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Alok Durgapal

Publications and source records attributed to Alok Durgapal.

18 recordsLinked to original sources

Blue Straggler Stars in Berkeley 18: A Multiwavelength Study of Their Physical Properties and Dynamical Evolution

Berkeley~18 is an old open cluster in the outer Galactic disk that hosts a population of blue straggler stars (BSSs). We present a comprehensive multiwavelength analysis of its BSS population using \textit{Gaia} DR3 astrometry, optical--infrared photometry, and time-domain TESS observations. Using a Gaussian Mixture Model (GMM) in astrometric space, we identify 798 high-probability cluster members ($p > 0.7$). Isochrone fitting yields an age of $3.2 \pm 0.2$ Gyr and a heliocentric distance of $5.01^{+0.75}_{-0.55}$ kpc. We identify 24 BSS candidates above the main-sequence turn-off. Spectral energy distribution (SED) modelling reveals effective temperatures of $6000$--$8500$ K, radii of $1.4$--$5.7\,R_\odot$, and luminosities of $3.3$--$38\,L_\odot$, indicating a heterogeneous population spanning multiple evolutionary stages. The BSS population exhibits only a mild central concentration, with a low $A^{+}$ parameter and an extremely low stellar collision-rate proxy, implying weak mass segregation and an inefficient collisional channel. We find no significant photometric variability among the BSS candidates within TESS's sensitivity limits. Although WISE W3/W4 data initially suggested possible mid-infrared excesses, detailed image inspection and SPHEREx spectrophotometry indicate that these are caused by background contamination and blending, with no clear evidence of circumstellar dust. The structural parameters derived from King-profile fitting ($r_c = 6.91^{+0.91}_{-0.73}$ arcmin, $r_t = 13.23^{+0.44}_{-0.43}$ arcmin) indicate a dynamically evolved, low-density system. Together, these results suggest that dynamical interactions are inefficient in Berkeley~18 and that binary evolution is likely the dominant formation channel of BSSs.

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Multiwavelength Study of Blue Straggler Stars in Tombaugh 2: Evidence for Binary Mass Transfer and Constraints on Cluster Dynamical State

We present a focused multiwavelength study of blue straggler stars (BSSs) in the intermediate-age open cluster Tombaugh 2, located in the outer Galactic disk, to constrain the dominant formation pathways of BSSs in a low-density environment. Cluster members are identified using Gaia DR3 astrometry through a Gaussian Mixture Model, yielding a clean sample of high-probability members. Color-magnitude diagram analysis indicates an age of 1.74 Gyr. The radial surface density profile is well described by a King model, indicating a centrally concentrated overall structure, while the cluster exhibits only weak or no clear evidence of mass segregation among its stellar populations. We identify 26 BSS candidates and 2 YSS candidates. Spectral energy distributions constructed from ultraviolet, optical, and infrared photometry reveal that 9 BSSs (32%) exhibit significant ultraviolet excess, indicating an additional hot component. Binary SED decomposition identifies stripped companions with effective temperatures Teff $\sim$ (1.5-8) $\times$ 10$^4$ K and radii R $\sim$ 0.04-0.28 R_$\odot$, consistent with proto-white dwarfs, extremely low-mass pre-helium white dwarfs, and young hot remnants formed through recent mass transfer. A slight central concentration of BSSs, together with stripped companions, suggests that binary mass transfer is an important formation channel, with no evidence for merger-driven formation. Multi-epoch VLT/FLAMES spectroscopy reveals radial-velocity variability in several systems, providing independent evidence for binarity. Our results highlight that optical-infrared photometric analyses alone may fail to detect hot compact companions, while spectroscopy and ultraviolet observations provide complementary constraints, with ultraviolet data offering a direct probe of such companions in intermediate-age open clusters.

