Globular Cluster System Research Articles

BEYOND THE BRIM OF THE HAT: KINEMATICS OF GLOBULAR CLUSTERS OUT TO LARGE RADII IN THE SOMBRERO GALAXY

We have obtained radial velocity measurements for 51 new globular clusters around the Sombrero galaxy. These measurements were obtained using spectroscopic observations from the AAOmega spectrograph on the Anglo-Australian Telescope and the Hydra spectrograph at WIYN. Combined with our own past measurements and velocity measurements obtained from the literature we have constructed a large database of radial velocities that contains a total of 360 confirmed globular clusters. Previous studies' analyses of the kinematics and mass profile of the Sombrero globular cluster system have been constrained to the inner ~9' (~24 kpc or ~5 effective radii), but our new measurements have increased the radial coverage of the data, allowing us to determine the kinematic properties of M104 out to ~15' (~41 kpc or ~9 effective radii). We use our set of radial velocities to study the GC system kinematics and to determine the mass profile and V-band mass-to-light profile of the galaxy. We find that the V-band mass-to-light ratio increases from 4.5 at the center to a value of 20.9 at 41 kpc (~9 effective radii or 15'), which implies that the dark matter halo extends to the edge of our available data set. We compare our mass profile at 20 kpc (~4 effective radii or ~7.4') to the mass computed from x-ray data and find good agreement. We also use our data to look for rotation in the globular cluster system as a whole, as well as in the red and blue subpopulations. We find no evidence for significant rotation in any of these samples.

Globular clusters: DNA of early-type galaxies?

This paper explores if the mean properties of Early-Type Galaxies (ETG) can be reconstructed from "genetic" information stored in their GCs (i.e., in their chemical abundances, spatial distributions and ages). This approach implies that the formation of each globular occurs in very massive stellar environments, as suggested by some models that aim at explaining the presence of multi-populations in these systems. The assumption that the relative number of globular clusters to diffuse stellar mass depends exponentially on chemical abundance, [Z/H], and the presence of two dominant GC sub-populations blue and red, allows the mapping of low metallicity halos and of higher metallicity (and more heterogeneous) bulges. In particular, the masses of the low-metallicity halos seem to scale up with dark matter mass through a constant. We also find a dependence of the globular cluster formation efficiency with the mean projected stellar mass density of the galaxies within their effective radii. The analysis is based on a selected sub-sample of galaxies observed within the ACS Virgo Cluster Survey of the {\it Hubble Space Telescope}. These systems were grouped, according to their absolute magnitudes, in order to define composite fiducial galaxies and look for a quantitative connection with their (also composite) globular clusters systems. The results strengthen the idea that globular clusters are good quantitative tracers of both baryonic and dark matter in ETGs.

How tidal erosion has shaped the relation between globular cluster specific frequency and galaxy luminosity

We quantify to what extent tidal erosion of globular clusters (GCs) has contributed to the observed u-shaped relation between GC specific frequencies S_N and host galaxy luminosity M_V. We used our MUESLI code to calculate GC survival rates for typical early-type galaxy potentials covering a wide range of observed galaxy properties. We do this for isotropic and radially anisotropic GC velocity distributions. We find that the calculated GC survival fraction, f_s, depends linearly on the logarithm of the 3D mass density, rho_3D, within the galaxy's half light radius, with f_s proportional to (rho_3D)^(-0.17). For a given galaxy, survival rates are lower for radially anisotropic configurations than for the isotropic GC cases. We apply these relations to a literature sample of 219 early-type galaxies from Harris et al. (2013) in the range M_V=[-24.5:-15.5] mag. The expected GC survival fraction ranges from ~50% for the most massive galaxies with the largest radii to ~10% for the most compact galaxies. We find that intermediate luminosity galaxies M_V=[-20.5:-17.5] mag have the strongest expected GC erosion. Within the considered literature sample, the predicted GC survival fraction therefore defines a u-shaped relation with M_V, similar to the relation between specific frequency S_N and M_V. As a consequence, the u-shape of S_N vs. M_V gets erased almost entirely when correcting the S_N values for the effect of GC erosion. We conclude that tidal erosion is an important contributor to the u-shaped relation between GC specific frequency and host galaxy luminosity. It must be taken into account when inferring primordial star cluster formation efficiencies from observations of GC systems in the nearby universe.

