W. S. Dias

Overlapping abundance gradients and azimuthal gradients related to the spiral structure of the Galaxy

The connection between some features of the metallicity gradient in the Galactic disc, best revealed by Open Clusters and Cepheids, and the spiral structure, has been explored. The step-like abrupt decrease in metallicity at 8.5kpc (with R0= 7.5kpc, or at 9.5kpc if R0= 8.5kpc is adopted) is well explained by the corotation ring-shaped gap in the density of gas, which isolates the internal and external regions of the disc one from the other. This solves the long-standing problem of a lack of understanding of the different chemical characteristics of the inner and outer parts of the disc. The time required to build up the metallicity difference between the two sides of the step is a measure of the minimal lifetime of the present grand-design spiral pattern structure, of the order of 3 Gyr. The plateaux observed on both sides of the step are interpreted in terms of the large-scale radial motion of the stars and of the gas flow induced by the spiral structure. The star formation rate revealed by the density of open clusters is maximum in the Galactic radial range from 6 to 12kpc (with an exception of a narrow gap at corotation), coinciding with the region where the four-arms mode is allowed to exist. We argue that most of the old open clusters situated at large Galactocentric radii were born in this inner region where conditions more favourable for star formation are found. The ratio of α-elements to Fe of the sample of Cepheids does not vary appreciably with the Galactic radius, which reveals a homogeneous history of star formation. Different arguments are forwarded to show that the usual approximations of chemical evolution models, which assume fast mixing of metallicity in the azimuthal direction and ignore the existence of the spiral arms, are poor ones.

Fitting isochrones to open cluster photometric data - A new global optimization tool

We present a new technique to fit color–magnitude diagrams of open clusters based on the cross-entropy global optimization algorithm. The method uses theoretical isochrones available in the literature and maximizes a weighted likelihood function based on distances measured in the color–magnitude space. The weights are obtained through a non parametric technique that takes into account the star distance to the observed center of the cluster, observed magnitude uncertainties, the stellar density profile of the cluster among others. The parameters determined simultaneously are distance, reddening, age and metallicity. The method takes binary fraction into account and uses a Monte-Carlo approach to obtain uncertainties on the determined parameters for the cluster by running the fitting algorithm many times with a re-sampled data set through a bootstrapping procedure. We present results for 9 well studied open clusters, based on 15 distinct data sets, and show that the results are consistent with previous studies. The method is shown to be reliable and free of the subjectivity of most previous visual isochrone fitting techniques.

Fitting isochrones to open cluster photometric data - II. Nonparametric open cluster membership likelihood estimation and its application in optical and 2MASS near-IR data

Aims. Open clusters are essential tools for understanding Galactic structure, as well as stellar evolution, because they are distributed over the whole Galactic plane, and because their ages, distances, and reddening can be determined. The values of derived cluster fundamental parameters can vary greatly because of the often subjective nature of both the isochrone fitting technique and member star selection. To minimize the subjectivity in the selection of stars and to improve the fitting procedure, our group has developed a nonparametric method that estimates the membership likelihood for apparent cluster stars. Methods. The cluster member selection method is based on the star position relative to the cluster center, the density of stars in the color–magnitude diagram (which can be multidimensional), the photometric errors, and the limiting magnitude of observations. We use this method, together with the global optimization tool developed in our previous articles, to fit theoretical isochrones to open cluster photometric data, making use of UBV and 2MASS data sets. Results. Using this likelihood estimation as a weight in the fitting procedure, we show that the method is robust in that it assigns low weights to most contaminating stars and high weights to the stars that are likely cluster members. Our results show that the fundamental parameters determined using 2MASS data agree with those from UBV data when both are determined from the global optimization fitting method, however, the analysis of the open cluster Dias 6 indicates that a revision of the determined parameters might be required for some cases.