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Dynamical and Photometric Analysis of NGC 146 and King 14: Evidence for a Co-Moving, Unbound Cluster Pair

To understand the nature of the NGC 146-King 14 cluster pair, we conducted a detailed photometric, astrometric, and dynamical study using multiwavelength data from Gaia DR3, Pan-STARRS1, WISE, and TESS. Using a probabilistic approach, we identified 770 and 690 high-probability members of NGC 146 and King 14, respectively. Both clusters exhibit well-defined radial density profiles consistent with King models. We estimate the cluster ages as 20 $\pm$ 5 Myr and 50 $\pm$ 10 Myr from isochrone fitting, and distances of 2.98 $\pm$ 0.33 kpc and 2.51 $\pm$ 0.23 kpc from parallaxes after applying the Bailer-Jones criteria. The clusters show consistent mean proper motions. The mass function slopes (1.51 $\pm$ 0.18 and 1.50 $\pm$ 0.15) are close to the Salpeter value, and the extinction follows a normal Galactic reddening law (RV ~ 3.1). Three-dimensional mapping gives a projected separation of ~ 9 pc. Orbit integration using the galpy MWPotential2014 model shows that NGC 146 and King 14 move in nearly circular, disk-like orbits with similar mean orbital radii (Rm ~ 9 kpc) and orbital periods of roughly 255 Myr. A dynamical separation of ~ 32 pc indicates that both clusters share a common spatial and kinematic association, consistent with a co-moving pair. However, their relative velocity exceeds the escape velocity set by their combined mass, indicating they are not gravitationally bound. TESS light curves reveal seven variable stars, including $γ$ Doradus, SPB stars, and eclipsing binaries, though only one is a likely member. Overall, the clusters likely formed within the same giant molecular cloud and now exist as an unbound co-moving pair.

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Unveiling Dynamics and Variability in Open Clusters: Insights from a Comprehensive Analysis of Six Galactic Clusters

We present a kinematic and dynamical analysis of six Galactic open clusters NGC~2204, NGC~2660, NGC~2262, Czernik~32, Pismis~18, and NGC~2437, using \textit{Gaia}~DR3. We used Bayesian and Gaussian Mixture Model (GMM) methods to identify cluster members, but chose GMM because it's more appropriate for low-mass stars. Estimated distances range from 1.76 to 4.20~kpc and ages from 0.199 to 1.95~Gyr, confirming their intermediate-age nature. King model fits indicate compact morphologies, with core radii of 1--10~arcmin and cluster radii of 5--24~arcmin. We identify 13 BSS and 3 YSS members, whose central concentrations suggest origins via mass transfer or stellar collisions. The mass function slopes (0.96--1.19) are flatter than the Salpeter value, which indicates that these clusters have undergone dynamical mass segregation. Orbit integration within a Galactic potential indicates nearly circular orbits (eccentricities 0.02--0.10), vertical excursions within $\pm$132~pc, and guiding radii near the solar circle, suggesting disk confinement. These clusters likely formed in the thin disk and are shaped by Galactic tidal perturbations, facilitating the rapid loss of low-mass members. Additionally, twelve variable stars were found across four clusters using \textit{TESS} light curves, including $γ$~Doradus and SPB pulsators, eclipsing binaries, and a yellow straggler candidate. Periods were derived via Lomb-Scargle analysis. Two eclipsing binaries (TIC~94229743 and TIC~318170024) were modeled using PHOEBE, yielding mass ratios of 1.37 and 2.16, respectively. Our findings demonstrate that integrating orbital dynamics and variable star studies presents valuable insights into the evolutionary pathways of open clusters.

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Investigating kinematics and dynamics of three open clusters towards Galactic anti-center

We present the intra-cluster kinematics and dynamics of three open clusters: NGC 1193, NGC 2355, and King 12 by incorporating kinematical and photometric data from Gaia DR3, as well as a ground-based telescope. After selecting cluster members based on proper motion data, clusters' fundamental and structural parameters are investigated. We found the clusters at distances of 4.45, 1.97, and 3.34 kpc from the Sun in the direction of the Galactic anticenter. The luminosity function of the cluster NGC 1193 is flat, whereas it advances towards the fainter ends of the other two clusters. We observed a dip in the luminosity function of King 12. The mass function slopes for all three clusters differ from the solar neighbourhood reported by Salpeter, with NGC 1193 and NGC 2355 being flatter and King 12 having a higher value than the Salpeter value. The intra-cluster kinematics depict that stars in King 12 are moving outwards due to tidal forces from the Galactic disc, which we confirmed by plotting the cluster's orbit in the Galaxy. Stars in NGC 2355 are moving with smaller relative velocities and have zero mean relative motion, which signifies that the cluster is neither contracting nor evaporating. The Galactic orbits of NGC 1193 suggest that it is orbiting farther from the Galactic disc, and so is less impacted by the Galactic tidal forces.

