Method for simultaneous determination of the metallicity and interstellar reddening of globular clusters using the <Emphasis Type="Italic">V</Emphasis> vs. (<Emphasis Type="Italic">B-R</Emphasis>) color-magnitude diagram

We describe a method for simultaneous determination of the metallicity and interstellar reddening of globular clusters that uses parameters of the giant branch on the V vs. (B-R) color-magnitude diagram: the slope of the giant branch, its color at the level of the horizontal branch, and the apparent magnitude V of the horizontal branch. Applying this method to the globular cluster NGC 7006 gives the metallicity [Fe/H] = −1.78 ± 0.11 and interstellar reddening E _B-R = 0.25 ± 0.02.     

Evolution of Population II stars

The current knowledge of the evolution of Population II stars, as observed in galactic halos and globular clusters, is outlined. The recent theoretical results provided by an improved physical understanding of the stars are reported, with a particular emphasis upon those stellar evolutionary phases which are the keystones of the interpretation of globular cluster stars. Within the up–to–date theoretical scenario, the luminosity of the turn–off stars and horizontal branch stars, which are of fundamental importance for distance and age determinations, turns out to be fainter and brighter, respectively, in comparison with previous theoretical computations. The predicted absolute magnitude of RR Lyrae stars is consistent with the bright values suggested from the long distance scale (Sandage 1993), but the slope of the relation between and metallicity ([Fe/H]) agrees with that suggested from the short distance scale (see, e.g., Carney et al. 1992, Clementini et al. 1995), at least with [Fe/H]-1.3. As to the globular cluster ages, the new computations provide younger ages ( 10 Gyr–13 Gyr), weakening the conflict with current cosmological estimates. The recent results derived from the fitting of HIPPARCOS parallaxes of field subdwarfs to the fiducial main sequence of globular clusters are consistent with the up–to–date theoretical models. However, the direct determinations of , which are based on the HIPPARCOS proper motions and trigonometric parallaxes of field RR Lyrae stars, give fainter absolute magnitudes than those obtained from the improved evolutionary models. This seems to suggest that the problem of the globular cluster distance and age is still open. Received 6 April 1998     

Metallicity distributions of globular cluster systems in galaxies

We collected a sample of 100 galaxies for which different observers have determined colour indices of globular cluster candidates. The sample includes representatives of galaxies of various morphological types and different luminosities. Colour indices (in most cases (V–I), but also (B–I) and (C–T1)) were transformed into metallicities [Fe/H] according to a relation by Kissler‐Patig (1998). These data were analysed with the KMM software in order to estimate similarity of the distribution with uni‐ or bimodal Gaussian distribution. We found that 45 of 100 systems have bimodal metallicity distributions. Mean metallicity of the metal‐poor component for these galaxies is 〈[Fe/H]〉 = –1.40 ± 0.02, of the metalrich component 〈[Fe/H]〉 = –0.69 ± 0.03. Dispersions of the distributions are 0.15 and 0.18, respectively. Distribution of unimodal metallicities is rather wide. These data will be analysed in a subsequent paper in order to find correlations with parameters of galaxies and galactic environment.     

Integrated colours of Milky Way globular clusters and horizontal branch morphology

Broadband colours are often used as metallicity proxies in the study of extragalactic globular clusters. A common concern is the effect of variations in horizontal branch (HB) morphology – the second‐parameter effect – on such colours. We have used UBVI, Washington, and DDO photometry for a compilation of over 80 Milky Way globular clusters to address this question. Our method is to fit linear relations between colour and [Fe/H], and study the correlations between the residuals about these fits and two quantitative measures of HB morphology. While there is a significant HB effect seen in U – B, for the commonly used colours B – V, V – I, and C – T₁, the deviations from the baseline colour‐[Fe/H] relations are less strongly related to HB morphology. There may be weak signatures in B –V and C –T₁, but these are at the limit of observational uncertainties. The results may favour the use of B –I in studies of extragalactic globular clusters, especially when its high [Fe/H]‐sensitivity is considered. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Horizontal branch stars: the interplay between observations and theory,and insights into the formation of the Galaxy

