinsically flatter than are the most luminous globulars associatedwith these objects. It would clearly be important to strengthen and confirm this preliminary conclusion byobtaining flattening data for the globular clusters hosted by other relatively nearby luminous galaxies. Data on the ellipticities of star clusters in the Large Magellanic Cloud have been taken from Geisler& Hodge (1980), Frenk & Fall (1982), Geyer et al. (1983), Zepka & Dottori (1987), Kontizas et al.(1989)and Bhatia & MacGillvray (1989). The averages of the published flattening values for each LMC cluster arelisted in Table 2. Data on the flattenings of 34 clusters in the Small Magellanic Cloud have been published byKontizas et al.(1990). For the SMC the flattening given in Table 3 refers to its value at the cluster half-lightradius. The photometry of the SMC clusters in Table 3 is from van den Bergh (1981). From the agreementbetween independent flattening observations of the same clusters in the LMC it is estimated that the meanerror of dividual estimates of ǫ is ∼ ∼ >
12 than they are for the bright clusters having V < i.e. that whichencloses half of the cluster luminosity in projection. (2) Background subtraction may be a problem for theleast luminous clusters in the densest regions of the Magellanic Clouds. (3) Stochastic effects will affect allattempts to determine the shapes of the isophotes of all clusters, particularly those that are faint or highlyresolved. Since only a single series of observations exists for the flattenings of SMC clusters (Kontizas et al.1990) it is not possible yet to derive an independent estimate for the errors in the quoted ellipticities of SMCclusters.In the LMC cluster age determinations, on a scale from I (very young) to VII (very old), were taken fromSearle et al. (1980). These were supplemented by assignment to age class VII for all of the globular clusters(van den Bergh 2000, p.104) in the LMC. Contrary to a previous result by Fall & Frenk (1984) the data,which are plotted in Figure 3, show no evidence for any correlation between the age class and the flatteningof clusters in the LMC. Also given in Tables 2 and 3 are values of the reddening-free parameter Q = (U-B)- 0.72 (B-V) introduced by Johnson & Morgan (1951). This parameter has good sensitivity to cluster agefor young clusters, but may be affected by metallicity for the oldest clusters. In the tables uncertain valuesare followed by a colon. The data in in Table 2 and Table 3 are plotted in Figure 4. This figure shows noevidence for any correlation between LMC and SMC cluster ellipticity and the parameter Q, which may beregarded as a proxy for age. This is so because young blue clusters have more negative Q values than doolder ones.Figure 5 shows a plot of the ellipticities of LMC clusters as a function of their luminosity. Contrary to aprevious result by van den Bergh (1983a) the data that are now available show no evidence for a correlationbetween cluster luminosity and cluster flattening. This result is true for both globular clusters (shown inthe figure as triangles) and for younger clusters, which are plotted as dots.The data in Table 1 clearly show that the Galactic globular clusters with A v < < M v > -7.0were drawn from the same flattening distribution as the LMC clusters. A comparison between all Galacticglobular clusters with A v < < ǫ = 0.30 (Geyer et al. 1983), or ǫ = 0.28 (Kontizas et al. 1990) - whichis flatter than any of the globular clusters in the LMC - which all have ǫ < < h ǫ i =0.26. If real, this trend would run counter to that in giant galaxies in which it thefaintest clusters that are the most flattened.
3. Cluster flattening and population type.
Mackey & van den Bergh (2005) have used the morphology of globular cluster horizontal branchesto assign these objects to different Galactic populations such as old halo (OH), young halo (YH) andbulge/disk(BD). Among clusters with A v < ǫ distribu-tions of 31 old halo clusters, 13 young halo objects and 16 bulge/disk clusters. It is noted in passing thatthe relaxation times of Galactic globular clusters (Webbink 1985) are uncorrelated with their flattenings,even though faint clusters are more flattened than luminous ones. The reason for this is that faint Galacticglobular clusters are, on average, larger than luminous ones. The longer relaxation time of clusters con-taining a large number of stars is therefore approximately compensated for by the fact that that luminousclusters tend to be more compact than dim ones. If tidal effects contribute to the flattening of globularclusters, then one might expect clusters close to the Galactic center to be more flattened than those in theouter Galactic halo. This is indeed observed to be the case. However, a K-S test shows that the differencein flattening distributions of clusters with A v < R gc <
12 kpc does not differ at a respectablelevel of statistical significance from that of the clusters with A v < R gc >
12 kpc. It is noted inpassing that the elimination of highly reddened globular clusters from the present sample has introduced abias against clusters with collapsed cores which are strongly concentrated behind the dust clouds that shroudthe Galactic center.
