Summer Research Fellowship Programme of India's Science Academies

Astrometry of open star clusters

Pawan Tiwari

Institute of Science, BHU, Varanasi 221005

Prof. Annapurni Subramaniam

Indian Institute of Astrophysics (IIA), Bengaluru 560034


​The main objective of this study is to analyse astrometric parameters of open cluster using software named TOPCAT from the data provided by European Space Agency Gaia Survey in Gaia Data Release 2. Astrometric parameters include distance of star cluster, parallax, their radial velocity, tangential velocity etc. Colour Magnitude Diagram of star cluster is constructed after analysing their proper motion and also isochrone fitting is done with CMD revealing about their ages, masses etc. Parallax, radial velocity, tangential velocity, space velocity are found with the help of proper motion of star cluster within limit of error. All the calculation, diagram, histogram, plane plot, sky plot etc. are constructed using TOPCAT.​

Keywords: open star cluster, astrometry, CMD, isochrone, GAIA, TOPCAT


Abbrevations and Acronoyms
pmRAProper Motion Right Ascension 
 pmDECProper Motion Declination 
 HRDHertzsprung Russell Diagram
 CMDColour Magnitude Diagram 
 GAIAGlobal Astrometric Interferometer for Astrophysics 
 DR2 Data Release 2 
ESA European Space Agency 
DMDistance Modulus 


Astronomy, one of the oldest branch of science, deals with the celestial objects, space and the physical universe as whole whereas Astrophysics is branch of astronomy concerned with physical nature of stars and other celestial bodies and the application of laws and theories of physics to the interpretation of astronomical observations.

The aim of this project to study about star clusters mainly open star clusters and derive their astrometric parameters from the data provided by GAIA DR2 using software TOPCAT. To measure distance of an astronomical object is one of the interesting and challenging subject of astrometry. Measurement of distance of astronomical object not only tells how that object is far from us but using distance we can predict luminosity of the object, masses of object from orbital motion, physical size of an object, true motion through stars etc. One of most fundamental technique for the distance measurement is determination of parallax. CMD and Isochrone fiting is done to find out ages of star cluster.

Open Star Cluster

Open star clusters are group of star cluster up to few thousand stars that were formed by same giant molecular cloud and have roughly same age. They are loosely bound by mutual gravitational attraction and become disrupted by the close encounters with other cluster and clouds of gas as they orbit the galactic centre. Pleiades, Hyades, Prasepes etc. are some open star cluster.

     Pleiades Open Star Cluster


    The most fundamental distance measurement comes from trigonometric parallax. The nearby stars appear move with respect to the distance stars due to the motion of Earth around Sun. This apparent motion is called Stellar Parallax. It is measured in arc sec. Relation between distance and parallax is -

    d = 1/p

    where 'd' is distance to the stars in pc and 'p' is parallax in arcsec.

    stellar parallax_1.png
      Method of Trignometric Parallax

      Hipparcos Mission

      Launched in August 1989 by ESA, Hipparcos was a pioneering space experiment dedicated to the precise measurement of position, parallax and proper motion of stars. Some of the following features of this mission are

      →Measured precision parallax upto accuracy about 0.001 arcsec.

      →Hipparcos measured parallax of about 10,000 stars.

      →Measured good distance upto 1000 pc.

      hipparcos satellite_1.jpg
        Hipparcos Satellite

        Gaia Mission

        Global Astrometric Inferomter for Astrophysics Mission was launched by ESA. The prime objective of this mission is to survey more than one billion stars in our Galaxy and beyond. Data from this astronomical census will allow astronomers to answer. Some fundamental questions about the formation and evolution of our Galaxy and will provide insight into many other topical areas of astronomy. Some of following features of this mission are

        →All sky survey of Galaxy that build up high precison angular measurement through repeated measurement.