We review and discuss horizontal branch (HB) stars in a broad astrophysical context, including both variable and non-variable stars. A reassessment of the Oosterhoff dichotomy is presented, which provides unprecedented detail regarding its origin and systematics. We show that the Oosterhoff dichotomy and the distribution of globular clusters in the HB morphology-metallicity plane both exclude, with high statistical significance, the possibility that the Galactic halo may have formed from the accretion of dwarf galaxies resembling present-day Milky Way satellites such as Fornax, Sagittarius, and the LMC—an argument which, due to its strong reliance on the ancient RR Lyrae stars, is essentially independent of the chemical evolution of these systems after the very earliest epochs in the Galaxy’s history. Convenient analytical fits to isochrones in the HB type–[Fe/H] plane are also provided. In this sense, a rediscussion of the second-parameter problem is also presented, focusing on the cases of NGC 288/NGC 362, M13/M3, the extreme outer-halo globular clusters with predominantly red HBs, and the metal-rich globular clusters NGC 6388 and NGC 6441. The recently revived possibility that the helium abundance may play an important role as a second parameter is also addressed, and possible constraints on this scenario discussed. We critically discuss the possibility that the observed properties of HB stars in NGC 6388 and NGC 6441 might be accounted for if these clusters possess a relatively minor population of helium-enriched stars. A technique is proposed to estimate the HB types of extragalactic globular clusters on the basis of integrated far-UV photometry. The importance of bright type II Cepheids as tracers of faint blue HB stars in distant systems is also emphasized. The relationship between the absolute V magnitude of the HB at the RR Lyrae level and metallicity, as obtained on the basis of trigonometric parallax measurements for the star RR Lyr, is also revisited. Taking into due account the evolutionary status of RR Lyr, the derived relation implies a true distance modulus to the LMC of (m–M)₀=18.44±0.11. Techniques providing discrepant slopes and zero points for the M _V (RRL)–[Fe/H] relation are briefly discussed. We provide a convenient analytical fit to theoretical model predictions for the period change rates of RR Lyrae stars in globular clusters, and compare the model results with the available data. Finally, the conductive opacities used in evolutionary calculations of low-mass stars are also investigated. M. Catelan is John Simon Guggenheim Memorial Foundation Fellow.     

Space distribution and metallicities of globular clusters: the distance to the galactic centre

The system of globular clusters in the Galaxy is used in order to locate the position of the galactic centre and, consequently, to determine the galacto-centric distance of the Sun,R ₀. The space distribution and metallicities of the whole sample of known globular clusters are taken into account, and the obtained results indicate that 8.6 >R ₀ (kpc) > 6.4. Analysis of a selected sample of clusters further suggests thatR ₀ = 7.6 ± 0.4 kpc.     

Ages and metallicities of globular clusters in NGC 4472

We have derived ages and metallicities from co-added spectra of 131 globular clusters associated with the giant elliptical galaxy NGC 4472. Based upon a calibration with Galactic globular clusters, we find that our sample of globular clusters in NGC 4472 span a metallicity range of approximately −1.6≤[Fe/H]≤0 dex. There is evidence of a radial metallicity gradient in the globular cluster system which is steeper than that seen in the underlying starlight. Determination of the absolute ages of the globular clusters is uncertain, but formally, the metal-poor population of globular clusters has an age of 14.5±4 Gyr and the metal-rich population is 13.8±6 Gyr old. Monte Carlo simulations indicate that the globular cluster populations present in these data are older than 6 Gyr at the 95 per cent confidence level. We find that within the uncertainties, the globular clusters are old and coeval, implying that the bimodality seen in the broadband colours primarily reflects metallicity and not age differences.     

Two-stage model for chemical evolution of galactic halo

We propose a model of chemical evolution of the galactic halo which consists of a succession of two different evolutionary stages; each stage is characterized by different outflow rate of gas from the star-forming region so that different metal-enrichment rate is resulted. The low-metal stars with [Fe/H]<–0.8 are formed mainly during the first 3×10⁸ yr, and most of the high-metal stars with [Fe/H]–0.8 are formed during the succeeding 2×10⁹ yr. This model naturally explains the metallicity distribution of globular clusters in the galactic halo including both the metal-rich and the metal-poor clusters. We also discuss the implications of the present model on the formation and evolution of the galactic halo.     

Time variation of ellipticity of globular clusters in the Large Magellanic Cloud

Dynamical evolution of globular clusters in the Large Magellanic Cloud (LMC) is investigated by means of N-body simulations; particular attention is paid to time evolution in the ellipticitical figure of globular clusters. The simulations were started with a binary globular cluster. It merged into a single cluster with ellipticity of about 0.3. The simulations were continued until the cluster became rounder due to the effects of two body relaxation and of tidal field of LMC. It is found that the outward angular momentum transport due to the gravothermal contraction makes the inner region rounder; the ellipticity at about the initial half-mass radius (r _h) decreases with the e-folding time of 20 relaxation times. On the other hand, the outer region becomes rounder due to the stripping of stars by the tidal field; the ellipticity at about 3r _h decreases with the e-folding time of 80 crossing times therein, though the time scale depends on the direction of the tidal field relative to the spin of the cluster. These two effects are comparable at about the half-mass radius. Taking account of such theoretical results we reanalyzed observed data for the ellipticity at about the half-mass radius of LMC clusters. We estimated the relaxation time and crossing time for each of the observed clusters, from which we calculated the effective time of getting round of the cluster. We plotted the observed ellipticity of the clusters against their non-dimensional age — i.e., the age normalized by the effective time. We found that observed ellipticity distribution is consistent with our picture.     

