Development of Multilayer Models of Globular Star Clusters and Study of Their Evolution

Usually, models of globular star clusters are created by analyzing their luminosity and other observation parameters. The goal of this work is to create stable models of globular clusters based on the laws of mechanics. It is necessary to set the coordinates, velocities and masses of the stars so that as a result of their gravitational interaction the globular cluster is not destroyed. This is not an easy task, and it has been solved in this paper. Using an exact solution of the axisymmetric gravitational interaction of N-bodies, single-layer spherical structures were created. They are combined into multilayer models of globular clusters. An algorithm and a program for their creation is described. As a result of solving the problem of gravitational interaction of N bodies, evolution of 5-, 10-, and 15-layer structures was studied. During the inter-body interaction, there proceeds a transition from the initial specially organized structure to a structure with bodies, uniformly distributed in space. The number of inter-body collisions decreases, and the globular cluster model passes into the stable form of its existence. The collisions of bodies and the acquisition of rotational motion and thermal energy by them are considered. As a result of the passage to scaled dimensions, the results were recalculated to the conditions of globular star clusters. The periods of rotation and the temperatures of merged stars are calculated. Attention is paid to a decreased central-body mass in the analyzed models of globular star clusters.

Age and Mass Estimates for 41 Star Clusters in M33

In this second paper of our series, we estimate the age of 41 star clusters, which were detected by Melnick & D'odorico in the nearby spiral galaxy M33, by comparing the integrated photometric measurements with theoretical stellar population synthesis models of Bruzual & Charlot. Also, we calculate the mass of these star clusters using the theoretical M/LV ratio. The results show that, these star clusters formed continuously in M33 from ~ 7 × 106–1010 years and have masses between ~ 103 and 2 × 106M☉. M33 frames were observed as a part of the BATC Multicolor Survey of the sky in 13 intermediate-band filters from 3800 to 10 000?. The relation between age and mass confirms that the sample star cluster masses systematically decrease from the oldest to the youngest.

Estimating the Metallicity of Old Star Clusters in M33

Based on the method proposed by Kong et al. and on the multi-color spectrophotometry by Ma et al., we estimate the metallicities of 16 old star clusters in the nearby spiral galaxy M33, ten of which are halo globular clusters. These old clusters are all metal poor, the range of metallicity ([Fe/H]) is from-0.14 to-2.12. In general, our results are consistent with those derived by other methods, such as integrated spectra and photometry, and our study confirms the reliability of the method of Kong et al.

Positions and Spectral Energy Distributions of 41 Star Clusters in M33

We present accurate positions and multi-color photometry for 41 star clusters detected by Melnick & D'odorico in the nearby spiral galaxy M33 as a part of the BATC Color Survey of the sky in 13 intermediate-band filters from 3800 to 10 000 A. The coordinates of the clusters are found from the HST Guide Star Catalog. By aperture photometry, we obtain the spectral energy distributions of the clusters. Using the relations between the BATC intermediate-band system and UBVRI broadband system, we derive their V magnitudes and B - V colors and find that most of them are blue, which is consistent with previous findings.

The Long-term Survival Chances of Young Massive Star Clusters

We review the long-term survival chances of young massive star clusters （YMCs）, hallmarks of intense starburst episodes often associated with Violent galaxy interactions. We address the key question as to whether at least some of these YMCs can be considered protoglobular clusters （GCs）, in which case these would be expected to evolve into counterparts of the ubiquitous old GCs believed to be among the oldest galactic building blocks. In the absence of significant external perturbations, the key factor determining a cluster＇s long-term survival chances is the shape of its stellar initial mass function （IMF）. It is, however, not straightforward to assess the IMF shape in unresolved extragalactic YMCs. We discuss in detail the promise of using high-resolution spectroscopy to make progress towards this goal, as well as the numerous pitfalls associated with this approach. We also discuss the latest progress in worldwide efforts to better understand the evolution of entire cluster systems, the disruption processes they are affected by, and whether we can use recently gained insights to determine the nature of at least some of the YMCs observed in extragalactic starbursts as proto-GCs. We conclude that there is an increasing body of evidence that GC formation appears to be continuing until today; their long-term evolution crucially depends on their environmental conditions, however.

