arXiv subjects

R. K. S. Yadav

Publications and source records attributed to R. K. S. Yadav.

At least 37 records · Page 2Linked to original sources

arXiv2021

Study of dynamical status of the globular cluster NGC 1851 using Ultraviolet Imaging Telescope

We present the study of dynamical status of the globular cluster NGC 1851. A combination of multiwavelength space and ground-based data sets are used for the present analysis. In order to select the genuine cluster members, we used the astro-photometric data available from HST and GAIA-DR2 catalogs. The BSS radial distribution of the cluster is plotted from the center of the cluster to the outskirts. The radial distribution of BSS shows a central peak, followed by a dip at the intermediate radii (rmin ~ 90'') and a rising trend in the outskirts. We also estimated A+rh parameter as 0.391 +/- 0.006 to validate the findings of the radial distribution study. On the basis of the minima in the BSS radial distribution and the value of A+rh parameter, we conclude that NGC 1851 belongs to Family II classification and is an intermediate dynamical state cluster.

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arXiv2020

A comprehensive analysis of NGC 2158 in Gaia era: photometric parameters, apex and orbit

We present an investigation of NGC 2158 using Gaia-DR2 data. We identified 800 most likely cluster members with membership probability higher than 90%. The mean proper motions of this object are determined as (mu_{x}=-0.203 \pm 0.003, mu_{y}=-1.99 \pm 0.004) mas yr^{-1}. The limiting radius, log(age), and distance of the cluster are obtained as 23.5 arcmin, 9.38 \pm 0.04 Gyr and 4.69 \pm 0.22 kpc, respectively. The overall mass function slope (0.93 \pm 0.14) is flatter than the Salpeter value (1.35) within the mass range 1.17-1.44 M_\odot. This cluster also shows the mass-segregation effect and our study demonstrates that NGC 2158 is a dynamically relaxed open cluster. Using the AD-diagram, the apex coordinates of the cluster are obtained in different ways and examined using (μ_{U},μ_{T}) diagram. The best value of apex coordinates is determined as A=87.24^\circ \pm 1.60^\circ, D=-36.61^\circ \pm 5.30 ^\circ. We also determined the orbit of the cluster and found that NGC 2158 moves almost in the Solar antapex direction. The resulting spatial velocity of NGC 2158 is 51 km s^{-1}. A significant oscillations along the Z-coordinate up to 529~pc is detected. Various scenarios regarding the origin of this cluster are also discussed.

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arXiv2020

Peculiarities in the horizontal branch stars of globular cluster NGC 1851: Discovery of a Blue straggler companion to an EHB star

We present a study of Far Ultraviolet (FUV) bright horizontal branch (HB) stars to understand the peculiarities seen in the HB sequence of the Globular Cluster NGC 1851, using ground and space based multi-wavelength data. Optical and UV color magnitude diagrams are used to classify HB stars and their membership from HST and Gaia DR2 data. The Spectral energy distributions (SEDs) of the hot HB stars located from the core to tidal radii are constructed. The SEDs reveal that the HB stars near the G-jump show a decrease in the FUV flux when atmospheric models of cluster metallicity are used for fitting, but a better fit is found with higher metallicity models, as expected due to atmospheric diffusion. We report on four particularly interesting extreme HB (EHB) stars, two each in inner and outer regions. We detect a sub-luminous EHB and a "blue-Hook" candidates with temperatures Teff ~ 25,000 K and 31,000 K, respectively. We found an EHB star (Teff ~ 17,000 K) with the radius lies between the BHB and normal EHB stars. The most peculiar of our EHB stars (Teff ~ 28,000 K) is found to be a photometric binary to a Blue Straggler star (BSS) (Teff ~ 7,000 K), which is an important target for spectroscopic study. This discovery of the candidate EHB+BSS binary system, could help to explain the mass loss in the RGB phase, leading to the formation of EHB stars.