DARK MATTER HALOS IN GALAXIES AND GLOBULAR CLUSTER POPULATIONS

We combine a new, comprehensive database for globular cluster populations in all types of galaxies with a new calibration of galaxy halo masses based entirely on weak lensing. Correlating these two sets of data, we find that the mass ratio $\eta \equiv M_{GCS}/M_{h}$ (total mass in globular clusters, divided by halo mass) is essentially constant at $\langle \eta \rangle \sim 4 \times 10^{-5}$, strongly confirming earlier suggestions in the literature. Globular clusters are the only known stellar population that formed in essentially direct proportion to host galaxy halo mass. The intrinsic scatter in $\eta$ appears to be at most 0.2 dex; we argue that some of this scatter is due to differing degrees of tidal stripping of the globular cluster systems between central and satellite galaxies. We suggest that this correlation can be understood if most globular clusters form at very early stages in galaxy evolution, largely avoiding the feedback processes that inhibited the bulk of field-star formation in their host galaxies. The actual mean value of $\eta$ also suggests that about $1/4$ of the \emph{initial} gas mass present in protogalaxies collected into GMCs large enough to form massive, dense star clusters. Finally, our calibration of $\langle \eta \rangle$ indicates that the halo masses of the Milky Way and M31 are $(1.2\pm0.5)\times 10^{12} M_{\odot}$ and $(3.9\pm1.8)\times 10^{12} M_{\odot}$ respectively.

Erosion of globular cluster systems: the influence of radial anisotropy, central black holes and dynamical friction

We present the adaptable MUESLI code for investigating dynamics and erosion processes of globular clusters (GCs) in galaxies. MUESLI follows the orbits of individual clusters and applies internal and external dissolution processes to them. Orbit integration is based on the self-consistent field method in combination with a time-transformed leapfrog scheme, allowing us to handle velocity-dependent forces like triaxial dynamical friction. In a first application, the erosion of globular cluster systems (GCSs) in elliptical galaxies is investigated. Observations show that massive ellipticals have rich, radially extended GCSs, while some compact dwarf ellipticals contain no GCs at all. For several representative examples, spanning the full mass scale of observed elliptical galaxies, we quantify the influence of radial anisotropy, galactic density profiles, SMBHs, and dynamical friction on the GC erosion rate. We find that GC number density profiles are centrally flattened in less than a Hubble time, naturally explaining observed cored GC distributions. The erosion rate depends primarily on a galaxy's mass, half-mass radius and radial anisotropy. The fraction of eroded GCs is nearly 100% in compact, M 32 like galaxies and lowest in extended and massive galaxies. Finally, we uncover the existence of a violent tidal disruption dominated phase which is important for the rapid build-up of halo stars.

WIDE-FIELDHUBBLE SPACE TELESCOPEOBSERVATIONS OF THE GLOBULAR CLUSTER SYSTEM IN NGC 1399

We present a comprehensive high spatial-resolution imaging study of globular clusters (GCs) in NGC1399, the central giant elliptical cD galaxy in the Fornax galaxy cluster, conducted with HST/ACS. Using a novel technique to construct drizzled PSF libraries for HST/ACS data, we accurately determine the fidelity of GC structural parameter measurements from detailed artificial star cluster experiments. The measurement of rh for the major fraction of the NGC1399 GC system reveals a trend of increasing rh versus galactocentric distance, Rgal, out to about 10 kpc and a flat relation beyond. This trend is very similar for blue and red GCs which are found to have a mean size ratio of rh(red)/rh(blue)=0.82+/-0.11 at all galactocentric radii from the core regions of the galaxy out to ~40 kpc. This suggests that the size difference between blue and red GCs is due to internal mechanisms related to the evolution of their constituent stellar populations. Modeling the mass density profile of NGC1399 shows that additional external dynamical mechanisms are required to limit the GC size in the galaxy halo regions to rh~2 pc. We suggest that this may be realized by an exotic GC orbit distribution function, an extended dark matter halo, and/or tidal stress induced by the increased stochasticity in the dwarf halo substructure at larger Rgal. We match our GC rh measurements with radial velocity data from the literature and find that compact GCs show a significantly smaller line-of-sight velocity dispersion, <sigma(cmp)>=225+/-25 km/s, than their extended counterparts, <sigma(ext)>=317+/-21 km/s. Considering the weaker statistical correlation in the GC rh-color and the GC rh-Rgal relations, the more significant GC size-dynamics relation appears to be astrophysically more relevant and hints at the dominant influence of the GC orbit distribution function on the evolution of GC structural parameters.