The NGC 7742 star cluster luminosity function： a population analysis revisited

We re-examine the properties of the star cluster population in the circumnuclear starburst ring in the face-on spiral galaxy NGC 7742, whose young cluster mass function has been reported to exhibit significant deviations from the canonical power law. We base our reassessment on the clusters＇ luminosi- ties （an observational quantity） rather than their masses （a derived quantity）, and confirm conclusively that the galaxy＇s starburst-ring clusters--and particularly the youngest subsample, log（t yr-1） ≤7.2- show evidence of a turnover in the cluster luminosity function well above the 90% completeness limit adopted to ensure the reliability of our results. This confirmation emphasizes the unique conundrum posed by this unusual cluster population.

Stellar populations in star clusters

Stellar populations contain the most important information about star cluster formation and evo- lution. Until several decades ago, star clusters were believed to be ideal laboratories for studies of simple stellar populations （SSPs）. However, discoveries of multiple stellar populations in Galactic globular clus- ters have expanded our view on stellar populations in star clusters. They have simultaneously generated a number of controversies, particularly as to whether young star clusters may have the same origin as old globular clusters. In addition, extensive studies have revealed that the SSP scenario does not seem to hold for some intermediate-age and young star clusters either, thus making the origin of multiple stellar popu- lations in star clusters even more complicated. Stellar population anomalies in numerous star clusters are well-documented, implying that the notion of star clusters as true SSPs faces serious challenges. In this review, we focus on stellar populations in massive clusters with different ages. We present the history and progress of research in this active field, as well as some of the most recent improvements, including ob- servational results and scenarios that have been proposed to explain the observations. Although our current ability to determine the origin of multiple stellar populations in star clusters is unsatisfactory, we propose a number of promising projects that may contribute to a significantly improved understanding of this subject.

Astrophysical parameters of ten poorly studied open star clusters

We present the fundamental parameters of ten open star clusters, nominated from Kronberger et al. who presented some newly discovered stellar groups on the basis of the Two Micron All Sky Survey photometry and Digitized Sky Survey visual images. Star counts and photometric parameters （radius, membership, distance, color excess, age, luminosity function, mass function, total mass, and dynamical relaxation time） have been determined for these ten clusters for the first time. In order to calibrate our procedures, the main parameters （distance, age, and color excess） have been reestimated for another five clusters, which are also studied by Kronberger et al.

Candidate members of star clusters from LAMOST DR2

In this work, we provide 2189 photometrically- and kinematically-selected candidate members of 24 star clusters from the LAMOST DR2 catalog. We perform two-step membership identification： selection along the stellar track in the colormagnitude diagram, i.e., photometric identification, and selection from the distribution of radial velocities, i.e. the kinematic identification. We find that the radial velocities from the LAMOST data are very helpful in the membership identification. The mean probability of membership is 40% for the sample selected with radial velocity. With these 24 star clusters, we investigate the performance of the radial velocity and metallicity estimated with the LAMOST pipeline. We find that the systematic offsets in radial velocity and metallicity are 0.85 ± 1.26 km s-1and-0.08 ± 0.04 dex, with dispersions of 5.47＋1.16-0.71 km s-1and 0.13＋0.04-0.02 dex, respectively. Finally, we propose that the photometrically-selected candidate members of the clusters covered by the LAMOST footprint should be assigned higher priority so that more candidate stars can be observed.

13 Galactic Star Clusters in Gaia DR3 Identified by An Improved FoF and UPMASK Hybrid Method Using MvC

Open clusters(OCs)serve as invaluable tracers for investigating the properties and evolution of stars and galaxies.Despite recent advancements in machine learning clustering algorithms,accurately discerning such clusters remains challenging.We re-visited the 3013 samples generated with a hybrid clustering algorithm of FoF and pyUPMASK.A multi-view clustering(MvC)ensemble method was applied,which analyzes each member star of the OC from three perspectives—proper motion,spatial position,and composite views—before integrating the clustering outcomes to deduce more reliable cluster memberships.Based on the MvC results,we further excluded cluster candidates with fewer than ten member stars and obtained 1256 OC candidates.After isochrone fitting and visual inspection,we identified 506 candidate OCs in the Milky Way.In addition to the 493 previously reported candidates,we finally discovered 13 high-confidence new candidate clusters.