4. Flattening and horizontal branch morphology
It has been known for many years (van den Bergh 1965, 1967, and Sandage & Wildey 1967) thatglobular clusters exhibit a “second parameter” effect with clusters of similar metallicity showing differingpopulation gradients along their horizontal branches. This effect has variously been attributed to differencesin helium abundance, CNO group abundances or stellar rotation. Surprisingly Norris (1983) found an 6 –apparent correlation between cluster flattening and horizontal branch gradient, in the sense that (amongclusters of intermediate metallicity) objects with blue horizontal branches can have any value of ǫ , whereasnearly round clusters all have red horizontal branches. A better way to look into this problem is providedby using the larger and more recent sample of ǫ and HB-index values listed by Mackey & van den Bergh.Their HB index is defined as (B-R)/B+V+R) in which B is the number of stars that lie to the blue ofHB instability strip, V is the number of stars in this strip, and R is the number of stars to the red of thehorizontal branch instability strip. After omitting (1) highly reddened clusters with A v > M v > -6.0 (in which flattening measurements are intrinsically uncertain because of low total stellar content), and(3) ω Cen and M54 (which might be stripped galaxy cores), one obtains a sample of 54 Galactic globularclusters. Half of these clusters have a horizontal branch index < +0.6 and half of them have an HB-index > +0.6. A Kolmogorov-Smirnov test shows that there is no statistically significant difference between theellipticity distributions of the Galactic globular clusters with red and with blue horizontal branches. Sincethe present sample is exactly twice as large as that used by Norris it is concluded that his result, which wassignificant at the 96% level, was probably due to the well-known perversity of small-number statistics. Inhis original paper Norris considered only those globular clusters with intermediate metallicities in the range1.4 [Fe/H] -1.9. If one applies the same restriction to the sample discussed above then one is left withonly 29 clusters. For these objects a K-S test again shows no significant difference between the flatteningdistributions of the clusters with HB-index < +0.6 and HB-index > +0.6. It is therefore concluded thatthe best presently available data provide no evidence to support the conclusion by Norris (1983) that theflattening of Galactic globular clusters is correlated with their horizontal branch morphology.About a quarter of all globular clusters exhibit an unusually extended horizontal branch (Lee et al.2007). This “blue hook” morphology probably indicates that such clusters had an unusual evolutionaryhistory. On average these clusters are of above-average luminosity. A comparison between the distributionof the small population of little reddened blue hook clusters with a similar population of luminous globularswith normal horizontal branches shows no statistically significant difference in the distribution of clusterflattenings. It should, however, be emphasized that this conclusion is based on small samples.
5. Conclusions
Data in the larger database that is now available do not confirm Norris’s (1983) surprising conclusion thatthe flattening of Galactic globular clusters correlates with their horizontal branch morphology. Furthermoreit is found that there is no difference between the flattening distributions among old halo, young halo andbulge/disk clusters (as defined by Mackey & van den Bergh (2005). Finally the present data strengthen andconfirm the conclusion of Davoust & Prugniel (1990) that luminous Galactic globular clusters are, on average,rounder than are less luminous globular clusters. In this respect the Galaxy appears to resembles M31 andNGC 5128, but differs from the Magellanic Clouds (Frenk & Fall 1982, van den Bergh 1983a, Goodewin1997). The reasons for these difference are presently not understood. The conclusions listed above couldbe greatly strengthened by obtaining (a-b)/a values for Galactic globular clusters with A v > REFERENCES
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This preprint was prepared with the AAS L A TEX macros v5.2.
Figure 1 -10.0-8.0-6.0-4.00.0 0.1 0.2 0.3 (cid:304) M V Fig. 1.— Luminosity versus flattening for Galactic globular clusters. Clusters with A v < A v > Figure 2 (cid:304)
Bright Faint