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Structural Analysis of Open Cluster Bochum 2

We present the results from our deep optical photometric observations of Bochum 2 (Boc2) star cluster obtained using the $1.3$m Devasthal Fast Optical Telescope along with archival photometric data from Pan-STARRS2/2MASS/UKIDSS surveys. We also used high-quality parallax and proper motion data from the $Gaia$ Data Release 3. We found that the Boc2 cluster has a small size ($\sim$1.1 pc) and circular morphology. Using $Gaia$ parallax of member stars and isochrone fitting method, the distance of this cluster is estimated as $3.8\pm0.4$ kpc. We have found that this cluster holds young ($\sim5$ Myr) and massive (O$7-$O$9$) stars as well as an older population of low mass stars. We found that the massive stars have formed in the inner region of the Boc2 cluster in a recent epoch of star formation. We have derived mass function slope ($Γ$) in the cluster region as $-2.42\pm0.13$ in the mass range $\sim0.72<$M/M$_{\odot}<2.8$. The tidal radius of the Boc2 cluster ($\sim7-9$) is much more than its observed radius ($\sim1.1$ pc). This suggests that most of the low-mass stars in this cluster are the remains of an older population of stars formed via an earlier epoch of star formation.

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A deep investigation of two poorly studied open clusters Haffner 22 and Melotte 71 in Gaia era

This paper presents a deep investigation of two open clusters, Haffner 22 and Melotte 71, using astrometric and photometric data from Gaia EDR3. We identified 382 and 597 most probable cluster members with membership probability higher than 50 percent. Mean proper motion in RA and DEC are estimated as -1.63 and 2.889 respectively for Haffner 22 and -2.398 and 4.210 for Melotte 71. A comparison of observed CMDs with theoretical isochrones leads to an age of 2.25 and 1.27 Gyr for these clusters. The distances 2.88 and 2.28 kpc based on parallax are comparable with the values derived by isochrone fitting method. Five and four blue straggler stars are identified as cluster members in Haffner 22 and Melotte 71 respectively. Based on the relative number of high velocity (binary) and single stars, we inferred binary fractions for both clusters. We found binary content is larger in core region. Mass function slope is in good agreement with the Salpeter's value while it is flat for Haffner 22. Evidence for the existence of mass segregation effect is observed in both clusters. Using the Galactic potential models, Galactic orbits are derived, indicating that both clusters follow a circular path around the Galactic center, evolving slowly.

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Detailed analysis of the poorly studied northern open cluster NGC 1348 using multi-color photometry and GAIA EDR3 astrometry

The membership determination for open clusters in noisy environments of the Milky Way is still an open problem. In this paper, our main aim is provide the membership probability of stars using proper motions and parallax values of stars using Gaia EDR3 astrometry. Apart from the Gaia astrometry, we have also used other photometric data sets like UKIDSS, WISE, APASS and Pan-STARRS1 in order to understand cluster properties from optical to mid-infrared regions. We selected 438 likely members with membership probability higher than $50\%$ and G$\le$20 mag. We obtained the mean value of proper motion as $μ_{x}=1.27\pm0.001$ and $μ_{y}=-0.73\pm0.002$ mas yr$^{-1}$. The cluster's radius is determined as 7.5 arcmin (5.67 pc) using radial density profile. Our analysis suggests that NGC 1348 is located at a distance of $2.6\pm0.05$ kpc. The mass function slope is found to be $1.30\pm0.18$ in the mass range 1.0$-$4.1 $M_\odot$, which is in fair agreement with Salpeter's value within the 1$σ$ uncertainty. The present study validates that NGC 1348 is a dynamically relaxed cluster. We computed the apex coordinates $(A, D)$ for NGC 1348 as $(A_\circ, D_\circ)$ = $(-23^{\textrm{o}}.815\pm 0^{\textrm{o}}.135$, $-22^{\textrm{o}}.228\pm 0^{\textrm{o}}.105)$. In addition, calculations of the velocity ellipsoid parameters (VEPs), matrix elements $μ_{ij}$, direction cosines ($l_j$, $m_j$, $n_j$) and the Galactic longitude of the vertex have been also conducted in this analysis.

