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Summer Research Fellowship Programme of India's Science Academies

Study of open clusters

Aparna K P

Christ College Irinjalakuda, Thrissur 680125

Annapurni Subramaniam

Indain Institute of Astrophysics, Sarjapur Main Road, 2nd Block, Karnataka 560034

Abstract

The project analyses open clusters finding their distances from Earth, predicts their evolution, general properties and probability of binaries. Topcat software is used to plot graphs and the data is obtained from Gaia the space observatory by European Space Agency (ESA). Studying cluster properties helps us to understand more about star, planetary formations. It also helps in improving our knowledge about the universe. Open clusters are young star clusters with vigorous activity going on within the cluster. This project studied 15 open clusters found out their general properties, distances to Earth and also checked the probability of binaries. Clusters Alphaper, NGC1039, NGC2232, NGC2422, NGC2516, NGC6405, Trumpler10, NGC2451, NGC2457, NGC2168 has higher probability of visual binaries in them and the clusters NGC2422, NGC2516, NGC6405, Trumpler 10, NGC1039 were found to be within the same distance range which explains their similar extinction values.

Abbrevations and Notations

Abbreviations
ADS Astrophysics Data System 
 AλExtinction coefficient 
 CMD Color-Magnitude Diagram
 Ddistance modulus 
DEC Declination 
 ESAEuropean Space Agency  
 E(B-V)Extinction
HIPPARCOS High Precesion PARrallaxCOllecting Satellite 
 ddistance of cluster from Earth 
Mo 1 solar mass=2*10^30kg 
 MAbsolute magnitude 
Myrs Million years 
 mApparent magnitude 
 RARight Ascension 
 YESYork Extinction Solver 

INTRODUCTION

Background

Stars are generally formed together in star clusters, which are very large group of stars gravitationally bound to each other. There are two kinds of star clusters: open and globular clusters. Globular clusters are tight groups of hundreds of stars and contain a large proportion of old stars (population II stars), while Open clusters are more loosely clustered groups of stars with fewer and younger (population I stars). Clusters being gravitationally bound move together and are often referred to as co-moving groups. Open clusters are often confined to the galactic plane and are almost always found within the spiral arms of galaxies. Studying young clusters like the open clusters help in understanding stellar evolution which can further improve our understanding of planetary systems. Open clusters play a vital role in transforming dust and gas to stars, hence studying them provides insight to star formation, as stars of a cluster have similar properties, since they are formed from the same molecular cloud cluster studies can inturn help in studying the individual stars of a cluster. This project is on studying Open clusters by plotting their color-magnitude diagrams (CMD), adding their best fit isochrones, plotting histograms in TOPCAT (It is a graphical viewer and editor of tabular data written in pure java and developed in U.K) to classify 15 open clusters within the Logage 7-8, that is logarithm(age) of clusters is in the range 7-8. In a CMD color is plotted in the X -axis which indicates temperature, bluer the star higher is it's core temperature against magnitude in Y-axis, which indicates the flux. Magnitudes of a star or cluster are generally expressed in terms of absolute and apparent magnitude. Apparent magnitude is the magnitude seen by the observer while Absolute magnitude is the magnitude seen when the corresponding star or cluster is at 10parsec (10pc) and Distance modulus is the difference between apparent and absolute magnitudes. The data for plotting is obtained from Gaia mission. Gaia is a space observatory launched in 2013 by European Space Agency (ESA) which uses astrometry to find positions of celestial objects. Gaia is considered to be a follow up mission to HIPPARCOS launched by ESA in 1989. Stars of a cluster have similar chemical composition and properties because they are formed from the same molecular clouds, since open clusters very young studying them can tell us about star formation and stellar evolution which can further help in explaining planetary formations and binary systems. Calculating distances to celestial bodies help classify them, find their luminosity and temperature.

Cluster Studies

Clusters studies has been done to predict the evolution of clusters and to learn cluster properties. Cluster studies is gaining large acceptance over the recent years, it began with observing clusters and constellations initially through naked eye Galileo had observed Pleaides and Orion through his telescope considering them as stars as the idea of clusters was unfamiliar during that time but with the improvements in technology observations were made through telescopes, from ground telescopes to today's space observatories. The idea of space observatories was to reduce the disturbances caused due to Earth's atmosphere. The formal proposal to make exact observation from space was put forward in1967 in "Proceedings of the 13th General assembly", Transactions of the International Astronomical Union. One of the major benefits if this idea was the launch of Hubble space telescope launched into lower Earth orbit in 1990, Hubble has identified thousands of star clusters in our galaxy and other galaxies in the universe, Although Hubble's contribution is significant it's data was insufficient to gather complete details of star clusters, one reason is that it operated in the optical region of the spectrum. There were also several space telescopes that observed the universe and today we have telescopes which operate in different regions like IR, UVetc. Astrosat is India's first multi wavelength space telescope that studies different celestial bodies in multi wavelength. Studying clusters involves different techniques which use different tools space telescopes give data to which mainly concentrates on spectral studies another common technique involves the distance and position measurements of clusters. HIPPARCOS launched by ESA in 1989 and was the first space mission dedicated to measuring parallaxes and positions based on astrometry, it operated until 1993 so it was followed by Gaia launched in 2013 the major advantage of Gaia is that it identifies cluster members by analysing co-moving groups, and gives an accuracy upto 1000pc. Using the observed distance we can identify general properties of the cluster, this project has used color-magnitude diagrams and parallax method and isochrones (whose mass, age, color index and magnitude are obtained from Gaia data) to study clusters, the advantage of the method is that almost all basic properties of the cluster can be found using this method with negligible errors. The method also allows to do comparative studies among different clusters. Astrometry has gained wider acceptance in the scientific community, future works are concentrated obtaining high quality astrometric positions and parallaxes, relative astrometry for exoplanet detection and probing of dark matter.