A NEW DISTANT MILKY WAY GLOBULAR CLUSTER IN THE PAN-STARRS1 3π SURVEY

We present a new satellite in the outer halo of the Galaxy, the first Milky Way satellite found in the stacked photometric catalog of the Panoramic Survey Telescope and Rapid Response System 1 (Pan-STARRS1) Survey. From follow-up photometry obtained with WFI on the MPG/ESO 2.2m telescope, we argue that the object, located at a heliocentric distance of 145+/-17 kpc, is the most distant Milky Way globular cluster yet known. With a total magnitude of M_V=-4.3+/-0.2 and a half-light radius of 20+/-2 pc, it shares the properties of extended globular clusters found in the outer halo of our Galaxy and the Andromeda galaxy. The discovery of this distant cluster shows that the full spatial extent of the Milky Way globular cluster system has not yet been fully explored.

HEAVY ELEMENTS IN GLOBULAR CLUSTERS: THE ROLE OF ASYMPTOTIC GIANT BRANCH STARS

Recent observations of heavy elements in Globular Clusters reveal intriguing deviations from the standard paradigm of the early galactic nucleosynthesis. If the r-process contamination is a common feature of halo stars, s-process enhancements are found in a few Globular Clusters only. We show that the combined pollution of AGB stars with mass ranging between 3 to 6 M$_\odot$ may account for most of the features of the s-process overabundance in M4 and M22. In these stars, the s process is a mixture of two different neutron-capture nucleosynthesis episodes. The first is due to the 13C(a,n)16O reaction and takes place during the interpulse periods. The second is due to the 22Ne(a,n)25Mg reaction and takes place in the convective zones generated by thermal pulses. The production of the heaviest s elements (from Ba to Pb) requires the first neutron burst, while the second produces large overabundances of light s (Sr, Y, Zr). The first mainly operates in the less-massive AGB stars, while the second dominates in the more-massive. From the heavy-s/light-s ratio, we derive that the pollution phase should last for $150\pm 50$ Myr, a period short enough compared to the formation timescale of the Globular Cluster system, but long enough to explain why the s-process pollution is observed in a few cases only. With few exceptions, our theoretical prediction provides a reasonable reproduction of the observed s-process abundances, from Sr to Hf. However, Ce is probably underproduced by our models, while Rb and Pb are overproduced. Possible solutions are discussed.

Globular Star Cluster Systems Around Galaxies. I. Search for Statistical Relationships

Our earlier composite catalog [1] of systems of globular star clusters around galaxies has been substantially extended with the addition of observational data published over the last decade and now includes 252 systems. The new catalog is analyzed statistically. Empirical relationships among the main physical parameters of systems of globular clusters and their host galaxies are found. These relationships apply with adequate accuracy to elliptical and lenticular galaxies in isolation. The problems with classifying systems of globular clusters and the relations of these systems to their host galaxies are discussed.

The SLUGGS survey: breaking degeneracies between dark matter, anisotropy and the IMF using globular cluster subpopulations in the giant elliptical NGC 5846

We study the mass and anisotropy distribution of the giant elliptical galaxy NGC 5846 using stars, as well as the red and blue globular cluster (GC) subpopulations. We break degeneracies in the dynamical models by taking advantage of the different phase space distributions of the two GC subpopulations to unambiguously constrain the mass of the galaxy and the anisotropy of the GC system. Red GCs show the same spatial distribution and behaviour as the starlight, whereas blue GCs have a shallower density profile, a larger velocity dispersion and a lower kurtosis, all of which suggest a different orbital distribution. We use a dispersion-kurtosis Jeans analysis and find that the solutions of separate analyses for the two GC subpopulations overlap in the halo parameter space. The solution converges on a massive dark matter halo, consistent with expectations from $\Lambda$CDM and WMAP7 cosmology in terms of virial mass ($\log M_{DM} \sim13.3 M_{sun}$) and concentration ($c_{vir}\sim8$). This is the first such analysis that solves the dynamics of the different GC subpopulations in a self-consistent manner. Our method improves the uncertainties on the halo parameter determination by a factor of two and opens new avenues for the use of elliptical galaxy dynamics as tests of predictions from cosmological simulations. The implied stellar mass-to-light ratio derived from the dynamical modelling is fully consistent with a Salpeter initial mass function (IMF) and rules out a bottom light IMF. The different GC subpopulations show markedly distinct orbital distributions at large radii, with red GCs having an anisotropy parameter $\beta\sim0.4$ outside $\sim3R_e$, and the blue GCs having $\beta\sim0.15$ at the same radii, while centrally ($\sim1R_e$) they are both isotropic. We discuss the implications of our findings within the two-phase formation scenario for early-type galaxies.