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Multi-colour photometry and Gaia EDR3 astrometry of two couples of binary clusters (NGC 5617 and Trumpler 22) and (NGC 3293 and NGC 3324)

This paper presents a comprehensive analysis of two pairs of binary clusters (NGC 5617 and Trumpler 22) and (NGC 3293 and NGC 3324) located in the fourth quadrant of our Galaxy. For this purpose we use different data taken from VVV survey, WISE, VPHAS, APASS, GLIMPSE along with Gaia~EDR3 astrometric data. We identified 584, 429, 692 and 273 most probable cluster members with membership probability higher than 80 % towards the region of clusters NGC 5617, Trumpler 22, NGC 3293 and NGC 3324. We estimated the value of R as ~ 3.1 for clusters NGC 5617 and Trumpler 22, which indicates normal extinction law. The value of R ~ 3.8 and 1.9 represent the abnormal extinction law towards the clusters NGC 3293 and NGC 3324. Our Kinematical analysis show that all these clusters have circular orbits. Ages are found to be 90\pm10 and 12\pm3 Myr for the cluster pairs (NGC 5617 and Trumpler 22) and (NGC 3293 and NGC 3324), respectively. The distances of 2.43\pm0.08, 2.64\pm0.07, 2.59\pm0.1 and 2.80\pm0.2 kpc estimated using parallax are alike to the values calculated by using the distance modulus. We have also identified 18 and 44 young stellar object candidates present in NGC 5617 and Trumpler 22, respectively. Mass function slopes are found to be in fair agreement with the Salpeter's value. The dynamical study of these objects shows a lack of faint stars in their inner regions, which leads to the mass-segregation effect. Our study indicates that NGC 5617 and Trumpler 22 are dynamically relaxed but the other pair of clusters are not. Orbital alongwith the physical parameters show that the clusters in both pairs are physically connected.

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A deep study of an intermediate age open cluster SAI 35 (Juchert 20) using ground based imaging and Gaia EDR3 astrometry

We present CCD $UBVI$ photometric study of poorly studied intermediate age open cluster SAI 35 (Juchert 20) for the first time. To accomplish this study, we also used LAMOST DR5, 2MASS, and Gaia EDR3 databases. We identified 214 most probable cluster members with membership probability higher than 50%. The mean proper motion of the cluster is found as μ_αcosδ=1.10 \pm 0.01 and μ_δ=-1.66 \pm 0.01 mas/yr. We find the normal interstellar extinction law using the various two-color diagrams. The age, distance, reddening, and radial velocity of the cluster are estimated to be 360 \pm 40 Myr, 2.9 \pm 0.15 kpc, 0.72 \pm 0.05 mag and -91.62 \pm 6.39 km/sec. The overall mass function slope for main-sequence stars is found to be 1.49\pm0.16 within the mass range 1.1-3.1 M_\odot, which is in agreement with Salpeter's value within uncertainty. The present study demonstrates that SAI 35 is a dynamically relaxed. Galactic orbital parameters are determined using Galactic potential models. We found that this object follows a circular path around the Galactic center.

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An investigation of poorly studied open cluster NGC 4337 using multi-color photometric and Gaia DR2 astrometric data