Metallicity Distributions of Elliptical Galaxies and Globular Cluster Systems

Gradients of absorption line indices are studied and mean stellar metallicities are estimated for 46 elliptical galaxies. The mean stellar metallicities range from 〈 [Fe/H] 〉 ≃ =0.8 to +0.2 and ellipticals with smaller central velocity dispersions tend to have lower 〈 [Fe/H] 〉 thus the mass-metallicity relation holds not only for the galaxy center but also for the whole part of the galaxy. There is an evidence that the magnesium is enhanced systematically in all ellipticals by 0.2 dex with respect to the iron. Giant elliptical galaxies show lack of metal-poor stars (the G-dwarf problem). Metal-poor globular clusters of ellipticals formed well in advance of the formation of metal-rich ones which formed simultaneously with the bulk of stars of mother galaxies under the influence of galaxy chemical enrichment. The bimodal [Fe/H] distribution of globular clusters does not necessarily mean that elliptical galaxies formed by the mergers of disc galaxies. This revised version was published online in July 2006 with corrections to the Cover Date.     

Photometric membership and metallicities of red giant candidates in selected open clusters

As part of a long‐term project to determine abundances and astrophysical properties of evolved red stars in open clusters, we present high‐precision DDO photoelectric observations for a sample of 33 red giant candidates projected in the fields of nine Galactic open clusters. These data are supplemented with UBV photoelectric photometry of 24 of these stars as well as with CORAVEL radial‐velocity observations for 13 red giant candidates in four of the clusters. We also present Washington photoelectric photometry of a small sample of red giant candidates of the open cluster Ruprecht 97. The likelihood of cluster membership for each star photometrically observed and for 23 additional red giant candidates with UBV and DDO data available in the literature, is evaluated by using two independent photometric criteria. Nearly 82% of the analysed stars are found to have a high probability of being cluster giants. Photometric membership probabilities show very good agreement with those obtained from CORAVEL radial velocities. While E (B –V) colour excesses were determined from combined B – V and DDO colours, calibrations of the DDO system were used to derive MK spectral types, effective temperatures and metallicities. The derived DDO metallicities range between values typical of moderately metal‐poor clusters ([Fe/H] = –0.19) to moderately metal‐rich ([Fe/H] = 0.25) ones. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

UBRI photometry of globular clusters in the Leo group galaxy NGC 3379

We present wide-area UBRI photometry for globular clusters around the Leo group galaxy NGC 3379. Globular cluster candidates are selected from their B -band magnitudes and their  ( U − B ) _o   versus  ( B − I ) _o   colours. A colour–colour selection region was defined from photometry of the Milky Way and M31 globular cluster systems. We detect 133 globular cluster candidates, which supports previous claims of a low specific frequency for NGC 3379.
The Milky Way and M31 reveal blue and red subpopulations, with  ( U − B ) _o   and  ( B − I ) _o   colours indicating mean metallicities similar to those expected based on previous spectroscopic work. The stellar population models of Maraston and Brocato et al. are consistent with both subpopulations being old, and with metallicities of  [Fe/H]∼−1.5  and −0.6 for the blue and red subpopulations, respectively. The models of Worthey do not reproduce the  ( U − B ) _o   colours of the red (metal-rich) subpopulation for any modelled age.
For NGC 3379 we detect a blue subpopulation with similar colours, and presumably age/metallicity, to that of the Milky Way and M31 globular cluster systems. The red subpopulation is less well defined, perhaps due to increased photometric errors, but indicates a mean metallicity of [Fe/H]∼−0.6.     