CONSTRAINING STELLAR POPULATION MODELS. I. AGE, METALLICITY AND ABUNDANCE PATTERN COMPILATION FOR GALACTIC GLOBULAR CLUSTERS

We present an extenstive literature compilation of age, metallicity, and chemical abundance pattern information for the 41 Galactic globular clusters (GGCs) studied by Schiavon et al. (2005). Our compilation constitutes a notable improvement over previous similar work, particularly in terms of chemical abundances. Its primary purpose is to enable detailed evaluations of and refinements to stellar population synthesis models designed to recover the above information for unresolved stellar systems based on their integrated spectra. However, since the Schiavon sample spans a wide range of the known GGC parameter space, our compilation may also benefit investigations related to a variety of astrophysical endeavours, such as the early formation of the Milky Way, the chemical evolution of GGCs, and stellar evolution and nucleosynthesis. For instance, we confirm with our compiled data that the GGC system has a bimodal metallicity distribution and is uniformly enhanced in the alpha-elements. When paired with the ages of our clusters, we find evidence that supports a scenario whereby the Milky Way obtained its globular clusters through two channels, in situ formation and accretion of satellite galaxies. The distributions of C, N, O, and Na abundances and the dispersions thereof per cluster corroborate the known fact that all GGCs studied so far with respect to multiple stellar populations have been found to harbour them. Finally, using data on individual stars, we also confirm that the atmospheres of stars become progressively polluted by CN(O)-processed material after they leave the main sequence and uncover evidence which suggests the alpha-elements Mg and Ca may originate from more than one nucleosynthetic production site. [abridged]

TOWARD A BETTER UNDERSTANDING OF THE DISTANCE SCALE FROM RR LYRAE VARIABLE STARS: A CASE STUDY FOR THE INNER HALO GLOBULAR CLUSTER NGC 6723

We present BV photometry for 54 variables in the metal-rich inner halo globular cluster NGC6723. With the discovery of new RR Lyrae variables (RRLs), we obtain <P_ab> = 0.541 +/- 0.066 and <P_c> = 0.292 +/- 0.030 day, n(c)/n(ab+c) = 0.167, and <V(RR)>_int = 15.459 +/- 0.055. We carry out the Fourier decomposition analysis and obtain [Fe/H]_ZW = -1.23 +/- 0.11 and E(B-V) = 0.063 +/- 0.015 for NGC 6723. By calibrating the zero-point from the recent absolute trigonometric parallax measurements for RR Lyr, we derive the revised M_V(RR)-[Fe/H] relation, providing M_V(RR)= 0.52 at [Fe/H] = -1.50 and (m-M)_0 = 18.54 for Large Magellanic Cloud (LMC), in excellent agreement with others. We obtain (m-M)_0 = 14.65 +/- 0.05, equivalent to the distance from the Sun of 8.47 +/- 0.17 kpc, for NGC 6723 from various distance measurement methods using RRLs. We find that RRLs in NGC 6723 do not have magnitude dependency on the radial distance, due to a not severe degree of the apparent crowdedness. Finally, we show that there exists a relation between the degree of photometric contamination and the apparent crowdedness of the central region of globular cluster systems. The use of this relation can play a significantly role on mitigating the discrepancy to establish a cosmic distance scale using RRLs in resolved stellar populations in the near-field cosmology.

The SLUGGS survey★: the globular cluster systems of three early-type galaxies using wide-field imaging

We present the results from a wide-field imaging study of globular cluster (GC) systems in three early-type galaxies. Combinations of Subaru/Suprime-Cam, CFHT/MegaCam and HST/WFPC2/ACS data were used to determine the GC system properties of three highly flattened galaxies NGC 720, NGC 1023 and NGC 2768. This work is the first investigation of the GC system in NGC 720 and NGC 2768 to very large galactocentric radius ($\sim$ 100 kpc). The three galaxies have clear blue and red GC subpopulations. The radial surface densities of the GC systems are fitted with Sersic profiles, and detected out to 15, 8 and 10 galaxy effective radii respectively. The total number of GCs and specific frequency are determined for each GC system. The ellipticity of the red subpopulation is in better agreement with the host galaxy properties than is the blue subpopulation, supporting the traditional view that metal-rich GCs are closely associated with the bulk of their host galaxies' field stars, while metal-poor GCs reflect a distinct stellar halo. With the addition of another 37 literature studied galaxies, we present a new correlation of GC system extent with host galaxy effective radius. We find a dependence of the relative fraction of blue to red GCs with host galaxy environmental density for lenticular galaxies (but not for elliptical or spiral galaxies). We propose that tidal interactions between galaxies in cluster environments might be the reason behind the observed trend for lenticular galaxies.