Here we are discussing about 15 open clusters.

✪ Alphaper also called Molette20 or Collinder39 is found in the constellation of Perseus. The most luminous member is a white yellow supergiant called Mirfak or Alpha Persei.

✪ NGC1039 also called Messier34 is found in the constellation of Perseus and was discovered by Giovanni Batista before 1654, it was included in the Messier catalog in 1764.

✪ NGC2232 found in the constellation of Monceros.

✪ NGC2422 also called Messier 47 is found in the constellation of Puppis and was discovered by Giovanni Batista.

✪ NGC2516 is found in the southern sky in the constellation Carina, it was discovered by Abbe Lacaille. It is often referred to as the Southern Beehive or Sprinter.

✪ NGC6405 often called the Butterfly Cluster is found in the constellation Scorpious. The cluster's existence was first recorded bu Giovanni Batista.

✪ Trumpler 10 is found in the constellation Vela, the cluster is said to be named after R.J trumpler who rediscovered the cluster after James Dunlop.

✪ Blanco1 located in the constellation Sculptor, it was discovered by Puerto Rican astronomer Victor Manuel Blanco in 1949.

✪ NGC2451 located in the constellation of Puppis it was discovered by Giovanni Batista and John Herschel. It was postulated to be two open clusters which was confirmed in 1996, they were named NGC2451A and NGC2451B.

✪ IC2602 often called as Southern Pleiades, it is located in the constellation Carina and was discovered by Abbe Lacaille.

✪ NGC0869 is an open cluster found in constellation Perseus. This along with NGC0884 is called "Double Perseus".

✪ NGC2391 found in the constellation of Gemini and discovered by Robert Stawell Ball in 1866.

✪ NGC2547 this southern sky cluster is found in the constellation Vela and was discovered by Nicolas de Lacaille.

✪ NGC0884 found in the open cluster Perseus. Along with NGC0869 it is referred to as the "Double Perseus".

✪ NGC2168 it is also known as Messier 35; a northern sky open cluster found in the constellation of Gemini and was independently discovered by Philip Loys and John Bevis. The cluster is known for its chemically peculiar cluster members.

LITERATURE REVIEW

From time immemorial humans have been fascinated about the sky, the drawing of ancient philosophers watching the night sky with bare eyes or Galileo with his telescopes is the first picture on most people's mind thinking about ancient astronomy. From watching the night sky, understanding the Earth is round etc. we have come a long way in the field of Astrophysics. Universe in its abundance and magnanimity has been revealing to us since then. Star clusters is one of the topics that has always stayed in discussion although the methods adopted to study them have evolved with time. From early observations of constellations through naked eye, now we have space telescopes observing star clusters at different wavelengths, astrometric projects like HIPPARCOS and Gaia which can help us determine cluster distances, but the major problems behind these are the possible errors in measurement that might arise, the insufficient technology (this insufficiency is the true motivation to betterment). The gaia data provides accuracy only upto 1000pc. The data also has a time lag between the collected data which may belong to the state of the region some time in the past, although the data can help predict the outcomes sometimes the prediction too comes with probabilities of being true or not. Even though this project also predicts the future of open clusters the prediction has higher probabilities of being true as it is analysed using a number of methods and takes into account the past data from other journals and papers to confirm the results, even though humans have a lot of limitations in studying the whole universe by occupying a tiny portion of it, we have come to a deeper understanding and are overcoming the limitations through innovative ideas.

METHODOLOGY

Data Collection and Analysis

Gaia data is collected from Gaia archive and using this data we plot CMD'S and histograms in TOPCAT. The cluster data is not directly used for plotting, initially negative parallaxes and 10% error in parallaxes are removed to obtain a more accurate cluster data this is then used for plotting. In plotting CMD's we use bp-rp (B-V index-indicating colour) in X- axis, but the value cannot be used as it is since there might be reddening effect (dust grains and other particles in interstellar medium can scatter and absorb light making objects dimmer and redder than they really are), to account for reddening effect we calculate G_BP,G-RP (which are extinction coefficients of respective colours-Obtained from YES: York Extiction Solver) from the extinction E (B-V) (it is the absorption and scattering of electromagnetic radiation by dust, gas etc between the astronomical object and observer.), obtained from webda and SAO/NASA ADS (Astrophysics data system). By subtracting the extinction coefficients from bp_rp we obtain the actual colour, removing colour excess. In the Y axis we have Gmag (indicating flux), but this magnitude is apparent magnitude, it will also have extinction effects, on subtracting the extinction effects and finding a suitable range of distance modulus (for which the isochrone is best fit) which on subtraction from Gmag along with extinction coefficient gives the absolute magnitude. The formula is

1.1) D = M-m = 5log (d/10)

D=distance modulus

d= distance in parsecs

M=absolute magnitude

m=apparent magnitude

since clusters are very far away,

1.2) D= M = 5log(d/10)

From the range of distance modulus the distance range of the cluster can be found, this is one method of finding distances another method involves finding parallaxes, here the corrected cluster data is plotted in a histogram (with Gaussian) with parallax in the X axis from the histogram we obtain mean parallax and it's standard deviation hence parallax range is (mean parallax+standard deviation) to (mean parallax-standard deviation), from parallax range distance range is obtained from the formula:

1.3) d=1/p

The turn of mass and age of the cluster are found by from its best fit isochrone where each isochrone refers to each unique age), it also helps to find the presence of white dwarfs, blue stragglers and other important properties of the cluster. The chance for visual binaries can also be checked using the CMD, for this 0.75 is subtracted from the Gmag of the best fit isochrone, the 0.75 subtraction can be explained by a simple derivation, consider two visual binaries of equal magnitude, we know that.