We present a comprehensive analysis (photometric and kinematical) of poorly studied open cluster NGC 4337 using 2MASS, WISE, APASS, and Gaia~DR2 database. By determining the membership probabilities of stars, we identified 624 most probable members with membership probability higher than $50\%$ by using proper motion and parallax data taken from Gaia~DR2. The mean proper motion of the cluster is obtained as $μ_{x}=-8.83\pm0.01$ and $μ_{y}=1.49\pm0.006$ mas yr$^{-1}$. We find the normal interstellar extinction towards the cluster region. The radial distribution of members provides a cluster radius of 7.75 arcmin (5.63 pc). The estimated age of $1600\pm180$ Myr indicates that NGC 4337 is an old open cluster with a bunch of red giant stars. The overall mass function slope for main-sequence stars is found as $1.46\pm0.18$ within the mass range 0.75$-$2.0 $M_\odot$, which is in fair agreement with Salpeter's value (x=1.35) within uncertainty. The present study demonstrates that NGC 4337 is a dynamically relaxed open cluster. Using the Galactic potential model, Galactic orbits are obtained for NGC 4337. We found that this object follows a circular path around the Galactic center. Under the kinematical analysis, we compute the apex coordinates $(A, D)$ by using two methods: (i) the classical convergent point method and (ii) the AD-diagram method. The obtained coordinates are: $(A_{conv}, D_{conv})$ = (96$^{\textrm{o}}$.27 $\pm$ 0$^{\textrm{o}}$.10, 13$^{\textrm{o}}$.14 $\pm$ 0$^{\textrm{o}}$.27) $\&$ $(A_\circ, D_\circ)$ = (100$^{\textrm{o}}$.282 $\pm$ 0$^{\textrm{o}}$.10, 9$^{\textrm{o}}$.577 $\pm$ 0$^{\textrm{o}}$.323) respectively. We also computed the Velocity Ellipsoid Parameters (VEPs), matrix elements ($μ_{ij}$), direction cosines ($l_j$, $m_j$, $n_j$) and the Galactic longitude of the vertex ($l_2$).

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Unveiling the physical conditions in NGC 6910

Deep and wide-field optical photometric observations along with multiwavelength archival datasets have been employed to study the physical properties of the cluster NGC 6910. The study also examines the impact of massive stars to their environment. The age, distance and reddening of the cluster are estimated to be $\sim$4.5 Myr, $1.72\pm0.08$ kpc, and $ E(B-V)_{min}= 0.95$ mag, respectively. The mass function slope ($Γ= -0.74\pm0.15$ in the cluster region is found to be flatter than the Salpeter value (-1.35), indicating the presence of excess number of massive stars. The cluster also shows mass segregation towards the central region due to their formation processes. The distribution of warm dust emission is investigated towards the central region of the cluster, showing the signature of the impact of massive stars within the cluster region. Radio continuum clumps powered by massive B-type stars (age range $\sim$ 0.07-0.12 Myr) are traced, which are located away from the center of the stellar cluster NGC 6910 (age $\sim$ 4.5 Myr). Based on the values of different pressure components exerted by massive stars, the photoionized gas associated with the cluster is found to be the dominant feedback mechanism in the cluster. Overall, the massive stars in the cluster might have triggered the birth of young massive B-type stars in the cluster. This argument is supported with evidence of the observed age gradient between the cluster and the powering sources of the radio clumps.

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Mid-infrared Variability of gamma-ray emitting blazars

Using data from the Wide-field Infrared Survey Explorer we studied the mid infrared 3.4 $μ$m (W1-band) and 4.6 $μ$m (W2-band) flux variability of $γ$-ray emitting blazars. Our sample consists of 460 flat spectrum radio quasars (FSRQs) and 575 BL Lacertae (BL Lac) objects. On intra-day timescales, the median amplitude of variability ($σ_{m}$) for FSRQs is 0.04$^{+0.03}_{-0.02}$ mag and 0.05$^{+0.03}_{-0.02}$ mag in W1 and W2 bands. For BL Lacs we found median $σ_{m}$ in W1(W2) bands of 0.04$^{+0.01}_{-0.02}$ (0.04$^{+0.02}_{-0.02}$) mag. On long timescales, for FSRQs we found a median $σ_{m}$ of 0.44$^{+0.28}_{-0.27}$ mag and 0.45$^{+0.27}_{-0.27}$ mag in W1 and W2 bands, while for BL Lacs the median values are 0.21$^{+0.18}_{-0.12}$ mag and 0.22$^{+0.18}_{-0.11}$ mag in W1 and W2 bands. From statistical tests, we found FSRQs to show larger $σ_m$ than BL Lacs on both intra-day and long timescales. Among blazars, low synchrotron peaked (LSP) sources showed larger $σ_m$ compared to intermediate synchrotron peaked (ISP) and high synchrotron peaked (HSP) sources.The larger $σ_{m}$ seen in FSRQs relative to BL Lacs on both intra-day and long timescales could be due to them having the most powerful relativistic jets and/or their mid infrared band coinciding with the peak of the electron energy distribution. BL Lacs have low power jets and the observational window too traces the emission from low energy electrons, thereby leading to low $σ_{m}$. In both FSRQs and BL Lacs predominantly a bluer when brighter behaviour was observed. No correlation is found between $σ_m$ and black hole mass.