Reddening, colour and metallicity of the M31 globular cluster system

Using metallicities from the literature, combined with the Revised Bologna Catalogue of photometric data for M31 clusters and cluster candidates [the latter of which is the most comprehensive catalogue of M31 clusters currently available, including 337 confirmed globular clusters (GCs) and 688 GC candidates], we determine 443 reddening values and intrinsic colours, and 209 metallicities for individual clusters without spectroscopic observations. This, the largest sample of M31 GCs presently available, is then used to analyse the metallicity distribution of M31 GCs, which is bimodal with peaks at [Fe/H]≈−1.7 and −0.7 dex. An exploration of metallicities as a function of radius from the M31 centre shows a metallicity gradient for the metal-poor GCs, but no such gradient for the metal-rich GCs. Our results show that the metal-rich clusters appear as a centrally concentrated spatial distribution; however, the metal-poor clusters tend to be less spatially concentrated. There is no correlation between luminosity and metallicity among the M31 sample clusters, which indicates that self-enrichment is indeed unimportant for cluster formation in M31.
The reddening distribution shows that slightly more than half of the GCs are affected by a reddening of E ( B − V ) ≲ 0.2 mag; the mean reddening value is   E ( B − V ) = 0.28^+0.23_−0.14 mag  . The spatial distribution of the reddening values indicates that the reddening on the north-western side of the M31 disc is more significant than that on the south-eastern side, which is consistent with the conclusion that the north-western side is nearer to us.     

Spectroscopy of the W Virginis star V1 (K 307 ) in the globular cluster M12

High-resolution CCD spectra have been obtained for the first time for the W Virginis star V1 (K 307) in the globular cluster M12 and its closest neighbor K 307b (m _pg=14^m; the angular distance from the W Vir star is δ<1 arcsec). We determined the fundamental parameters (T _eff=5600 K, logg=1.3, and T _eff=4200 K, logg=1.0 for the W Vir star and the neighboring star, respectively) and their detailed chemical composition. The derived metallicities of the two stars ([Fe/H]=?1.27 and ?1.22 relative to the solar value) are in good agreement with the metallicities of other cluster members. Changed CNO abundances were found in the atmosphere of the W Vir star: a small carbon overabundance, [C/Fe]=+0.30 dex, and a large nitrogen overabundance, [N/Fe]=+1.15 dex, with oxygen being underabundant, [O/Fe]≈?0.2 dex. The C/O ratio is ≥1. Na and the α-process elements Mg, Al, Si, Ca, and Ti are variously enhanced with respect to iron. We found an enhanced abundance of s-process metals relative to iron: [X/Fe]=+0.34 for Y, Zr, and Ba. The overabundance of the heavier metals La, Ce, and Nd with respect to iron is larger: [X/Fe]=+0.49. The largest overabundance was found for the r-process element europium, [Eu/Fe]=+0.82. The spectrum of the W Vir star exhibits the Hα and Hβ absorption-emission profiles and the He I λ5876 Å emission line, which are traditionally interpreted as a result of shock passage in the atmosphere. However, the radial velocities determined from absorption and emission features are in conflict with the formation pattern of a strong shock. The high luminosity log L/L _⊙ = 2.98, the chemica peculiarities, and the spectral peculiarity are consistent with the post-AGB evolution in the instability strip. The pattern of relative elemental abundances [X/Fe]in the atmosphere of the neighboring star K 307b is solar. Statistically significant differences were found only for sodium and α-process elements: the mean overabundance of light metals is [X/Fe]=+0.35.     

Pulsational MV versus [Fe/H] relation(s) for globular cluster RR Lyrae variables

We use the results from recent computations of updated non-linear convective pulsating models to constrain the distance modulus of Galactic globular clusters through the observed periods of first-overtone (RR _c ) pulsators. The resulting relation between the mean absolute magnitude of RR Lyrae stars 〈 M _V (RR)〉 and the heavy element content [Fe/H] appears well in the range of several previous empirical calibrations, but with a non-linear dependence on [Fe/H] so that the slope of the relation increases when moving towards larger metallicities. On this ground, our results suggest that metal-poor ([Fe/H]<−1.5) and metal-rich ([Fe/H]>−1.5) variables follow two different linear 〈 M _V (RR)〉−[Fe/H] relations. Application to RR Lyrae stars in the metal-poor globular clusters of the Large Magellanic Cloud (LMC) provides an LMC distance modulus of the order of 18.6 mag, thus supporting the 'long' distance scale. The comparison with recent predictions based on updated stellar evolution theory is briefly presented and discussed.     

Warped discs and the directional stability of jets in active galactic nuclei

The radial distribution of globular clusters in galaxies is always less peaked to the centre than that of the halo stars. Extending previous work to a sample of Hubble Space Telescope globular cluster systems in ellipticals, we evaluate the number of clusters potentially lost to the galactic centre as the integrals of the difference between the observed globular cluster system distribution and the underlying halo light profile. In the sample of galaxies examined it is found that the initial populations of globular clusters may have been ∼30 per cent to 50 per cent richer than now. If these 'missing' globular clusters have decayed and have been partly destroyed in the very central galactic zones, they have carried there a significant quantity of mass that, plausibly, contributed to the formation and feeding of a massive object therein. It is relevant to note that the observed correlation between the core radius of the globular cluster system and the parent galaxy luminosity can be interpreted as a result of evolution.     