M = −2.5log (f1/f2) in case of equal magnitude f1=f2 .f1 and f2 are fluxes of the two visual binaries.

hence M = −2.5 log(2f1/f2) = −2.5(log2 + log(f1/f2))=M-0.75

This is the maximum net magnitude obtained in the case of visual binaries, hence for all visual binaries magnitude would lie between that of the first isochrone which stands for single star evolution and the binary isochrone. Dust particles in the interstellar medium has size comparable to that of the wavelength of light in the blue region, as a result the dust particles scatter and absorb blue light making them appear redder this is called interstellar reddening. Extinction refers to the absorption and scattering of interstellar medium and accounts for the reddening effect. In the project the extinction values are found using YES: York Extinction Solver (Developed at York University, Canada) the extinction takes into account of the reddening effect which can be used in the CMD to obtain actual colour of the cluster.

Cluster Analysis

Alphaper

The cluster is found in constellation Perseus.

RA: 03hrs 20min 00sec

DEC: 49deg 51min 40sec

→CMD

A

A is the Color- magnitude diagram for Alphaper cluster

It's E(B-V)= 0.09 (Author: Malysheva L K, journal: Astronomy letters Sept 1997, SAO/NASA Astrophysics Data System)

For G_BP,Aλ/E(B-V)=5.113 (YES: York Extinction Solver), hence Aλ=5.113*E(B-V) extinction coefficient Aλ=0.46 mag

For R_BP, Aλ/E(B-V)=2.474 (YES: York Extinction Solver), hence Aλ= 2.474*E(B-V) extinction coefficient Aλ=0.22 mag

For G, Aλ/E(B-V)=5.082 (YES: York Extinction Solver), hence Aλ= 5.082*E (B-V)=0.46mag

X axis: bp_rp- (G_BP-G_RP)= bp_rp-0.46+0.22

Y axis: Gmag-D-G=Gmag-6.5-0.46

Range of distance modulus D obtained from the plot is 6.2-6.5 applying equation 1.2,

antlog (6.2/5)=d/10, d=174pc antlog(6.5/5)=d/10, d=200pc

✹The distance range of the cluster 174-200pc.

✹The red line represents the isochrone of logage 7.8 so the cluster logage is 7.8, age of the cluster is antlog (7.8)=63Myrs, It shows the path of single star evolution which the stars in the cluster is predicted to follow.

✹The turn-off mass of the cluster would be the turn off mass of it's isochrone which is 5.1Mo (Mo -solar mass =2* 10^30kg).

✹The blue dashed line represents the isochrone of visual binaries, as there are lot of stars which fit exactly between the two isochrones, there could be a lot of visual binaries in the cluster.

✹The plot also shows that the cluster has comparitively less number of stars with some stars in the turn-off signifying that they have exhausted their fuel and is entering the gaint phase.

→Histogram

Table B shows the histogram representing the Alphaper cluster and the cluster after removing it's parallax error.

B

Parallax Mean 5.7milliarcsec Standard Deviation =0.2milliarcsec

Lower limit of distance range =1/(5.7+0.2) = 168 pc

Upper limit of distance range=1/(5.7-0.2) =181pc

✹Distance range of the cluster using parallax method is 168-181pc.

NGC 1039

The cluster also called M34 (in Messier catalog) is found in constellation perseus

RA:02hrs 42min 00sec

Dec:42deg 45min 42sec

→CMD

C

This is the colour - magnitude diagram for NGC1039 cluster

It's E(B-V) = 0.06 (Author: Malysheva L K, journal: Astronomy Letters Sept 1997,SAO/NASA ADS)

For G_BP, Aλ/E(B-V) = 5.113 (YES:York Extinction Solver), hence Aλ=5.113*0.06=0.34mag

For G_RP, Aλ/E(B-V) = 2.474 (YES:York Extinction Solver), hence Aλ=2.474*0.06=0.2mag

For G , Aλ/E(B-V) = 5.082 (YES:York Extinction Solver), hence Aλ=5.082*0.06=0.34mag

X axis: bp_rp- (G_BP-G_RP)=bp_rp-0.34+0.2

Y axis: Gmag- D- G=Gmag-8.5-0.2

✹The distance modulus range found from the plot is 8.1-8.6, applying equation 1.2

antlog (8.1)=d/10, d=417pc antlog(8.6)=d/10, d=525pc

Therefore, distance range of the cluster from the CMD is 417-525pc.

✹The red line represents the isochrone of single star evolution of logage 7.8, so the cluster logage is 7.8 implying the cluster age is antlog(7.8)=63Myrs.

✹The cluster turn off mass found from the isochrone is 5.1Mo.

✹The blue dashed line represents the visual binary isochrone, since there are lot of stars in between the two isochrones the cluster could be rich in visual binaries.

✹Almost all stars in the cluster fits in well with the stellar evolution and the CMD plot shows no stars outside the main sequence, it also shows a few stars turning off from the main sequence.

→Histogram

D

Mean =1.9 milliarcsec Standard Deviation = 0.23 milliarcsec

Lowerlimit of distance range, d=1/p=1/(1.98+0.23) =4 52pc.

Upperlimit of distance range, d=1/p=1/(1.98-0.23) = 571pc.

