Astrometry of open star clusters
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
|pmRA||Proper Motion Right Ascension|
|pmDEC||Proper Motion Declination|
|HRD||Hertzsprung Russell Diagram|
|CMD||Colour Magnitude Diagram|
|GAIA||Global Astrometric Interferometer for Astrophysics|
|DR2||Data Release 2|
|ESA||European Space Agency|
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.
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 -
where 'd' is distance to the stars in pc and 'p' is parallax in arcsec.
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.
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.
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.
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 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
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
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
HERE I HAVE CHOOSEN PLEIADES STAR CLUSTER TO CARRY OUT AND LEARN ASTROMETRY
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 -
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.
ASTROMETRY OF PLEAIDES STAR CLUSTER- METHOD, OBSERVATION AND CALCULATION
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.
Now we can analysis the data further.
Proper motion analysis
✱Graphics | Plane Plot
Note overdensity far from (0,0)
† Graphically selecting this comoving cluster as NEW SUBSET
Now we have cluster and we do further its analysis.
Drawing parallax histrogram
†Plotting parallax histogram of comoving subset
✱Graphics: Histogram Plot
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
†Clicking New Toolbar button to create new algebric subset and naming it: “cluster” and
writing expression :“Comoving && parallax >6.2 && parallax<8.8 ”
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
†Subset for Calculation cluster
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.
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
☆TANGENTIAL VELOCITY ESTIMATION
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
COLOR MAGNITUDE DIAGRAM OF PLEIADES
CMD of Pleiades Star cluster from given data is drawn in TOPCAT which is
Now we can do isochrone fitting on CMD.
The theoretical isochrones for the cluster are obtained from the . 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.
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.
ANALYSING PROPER MOTION OF PLEIADES STAR CLUSTER IN SPACE
We analysing Proper Motion of Pleiades Star Cluster by drawing sky plot.
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
|Log age||8.0 ( 100 million years)||-|
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.
★ 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 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.