Spatial structure of the old open cluster NGC 2420

The spatial structure of the intermediate and outer regions of the old open cluster NGC 2420 is analyzed using data from the catalog of Paparó. The differential and integrated distributions of the projected [ΔF(r) and F(r)] and spatial [Δf(r) and f(r)] stellar densities are obtained for various subsystems of cluster stars using Kholopov’s star-count method. Analysis of these curves shows that: (1) the cluster has at least three distinct spatial zones with different stellar-density gradients, (2) the each cluster subsystem has a layered structure, and (3) the spatial structure of the cluster changes systematically in the transition to subsystems containing fainter main-sequence stars. Empirical relations describing the structure of the cluster are also derived. Similar structural features can also be found in other globular and open clusters.     

Modeling and analysis of the spectrum of the globular cluster NGC 2419

The properties of the stellar population of the unusual object NGC 2419 are studied; this is the most distant high-mass globular cluster of the Galaxy’s outer halo, and a spectrum taken with the 1.93-m telescope of the Haute Provence Observatory displays elemental abundance anomalies. Since traditional high-resolution spectroscopicmethods are applicable to bright stars only, spectroscopic information for the cluster’s stellar population as a whole, integrated along the spectrograph slit placed in various positions, is used. Population synthesis is carried out for the spectrum of NGC 2419 using synthetic spectra calculated from a grid of stellar model atmospheres, based on the theoretical isochrone from the literature that best fits the color-magnitude diagram of the cluster. The derived age (12.6 billion years), metallicity ([Fe/H] = ?2.25 dex), and abundances of helium (Y = 0.26) and other chemical elements (a total of 14) are in a good qualitative agreement with estimates from the literature made from high-resolution spectra of eight red giants in the cluster. The influence on the spectrum of deviations from local thermodynamic equilibrium is considered for several elements. The derived abundance of α-elements ([α/Fe] = 0.13 dex, as the mean of [O/Fe], [Mg/Fe], and [Ca/Fe]) differs from the mean value in the literature ([α/Fe] = 0.4 for the eight brightest red giants) and may be explained by recently discovered in NGC2419 large [a/Fe] dispersion. Further studies of the integrated properties of the stellar population in NGC 2419 using higher-resolution spectrographs in various wavelength ranges should help improve our understanding of the cluster’s chemical anomalies.     

The chemical composition of stars in the globular clusters M 10, M 12, and M 71

The abundances of 19 chemical elements in the atmospheres of five stars belonging to three globular clusters have been determined by applying the model-atmospheremethod to 430.0–790.0 nm spectra obtained with the échelle spectrometer of the 6-m telescope of the Special Astrophysical Observatory. The abundances of silicon, calcium, iron-peak elements, copper, zinc, and neutron-capture elements follow the abundance patterns for halo stars. The abundance of sodium in M 10 giants provides evidence that different mixing mechanisms operate in halo and cluster stars or that light elements are enriched in different ways in the pre-stellar matter from which some globular clusters and halo stars were formed.     

The motion of a star in the vicinity of a globular cluster in an elliptical galaxy

The spatial motion of a star in the vicinity of a globular cluster located in an inhomogeneous, rotating elliptical galaxy (EG) is considered. Perturbations due to the gravitation of the galaxy are taken into account, taking it to be a two-layer system together with its halo: an inner ellipsoid, representing the lumious part of the galaxy, and a homeoid, representing space filled with dark matter between inner and outer ellipsoidal boundaries. The ellipsoids are taken to be homothetic and to have a common center, with the boundary of the outer ellipsoid coincident with the boundary of the galactic halo. The luminous part of the EG and the homeoid have different densities. The motion of the star near a globular cluster occurs outside the luminous part of the EG, but inside the homeoid. The concept of the “vicinity of the globular cluster” is concretized using the concept of a “sphere of influence” (and the gravitational sphere and Hill gravitational sphere). Stellar motions inside and outside the sphere of influence of the globular cluster are considered, and the region of possible motions is determined. A quasi-integral and surfaces of minimum energy are found, which under certain conditions can be transformed into an analog of the Jacobi integral and surfaces of zero velocity. The Lyapunov stability of the stationary solutions obtained is established. The results are applied to model EGs whose parameters coincide with those of NGC 4472 (M49), NGC 4636, and NGC 4374, which contain a large number of globular clusters, and are presented in the form of figures and tables. Using these galaxies as examples, it is shown that studying stellar motions, and also determining the libration points and establishing their stability, requires use of an exact, rather than an approximate, expression for the potential of the luminous part of the elliptical galaxy.     