Open clusters in the Third Galactic Quadrant III. Alleged binary clusters

Aims. We aim to determine accurate distances and ages of eight open clusters in order to: (1) assess their possible binarity (2) provide probes to trace the structure of the Third Galactic Quadrant. Methods. Cluster reddenings, distances, ages and metallicities are derived from ZAMS and isochrone fits in UBVRI photometric diagrams. Field contamination is reduced by restricting analysis to stars within the cluster limits derived from star counts. Further membership control is done by requiring that stars have consistent positions in several diagrams and by using published spectral types. Results. The derived distances, ages and metallicities have shown that none of the analysed clusters compose binary/double systems. Of the four candidate pairs, only NGC 2383/NGC 2384 are close to each other, but have different metallicities and ages. Ruprecht 72 and Ruprecht 158 are not clusters but fluctuations of the field stellar density. Haffner 18 is found to be the superposition of two stellar groups at different distances: Haffner 18(1) at 4.5 kpc and Haffner 18(2) between 9.5 and 11.4 kpc from the Sun. The derived distances and ages have been used to situate the clusters in the Galactic context. In particular, young stellar groups trace spiral structure at large Galactocentric radii. At least two clusters formed during the last few 10 8 yr in an interstellar medium with less than solar abundances. Conclusions. In contrast with the LMC, double clusters are apparently rare, or even non existent, in the undisturbed environment of the Third Galactic Quadrant. This leaves open the question of whether binary clusters form more easily toward denser and more violent regions of the Milky Way such as the inner Galaxy.

The possibility of determining open-cluster parameters from BVRI photometry

In the last decades we witnessed an increase in studies of open clusters of the Galaxy, especially because of the good determination for a wide range of values of parameters such as age, distance, reddening, and proper motion. The reliable determination of the parameters strongly depends on the photometry available and especially on the U filter, which is used to obtain the color excess E(B-V) through the color-color diagram (U-B) by (B-V) by fitting a zero age main-sequence. Owing to the difficulty of performing photometry in the U band, many authors have tried to obtain E(B-V) without the filter. But because of the near linearity of the color-color diagrams that use the other bands, combined with the fact that most fitting procedures are highly subjective (many done by eye) the reliability of those results has always been questioned. Our group has recently developed, a tool that performs isochrone fitting in open-cluster photometric data with a global optimization algorithm, which removes the need to visually perform the fits and thus removes most of the related subjectivity. Here we apply our method to a set of synthetic clusters and two observed open clusters (Trumpler 1 and Melotte 105) using only photometry for the BVRI bands. Our results show that, considering the cluster structural variance caused only by photometric and Poisson sampling errors, our method is able to recover the synthetic cluster parameters with errors of less than 10% for a wide range of ages, distances, and reddening, which clearly demonstrates its potential. The results obtained for Trumpler 1 and Melotte 105 also agree well with previous literature values.

Fitting isochrones to open cluster photometric data - III. Estimating metallicities from UBV photometry

The metallicity is a critical parameter that affects the correct determination fundamental characteristics stellar cluster and has important implications in Galactic and Stellar evolution research. Fewer than 10 % of the 2174 currently catalog open clusters have their metallicity determined in the literature. In this work we present a method for estimating the metallicity of open clusters via non-subjective isochrone fitting using the cross-entropy global optimization algorithm applied to UBV photometric data. The free parameters distance, reddening, age, and metallicity simultaneously determined by the fitting method. The fitting procedure uses weights for the observational data based on the estimation of membership likelihood for each star, which considers the observational magnitude limit, the density profile of stars as a function of radius from the center of the cluster, and the density of stars in multi-dimensional magnitude space. We present results of [Fe/H] for nine well-studied open clusters based on 15 distinct UBV data sets. The [Fe/H] values obtained in the ten cases for which spectroscopic determinations were available in the literature agree, indicating that our method provides a good alternative to determining [Fe/H] by using an objective isochrone fitting. Our results show that the typical precision is about 0.1 dex.

Highly dynamically evolved intermediate-age open clusters

We present a comprehensive UBVRI and Washington CT1T2 photometric analysis of seven catalogued open clusters, namely: Ruprecht 3, 9, 37, 74, 150, ESO 324-15 and 436-2. The multi-band photometric data sets in combination with 2MASS photometry and Gaia astrometry for the brighter stars were used to estimate their structural parameters and fundamental astrophysical properties. We found that Ruprecht 3 and ESO 436-2 do not show self-consistent evidence of being physical systems. The remained studied objects are open clusters of intermediate-age (9.0 < log(t yr-1) < 9.6), of relatively small size (r_cls ~ 0.4 - 1.3 pc) and placed between 0.6 and 2.9 kpc from the Sun. We analized the relationships between core, half-mass, tidal and Jacoby radii as well as half-mass relaxation times to conclude that the studied clusters are in an evolved dynamical stage. The cluster masses obtained by summing those of the observed cluster stars resulted to be ~ 10-15 per cent of the masses of open clusters of similar age located closer than 2 kpc from the Sun. We found that cluster stars occupy volumes as large as those for tidally filled clusters.