Metallicity field and selection effects in spatial distribution of the Galactic globular cluster system

AbstractThe prospects for using the present‐day data on metallicity of globular clusters (GCs) of the Galaxy to put constraints on the distance to the Galactic center, R0, are considered. We have found that the GCs of the metal‐rich and metal‐poor subsystems separately form a bar‐like structure in metallicity maps whose parameters are very close to those for the Galactic bar. The results indicate the existence of a bar component within both the metal‐rich and metal‐poor subsystems of GCs. The bar GCs could have formed within the already existing Galactic bar or could have later been locked in resonance with the bar. We conclude that substantial constraints on the R0 value can be obtained only with non‐axisymmetric models for the space distribution of GC metallicities with the allowance for the subdivision of GCs into subsystems. We found evidence for a bar extinction component that causes the observational incompleteness of GCs in the far side of the Galactic bar and in the “post‐central” region. This selection effect should be taken into account when determining R0 from the spatial distribution of GCs. (© 2013 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

The SLUGGS Survey: wide field imaging of the globular cluster system of NGC 4278

We use multi-pointing HST ACS and wide field Subaru Suprime-Cam imaging to study the globular cluster system of the L* elliptical galaxy NGC 4278. We have also obtained a handful of new globular cluster spectra with Keck/DEIMOS. We determine the globular cluster surface density profile and use it to calculate the total number of globular clusters, finding the system to be slightly more populous than average for galaxies of its luminosity. We find clear evidence for bimodality in the globular cluster colour distribution and for a colour-magnitude relation in the blue subpopulation (a 'blue tilt'). We also find negative radial colour gradients in both colour subpopulations of equal strength which are similar in strength to those reported in other galaxies. The sizes of NGC 4278's globular clusters decrease with redder colours and increase with galactocentric radius. The ratio of the sizes of blue to red globular clusters is independent of galactocentric radius demonstrating that internal effects are responsible for the size difference with colour.

Signatures of accretion events in the haloes of early-type galaxies from comparing PNe and GCs kinematics

We have compared the halo kinematics traced by globular clusters (GCs) and planetary nebulae (PNe) for two elliptical galaxies in the Fornax and Virgo clusters NGC 1399 and NGC 4649, and for the merger remnant NGC 5128 (Centaurus A). We find differences in the rotational properties of the PN, red GC, and blue GC systems in all these three galaxies. NGC 1399 PNe and GCs show line of sight velocity distributions in specific regions that are significantly different, based on Kolmogorov-Smirnov tests. The PN system shows multi-spin components, with nearly opposite direction of rotation in the inner and the outer parts. The GCs velocity field is not point-symmetric in the outer regions of the galaxy, indicating that the system has not reached dynamical equilibrium yet. In NGC 4649 PNe, red and blue GCs have different rotation axes and rotational velocities. Finally, in NGC 5128 both PNe and GCs deviate from equilibrium in the outer regions of the galaxy, and in the inner regions the PN system is rotationally supported, whereas the GC system is dominated by velocity dispersion. The observed different kinematic properties, including deviations from point-symmetry, between PNe and GCs suggest that these systems are accreted at different times by the host galaxy, and the most recent accretion took place only few Gyr ago.We discuss two scenarios which may explain some of these differences: i) tidal stripping of loosely-bound GCs, and ii) multiple accretion of low luminosity and dwarf galaxies. Because these two mechanisms affect mostly the GC system, differences with the PNe kinematics can be expected.

Newly discovered globular clusters in NGC 147 and NGC 185 from PAndAS

Using data from the Pan-Andromeda Archaeological Survey (PAndAS), we have discovered four new globular clusters (GCs) associated with the M31 dwarf elliptical (dE) satellites NGC 147 and NGC 185. Three of these are associated with NGC 147 and one with NGC 185. All lie beyond the main optical boundaries of the galaxies and are the most remote clusters yet known in these systems. Radial velocities derived from low-resolution spectra are used to argue that the GCs are bound to the dwarfs and are not part of the M31 halo population. Combining PAndAS with United Kingdom Infrared Telescope (UKIRT)/WFCAM (Wide-Field Camera) data, we present the first homogeneous optical and near-IR photometry for the entire GC systems of these dEs. Colour–colour plots and published colour–metallicity relations are employed to constrain GC ages and metallicities. It is demonstrated that the clusters are in general metal poor ([Fe/H] < −1.25 dex), while the ages are more difficult to constrain. The mean (V − I)0 colours of the two GC systems are very similar to those of the GC systems of dEs in the Virgo and Fornax clusters, as well as the extended halo GC population in M31. The new clusters bring the GC-specific frequency (SN) to ∼9 in NGC 147 and ∼5 in NGC 185, consistent with values found for dEs of similar luminosity residing in a range of environments.