        →Measured precision parallax up to accuracy of 0.01 milliarcsec.

        gaia satellite.jpg
          Gaia Satellite

          Proper Motion of Stars

          Proper motion of star is the angular motion of that star across the sky with respect to more distant stars. It is measured in arcsec per year and denoted by usually μ. Typical proper motion of stars is ≈0.1 arc sec per year. Proper motion of stars can be calculated using

          μ2 = μδ2 + μα2

          where μδ is component of proper motion along DEC.

          μα is component along RA.

            Proper Motion Of Stars

            Radial Velocity

            Radial Velocity of stars is the velocity of stars along the line of sight. It tells us how fast it is moving towards or away from us. Radial velocity is measured using DOPPLER SHIFT'S of star spectrum. It is denoted by vr and measured in km/sec.

            Tangential Velocity

            Tangential Velocity is the real velocity across our line of sight. To calculate we need both proper motion of star and distance to the stars. It is denoted by vt and measured in km/sec. It is calculated by using formula

            vt = 4.74 μ / p

            Space Velocity

            Velocity and direction with which stars move in space is called its space motion or space velocity. It is denoted by vs and measured in km/sec. Space velocity is obtained by vector addition of radial velocity and tangential velocity of star. Magnitude of space velocity is determined by using formula

            vs = √ vt2 + vr2

              Space velocity and its component

              Objectives of the Project

              The objective of this report is to learn astrometry of stars clusters data provided by Gaia and determine fundamental astrometrical parameters of stars cluster. Also to study about basic of astronomy and astrophysics which include magnitude of stars, telescope, brief introduction to photometry etc.

              List the objectives of this project is -

              →To identify members with proper motion analysis.

              →To determine parallax and distance to the stars under limit of error.

              →To plot CMD of star cluster

              →To fit isochrone to find age, metallicity and extinction of cluster.

              →To study about magnitude of stars, telescope and brief introduction to photometry




              The basic information or literature about Pleiades cluster is taken from GAIA DR2 and its article is found to be on www.aanda.org/articles/aa/abs/2018/08/aa32843-18. Information is listed as follows -

              Parameters of Pleiades Star Cluster
              Parameter  Value Unit
              pmRA 19.997  mas/yr
              pmDEC  -45.548 mas/yr
              parallax 7.364 mas 
               Distance Modulus 5.667 -
               Radial Velocity 5.65km/sec 
               E(B-V)0.045  -
              log age  8.04 - 


              The section answers how the data was collected and how it was analyzed.

              Collection of Data

              The data about star cluster which has been analysed is collected from source catalog GAIA DR2. Gaia is successor to Hipparcos mission and telescope is part of ESA's Horizon 2000+ long term scientific program. The 1.7 billion source catalog of Gaia DR2 is unprecedented form for an astronomical datasheet in term of sheer size, high dimensionality and astrometric precision and accuracy. The data is collected from Gaia archive query search where we chose the parameters we need.


              Most of the analysis is done using the help of software TOPCAT which is described below


              TOPCAT is an interactive graphical viewer and editor for tabular data. Its aim is to provide most of facilities that astronomers need to analysis and manipulation of source catalogs and other tables. It can also be used for non-astronomical data as well. All the tables, figures, histogram and plots in this project are made using TOPCAT.


              Downloading of pleaides star cluster data using TOPCAT

              Data is downloaded using TOPCAT Cone Search Window and method and diagram with respect to that step by step are listed below -

              † Querying TGAS source within 5 degree of Pleiades

              † Opening TOPCAT Cone Search Window and performing following command-

              ✱VO|Cone Search menu item

              ✱Keywords: “ tgas”

              ✱Object Name: “pleiades” and then resolve

              ✱Radius: “ 5”

              On Clicking OK, data about star cluster Pleiades will be downloaded.

              vo search_1.PNG
                VO search window

                Now we can analysis the data further.

                Proper motion analysis

                ✱Graphics | Plane Plot

                menu item

                ✱X: pmra

                ✱Y :pmdec

                Note overdensity far from (0,0)

                † Graphically selecting this comoving cluster as NEW SUBSET

                  Plane Plot between pmRA and pmDEC

                  Now we have cluster and we do further its analysis.