Fig. 2.— Normalized frequency distributions of the apparent flattening values for luminous ( M v < -7.0) andfaint ( M v > -7.0) Galactic globular clusters. [For reasons outlined in the text ω Centauri and M54 havebeen excluded from the samples plotted in Figures 1 and 2.] The figure shows that the apparent flatteningvalues of the faint globular clusters are significantly greater than those of the more luminous ones. 11 –
Figure 3 (cid:304)
IIIIIVVVIVI
Fig. 3.— Relation between the flattening and the Searle age class of globular clusters in the MagellanicClouds. NGC 121 in the SMC is shown as a plus sign. The figure shows no evidence for a dependence ofcluster flattening on age, i.e. both the old and the young star clusters in the Magellanic Clouds are flatterthan their Galactic counterparts. 12 –
Figure 4 -1.0-0.50.00.0 0.1 0.2 0.3 (cid:304) Q Fig. 4.— Relation between ellipticity and the reddening-free parameter Q for clusters in the LMC (dots)and SMC (plus signs). In neither of these galaxies does the cluster flattening appear to be correlated withcluster age. 13 –
Figure 5 . . . . (cid:304) V Fig. 5.— Relation between luminosity and flattening of LMC clusters. Globular clusters of Searle ageclass VII clusters are shown as triangles, younger clusters as circles. Contrary to some previous results thefigure shows no evidence for a correlation between the luminosity and the flattening of clusters in the LargeMagellanic Cloud. 14 –Table 1. Normalized integral frequency distributions of flattening distributions for little-reddened globularclusters with A v < (a-b)/a Galaxy Galaxy M31 M31luminous clusters faint clusters luminous clusters faint clustersM v < -7.0 M v > -7.0 M v < -8.0 M v > -8.0 < < < < < < < < < < < < < < -8.0 Mv > -7.0 < < < < < < < < < < < < < < ǫ > N1466 VII 11.59 -0.35 0.09N1644 V 12.89 -0.24 0.11N1651 ... 12.67 -0.20 0.17:N1652 ... 13.13 -0.29: 0.26N1696 ... ... ... 0.21N1698 ... ... -0.54: 0.15N1711 II 10.11 -0.46 0.20N1718 ... 12.25 -0.29 0.12N1734 ... ... ... 0.25N1749 ... ... ... 0.32N1751 V 12.11 -0.19: 0.18N1754 GC 11.96 -0.35: 0.08N1755 II-III 9.85 -0.32 0.18N1783 V 10.93 -0.22 0.20N1786 GC 10.88 -0.43 0.08NN1786 GC 10.88 -0.43 0.08N1795 ... ... -0.13: 0.23N1801 ... 12.16 -0.10 0.16N1805 ... 10.63 -0.63 0.17N1806 V 11.10 -0.27 0.12N1818 I 9.70 -0.60 0.24N1828 ... 12.52 -0.25 0.18N1831 V 11.18 -0.11 0.17N1835 VII 10.13 -0.37 0.16N1838 ... ... ... 0.17N1839 ... ... ... 0.10N1842 ... ... ... 0.16N1844 ... 12.08 -0.29 0.14N1846 V 11.31 -0.13 0.24N1847 ... 11.06 -0.47 0.20N1849 ... 12.80 -0.02 0.07N1850 ... 8.96 -0.44 0.09N1852 ... 12.01 -0.28 0.10N1854 II 10.39 -0.37 0.12N1856 IV 10.06 -0.17 0.10N1860 ... 11.04 -0.49 0.11N1861 ... ... ... 0.14N1863 ... 10.98 -0.45 0.25 17 –Table 2—ContinuedName Age class V Q < ǫ >
N1864 ... ... ... 0.16N1865 ... ... ... 0.18N1866 III 9.73 -0.22 0.08N1868 ... 11.56 -0.17 0.04N1870 ... 11.26 -0.35 0.19N1871 ... ... ... 0.20N1878 ... ... ... 0.21N1885 ... 11.97 -0.32 0.13N1897 ... ... ... 0.12N1898 GC 11.42 -0.56 0.18N1903 II 11.86 -0.35 0.10N1905 ... ... ... 0.19N1916 GC 10.38 -0.38 0.13N1917 ... 10.25 -0.17: 0.15N1943 III 11.88 -0.36 0.26N1953 ... 11.74 -0.11 0.14N1978 VI 10.70 -0.33 0.29N1983 ... 9.94 -0.83 0.12N1984 ... 9.72 -0.82 0.12N1987 IV 12.08 -0.17 0.13N2004 I 9.60 -0.80 0.20N2005 GC 11.57 -0.33 0.14N2019 VII 10.86 -0.36 0.16N2031 ... 10.83 -0.24 0.19N2038 ... ... ... 0.16N2041 III 10.36 =3D0.33 0.05N2056 ... 12.34 -0.09 0.07N2065 III 11.24 -0.29 0.15N2098 ... 10.73 -0.70 0.11:N2107 IV 11.51 -0.14 0.08N2108 ... 12.32 -0.20 0.15N2109 ∗ VII ... ... 0.18N2114 ... ... ... 0.42N2116 ... ... ... 0.29N2117 ... ... ... 0.41N2121 VI 12.37 -0.36 0.25N2134 IV 11.05 -0.20 0.06N2135 ... ... ... 0.48 18 –Table 2—ContinuedName Age class V Q < ǫ >
N2140 ... ... ... 0.27N2154 V 12.13 =3D0.19 0.17N2155 VI 12.60 -0.35 0.18N2156 ... 11.38 -0.16 0.17N2157 ... 10.16 -0.30 0.07N2159 ... 11.38 -0.34 0.16N2160 ... ... ... 0.19N2162 V 12.70 -0.18 0.06N2164 III 10.34 -0.31 0.12N2166 ... ... ... 0.22N2172 ... 11.75 -0.29 0.17N2173 V-VI 12.30 -0.26: 0.16:N2177 ... ... ... 0.08N2193 ... ... ... 0.33N2209 III-I V 13.15 -0.18 0.04N2210 VII 10.94 -0.40 0.10N2213 V-VI 12.38 -0.22 0.14:N2214 II 10.93 -0.35 0.22N2231 V 13.20 =3D0.21 0.10N2249 ... 12,23 =3D0.11 0.08H11 VII 11.98 -0.47 0.09SL363 ... ... -0.24 0.25SL885 ... 14.3 ... 0.18 ∗ The cluster NGC 2109 is misidentified as NGC2019 in Bhatia and MacGillivray (1989) 19 –Table 3. Flattening of clusters in the SMC measured at the half-light isophoteCluster V Q ǫǫ