✹Disance range found using parallax method is 452-571pc

NGC 2232

This cluster is found in constellation Monoceros

RA: 06hrs 28min 00sec

Dec: 04deg 50min 48sec

→CMD

E

This is the color - magnitude diagram of the cluster

It's E (B-V) = 0.03 (Author: Malysheva L k, journal: Astronomy Letters Sept 1997)

For G_BP, Aλ/E(B-V)=5.113(YES), Aλ=5.113*0.03=0.15mag

For G_RP, Aλ/E(B-V)=2.474(YES), Aλ=2.474*0.03=0.1mag

For G, Aλ/E(B-V)= 5.082(YES), Aλ=5.082*0.03=0.15mag

X axis: bp_rp-(G_BP-G_RP)=bp_rp-0.15+0.1

Y axis: Gmag-D-G=Gmag-7.5-0.1

✹The D range for the cluster from the plot is 7.4-7.8, by applying equation 1.2,

antlog (7.4/5)=d/10, d=302pc antlog (7.8/5)=d/10, d=363pc

Hence the distance range of the cluster is 302-363pc.

✹The peacock green line represents the isochrone of single star evolution, the logage of isochrone is 7.6, so the logage of the cluster is around 7.6; age of the cluster is about 39 Mys.

✹The turn off mass of the cluster, found from its isochrone is approximately 7 Mo.

✹The blue dashed line representing the isochrone of visual binaries has lots of stars in between it and green line, the cluster has larger probability of visual binaries.

→Histogram

F

Mean parallax = 3.05 milliarcsec Standard Deviation = 0.23 milliarcsec

Lower limit of distance range, d=1/p=1/(3.05+0.23)=310pc.

Upper limit of distance range, d=1/p=1/(3.05-0.23)=361pc.

✹ Distance range found using parallax method is 310-361pc.

NGC 2422

This star cluster also referred to as M47 is found in constellation puppis.

RA:07hrs 36min 35sec

DEC:14deg 29min 00 sec

→CMD

G

This is the color-magnitude diagram for the cluster.

It's E(B-V) = 0.07 (Author: Malysheva L K, journal: Astronomy Letters Sept 1997)

For G_BP, Aλ/E(B-V)=5.113 (from YES), so Aλ=5.113*0.07 =0.36mag

For G_RP, Aλ/E(B-V)=2.474 (from YES), so Aλ=2.474*0.07=0.17mag

For G, Aλ/E(B-V)=5.082 (from YES), so Aλ=5.082*0.07=0.35mag

X axis: bp_rp-(G_BP-G_RP)=bp_rp-0.36-0.17

Y axis:Gmag-D-G=Gmag-8.7-0.35

✹The range of distance modulus found from the plot is 8.3-8.5, by applying equation 1.2

antlog(8.3/5)=d/10, d=457pc

antlog(8.5/5)=d/10, d=501pc

Therefore the distance range is found to be 457-501pc.

✹The pink line shows the isochrone of single star evolution, the logage of the cluster is 8 so the logage of the cluster is around 8; age of the cluster is around antlog(8)= 100Myrs

✹The turn off mass of the isochrone is 5Mo, therefore the turn of mass of the cluster is approximately 5Mo.

✹The yellow dashed line is the isochrone of visual binaries, as there are lot of stars between the two isochrones, the cluster has large probability of visual binaries in it.

✹All the stars of the cluster are together fitting with the isochrone, so all the stars should have the predicted evolution.

→Histogram

H

Mean parallax = 2.09 milliarcsec Standard Deviation = 0.17 milliarcsec

Lower limit of distance range, d=1/p=1/(2.09+0.17)=442pc.

Upper limit of distance range, d=1/p=1/(2.09-0.17)=521pc.

✹The distance range found using parallax method is 442-521pc.

NGC2516

This star cluster is found in constellation Carina

RA: 07hrs 58min 04sec

Dec: 60 deg 45min 12 sec

→CMD

I

This is the color- magnitude diagram for the cluster.

It's E(B-V) = 0.124 (Author: Malysheva L K, journal: Astronomy Letters Sept 1997)

For G_BP, Aλ/E(B-V)=5.113 (YES), so Aλ=5.113*0.124= 0.63mag

For G_RP, Aλ/E(B-V)=2.474 (YES), so Aλ=2.474*0.124=0.31mag

For G, Aλ/E(B-V)=5.082(YES), so Aλ=5.082*0.124=0.63mag

X axis: bp-rp- (G_BP-G_RP)=bp_rp-0.63+0.31

Y axis: Gmag-D-G=Gmag-8.5-0.63

✹ The range of distance modulus found from the plot is 8-8.5, by applying equation 1.2,

antlog(8/5)=d/10, d=398pc antlog(8.5/5)=d/10, d=501pc

Therefore the distance range of the cluster is found to be 398-501pc.

✹ The peacock green line represents the isochrone of single star evolution, the logage of the isochrone is 7.6 so the logage of the cluster would be 7.6; the age of the cluster is about antlog(7.6)= 39.8Myrs.

✹ The turn off mass of the isochrone is 7Mo, hence the turn off mass ofthe cluster is approximately 7Mo.

✹ The yellow dashed line is the isochrone of visual binaries, as there are stars that fit between the two isochrones they can be visual binaries.

→Histogram

J

Mean parallax = 2.39 milliarcsec Standard Deviation = 0.17 milliarcsec

Lower limit of distance range, d=1/p=1/(2.39+0.17)=391pc

Upper limit of distance range, d=1/p=1/(2.39-0.17)=450pc

✹The distance range of the cluster found using parallax method is 391-450pc.

NGC 6405

This cluster is found in constellation scorpius.

RA: 17hrs 40min 20sec

DEC: -32deg 45min 12sec

→CMD

K

This is the color-magnitude diagram of the cluster

It's E(B-V) = 0.16 (Author: Malysheva L K, journal: Astronomy Letters Sept 1997)

For G-BP, Aλ/E(B-V)=5.113 (YES), so Aλ=5.113*0.16=0.80mag

For G_RP, Aλ/E(B-V)=2.474 (YES), so Aλ=2.474*0.16=0.40mag

For G , Aλ/E(B-V)=5.082 (YES), so Aλ=5.082*0.16=0.80mag

X axis: bp_rp-(G_BP-G_RP)=bp-rp-0.80+0.40

Y axis:Gmag-D-G=Gmag-8.6-0.80

✹The range of D is found to be 8.3-8.6, by applying equation 1.2,

antlog (8.3/5)=d/10, d=457 antlog(8.6/5)=d/10, d=525

Therefore the distance range of the cluster is 457-525pc.