THE RICH GLOBULAR CLUSTER SYSTEM OF ABELL 1689 AND THE RADIAL DEPENDENCE OF THE GLOBULAR CLUSTER FORMATION EFFICIENCY

We study the rich globular cluster (GC) system in the center of the massive cluster of galaxies Abell 1689 (z=0.18), one of the most powerful gravitational lenses known. With 28 HST/ACS orbits in the F814W bandpass, we reach magnitude I_814=29 with >90% completeness and sample the brightest ~5% of the GC system. Assuming the well-known Gaussian form of the GC luminosity function (GCLF), we estimate a total population of N(GC_total) = 162,850 GCs within a projected radius of 400kpc. As many as half may comprise an intracluster component. Even with the sizable uncertainties, which mainly result from the uncertain GCLF parameters, this is by far the largest GC system studied to date. The specific frequency S_N is high, but not uncommon for central galaxies in massive clusters, rising from S_N~5 near the center to ~12 at large radii. Passive galaxy fading would increase S_N by ~20% at z=0. We construct the radial mass profiles of the GCs, stars, intracluster gas, and lensing-derived total mass, and we compare the mass fractions as a function of radius. The estimated mass in GCs, M(GC_total)=3.9x10^10 Msun, is comparable to ~80% of the total stellar mass of the Milky Way. The shape of the GC mass profile appears intermediate between those of the stellar light and total cluster mass. Despite the extreme nature of this system, the ratios of the GC mass to the baryonic and total masses, and thus the GC formation efficiency, are typical of those in other rich clusters when comparing at the same physical radii. The GC formation efficiency is not constant, but varies with radius, in a manner that appears similar for different clusters; we speculate on the reasons for this similarity in profile.

The specific frequency and the globular cluster formation efficiency in Milgromian dynamics

Previous studies of globular cluster (GC) systems show that there appears to be a universal specific GC formation efficiency $\eta$ which relates the total mass of GCs to the virial mass of host dark matter halos, $M_{vir}$ (Georgiev et al 2010, Spitler & Forbes2009). In this paper, the specific frequency, $S_N$, and specific GC formation efficiency, $\eta$, are derived as functions of $M_{vir}$ in Milgromian dynamics, i.e., in modified Newtonian dynamics (MOND). In Milgromian dynamics, for the galaxies with GCs, the mass of the GC system, $M_{GC}$, is a two-component function of $M_{vir}$ instead of a simple linear relation. An observer in a Milgromian universe, who interprets this universe as being Newtonian/Einsteinian, will incorrectly infer a universal constant fraction between the mass of the GC system and a (false) dark matter halo of the baryonic galaxy. In contrast to a universal constant of $\eta$, in a Milgromian universe, for galaxies with $M_{vir} <= 10^{12}\msun$, $\eta$ decreases with the increase of $M_{vir}$, while for massive galaxies with $M_{vir}>10^{12}\msun$, $\eta$ increases with the increase of $M_{vir}$.

DUAL HALOS AND FORMATION OF EARLY-TYPE GALAXIES

We present a determination of the two-dimensional shape parameters of the blue and red globular cluster systems (GCSs) in a large number of elliptical galaxies and lenticular galaxies (early-type galaxies, called ETGs). We use a homogeneous data set of the globular clusters in 23 ETGs obtained from the HST/ACS Virgo Cluster Survey. The position angles of both blue and red GCSs show a correlation with those of the stellar light distribution, showing that the major axes of the GCSs are well aligned with those of their host galaxies. However, the shapes of the red GCSs show a tight correlation with the stellar light distribution as well as with the rotation property of their host galaxies, while the shapes of the blue GCSs do much less. These provide clear geometric evidence that the origins of the blue and red globular clusters are distinct and that ETGs may have dual halos: a blue (metal-poor) halo and a red (metal-rich) halo. These two halos show significant differences in metallicity, structure, and kinematics, indicating that they are formed in two distinguishable ways. The red halos might have formed via dissipational processes with rotation, while the blue halos are through accretion.