                  Drawing parallax histrogram

                  †Plotting parallax histogram of comoving subset

                  ✱Graphics: Histogram Plot

                  menu item

                  ✱X: parallax

                    Histogram of Parallax

                    We observe some outliers in histogram. So we have to exclude that.

                    Excluding proper motion outliers

                    †Restricting comoving subset further to exclude parallax outlier

                    ✱Views † Row Subsets

                    menu item

                    †Clicking New Toolbar button to create new algebric subset and naming it: “cluster” and

                    writing expression :“Comoving && parallax >6.2 && parallax<8.8 ”

                    cluster 1_1.PNG
                      Histogram of Cluster

                      Now we have histogram of data excluding its outlier. Now we can check the value of parameters by opening column statistics of the data or we can check by drawing Gaussian. Here we have checked by both and the result will be same from both the way.

                      Checking for cluster proper motion statistics

                      It is done by following command

                      ✱Views| Column Statistics

                      menu item

                      †Subset for Calculation cluster

                      row (2).PNG
                        Column Statistics


                        Pleiades parallax ≈ 7.36 ± 0.14 mas

                        Radial Velocity ≈ 5.79 ± 2.86 km/sec.

                        pmRA ≈ 19.96 ±0.26 mas/yr

                        pmDEC ≈ -45.51±0.18 mas/yr

                        This observation helps to do further calculation and find parameters which are directly or indirectly related to above observation parameters.


                        ☆DISTANCE ESTIMATION

                        Since the parallax error is less than 10% and the mean of data is much greater than standard deviation, so we can invert the parallax to estimate the distance-

                        d = 1000/ p

                        and error in distance is calculated by using formula

                        ∆d = (∆p/p) d

                        DISTANCE TO STAR CLUSTER PLEIADES IS FOUND TO BE ≈ 135.50 ± 6.42 pc

                        ☆PROPER MOTION OF PLEIADES

                        Proper motion of Pleiades was found to be using formula

                        μ2 = μδ2 + μα2

                        and for error in it we use-

                        ∂μ = (∂μδ + ∂μα)/√ μδ2 + μα2

                        So, Proper motion of star cluster PLEIADES is = 49.69 ± 0.02 mas/yr


                        We found the Radial velocity and parallax of Pleiades Star Cluster. Now using formula for tangential velocity we will find that-

                        vt = 4.74 μ / p

                        and error in it is estimated by using

                        ∂vt = vt ( ∂μ/μ +∂p/p )

                        So, Tangential Velocity of PLEIADES star cluster was found to be = 32.00 ± 0.59 km/sec.

                        ☆ SPACE VELOCITY ESTIMATION

                        Space velocity of Pleiades Star Cluster is calculated using formula

                        vs = √ vt2 + vr2

                        and error in space velocity is given by-

                        vs =( ∂vt + ∂ vr ) / √ vt2 + vr2

                        Hence, Space Velocity of Pleiades Star Cluster was found to be = 32.52 ± 0.21 km/sec.

                        ☆ DISTANCE MODULUS

                        Distance modulus of star cluster is found using formula

                        DM = m-M = 5logd-5

                        Hence, DM of Pleiades star cluster was found to be= 5.66


                        CMD of Pleiades Star cluster from given data is drawn in TOPCAT which is

                          CMD of Pleiades Star Cluster

                          Now we can do isochrone fitting on CMD.

                          ISOCHRONE FITTING

                          The theoretical isochrones for the cluster are obtained from the http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/616/A10. The best fitted isochrone for Pleiades Star cluster was of logage = 8.0. Before that we subtracted extinction and distance modulus from magnitude of stars cluster. But still it was not matched, so we do it by hit and trial and fit the cmd with theoretical isochrone.