✹The pink line is the isochrone of the single star evolution, the logage of isochrone is 7.6, so the logage of the cluster is about 7.6; the age of the cluster is about antlog (7.6)=39.8Myrs

✹The yellow dashed line represents the visual binary isochrone, from the plot this cluster has a larger probability of visual binaries.

✹The CMD also shows a spread of stars at the bottom this indicates that the newly formed stars in the cluster has more spread color index.

→Histogram

L

Mean parallax = 2.17 milliarcsec Standard deviation = 0.22 milliarcsec

Lower limit of distance range, d=1/p=1/(2.17+0.22)=418pc

Upper limit of distance range d=1/p=1/(2.17-0.22)=508pc

✹Diastance range found using parallax method is 418-508pc.

TRUMPLER 10

This cluster is located in constellation Vela.

RA: 08hrs 47min 54sec

Dec: −42deg 27min 00sec

→CMD

M

This is the color-magnitude diagram of the cluster.

It's E(B-V) = 0.05 (Author: Malysheva L K, journal: Astronomy Letters Sept 1997)

For G_BP, Aλ/E(B-V)=5.113, so Aλ=5.113*0.05=0.25mag

For G_RP, Aλ/E(B-V)=2.474, so Aλ=2.474*0.05=.12mag

For G, Aλ/E(B-V)=5.082, so Aλ=5.082*0.05=.25mag

X axis: bp_rp-(G_BP-G_RP)=bp_rp-0.25+0.12mag

Y axis: Gmag-D-G=Gmag-8.5-0.25

✹The range of D found from the CMD is 8.1-8.6pc, by applying equation 1.2,

antlog (8.1/5)=d/10, d=417pc antlog(8.6/5)=d/10, d=525pc

Therefore the distance range is 417-525pc.

✹The peacock green line is the isochrone of single star evolution, the logage of the cluster found from it's isochrone is 7.6, so the age of the cluster is 39.8Myrs.

✹The turn of mass of the cluster would be that of the isochrone which is at 7Mo.

✹The yellow dashed line is the visual binary isochrone, from the CMD the cluster has high probability of visual binaries.

→Histogram

N

Mean parallax = 2.28 milliarcsec Standard Deviation = 0.24 milliarcsec

Lower limit of distance range, d=1/p=1/(2.28+0.24)=400pc

Upper limit of distance range , d=1/p=1/(2.28-0.24)=476pc

✹ The distance range found using the parallax is 400-476pc.

BLANCO 1

This cluster is located in sculptor constellation.

RA: 00hrs 04min 07sec

DEC: -29deg 50min

→CMD

O

This is the color-magnitude diagram of the cluster.

It's E(B-V) = 0.01 (Author: Malysheva L K, journal: Astronomy Letters Sept 1997)

For G_BP , Aλ/E(B-V)=5.113(YES), so Aλ=5.113*0.01=0.05mag

For G_RP, Aλ/E(B-V)=2.474(YES), so Aλ=2.474*0.01=0.02mag

For G, Aλ/E(B-V)=5.082(YES), so Aλ=5.082*0.01=0.05mag

X axis: bp-rp-(G_BP-G_RP)-bp_rp-0.05+0.02

Y axis: Gmag-D-G=Gmag-7.0-0.05

✹The range of D found from the CMD is 6.8-7.2, by applying equation 1.2,

antlog(6.8/5)=d/10, d=229pc antlog(7.2/5)=d/10, d=275pc

Therefore the distance range obtained is 229-279pc.

✹The blue line represents the isochrone of single star evolution, its logage is 8.0, so the logage of the cluster is about 8.0; age of the cluster is about antlog(8)=100Myrs.

✹ The red dashed line represents the visual binary isochrone the cluster, from the plot cluster has a few stars which can be visual binaries.

→Histogram

P

Mean parallax = 4.2 milliarcsec Standard Deviation = 0.12 milliarcsec

Lower limit of distance range, d=1/p=1/(4.2+0.12)=231pc.

Upper limit of distance range, d=1/p=1/(4.2-0.12)=245pc.

✹The distance range found using parallax method is 231-245pc.

NGC 2451

This cluster is located in the Puppis constellation

RA: o7hrs 44min 27sec

DEC: -37deg 40min 00sec

→CMD

8PRONGC2451PLOT.PNG
    Q

    Cluster's E(B-V) = 0.055 (Author: Malysheva L K, Astronomy Letters Sept 1997)

    For G_BP, Aλ/E(B-V)=5.113(YES) , Aλ=5.113*0.055=0.28mag

    For G_RP, Aλ/E(B-V)=2.474(YES, Aλ=2.474*0.055=0.14mag

    For G, Aλ/E(B-V)=5.082(YES), Aλ=5.082*0.055=0.28mag

    X axis:bp_rp-(G_BP-G_RP)=bp_rp-0.28-0.14

    Y axis:Gmag-D-G=Gmag-6.8-0.28

    ✹ The range of D found from the plot is 6.5-6.8, applying equation 1.2

    antlog (6.5/5)=d/10, d=200 pc

    antlog (6.8/5)=d/10, d=245pc

    Therefore the distance range of the cluster is 200-245pc.

    ✹ The green line represents the isochrone of a single star evolution its logage is 7.6, so the logage of the cluster is around 7.6; age of the cluster is antlog (7.6) 39.8M yrs.