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A Search for variable stars in the four open star clusters

We present a CCD photometric survey for the search of variable stars in four open clusters namely Berkeley 69, King 5, King 7, and Berkeley 20. The time series observations were carried out for 1 and/or 2 nights for each of the clusters in the year 1998, which have led to identify nineteen variable stars in these clusters. Out of these 19 variable stars, five stars show delta Scuti like variability and two stars show W UMa type variability. In other stars, we could not find the periods and hence the type of variability due to the lack of sufficient data. The periods of delta Scuti type stars are found to be in the range of 0.13 to 0.21 days, whereas the two stars in the cluster Berkeley 20, which showed W UMa type variability have orbital periods of 0.396 and 0.418 days, respectively. Using the Gaia data, the basic parameters of the clusters Berkeley 69, King 7 and King 5 are also revised. The age and reddening are estimated to be 0.79 \pm 0.09 Gyr and 0.68 \pm 0.03 mag for Berkeley 69, 0.79 \pm 0.09 Gyr and 1.22 \pm 0.03mag for the cluster King 7 and 1.59 \pm 0.19 Gyr and 0.63 \pm 0.02 mag for the cluster King 5, respectively. Signature of mass segregation is found in the clusters King 7 and King 5.

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A Comprehensive study of open clusters Czernik 14, Haffner 14, Haffner 17 and King 10 using multicolour photometry and Gaia DR2 astrometry

This paper presents an investigation on the four open clusters Czernik 14, Haffner 14, Haffner 17 and King 10 located near the Perseus arm of Milky Way Galaxy using Gaia DR2, 2MASS, WISE, APASS and Pan-STARRS1 data sets. We find normal interstellar extinction in twelve photometric bands for these clusters. Likely cluster members are identified as 225, 353, 350 and 395 for Czernik 14, Haffner 14, Haffner 17 and King 10, respectively by using Gaia DR2 proper motion data. Radii are determined as 3.5, 3.7, 6.2 and 5.7 arcmin for Czernik 14, Haffner 14, Haffner 17 and King 10 respectively. Mean proper motions in RA and DEC are estimated as (-0.42 \pm 0.02, -0.38 \pm 0.01), (-1.82 \pm 0.009, 1.73 \pm 0.008), (-1.17 \pm 0.007, 1.88 \pm 0.006) and (-2.75 \pm 0.008, -2.04 \pm 0.006) mas/yr for Czernik 14, Haffner 14, Haffner 17 and King 10, respectively. The comparison of observed CMDs with solar metallicity isochrones leads to an age of 570 \pm 60, 320 \pm 35, 90 \pm 10 and 45 \pm 5 Myr for these clusters. The distances 2.9 \pm 0.1, 4.8 \pm 0.4, 3.6 \pm 0.1 and 3.8 \pm 0.1 kpc determined using parallax are comparable with the values derived by the isochrone fitting method. Mass function slopes are found to be in good agreement with the Salpeter value. The total masses are derived as 348, 595, 763 and 1088 solar mass for the clusters Czernik 14, Haffner 14, Haffner 17 and King 10, respectively. Evidence for the existence of mass-segregation effect is observed in each cluster. Using the Galactic potential model, Galactic orbits are derived for the clusters. The present study indicates that all clusters under study fallow a circular path around the Galactic center.