Steady-state solutions for the motion of a globular cluster in an inhomogeneous, rotating elliptical galaxy

Steady-state solutions for the motion of a passively gravitating globular cluster (GC) inside an inhomogeneous, rotating, ellipsoidal elliptical galaxy (EG) are considered. It is assumed that an EG with a halo is comprised of a triaxial ellipsoid consisting of two layers. The first is formed by an inner, uniform ellipsoid representing the luminous part of the galaxy, while the second corresponds to the space between an inner and outer ellipsoid, which is uniformly filled with dark matter. The triaxial ellipsoids are taken to be homothetic and to have a common center; the space between them is called a homeoid. The outer boundary of the homeoid is the boundary of the galaxy halo. The densities of the luminous part of the EG and the homeoid are different. This picture of an EG is in agreement with our current understanding of galactic structure. The motion of the GC occurs outside the luminous part of the EG, but inside the homeoid, which is treated like a perturbing body. Steady-state solutions (libration points) are found for the GC, and its Lyapunov stability determined. The elliptical galaxies NGC 4472 (M49), NGC 4636, and NGC 4374, which contain a large number of GCs, are used as examples. Analysis of these galaxies shows that the exact expression for the potential of the luminous part of the EG must be used to find the libration points and study their stability, rather than an approximate expression for this potential.     

Spatial variations of groundwater vulnerability using cluster analysis

An investigation on quality of groundwater has been carried out in the river basin of Varaha located in Visakhapatnam District, Andhra Pradesh to find out the factors that are responsible for spatial variations of water vulnerability. The study area is underlain by the Precambrian rocks of Eastern Ghats over which the Recent Formations occur. Groundwater is a prime source for drinking and irrigation. The quality of groundwater is fresh and brackish with dominance of the latter. Groundwater samples are categorized into two major clusters A and B, using the dendrogram of cluster analyses. Out of these two major clusters, five sub-clusters I to V in the pre-monsoon season and six sub-clusters I to VI in the post-monsoon season are identified. The sub-clusters I to IV of pre-monsoon and I to V of post-monsoon seasons of the cluster A are characterized by less mineralized groundwater compared to those of V of pre-monsoon and VI of post-monsoon seasons of the cluster B, which represent highly mineralized groundwater. The low to high mineral content follows gradually from upstream to the downstream area, being higher in post-monsoon season in both the clusters A and B, depending upon the source, mineral dissolution, and precipitation, solubility and leaching of ions, ion exchange and adsorption processes. Spatial distributions of the sub-clusters give clues to understand the factors that cause variations of groundwater vulnerability at a specific site, vis-a-vis local and regional lithological and non-lithological influences. As a result, the quality of groundwater on a regional scale changes from Na⁺ > Mg²⁺ >Ca²⁺ > K⁺: HCO ₃ ^? > Cl^? > SO ₄ ^2? > NO ₃ ^? > F^? in the cluster A to Na⁺ > Mg²⁺ >Ca²⁺ > K⁺: Cl^? > HCO ₃ ^? > SO ₄ ^2? > NO ₃ ^? > F^? in the cluster B, following the topography. The classification of the area into the zones of relative groundwater vulnerability with respect to drinking water quality of the chemical composition of the sub-clusters helps the planners to identify the specific locations, where the inferior quality of groundwater can occur, for taking the remedial measures.     