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arXiv2020

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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arXiv2020

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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arXiv2020

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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arXiv2020

Optical Linear Polarization toward the Open Star Cluster Casado Alessi 1

We present B-, V-, R-, and I-bands linear polarimetric observations of 73 stars in the direction of open star cluster Casado Alessi 1 (hereafter Alessi 1). We aim to use polarimetry as a tool to investigate the properties and distribution of dust grains toward the direction of the cluster. The polarimetric observations were carried out using the ARIES IMaging POLarimeter mounted at the 104 cm telescope of ARIES, Nainital (India). Using the Gaia photometric data the age and distance of the cluster are estimated to be $0.8\pm0.1$ Gyr and $673\pm98$ pc, respectively. A total of 66 stars with a 26 arcmin radius from the cluster are identified as members of the cluster using the astrometric approach. Out of these 66 members, 15 stars were observed polarimetrically and found to have the same value of polarization. The majority of the stars in the region follow the general law of the polarization for the interstellar medium, indicating that polarization toward the cluster Alessi 1 is dominated by foreground dust grains. The average values of the maximum polarization ($P_{max}$) and the wavelength corresponding to the maximum polarization ($λ_{max}$) toward the cluster are found to be $0.83\pm0.03$% and $0.59\pm0.04$ $μ$m, respectively. Also, dust grains toward the cluster appear to be aligned, possibly due to the galactic magnetic field.

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arXiv2020

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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arXiv2019

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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arXiv2019

VR CCD photometry of variable stars in globular cluster NGC 4147

We present results of a search for variable stars in a region of the globular cluster NGC 4147 based on photometric observations with 4k x 4k CCD imager mounted at the axial port of the recently installed 3.6 m Devasthal optical telescope at Aryabhatta Research Institute of Observational Sciences, Nainital, India. We performed time series photometry of NGC 4147 in V and R bands, and identified 42 periodic variables in the region of NGC 4147, 28 of which have been detected for the first time. Seventeen variable stars are located within the half light radius $\lesssim$ 0.48 arcmin, of which 10 stars are newly identified variables. Two of 10 variables are located within the core radius $\lesssim$ 0.09 arcmin. Based on the location in the $V/(V-R)$ colour magnitude diagram and variability characteristics, 7, 8, 5 and 1 newly identified probable member variables are classified as RRc, EA/E, EW and SX Phe, respectively. The metallicity of NGC 4147 estimated from light curves of RRab and RRc stars with the help of Fourier decomposition is found to be characteristics of Oosterhoff II. The distance derived using light curves of RRab stars is consistent with that obtained from the observed $V/(V-R)$ colour-magnitude diagram.

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arXiv2018

The radial distribution of Blue stragglers in Galactic Globular Cluster NGC 6656 $-$ Clues on the dynamical status

We present dynamical status of the Galactic globular cluster NGC 6656 using spatial distribution of Blue Straggler Stars (BSSs). A combination of multi-wavelength high-resolution space and ground-based data are used to cover a large cluster region. We determine the centre of gravity ($C_{grav}$) and construct the projected density profile of the cluster using the probable cluster members selected from HST and Gaia DR2 proper motion data sets. The projected density profile in the investigated region is nicely reproduced by a single mass King model, with core ($r_{c}$) and tidal ($r_{t}$) radius as $75^{\prime\prime}.2$ $\pm$ $3^{\prime\prime}.1$ and $35^{\prime}.6$ $\pm$ $1^{\prime}.1$ respectively. In total, 90 BSSs are identified on the basis of proper motion data in the region of radius $625^{\prime\prime}$. An average mass of the BSSs is determined as $1.06$ $\pm$ $0.09$ $M_{\odot}$ and with an age range of 0.5 to 7 Gyrs. The BSS radial distribution shows a bimodal trend, with a peak in the centre, a minimum at $r \sim r_c$ and a rising tendency in the outer region. The BSS radial distribution shows a flat behaviour in the outermost region of the cluster. We also estimate $A^{+}_{rh}$ parameter as an alternative indicator of the dynamical status of the cluster and is found to be $0.038$ $\pm$ $0.016$. Based on the radial distribution and $A^{+}_{rh}$ parameter, we conclude that NGC 6656 is an intermediate dynamical age cluster.