    ✹ The turn off mass of the cluster found from it's isochrone is approximately 7Mo.

    ✹ The blue dashed line represents the visual binary isochrone, from the plot there are lots of stars which can be visual binaries.

    →Histogram

    R

    Mean parallax = 5.15 milliarcsec Standard Deviation = 0.15 milliarcsec

    Lower limit of distance range, d=1/p=1/(5.15+0.15)=189pc

    Upper limit of distance range, d=1/p=1/(5.15-0.15)=200pc

    ✹ Distance range found from the parallax method is 189-200pc.

    IC 2602

    Cluster is found in constellation Carina

    RA: 07hrs 44min 27sec

    Dec:37deg 40min 00sec

    →CMD

    S

    This is the colour-magnitude diagram of IC 2602 cluster.

    It's E(B-V) = 0.024 (Author: Malysheva L K, Journal: Astronomy Letters Sept 1997, SAO/NASA Astrophysics Data System)

    For G_BP, Aλ/E(B-V)=5.113( YES), hence Aλ=5.113*0.024=0.12mag

    For G_RP, Aλ/E(B-V)=2.474,(YES), hence Aλ=2.474*0.024=0.06mag

    For G, Aλ/E(B-V)=5.082(YES), hence Av=5.082*0.024=0.12mag

    X axis - bp_rp-(G_BP-G_RP)= bp_rp-0.12+0.06

    Y axis - Gmag- D - G=Gmag-6-0.12

    ✹ The D range for the cluster from the plot is 6-6.1, by applying equation 1.2,

    antlog (6/5)=d/10, d=158pc

    antlog (6.1/10)=d/10, d=166pc

    So the distance range found from the CMD is 158-166pc.

    ✹ The green line indicates the best fit isochrone of single star evolution of logage 7.6, hence logage of the cluster is 7.6 and age is antlog (7.6)=39.8 Myrs.

    ✹ Turn off mass of the cluster is that of the isochrone which is 7Mo.

    ✹ The red dashed line represents the isochrone of the visual binary, although there are not much but there are a few stars which fall between the two isochrones which can be visual binaries.

    →Histogram

    T

    Mean parallax = 6.56 milliarcsec Standard Deviation = 0.22 milliarcsec

    Lower limit of distance range= 1/p=1/(6.56+0.22)=147pc

    Upper limit of distance range= 1/p=1/(6.56-0.22)=158pc

    ✹ Distance range found using parallax method is 147-158pc.

    NGC 0869

    This cluster is found in Perseus constellation.

    RA:02hrs 19min 00sec

    DEC:57deg 07min 42sec

    →CMD

    8PRONGC0869PLOT.PNG
      U

      ​This is the color-magnitude diagram of the cluster.

      It's E(B-V)= 0.58 (WEBDA)

      For G_BP, Aλ/E(B-V) =5.113, so Aλ=5.113*0.58=2.5mag

      For G_RP, Aλ/E(B-V)=2.474, so Aλ=2.474*0.58=1.5mag

      For G, Aλ/E(B-V)=5.082, so Aλ=5.082*0.58=2.5mag

      X axis: bp_rp-(G_BP-G_RP)=bp_rp-2.5+1.5

      Y axis: Gmag-D-G=Gmag-11.5-2.5

      ✹ The range of D found from the CMD is 11.4-11.6, by applying equation 1.2,

      antlog (11.4/5)=d/10, d=1905

      antlog (11.6/5)=d/10, d=2089

      Therefore the distance range of the cluster is 1905-2089pc.

      ✹ The red line represents the isochrone for single star evolution, whose logage is 7.0, so the cluster logage is about 7.0; age of the cluster is antlog(7.0)=10Myrs

      ✹ The turn off mass of the cluster is would be that of the isochrone which is approximately at 17.8Mo.

      ✹ The blue dashed line represents the isochrone of visual binaries, from the plot there is a probability of finding visual binaries in newly formed stars in the cluster which occupy the lower portion of the CMD, but not in later stages.

      ✹ The distance range has increased because Gaia provides accuracy only upto 1000pc.

      →Histogram

      NEW1PROHISNGC0869PLOT.PNG
        V

        Mean parallax = 0.4 milliarcsec Standard Deviation = 0.1 milliarcsec

        Lower limit of distance range, d=1/p=1/(0.4+0.1)=2000pc

        Upper limit of distance range, d=1/p=1/(0.4-0.1)=3000pc

        ✹ The distance range found using parallax method is 2000-3000pc, the distance range has increased becuase Gaia gives accuracy only upto 1000pc.

        IC 2391

        This cluster is located in Vela constellation

        RA: 08hrs 40min 32 sec

        DEC: -53deg 02min 00sec

        →CMD

        8PROIC2391PLOT.PNG
          W

          Cluster's E(B-V) = 0.08 (Author: Malysheva L K journal: Astronomy Letters Sept 1997)

          For G_BP, Aλ/E(B-V)=5.113(YES), so Aλ=5.113*0.08=0.41mag

          For G_RP, Aλ/E(B-V)=2.474 (YES), so Aλ=2.474*0.08=0.2mag

          For G, Aλ/E(B-V)=5.082 (YES), so Aλ=5.082*0.08=0.41mag

          X axis: bp_rp -(G_BP-G_RP)=bp_rp-0.41+0.2

          Y axis: Gmag-D-G=Gmag-6.4-0.41

          ✹ The range of D from the plot is 6-6.4, by applying equation 1.2

          antlog(6/5)=d/10, d=158pc

          antlog(6.4/5)=d/10, d=190pc

          Therefore the distance range of the cluster is 158-190pc.

          ✹ The peacock green line is the isochrone of single star evolution whose logage is 7.2 so the logage of the cluster is about 7.2; age of the cluster is 15Myrs.