                          isochrone fitting of pleiades.PNG
                            Isochrone fitting of Pleiades Star Cluster

                            Here we are observing that CMD of experimental Pleiades Star Cluster data matches with theoretical isochrone of logage =8.0. Hence, we can find age of given star cluster with the masses we can check the table or column statistics of that theoretical isochrone.


                            We analysing Proper Motion of Pleiades Star Cluster by drawing sky plot.

                            sky plot.PNG
                              Sky Plot of Pleiades Star Cluster

                              RESULTS AND DISCUSSION

                              We have analysed, observed the data of Pleiades Star Cluster and calculated some fundamental parameters of Pleiades Star Cluster which is listed in given table

                               Parameters Value Units
                               pmRA 19.96±0.26 mas/yr
                               pmDEC-45.51±0.18   mas/yr 
                               Proper Motion49.69±0.02 mas/yr 
                               Parallax 7.36±0.14 mas
                               Distance135.50  pc
                               Log age8.0 ( 100 million years)- 
                               Radial Velocity 5.79±2.86km/sec 
                               Tangential Velocity 32.00±0.59km/sec 
                               Space Velocity 32.52±0.21 km/sec
                               DM 5.667 -

                              This is result of some fundamental astrometric parameters Pleiades Star Cluster. By this method we can collect, observe and analyse the data of other open star cluster as well as globular star cluster. On comparing with the result of literature we have concerned, the result which is found to be matching within limit of uncertainty or error.


                              The main aim of this project was to use data collected from the Gaia DR2 to find some astrometric parameters of Pleiades open star cluster by analysing it on software TOPCAT. By analysing proper motion etc, we are able to find distance to star cluster with radial velocity, tangential velocity and space velocity of Pleiades. As we were gradually proceeding by filtering the data by proper motion analysis and taking the stars within 1 sigma uncertainty of parallax, the stars beyond the main sequence (possible blue stragglers) were gone; so we could not study them. The cluster age is about 100 million year with E(B-V)=0.045. The positive radial velocity tells that star cluster is moving away from us. We can also estimates binaries on the main sequence, can plot spatial stellar density of star cluster and can estimate Galactic Space Velocity of Star Cluster. I have learned about binary stars and methods to estimate stellar magnitudes, which are not included in this report. Now, I have sound knowledge in basic of astronomy and astrophysics and basic parameters of star clusters and how to estimate them. In future, I would like to extend this to Globular Cluster and learn how to perform photometry using IRAF and perform advance research in this field.


                              ★ Inroduction to Stars, Galaxies and the Universe, Prof. Richard Pogge

                              ★Topcat Tutorial -University of Bristol

                              ★Exploring Gaia Data with Topcat, Mark Taylor

                              ★Inroduction to stellar Astrophysics, Erika-Bohm Vitense




                              I would like to express my thanks of gratitude to the IASc-INSA-NASI Summer Research Fellowship Program 2019 for selecting me and providing me an opportunity to work under the guidance of Prof. Annapurni Subramaniam,IIA, Bengaluru. I express my sincere gratitude to Prof. Annapurni Subramaniam for giving me opportunity as her intern and for her valuable guidance and support throughout project. I thank to IIA and their staff for their support. I specially thank to PhD. scholar Vikrant Jadav at IIA for his support.

                              I would also like to thank Dr. Amit Pathak, Associate Professor at BHU, Varanasi for his recommendation without which this internship will not be possible.

                              At last, I would like to thank my family and friends who motivated and supported me throughout this project.


                              • Fig 1: wikipedia
                              • Fig 2: google
                              • Fig 3: www.esa.com
                              • Fig 4: esa
                              • Fig 5: google images for proper motion
                              • Fig 6: google images
                              • Table 1: Gaia data release 2
                              • Fig 7: TOPCAT
                              • Fig 8: TOPCAT
                              • Fig 9: TOPCAT
                              • Fig 10: TOPCAT
                              • Fig 11: TOPCAT
                              • Fig 12: TOPCAT
                              • Fig 13: TOPCAT
                              • Fig 14: TOPCAT
                              Written, reviewed, revised, proofed and published with