The time-scale for core collapse in spherical star clusters

The collapse time for a cluster of equal-mass stars is usually stated to be either 330 central relaxation times (t_rc) or 12-19 half-mass relaxation times (t_rh). But the first of these times applies only to the late stage of core collapse, and the second only to low-concentration clusters. To clarify how the time depends on the density profile, the Fokker-Planck equation is solved for the evolution of a variety of isotropic cluster models, including King models, models with power-law density cusps of ρ ∼ r^−γ, and models with nuclei. The collapse times for King models vary considerably with the cluster concentration when expressed in units of t_rc or t_rh, but vary much less when expressed in units of t_rc divided by a dimensionless measure of the temperature gradient in the core. Models with cusps have larger temperature gradients and evolve faster than King models, but not all of them collapse: those with 0 < γ < 2 expand because they start with a temperature inversion. Models with nuclei collapse or expand as the nuclei would in isolation if their central relaxation times are short; otherwise their evolution is more complicated. Suggestions are made for how the results can be applied to globular clusters, galaxies, and clusters of dark objects in the centers of galaxies.Scott D. Tremaine     

Analysis and calibration of Ca ii triplet spectroscopy of red giant branch stars from VLT/FLAMES observations

We demonstrate that low-resolution Ca  ii triplet (CaT) spectroscopic estimates of the overall metallicity ([Fe/H]) of individual red giant branch (RGB) stars in two nearby dwarf spheroidal galaxies (dSphs) agree to ±0.1–0.2 dex with detailed high-resolution spectroscopic determinations for the same stars over the range  −2.5 < [Fe/H] < −0.5  . For this study, we used a sample of 129 stars observed in low- and high-resolution modes with VLT/FLAMES in the Sculptor and Fornax dSphs. We also present the data-reduction steps we used in our low-resolution analysis and show that the typical accuracy of our velocity and CaT [Fe/H] measurement is ∼2 km s⁻¹ and 0.1 dex, respectively. We conclude that CaT–[Fe/H] relations calibrated on globular clusters can be applied with confidence to RGB stars in composite stellar populations over the range  −2.5 < [Fe/H] < −0.5  .     

银河系中球状星团的空间分布和运动轨道

选用银河系中29个累积光谱型为F型的球状星团样本。根据它们的视向速度，绝对自行等参数，归算处理后得出了各样本星团的空间分布和运动速度。并以此作为初始条件，在给定的3种银河系引力势模型中，采用数值积分方法计算出各样本星团的运动轨道。计算结果表明：（1）大部分样本星团都位于银心距5kpc-10kpc的范围内，相对于银心呈球对称分布，它们的速度也呈椭球分布；（2）29个样本星团按其金属度大小和基本性发类，可分属HB和MP两个次系，且样本星团数随金属度[Fe/H]而变化，在[Fe/H]＝－1．6处出现一个峰值；（3）所有样本星团的轨道运动都呈周期性，大都在一个有界而不封闭的周期轨道上运动，其最大银心距大都在40kpc以内。不同的引力势模型对球状星团轨道的具体形态影响不大，在给定的引力势模型下，当某些星团的运动轨道穿越距银心1kpc附近的区域时会出现“混沌”行为。而样本星团的金属度与其轨道形态之间的相关性并不明显；（4）29个样本星团的轨道半长轴、远银心距和方位周期随金属度的变化规律基本相似。轨道偏心率与金属度有关，对于所选的晕族样本星团而言，大约有24％的样本星团的轨道偏心率低于0．4，不同的引力势模型对近银心距、偏心率和参数的不确定度等量影响较小，但是对远银心距、径向周期和方位周期等参数影响较为明显。     

Two-dimensional classification of globular clusters

The metallicities of 75 globular clusters are determined in the Pilachowskiet al. scale from the slopes of their giant branches in theV, B-V diagram. In the diagram giant branch slope, horizontal branch morphology type, the clusters form two sequences: a vertical sequence (group I) with blue horizontal branches and [Fe/H] from –2.2 to –1.2 and a diagonal sequence (group II) with horizontal branches changing from the blue to the red parallel with an increase of metallicity from –1.8 to –1.0. The differences in horizontal branch morphology of both cluster groups are probably caused by the difference in age, which is found to be of the order 1–2 billion years. It is shown that integrated reddening-free quantitiesQ and integrated spectral types cannot be used to determine metalicity without a previous division of clusters into groups.