          ✹ The turn off mass of the cluster is that of the isochrone which is approximately at 13Mo.

          ✹ The dashed line represents the isochrone of the visual binary and from the plot there is less probability of visual binaries in the cluster.

          →Histogram

          NEW1PROHISIC2391PLOT.PNG
            X

            Mean parallax = 6.6 milliarcsec Standard Deviation = 0.2 milliarcsec

            Lower limit of distance range, d=1/p=1/(6.6+0.2)=147pc

            Upper limit of distance range, d=1/p=1/(6.6-0.2)=156pc

            ✹ The distance range of the cluster found by parallax method is 147-156pc.

            NGC 2547

            This cluster is found in constellation Vela.

            RA:08hrs 10min 09sec

            DEC: -49deg 12min 54sec

            →CMD

            8PRONGC2547PLOT.PNG
              Y

              Cluster's E(B-V) = 0.06 (Author: Malysheva L K, journal: Astronomy Letters Sept 1997)

              For G_BP, Aλ/E(B-V)=5.113 (YES), so Aλ=5.113*0.06=0.31mag

              For G_RP, Aλ/E(B-V)=2.474 (YES), so Aλ=2.474*0.06=0.15mag

              For G, Aλ/E(B-V)=5.082 (YES), so Aλ=5082*0.06=0.30mag

              X axis: bp_rp-(G_BP-G_RP)=bp_rp-.31+.15

              Y axis: Gmag-D-G=Gmag-8.4-0.30

              ✹ The range of D obtained from the CMD is 8.1-8.4, by applying equation 1.2

              antlog (8.1/5)=d/10, d=417pc

              antlog (8.4/5)=d/10, d=479pc.

              Therefore the range of distance of the cluster is 417-479pc.

              ✹ The peacock green line represents the isochrone of single star evolution, from the isochrone the logage of the cluster is 7.2, age of the cluster is antlog(7.2)=15Myrs

              ✹ The turn off mass of the cluster is that of the isochrone which is approximately at 14Mo.

              ✹ The blue dashed line represents the visual binary isochrone, from the plot the cluster has stars which can be visual binaries.

              →Histogram

              MY1PROHISNGC2602REALPLOT.PNG
                Z

                Mean parallax = 2.5 milliarcsec Standard Deviation = 0.15 milliarcsec

                Lower limit of distance range, d=1/p=1/(2.5+0.15)=377pc

                Upper limit of distance range, d=1/p=1/(2.5-0.15)=426pc

                ✹ The distance range found by parallax method is 377-426pc.

                NGC 0884

                This cluster is found in Persues constellation.

                RA: 02hrs 22min 18sec

                DEC: 57deg 08min 12sec

                →CMD

                8PRONGC0884PLOT.PNG
                  Φ

                  Cluster's E(B-V)=0.56 (WEBDA)

                  For G_BP, Aλ/E(B-V)=5.113 (YES), so Aλ=5.113*0.56=2.5mag

                  For G_RP, Aλ/E(B-V)=2.474 (YES), so Aλ=2.474*0.56=1.24mag

                  For G , Aλ/E(B-V)=5.082 (YES), so Aλ=5.082*0.56=2.5mag

                  X axis: bp_rp-(G_BP-G_RP)=bp_rp-2.5+1.24

                  Y axis: Gmag-D-G= Gmag-11.7-2.5

                  ✹ The range of D from the plot is 11.3-11.7, by applying equation 1.2,

                  antlog (11.3/5)=d/10, d=1905pc

                  antlog (11.7)=d/10, d=2399pc

                  Therefore the distance range is 1905-2399pc

                  ✹ The distance range has increased because gaia gives accuracy only upto 1000pc.

                  ✹ The red line represents the isochrone of single star evolution whose logage is 7.0, so the logage of the cluster is 7.0; age of the cluster is antlog(7.0)=10Myrs.

                  ✹ The turn of mass of the cluster is that of the isochrone which is 17.8Mo

                  ✹ The blue dashed line is the isochrone of the visual binary, from the plot there is less probability visual binaries in the cluster.

                  →Histogram

                  MY1PROHISSNGC0884REALPLOT.PNG
                    π

                    Mean parallax = 0.39 milliarcsec Standard Deviation = 0.07 milliarcsec

                    Lower limit of distance range, d=1/p=1/(0.39+0.07)=2174pc

                    Upper limit of distance range , d=1/p=1/(0.39-0.07)=3125pc

                    ✹ Distance range found by parallax method is 2174-3125pc, the range has increased because gaia gives accuracy only upto 1000pc.

                    NGC 2168

                    This cluster is located in the constellation of Gemini, the cluster is often called M35.

                    RA: 06hrs 09min 00sec

                    DEC: 24deg 21min 00 sec

                    →CMD

                    8PRONGC2168PLOT.PNG
                      Δ

                      Cluster's E(B-V)= 0.26 (WEBDA)

                      For G_BP, Aλ/E(B-V)=5.113 (YES) , so Aλ=5.113*0.26=1.53mag

                      For G_RP, Aλ/E(B-V)=2.474(YES), so Aλ=2.474*0.26=0.74mag

                      For G, Aλ/E(B-V)=5.082 (YES) , so Aλ=5.082*0.26=1.52mag

                      X axis: bp_rp- (G_BP-G_RP)=bp_rp-1.53+0.74

                      Y axis: Gmag-D-G=Gmag-9.3-1.52

                      ✹ The D range obtained from the plot is 9.3-9.6, by applying equation 1.2,

                      antlog (9.3/5)=d/10, d=724 pc.

                      antlog (9.6/5)=d/10, d=832 pc.

                      Therefore the distance range of the cluster is 724-832pc.