Kinematics of stars in the old open cluster M67

We report an analysis of the kinematic properties of stars in the old open cluster M67 based on proper motions taken from a master catalog made up of nine different catalogs containing proper motions of stars in the cluster field. A modified Sanders method is used to identify 511 probable cluster members. The dependence of the mean radial components of the proper motions of cluster members on clustercentric radius indicates that the cluster core is expanding with a velocity of 0.4 km/s. The radial dependence of the mean tangential components of the proper motions suggests the possible rotation of the cluster core. The dispersions of the velocity components of the cluster members show no evidence for the dominance of elongated stellar orbits in the cluster. The kinetic energy of the cluster stars depends strongly on their mass.     

The motion of a globular cluster inside a rotating,layered, inhomogeneous elliptical galaxy

We consider the spatial motion of a globular cluster with a constant or variable mass inside a rotating, layered, inhomogenous elliptical galaxy with a constant or variable mass. An analog to the Jacobi integral is found, regions of possiblemotion are determined, and zero-velocity surfaces constructed. Stationary solutions (libration points) are determined, together with their stability according to the Lyapunov criterion. In the case of variable mass, the autonomization method is used to solve the equations of motion, and the autonomization criteria used to establish an analog of the Eddington-Jeans law for the variation of the density of the galaxy.     

Spatial structure analysis of regionalized compositions

Like compositions in general, regionalized compositions present the problem of spurious spatial correlation. To avoid this problem, this paper uses the additive-logratio transformation of regionalized compositions, following techniques introduced over the last few years for the statistical analysis of compositional data. It leads to an appropriate definition of a spatial covariance structure to describe spatial dependence between regionalized variables subject to constant-sum constraints in the case of weak stationarity. To illustrate stated problems, simulated data are used.     

Logarithmic density range and the percentage of stars in the cores of various subsystems of the globular clusters M56, M12, NGC 6535, NGC 6171, NGC 5466, and M92

Lower limits for the percentages of stars with various luminosities in the cores of six globular clusters are derived using stellar spatial density distributions f(r) to deep limiting B magnitudes obtained earlier. For NGC 6535 and NGC 5466, the logarithmic density range and Kholopov parameters D_f and D_r are also determined. These two parameters are correlated with the mean masses of stars of various subsystems and the total mass (number) of stars in the cluster.     

Spatial dynamics of retail structure and the venerable retail hierarchy

The retail system is continuously adapting itself to changing demographic conditions, consumer behavior and economic conditions. Existing retail units, getting larger in order to achieve economics of scale, and new forms of large-scale retailing do not fit easily in the traditional spatial pattern of retail concentrations. Neverteless the spatial distribution of retailing in urban areas, as schematized by Berry thirty-five years ago, still has its value. Through an upward hierarchical movement the retail system has adapted itself to an inflexible spatial system, in which downtown has still a dominant position. Future developments, however, may weaken the position of central shopping areas in favour of peripheral locations. This revised version was published online in July 2006 with corrections to the Cover Date.     

Electronic and magnetic structure of vivianite: cluster molecular orbital calculations

The electronic and magnetic structure of the octahydrophosphate vivianite, Fe₃(PO₄)₂·8H₂O, has been investigated by cluster molecular orbital calculations in local spin density approximation. Optical and Mössbauer spectra are well reproduced by the calculations, and the differences between the two iron sites can be correlated with differences in the geometrical structure of the first coordination sphere. The spin structure within the crystallographic ac plane is derived and explained on the basis of different superexchange pathways via edges of the phosphate tetrahedra. The calculations demonstrate that quite large clusters (up to 118 atoms) are necessary to arrive at reliable results.     

