We present a comprehensive photometric analysis of a young open cluster NGC 1960 (= M36) along with the long-term variability study of this cluster. Based on the kinematic data of Gaia DR2, the membership probabilities of 3871 stars are ascertained in the cluster field among which 262 stars are found to be cluster members. Considering the kinematic and trigonometric measurements of the cluster members, we estimate a mean cluster parallax of 0.86±0.05 mas and mean proper motions of µ RA = -0.143±0.008 mas yr −1 , µ Dec = -3.395±0.008 mas yr −1 . We obtain basic parameters of the cluster such as E(B − V) = 0.24±0.02 mag, log(Age/yr)=7.44±0.02, and d = 1.17±0.06 kpc. The mass function slope in the cluster for the stars in the mass range of 0.72-7.32 M ⊙ is found to be γ = -1.26±0.19. We find that mass segregation is still taking place in the cluster which is yet to be dynamically relaxed. This work also presents first high-precision variability survey in the central 13 ′ × 13 ′ region of the cluster. The V band photometric data accumulated on 43 nights over a period of more than 3 years reveals 76 variable stars among which 72 are periodic variables. Among them, 59 are short-period (P < 1 day)and 13 are long-period (P > 1 day). The variable stars have V magnitudes ranging between 9.1 to 19.4 mag and periods between 41 minutes to 10.74 days. On the basis of their locations in the H-R diagram, periods and characteristic light curves, the 20 periodic variables belong to the cluster. We classified them as 2 δ-Scuti, 3 γ-Dor, 2 slowly pulsating B stars, 5 rotational variables, 2 non-pulsating B stars and 6 as miscellaneous variables.

We present UBVR c I c photometric study of three intermediate age open star clusters NGC 381, NGC 2360, and Berkeley 68 (Be 68). We examine the cluster membership of stars using recently released Gaia DR2 proper motions and obtain a total of 116, 332, and 264 member stars in these three clusters. The mean reddening of E(B − V) = 0.36±0.04, 0.08±0.03, and 0.52±0.04 mag are found in the direction of these clusters where we observe an anomalous reddening towards NGC 381. We fitted the solar metallicity isochrones to determine age and distance of the clusters which are found to be log(Age) = 8.65±0.05, 8.95±0.05, and 9.25±0.05 yr with the respective distance of 957±152, 982±132, and 2554±387 pc for the clusters NGC 381, NGC 2360, and Be 68. A two-stage power law in the mass function (MF) slope is observed in the cluster NGC 381, however, we observe only a single MF slope in the clusters NGC 2360 and Be68. To study a possible spatial variation in the slope of MF we estimate slopes separately in the inner and the outer regions of these clusters and notice a steeper slope in outer region. The dynamic study of these clusters reveals deficiency of lowmass stars in their inner regions suggesting the mass segregation process in all these clusters. The relaxation times of 48.5, 78.9, and 87.6 Myr are obtained for the clusters NGC 381, NGC 2360, and Be 68, respectively which are well below to their respective ages. This suggests that all the clusters are dynamically relaxed.

This work presents the first long-term photometric variability survey of the intermediate-age open cluster NGC 559. Time-series V band photometric observations on 40 nights taken over more than three years with three different telescopes are analyzed to search for variable stars in the cluster. We investigate the data for the periodicity analysis and reveal 70 variable stars including 67 periodic variables in the target field, all of them are newly discovered. The membership analysis of the periodic variables reveal that 30 of them belong to the cluster and remaining 37 are identified as field variables. Out of the 67 periodic variables, 48 are short-period (P &lt; 1 day) variables and 19 are long-period (P &gt; 1 day) variables. The variable stars have periodicity between 3 hours to 41 days and their brightness ranges from V = 10.9 to 19.3 mag. The periodic variables belonging to the cluster are then classified into different variability types on the basis of observational properties such as shape of the light curves, periods, amplitudes, as well as their positions in the Hertzsprung-Russell (H-R) diagram. As a result, we identify one Algol type eclipsing binary, one possible blue straggler star, 3 slowly pulsating B type stars, 5 rotational variables, 11 non-pulsating variables, 2 FKCOM variables and remaining 7 are characterized as miscellaneous variables. We also identify three Eclipsing Binary stars (EBs) belonging to the field star population. The PHOEBE package is used to analyse the light curve of all four EBs in order to determine the parameters of the binary systems such as masses, temperatures and radii.