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arXiv2018

Mass function and dynamical study of the open clusters Berkeley 24 and Czernik 27

We present a $UBVI$ photometric study of the open clusters Berkeley 24 (Be 24) and Czernik 27 (Cz 27). The radii of the clusters are determined as 2\farcm7 and 2\farcm3 for Be 24 and Cz 27, respectively. We use the Gaia Data Release 2 (GDR2) catalogue to estimate the mean proper motions for the clusters. We found the mean proper motion of Be 24 as $0.35\pm0.06$ mas yr$^{-1}$ and $1.20\pm0.08$ mas yr$^{-1}$ in right ascension and declination for Be 24 and $-0.52\pm0.05$ mas yr$^{-1}$ and $-1.30\pm0.05$ mas yr$^{-1}$ for Cz 27. We used probable cluster members selected from proper motion data for the estimation of fundamental parameters. We infer reddenings $E(B-V)$ = $0.45\pm0.05$ mag and $0.15\pm0.05$ mag for the two clusters. Analysis of extinction curves towards the two clusters show that both have normal interstellar extinction laws in the optical as well as in the near-IR band. From the ultraviolet excess measurement, we derive metallicities of [Fe/H]= $-0.025\pm0.01$ dex and $-0.042\pm0.01$ dex for the clusters Be 24 and Cz 27, respectively. The distances, as determined from main sequence fitting, are $4.4\pm0.5$ kpc and $5.6\pm0.2$ kpc. The comparison of observed CMDs with $Z=0.01$ isochrones, leads to an age of $2.0\pm0.2$ Gyr and $0.6\pm0.1$ Gyr for Be 24 and Cz 27, respectively. In addition to this, we have also studied the mass function and dynamical state of these two clusters for the first time using probable cluster members. The mass function is derived after including the corrections for data incompleteness and field star contamination. Our analysis shows that both clusters are now dynamically relaxed

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arXiv2018

A Proper Motions Study of the Globular Cluster M12 (NGC 6218)

Using astrometric techniques developed by Anderson et al., we determine proper motions (PMs) in 14.60 arcmin X 16.53 arcmin area of the kinematically "thick-disk" globular cluster M12. The cluster's proximity and sparse nature makes it a suitable target for ground-based telescopes. Archive images with time gap of 11.1 years were observed with wide-field imager (WFI) mosaic camera mounted on ESO 2.2 m telescope. The median value of PM error in both components is 0.7 mas/yr for the stars having V less than or equal to 20 mag. PMs are used to determine membership probabilities and to separate field stars from the cluster sample. In electronic form, a membership catalog of 3725 stars with precise coordinates, PMs, BVRI photometry is being provided. One of the possible applications of the catalog was shown by gathering the membership information of the variable stars, blue stragglers and X-ray sources reported earlier in the cluster's region.

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arXiv2018

The Pleiades apex and its kinematical structure

A study of cluster characteristics and internal kinematical structure of the middle-aged Pleiades open star cluster is presented. The individual star apexes and various cluster kinematical parameters including the velocity ellipsoid parameters are determined using both Hipparcos and Gaia data. Modern astrometric parameters were taken from the Gaia Data Release 1 (DR1) in combination with the Radial Velocity Experiment Fifth Data Release (DR5). The necessary set of parameters including parallaxes, proper motions and radial velocities are used for n=17 stars from Gaia DR1+RAVE DR5 and for n=19 stars from the Hipparcos catalog using SIMBAD data base. Single stars are used to improve accuracy by eliminating orbital movements. RAVE DR5 measurements were taken only for the stars with the radial velocity errors not exceeding $2$~km/s. For the Pleiades stars taken from Gaia, we found mean heliocentric distance as $136.8 \pm 6.4$~pc, and the apex position is calculated as: $A_{CP}=92^\circ.52\pm1^\circ.72$, $D_{CP}=-42^\circ.28\pm2^\circ.56$ by the convergent point method and $A_0=95^\circ.59\pm2^\circ.30$ and $D_0=-50^\circ.90\pm2^\circ.04$ using AD-diagram method (n=17 in both cases). The results are compared with those obtained historically before the Gaia mission era.