The crystal structure of a 1M lepidolite

Summary The crystal structure of a 1M lepidolite coexisting with the 2M ₂ form, from the Island of Elba, Tuscany, Italy has been determined and refined by least-squares methods using three-dimensional data collected by the Weissenberg method with CuK radiation. The lattice parameters are:a=5.20(2),b=9.01(2),c=10.09(1) Å and =99.28°(33). The space group isC2/m. The final residual isR=6.7% using isotropic temperature factors. Comparison of the 1M lepidolite structure with that of the coexisting 2M ₂ polymorph shows the absence of significant differences both in chemical composition and in structural parameters; also for the 1M structure the main features are, in fact, a remarkable octahedral ordering and a considerable distortion of the tetrahedra joined with a relatively low ditrigonality (=7.41°) of their arrangement.

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Structure cristalline d'une lépidolite 1M

Résumé La structure cristalline d'une lépidolite 1M de l'Île d'Elbe, Toscane, Italie, coexistant dans le même échantillon avec le polymorphe 2M ₂, a été resolue et affinée par la methode des moindres carrés en utilisant les données recueillies à partir de clichés de Weissenberg, enregistrés sous rayonnement CuK. Les dimensions de la maille sont les suivantes:a=5.20(2),b=9.01(2),c=10.09(1) Å, =99.28°(33). Le groupe d'espace estC2/m. L'affinement de la structure en isotropie des facteurs d'agitation thermique a amené à une valeur finale du facteurR de 6.7%. En comparant la structure de la lépidolite 1M avec celle du polymorphe 2M ₂ présent dans le même échantillon on peut noter qu'il n'y a pas, pratiquement, des differences significatives entre les deux, soit en composition chimique soit en paramètres structuraux; en effet on remarque que la lépidolite 1M aussi est caractérisée par un considerable ordre dans la distribution des cations dans la couche octaèdrique, par une forte déformation des tetraèdres et par une faible déviation de l'héxagonalitè (=7.41°) de la disposition de ces dernier polyèdres.

     

The chemical evolution of globular clusters

The sequence of events determining the initial stages of star formation is analyzed in framework of the self-enrichment scenario. The computations are based on a single-zone chemo-dynamical model. It is shown that the first episode of star formation was characterized by an initial mass function shifted toward massive stars (M ≥ 8M_⊙). We argue that the transition to a star formation with a normal (Salpeter) initial mass function was due to more efficient radiative cooling of the proto-globular cluster gas after its enrichment to a metallicity of Z ～ 0.02 Z_⊙ in agreement with those observed in globular clusters.     

地热流体水化学特征与地质构造关系的Q型聚类分析

以天津地区大量的地热流体水化学数据为研究对象,利用Q-型聚类分析法,以构造单元及热储层为分类依据,将研究区分为17个亚类进行逐级聚类.结果表明:地热流体的水化学特征与地质构造单元、热储层特征有着较好的相关关系,与传统地球化学研究方法的结论一致.而且该方法具有客观、高效、直观的特点,所以对水质数据积累较多的地区,利用聚类分析法研究地下水的地球化学特征具有很好的应用前景.     

Source zones of the catastrophic Simushir earthquakes on November 15, 2006 (M w = 8.3) and January 13, 2007 (M w = 8.1) and the deep crust structure beneath the Middle Kuril segment

The data on catastrophic earthquakes with magnitudes of 8.3 and 8.1 that occurred in the Simushir Island area on November 15, 2006, and January 13, 2007, respectively, were compared with the results of land-sea deep seismic studies by different methods (deep seismic sounding, the correlation method of refracted waves, the earthquake converted-wave method, the common mid-point) in the Central Kuril segment. The structure of the Earth’s crust and the hypocentral zones of these earthquakes were analyzed. It was established that the hypocenter of the main shock of the first earthquake was located at the bend of the seismofocal zone under the island slope of the trench on the outer side of the subsiding lithospheric plate in the rapidly rising granulite-basite (ìbasalticî) crustal layer, which, at depths of 7–15 km, replaced the granulite-gneiss layer. This was accompanied by an increase of the seismic wave velocity from 6.4 to 7.1 km/s. The focus of the second earthquake was located beneath the axis of the deep-sea trench. The aftershocks were concentrated in two bands 60–120 km wide that extend along the trench, as well as in the third zone orthogonal to the island arc. It was shown that the epicenters of the earthquakes are linked with regional faults. The main shock of the first earthquake (November 15, 2006) was interpreted as a thrust fault and the second one (January 13, 2007) was attributed to a normal fault.     