We carry out a detailed photometric and kinematic study of the poorly studied sparse open clusters SAI 44 and SAI 45 using ground-based BVR c I c data supplemented by archival data from Gaia eDR3 and Pan-STARRS. The stellar memberships are determined using a statistical method based on Gaia eDR3 kinematic data, and we found 204 members in SAI 44 while only 74 members are identified in SAI 45. The average distances to SAI 44 and SAI 45 are calculated to be 3670 ± 184 and 1668 ± 47 pc. The logarithmic age of the clusters are determined to be 8.82 ± 0.10 and 9.07 ± 0.10 yr for SAI 44 and SAI 45, respectively. The color–magnitude diagram of SAI 45 hosts an extended main-sequence turnoff (eMSTO). The apparent age spread is found to be similar to the apparent age spread predicted on the basis of the age spread and cluster age relation predicted by rotation models. This indicates that eMSTO is a stellar evolution rather than star formation phenomenon in SAI 45. We conclude that eMSTO in SAI 45 is mainly caused by the different rotation rates of stars as the SYCLIST synthetic population with different rotation rates was able to reproduce the observed eMSTO, and stars in the red part of the eMSTO were preferentially concentrated in the inner region, which again hints at different rotations being the reason for the extension in the upper MS. This finding supports the theory attributing the origin of eMSTO to the different rotations of eMSTO stars. The mass function slopes are obtained as −2.24 ± 0.66 and −2.58 ± 3.20 in the mass rages 2.426–0.990 M ⊙ and 2.167–1.202 M ⊙ for SAI 44 and SAI 45, respectively. SAI 44 exhibits the signature of mass segregation while we found weak evidence of mass segregation in SAI 45 possibly due to tidal stripping. The dynamical relaxation times of these clusters indicate that both clusters are in a dynamically relaxed state. Using the AD-diagram method, the apex coordinates are found to be ( 69 .° 79 ± 0 .° 11 , − 30 .° 82 ± 0 .° 15 ) for SAI 44 and (− 56 .° 22 ± 0 .° 13 , − 56 .° 62 ± 0 .° 13 ) for SAI 45. The average space velocity components of the clusters SAI 44 and SAI 45 are calculated in units of km s−1 as (−15.14 ± 3.90, −19.43 ± 4.41, −20.85 ± 4.57) and (28.13 ± 5.30, −9.78 ± 3.13, −19.59 ± 4.43), respectively.

We carried out the UBVRcIc photometric study of three poorly studied young open clusters IC 1442, King 21, and Trumpler 7 (Tr 7). We obtained 263, 244, and 128 member stars using Gaia Data Release 2 proper motions and parallaxes in IC 1442, King 21, and Tr 7, respectively. The reddening, E(B − V), was derived to be 0.54 ± 0.04, 0.76 ± 0.06, and 0.38 ± 0.04 mag for these clusters. The comparison of observed colour–magnitude diagrams with solar metallicity isochrones yields log(age) = 7.40 ± 0.30, 7.70 ± 0.20, and 7.85 ± 0.25 yr and corresponding distances of 2847 ± 238, 2622 ± 156, and 1561 ± 74 pc for IC 1442, King 21, and Tr 7, respectively. The estimated mass function (MF) slopes are found to be −1.94 ± 0.18, −1.54 ± 0.32, and −2.31 ± 0.29 for IC 1442, King 21, and Tr 7, respectively. The study of MF slopes done separately in the inner and the outer regions of these clusters gives a steeper slope in the outer region, which suggests spatial variation in slope and mass segregation in the clusters. We found evidence of mass segregation after the dynamical study in these clusters. The obtained relaxation time, TE, is 74, 26, and 34 Myr for the clusters IC 1442, King 21, and Tr 7, respectively. The mass segregation in IC 1442 may be caused by early dynamical relaxation. The estimated TE is well below the ages of King 21 and Tr 7, which indicates that these clusters are dynamically relaxed.

We study variable stars in the field of the open cluster NGC 381 using photometric data observed over 27 nights and identify a total of 57 variable stars, six of which are member stars. The variable stars are classified based on their periods, amplitudes, light-curve shapes, and locations in the H-R diagram. We found a rich variety of variable stars in the cluster. We identified a total of 10 eclipsing binaries, of which two are of Algol type while eight are of W UMa type (EW). The estimated ages of these EW binaries are greater than 0.6 Gyr, which is in agreement with the formation time constraint of ≥0.6 Gyr on short-period eclipsing binaries. The physical parameters of the two EW-type binaries are estimated using PHOEBE model-fitting software. The pulsating variable stars include one each from the δ Scuti and γ Dor variability classes. We determined the pulsation modes of pulsating variables with the help of the FAMIAS package. We obtained 15 rotational variable stars comprising four dwarf stars identified on the basis of their log(g) versus log(T eff) diagram. These dwarf stars are found to have generally longer periods than the remaining rotational variables.

We carry out detailed photometric and kinematic study of the poorly studied sparse open clusters SAI 44 and SAI 45 using ground based BVR c I c data supplemented by archival data from Gaia eDR3 and Pan-STARRS. The stellar membership are determined using a statistical method based on Gaia eDR3 kinematic data and we found 204 members in SAI 44 while only 74 members are identified in SAI 45. The average distances to SAI 44 and SAI 45 are calculated as 3670±184 and 1668±47 pc. The logarithmic age of the clusters are determined as 8.82±0.10 and 9.07±0.10 years for SAI 44 and SAI 45, respectively. The color-magnitude diagram of SAI 45 hosts an extended main-sequence turn-off (eMSTO) which may be originated through differential rotation rates of member stars. The mass function slopes are obtained as -1.75±0.72 and -2.58±3.20 in the mass rages 2.426-0.990 M and 2.167-1.202 M for SAI 44 and SAI 45, respectively. SAI 44 exhibit the signature of mass segregation while we found a weak evidence of the mass segregation in SAI 45 possibly due to tidal striping. The dynamical relaxation times of these clusters indicate that both the clusters are in dynamically relaxed state. Using AD-diagram method, the apex coordinates are found to be (69. • 79 ± 0. • 11, -30. • 82 ± 0. • 15) for SAI 44 and (-56. • 22 ± 0. • 13, -56. • 62 ± 0. • 13) for SAI 45. The average space velocity components of the clusters SAI 44 and SAI 45 are calculated in units of km s −1

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