Studies of a possible new Herbig Ae/Be star in the open cluster NGC 7380

We present a study of the star 2MASS J22472238＋5801214 with the aim of identifying its true nature which has hitherto been uncertain. This object, which is a member of the young cluster NGC 7380, has been variously proposed to be a Be star, a D-type symbiotic and a Herbig Ae/Be star in separate studies. Here we present optical spectroscopy, near-IR photometry and narrow band Hα imaging of the nebulosity in its environment. Analysis of all these results, including the spectral energy distribution constructed from available data, strongly indicate the source to be a Herbig Ae/Be star. The star is found to be accompanied by a nebulosity with an interesting structure. A bow-shock shaped structure, similar to a cometary nebula, is seen very close to the star with its apex oriented towards the photoionizing source of this region （i.e. the star DH Cep）. An interesting spectroscopic finding, from the forbidden [StI] 6716, 6731A and [OI] 6300A lines, is the detection of a blue-shifted high velocity outflow （200 -t-50 km s-1） from the star.

A study of variable stars in the open cluster NGC 1582 and its surrounding field

This paper presents Charge-Coupled Device time-series photometric observations of the open cluster NGC 1582 and its surrounding field with Johnson B, V and R filters by using the Nanshan 1 m telescope administered by Xinjiang Astronomical Observatory. 19 variable stars and three variable candi- dates were detected in a 45＇ - 48.75＇ field around the cluster. 12 of the variable stars are newly-discovered variable objects. The physical properties, classifications and memberships of these 22 objects are studied through their light curves, their positions on the color-magnitude diagram and with archival data from the Naval Observatory Merged Astrometric Dataset. Among these objects, five are eclipsing binary systems, six are pulsating variable stars including one known 6 Scuti star and one newly-discovered RR Lyrae star. The distance to the RR Lyrae star is estimated to be 7.9 - 0.3 kpc, indicating that the star is located far behind the cluster. Four variable stars are probable members of the cluster, and 13 of the 22 objects are confirmed to be field stars.

Variable stars in the open cluster NGC 2141

We report the results of a search for variable stars in the open cluster NGC 2141. Ten variable stars are detected, among which nine are new variable stars and they are classified as three short-period W UMa-type eclipsing binaries, two EA- type eclipsing binaries, one EB-type eclipsing binary, one very short-period RS CVn- type eclipsing binary, one d-type RR Lyrae variable star, and one unknown type of variable star. The membership and physical properties are discussed, based on their light curves, positions in the color magnitude diagrams, spatial locations and periods. A known EB-type eclipsing binary is also identified as a blue straggler candidate in the cluster. Furthermore, we find that all eclipsing contact binaries have prominent asymmetric eclipses and display the O＇Connell effect, which increases with a decrease in orbital periods. This suggests that the O＇Connell effect is probably related to the evolution of the orbital period in short period eclipsing binary systems.

Variable stars in the field of open cluster NGC 2126

We report the results of a time-series CCD photometric survey of variable stars in the field of open cluster NGC 2126. In about a one square degree field covering the cluster, a total of 21 variable candidates are detected during this survey, of which 16 are newly found. The periods, classifications and spectral types of 14 newly discovered variables are discussed, which consist of six eclipsing binary systems, three pulsating variable stars, three long period variables, one RS CVn star, and one W UMa or δ Scuff star. In addition, there are two variable candidates, the properties of which cannot be determined. By a method based on fitting observed spectral energy distributions of stars with theoretical ones, the membership probabilities and the fundamental parameters of this cluster are determined. As a result, five variables are probably members of NGC 2126. The fundamental parameters of this cluster are determined as： metallicity to be 0.008 Z, age log（t） = 8.95, distance modulus （m - M）0 = 10.34 and reddening value E（B - V） = 0.55 mag.

Binary star detection in the open cluster King 1 field

A rarely studied open cluster,King 1 is observed using the 1.3-m telescope equipped with a 2 k×4 k CCD at Vainu Bappu Observatory,India.We analyze the photometric data obtained from CCD observations in both B and V bands.Out of 132 detected stars in the open cluster King 1 field,we have identified four stellar variables,and two among them are reported as newly detected binary systems.The parallax values from Gaia DR2 suggest that the open cluster King 1 is in the background of these two detected binary systems,falling along the same line of sight,giving rise to different parallax values.Periodogram analysis was carried out using Phase Dispersion Minimization(PDM)and the Lomb-Scargle(LS)method for all the detected variables.PHysics Of Eclipsing Binari Es(PHOEBE)is extensively employed to model various stellar parameters of both the detected binary systems.Based on the modeling results obtained from this work,one of the binary systems is reported for the first time as an Eclipsing Detached(ED)and the other as an Eclipsing Contact(EC)binary of W-type W UMa.