Mössbauer effect study of the spin structure in natural hematites

Three natural hematites, α-Fe₂O₃, from the region of Elba have been investigated by means of ⁵⁷Fe Mössbauer spectroscopy at variable temperatures between 80 and 400K. The samples were selected on the basis of their different morphology as observed from powder X-ray diffraction and transmission electron microscopy. The mean crystallite diameters (MCD) along [104] are 1000, 280 and 40 nm respectively. Energy-dispersive analyses of X-rays revealed the presence of minor amounts of Si impurities in those two hematites having the largest MCD. All three hematites show the coexistence at low temperatures of antiferromagnetic-like (AF) and weakly-ferromagnetic-like (WF) spin states. The saturation values of the AF and WF magnetic hyperfine fields and quadrupole shifts have been determined, from which conclusions are drawn concerning the spin structure in relation to the crystallinity of the samples. The variations of the hyperfine parameters in the Morin-transition region indicate a gradual reorientation of both AF and WF spins towards the basal plane. As expected, the Morin transition itself is affected by the particle size. The two hematites exhibiting the largest particle dimensions still show an AF contribution for T>270K. It is suggested, and argued that this unusual behaviour is due to the presence of Si⁴⁺, and hence Fe²⁺, in the lattice. The characteristic Mössbauer temperatures and the intrinsic isomer shifts were evaluated from the temperature variation of the observed isomer shifts. Both parameters are not significantly affected by the morphology and are in excellent agreement with data obtained for synthetic hematites.     

承德市土壤重金属空间结构与分布特征

基于地统计学和GIS相结合的方法,对承德全域表层土壤重金属As、Cd、Cr、Cu、Hg、Ni、Pb、Zn、微量元素Se正态分布特征、主导分布趋势及相互作用规律进行了分析,确定了不同元素最适宜的地统计插值模型并厘定出其空间分布规律。结果表明：As、Cd、Cr、Cu、Hg、Ni、Pb、Zn的质量含量平均值分别为8.28,0.200,60.85,24.37,0.034,27.76,26.65,77.10 mg/kg,Cd、Cu、Hg和Pb变异系数分别为385%、143%、350%、118%,分异性强。Zn含量均值受土壤类型影响显著,Cr、Cu、Ni含量均值则受土地利用类型影响显著。经过不同趋势阶数元素插值误差的综合对比,确定As、Cr、Pb、Zn、Ni、Se适宜选择无趋势参数,Hg和Cu适宜选择一阶趋势参数,而Cd适宜选择二阶趋势参数。As的理论模型为指数模型,主要受到结构性因素的影响;Cd、Cr、Cu、Hg、Ni、Pb、Zn、Se的理论模型为线性模型,主要受到随机性因素的影响。通过普通克里格插值图可见区内9种元素具有北低南高的特点,中部地区形成了一条较宽的Pb高值带,与Cd相似。按照含量分布特点,土壤中Cr和Ni、Cu和Hg、Zn和Pb、Se和Cd之间的高值空间展布区具有相似性且来源相同,仅As具有个性,分析结果与传统统计学结果数据保持部分一致性。     

Multiplicity of main-sequence turn-offs in globular clusters

We present color-magnitude diagrams of globular clusters for models with self-enrichment and primordial enrichment. The models with self-enrichment turn out to have two or more main-sequence turn-off points in the color-magnitude diagram if the fraction of mass lost by the globular cluster as a result of supernova explosions does not exceed 95–97%. The models with primordial enrichment can have only one main-sequence turn-off point. We argue that the cluster ω Cen evolved according to a self-enrichment scenario.