                      ✹ The yellow line represents the isochrone of single star evolution of logage 7.8, so the logage of the cluster is 7.8; age of the cluster is antlog(7.8)=63Myrs.

                      ✹ Turn off mass of the cluster is that of the isochrone which is 5.1Mo.

                      ✹ The dashed red line represents the visual binary isochrone, from the plot the cluster has a higher probability of visual binaries in it.

                      →Histogram

                      MY1PROHISNGC2168REALPLOT_1.PNG
                        λ

                        Mean parallax = 1.12 milliarsec Standard Deviation = 0.25 milliarcsec

                        Lower limit of distance range, d=1/p=1/(1.12+0.25)=732pc

                        Upper limit of distance range, d=1/p=1/(1.12-0.25)=1149pc

                        ✹ Distance range of the cluster found by parallax method is 732-1149pc

                        RESULTS AND DISCUSSIONS

                        Distance Calculation

                        ✹ The distances calculated from CMD and by parallax method is summarised in the table below with data obtained from journal and authorised site.

                        Cluster Analysis
                        CLUSTERDISTANCE FROM CMD(pc)DISTANCE FROM PARALLAX METHOD(pc)DISTANCE FROM JOURNAL OR AUTHORISED SITEAGE OF CLUSTER(Myrs)APPROX .TURN OF MASS(Mo-solar mass)
                        IC2602158-166147-1581637.67Mo
                        NGC2391158-190147-1571667.212.9Mo
                        ALPHAPER174-200168-1811787.85.1Mo
                        NGC2451199-245189-2002097.67Mo
                        BLANCO1229-275231-24526384.8Mo
                        NGC2232302-363310-3613597.67Mo
                        NGC2516398-501391-4504207.67Mo
                        TRUMPLER 10417-525397-4954277.67Mo
                        NGC2547417-479377-4264587.212.9Mo
                        NGC2422457-501442-52146284.8Mo
                        NGC6405457-525418-5084837.67Mo
                        NGC1039417-525452-5715007.85.1Mo
                        NGC2168724-832732-11498167.85.1Mo
                        NGC08691905-20892000-30002079717.8Mo
                        NGC08841905-23992174-31252345717.8Mo

                        Clusters: Alphaper, NGC1039. NGC2232, NGC2422, NGC2516, NGC6405, Trumpler 10, Blanco1, NGC2451, NGC2547. IC2602, NGC2391 the 3rd column distance from the data is taken from Author: Malysheva L K, journal: Astronomy Letters Sept 1997, and for clusters NGC0869. NGC0884, NGC2168 it is taken from WEBDA.

                        From the chart we have:-

                        ✹ The distances of 15 clusters are comparable to the journal data.

                        ✹ The range of distance in the case of NGC0869, NGC0884 has increased this is because Gaia data gives accuracy only upto 1000pc.

                        ✹ The age and approximate turn off mass of the cluster is found.

                        →From the CMD clusters

                        ✹ Alphaper, NGC1039, NGC2232, NGC2422, NGC2516, NGC6405, Trumpler 10, NGC2451. NGC2457, NGC2168 have high probability of visual binaries while clusters NGC0869, NGC0884 have lower probability of visual binaries and clusters IC2602, Blanco1, IC2391 has a few region of the cluster where visual binaries can be found.

                        ✹ The CMD cluster predicts the path of evolution of stars in the cluster.

                        Comparison of Clusters in the Similar Distance Ranges

                        The clusters NGC2422, NGC2516, NGC6405, Trumpler 10, NGC1039 are all clusters within the distance range of 300-500pc these have E(B-V) in the range of 0.05-0.1 this is because as they are in the same distance range from us the amount of dust particles that the light passes to reach Earth would be comparable for each cluster, so the clusters have similar extinction values.

                        CONCLUSION AND RECOMMENDATIONS

                        ❅The distance of clusters can be found very efficiently using Gaia data.

                        ❄The CMD plots can be used to find the general properties of the cluster, which can tell about stellar formation and chemical composition of the cluster.

                        ❅The CMD plot can predict prescence of visual binaries in a cluster, which can be further worked to see if they are real binaries.

                        ❅The distance obtained from the method can be later used to find luminoscity and temperature functions of the cluster.

                        ✳Cross-checked that clusters at similar distance ranges will have similar extinction.

                        REFERENCES

                        Web Journal

                        1. Malysheva L K, (Sept 1997) (SAO/NASA Astrophysics Data System), Parameters of open clusters uvbyβ photometry.Astronomy letters(http://articles.adssabs.harvard.edu//full/1997AstL...23..585M/0000588.000.html

                        Online site

                        2. Marshall L McCall , Ennio Caelluci, Shaun Deleaney, Robin Fingerhut, Kris Kilonski, Azadeh Mahinpou, Ovidiu Vaduvescu:York Extiction Solver ?http://www.cdac-ccda.hia.nrc-cnrc.gc.ca/community/YorkExtinctionSolver/output.cgi​

                        3. Jean -Claude Mermilliod WEBDA navigation- webda.physics.muni.cz?

                        BIBLIOGRAPHY

                        Erica Bohm Vitenese(1992) Introduction to Stellar Astrophysics volume 3 (pages 70-84, 113-126,155-164,172-202,216)

                        ACKNOWLEDGEMENTS

                        I extend my sincere gratitude to my guide Prof.Annapurni Subramaniam for her guidance, motivation and support without which this project would not be possible. I express my gratitude to Indian Institute of Astrophysics for providing me institute facilities and hosting me as an intern here, I thank Indian Academy of sciences for the internship opportunity and fellowship, I also use this opportunity to thank my HOD-Prof. V.P Joseph (Christ College Irinjalakuda) and my class teacher Mr. Edwin Jose for their kind support.

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