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Study of open cluster King 13 using CCD VI, 2MASS and Gaia DR2 Astrometry

In this paper, we present astrophysical parameters of the open cluster King 13 based on the VI CCD and 2MASS JHKs photometric data. This is a poorly studied cluster, for which new results have been found in the present work. To identify probable members, we use proper motion data from Gaia DR2 catalogue. The mean proper motion of the cluster is determined as -2.8 \pm 0.2 and -0.88 \pm 0.14 mas yr{-1} and cluster extent is derived as 3'.2. Using color-magnitude diagrams, we estimate the age and distance of the cluster as 510 \pm 60 Myr and 3.84 \pm 0.15 kpc respectively. Interstellar reddening E(B-V) in the direction of the cluster is determined as 0.80 \pm 0.2 mag using color-color diagram. Mass function slope of the cluster is found to be comparable with the Salpeter value. The total mass of this cluster is derived as 270 M_{\odot}. The present analysis shows that King 13 is a dynamically relaxed cluster.

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Astrometric and photometric study of NGC 6067, NGC 2506 and IC 4651 open clusters based on wide-field ground and Gaia DR2 data

We present an analysis of three southern open star clusters NGC 6067, NGC 2506 and IC 4651 using wide-field photometric and Gaia DR2 astrometric data. They are poorly studied clusters. We took advantage of the synergy between Gaia DR2 high precision astrometric measurements and ground based wide-field photometry to isolate cluster members and further study these clusters. We identify the cluster members using proper motions, parallax and colour-magnitude diagrams. Mean proper motion of the clusters in RA and DEC is estimated as -1.90 \pm 0.01 and -2.57 \pm 0.01 mas/yr for NGC 6067, -2.57 \pm 0.01 and 3.92 \pm 0.01 mas/yr for NGC 2506 and -2.41 \pm 0.01 and -5.05 \pm 0.02 mas/yr for IC 4651. Distances are estimated as 3.01 \pm 0.87, 3.88 \pm 0.42 and 1.00 \pm 0.08 kpc for the clusters NGC 6067, NGC 2506 and IC 4651 respectively using parallaxes taken from Gaia DR2 catalogue. Galactic orbits are determined for these clusters using Galactic potential models.We find that these clusters have circular orbits. Cluster radii are determined as 10 arcmin for NGC 6067, 12 arcmin for NGC 2506 and 11 arcmin for IC 4651. Ages of the clusters estimated by isochrones fitting are 66 \pm 8 Myr, 2.09 \pm 0.14 Gyr and 1.59 \pm 0.14 Gyr for NGC 6067, NGC 2506 and IC 4651 respectively. Mass function slope for the entire region of cluster NGC 2506 is found to be comparable with the Salpeter value in the mass range 0.77 - 1.54 Solar mass. The mass function analysis shows that the slope becomes flat when one goes from halo to core region in all the three clusters. A comparison of dynamical age with cluster's age indicates that NGC 2506 and IC 4651 are dynamically relaxed clusters.

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Interstellar extinction in twenty open star clusters

The interstellar extinction law in twenty open star clusters namely Berkeley 7, Collinder 69, Hogg 10, NGC 2362, Czernik 43, NGC 6530, NGC 6871, Bochum 10, Haffner 18, IC 4996, NGC 2384, NGC 6193, NGC 6618, NGC 7160, Collinder 232, Haffner 19, NGC 2401, NGC 6231, NGC 6823 and NGC 7380 have been studied in the optical and near-IR wavelength ranges. The difference between maximum and minimum values of E(B-V) indicates the presence of non-uniform extinction in all the clusters except Collinder 69, NGC 2362 and NGC 2384. The colour excess ratios are consistent with a normal extinction law for the clusters NGC 6823, Haffner 18, Haffner 19, NGC 7160, NGC 6193, NGC 2401, NGC 2384, NGC 6871, NGC 7380, Berkeley 7, Collinder 69 and IC 4996. We found that differential colour-excess which may be due to the occurrence of dust and gas inside the clusters, decreases with age of the clusters. A spatial variation of colour excess is found in NGC 6193 in sense that it decreases from east to west in cluster region. For cluster Berkeley 7, NGC 7380 and NGC 6871, a dependence of colour excess with spectral class and luminosity is observed. Eight stars in Collinder 232, four stars in NGC 6530 and one star in NGC 6231 have colour excess flux in near-IR. This indicates that these stars may have circumstellar material around them.

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