Discovery of 13 New Variable Stars in the Field of the Open Cluster NGC 2168 (M35)

A wide-field time-series CCD photometric survey of variable stars in the field of the open cluster NGC 2168 was carried out using the BATC Schmidt telescope. In total 13 new variable stars are discovered with three W UMa systems,one EA type and two EB type eclipsing binaries （one of them could be a W UMa system）, and seven pulsating stars including three candidates of δ Scuti stars.

Searching for Variable Stars in and around Open Clusters

We present a snapshot-of our recent results of a variable star survey in 1 degree fields around three open clusters: NGC 188, NGC 7789 and M67. A total number of 39 variable stars are newly discovered, including 22 W UMa stars, 10 EA (Algol) type binaries, one RR-1yr and one RRd pulsator, and five unclassified variables.

p-capture reaction cycles in rotating massive stars and their impact on elemental abundances in globular cluster stars: A case study of O, Na and Al

Elemental abundance patterns of globular cluster stars can provide important clues for understanding cluster formation and early chemical evolution.The origin of the abundance patterns,however,still remains poorly understood.We have studied the impact of p-capture reaction cycles on the abundances of oxygen,sodium and aluminium considering nuclear reaction cycles of carbon-nitrogenoxygen-fluorine,neon-sodium and magnesium-aluminium in massive stars in stellar conditions of temperature range 2×107to 10×107K and typical density of 102gm cc-1.We have estimated abundances of oxygen,sodium and aluminium with respect to Fe,which are then assumed to be ejected from those stars because of rotation reaching a critical limit.These ejected abundances of elements are then compared with their counterparts that have been observed in some metal-poor evolved stars,mainly giants and red giants,of globular clusters M3,M4,M13 and NGC 6752.We observe an excellent agreement with[O/Fe]between the estimated and observed abundance values for globular clusters M3 and M4 with a correlation coefficient above 0.9 and a strong linear correlation for the remaining two clusters with a correlation coefficient above 0.7.The estimated[Na/Fe]is found to have a correlation coefficient above 0.7,thus implying a strong correlation for all four globular clusters.As far as[Al/Fe]is concerned,it also shows a strong correlation between the estimated abundance and the observed abundance for globular clusters M13 and NGC 6752,since here also the correlation coefficient is above 0.7 whereas for globular cluster M4 there is a moderate correlation found with a correlation coefficient above 0.6.Possible sources of these discrepancies are discussed.

LISC Catalog of Open ClustersⅢ.83 Newly Found Galactic Disk Open Clusters Using Gaia EDR3

As groups of coeval stars born from the same molecular cloud,an open cluster(OC)is an ideal laboratory for studying the structure and dynamical evolution of the Milky Way.The release of high-precision Gaia Early Data Release 3(Gaia EDR3)and modern machine-learning methods offer unprecedented opportunities to identify OCs.In this study,we extended conventional HDBSCAN(e-HDBSCAN)for searching for new OCs in Gaia EDR3.A pipeline was developed based on the parallel computing technique to blindly search for OCs from Gaia EDR3within Galactic latitudes∣b∣<25°.As a result,we obtained 3787 star clusters,of which 83 new OCs were reported after cross-match and visual inspection.At the same time,the main star cluster parameters are estimated by color-magnitude diagram fitting.The study significantly increases the sample size and physical parameters of OCs in the catalog of OCs.It shows the incompleteness of the census of OCs across our Galaxy.

A binary study of color-magnitude diagrams of 12 globular clusters

Binary stars are common in star clusters and galaxies, but the detailed ef- fects of binary evolution are not taken into account in some color-magnitude diagram （CMD） studies. This paper studies the CMDs of twelve globular clusters via binary- star stellar populations. The observational CMDs of the star clusters are compared to those of binary-star populations, and then the stellar metallicities, ages, distances and reddenings of these star clusters are obtained. The paper also tests the different effects of binary and single stars on CMD studies. It is shown that binaries can better fit the observational CMDs of the sample globular clusters compared to single stars. This suggests that the effects of binary evolution should be considered when modeling the CMDs and stellar populations of star clusters and galaxies.