A multimembership catalogue for 1876 open clusters using UCAC4 data

We acknowledge financial support from the Spanish Ministry for Economy and Competitiveness and FEDER funds through grants AYA-2010-17631, BES-2011-049077, AYA-2013-40611-P and AYA016-75931-C2-1-P. LS acknowledges financial support from the Brazilian funding agency FAPESP (postdoc fellowship process number 2016/21664-2). AM acknowledges financial support from the Brazilian funding agency FAPESP (postdoc fellowship process number 2014/11806-9).

UBV(RI)C photometry of the open clusters Be 15, Be 80 and NGC 2192

The three open clusters Be 15, Be 80 and NGC 2192 have been observed using CCD UBV(RI) C photometry at the San Pedro Martir Observatory, Mexico within the framework of our open-cluster survey. The fundamental parameters of interstellar reddening, distance and age have been derived, and also the metallicity for NGC 2192 (solar metallicity has been assumed for the other two). By shifting the colours of Schmidt-Kaler in the (U - B, B ― V) two-colour diagram along the appropriate reddening vector, the interstellar reddenings have been derived as E(B - V) = 0.23 ± 0.03 mag for Be 15, 1.31 ± 0.05 for Be 80, and 0.16 ± 0.03 for NGC 2192. Evidence is shown for a variable interstellar extinction across the cluster Be 80. For NGC 2192, a nicely consistent fit is obtained for both the interstellar reddening and the metallicity ([Fe/H] = ―0.31) using simultaneously the F-type and red-clump stars. By fitting isochrones to the observed sequences of these three clusters in various colour-magnitude diagrams of different colour indices (B ― V, V ― I or V ― R), the averages of distance moduli and heliocentric distances [( V — M V ) o (mag); d(pc)] are the following: (10.74 ± 0.01; 1202) for Be 15, (10.75 ± 0.01; 1413) for Be 80 and (12.7 ± 0.01; 3467) for NGC 2192, and the averages of the inferred best ages [log(age); age(Gyr)] are (8.6 ± 0.05; 0.4) for Be 80 and (9.15 ± 0.05; 1.4) for NGC 2192; for Be 15 there are two distinct possibilities for the age fit, depending on the membership of three brighter stars (9.35 or 9.95 ± 0.05; 2.2 or 8.9). The need for spectroscopic observations in Be 15 is emphasized to select between alternate reddening and age solutions, and for deeper UBV observations in Be 80 to study in greater detail the variable interstellar, or intracluster, reddening across this cluster.

Models for the 3D axisymmetric gravitational potential of the Milky Way galaxy - A detailed modelling of the Galactic disk

Aims. Galaxy mass models based on simple and analytical functions for density and potential pairs have been widely proposed in the literature. Disk models that are constrained solely by kinematic data only provide information about the global disk structure very near the Galactic plane. We attempt to circumvent this issue by constructing disk mass models whose three-dimensional structures are constrained by a recent Galactic star counts model in the near-infrared and also by observations of the hydrogen distribution in the disk. Our main aim is to provide models for the gravitational potential of the Galaxy that are fully analytical but also give a more realistic description of the density distribution in the disk component. Methods. We produced fitted mass models from the disk model, which is directly based on the observations divided into thin and thick stellar disks and Hu2009I and H 2 disks subcomponents, by combining three Miyamoto-Nagai disk profiles of any model order (1, 2, or 3) for each disk subcomponent. The Miyamoto-Nagai disks are combined with models for the bulge and dark halo components and the total set of parameters is adjusted by observational kinematic constraints. A model that includes a ring density structure in the disk, beyond the solar Galactic radius, is also investigated. Results. The Galactic mass models return very good matches to the imposed observational constraints. In particular, the model with the ring density structure provides a greater contribution of the disk to the rotational support inside the solar circle. The gravitational potential models and their associated force-fields are described in analytically closed forms. Conclusions. The simple and analytical models for the mass distribution in the Milky Way and their associated three-dimensional gravitational potential are able to reproduce the observed kinematic constraints and, in addition, they are also compatible with our best knowledge of the stellar and gas distributions in the disk component. The gravitational potential models are suited for investigations of orbits in the Galactic disk.