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arXiv2017

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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arXiv2017

First-light instrument for the 3.6m DOT: 4Kx4K CCD Imager

As an in-house instrument developmental activity at ARIES, the 4Kx4K CCD Imager is designed and developed as a first-light instrument for the axial port of the 3.6m DOT. The f/9 beam of the telescope having a plate-scale of ~ 6.4 arc-sec/mm is utilized to conduct deeper photometry within the central 10 arc-min field of view. The pixel size of the blue-enhanced liquid Nitrogen cooled STA4150 4Kx4K CCD chip is 15 micron, with options to select gain and speed values to utilize the dynamic range. Using the Imager, it is planned to image the central ~ 6.5x6.5 arc-min^2 field of view of the telescope for various science goals by getting deeper images in several broad-band filters for point sources and objects with low surface brightness. The fully assembled Imager along with automated filter wheels having Bessel UBVRI and SDSS ugriz filters was tested in late 2015 at the axial port of the 3.6m DOT. This instrument was finally mounted at the axial port of the 3.6m DOT on 30th March 2016 when the telescope was technically activated jointly by the Prime Ministers of India and Belgium. This instrument is expected to serve as a general purpose multi-band deep imaging instrument for variety of science goals including studies of cosmic transients, active galaxies, star clusters and optical monitoring of X-ray sources discovered by the newly launched Indian space-mission called ASTROSAT and follow-up of radio bright objects discovered by the GMRT.

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arXiv2017

A proper motions study of the globular cluster NGC 3201

With a high value of heliocentric radial velocity, a retrograde orbit, and being suspected to have an extragalactic origin, NGC 3201 is an interesting globular cluster for kinematical studies. Our purpose is to calculate the relative proper motions (PMs) and membership probability for the stars in the wide region of globular cluster NGC 3201. Proper motion based membership probabilities are used to isolate the cluster sample from the field stars. The membership catalogue will help address the question of chemical inhomogeneity in the cluster. Archive CCD data taken with a wide-field imager (WFI) mounted on the ESO 2.2m telescope are reduced using the high-precision astrometric software developed by Anderson et al. for the WFI images. The epoch gap between the two observational runs is $\sim$14.3 years. To standardize the $BVI$ photometry, Stetson's secondary standard stars are used. The CCD data with an epoch gap of $\sim$14.3 years enables us to decontaminate the cluster stars from field stars efficiently. The median precision of PMs is better than $\sim$0.8 mas~yr$^{-1}$ for stars having $V<$18 mag that increases up to $\sim$1.5 mas~yr$^{-1}$ for stars with $18<V<20$ mag. Kinematic membership probabilities are calculated using proper motions for stars brighter than $V\sim$20 mag. An electronic catalogue of positions, relative PMs, $BVI$ magnitudes and membership probabilities in $\sim$19.7$\times$17 arcmin$^2$ region of NGC 3201 is presented. We use our membership catalogue to identify probable cluster members among the known variables and $X$-ray sources in the direction of NGC 3201.

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arXiv2016

2MASS photometry and kinematical studies of open cluster NGC 188

In this paper, we present our results for the photometric and kinematical studies of old open cluster NGC 188. We determined various astrophysical parameters like limited radius, core and tidal radii, distance, luminosity and mass functions, total mass, relaxation time etc. for the cluster using 2MASS catalog. We obtained the cluster's distance from the Sun as 1721+/-41 pc and log (age)= 9.85+/-0.05 at Solar metallicity. The relaxation time of the cluster is smaller than the estimated cluster age which suggests that the cluster is dynamically relaxed. Our results agree with the values mentioned in the literature. We also determined the cluster's apex coordinates as (281.88 deg, -44.76 deg) using AD-diagram method. Other kinematical parameters like space velocity components, cluster center and elements of Solar motion etc. have also been computed.

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