Re-estimation Of Open Star Cluster Parameters Using 2MASS Photometry

Under Graduate Project Report

Re-estimation Of Open Star ClusterParameters Using 2MASS

Photometry

By

Dinil Bose P

B. Sc. 2013 Registration No: 11123706

Supervisor: Prof. Raju Mathew

October 2013

This proposal is submitted in partial fulfillment of the requirement ofBachelor of Science in Physics

Department of PhysicsSt Thomas College

Pala

CERTIFICATE

This is to certify that the project report entitled “Re-estimation Of Open Star Clus-

ter Parameters Using 2MASS Photometry”, submitted to the Mahatma Gandhi

University, in partial fulfillment of the requirements for the award of the Bachelor of Sci-

ence in Physics, is a record of original work done by Dinil Bose P during the academic

year 2011 to 2014 of his study in the Department of Physics, St. Thomas College Pala,

under my supervision and guidance.

Dr. Michael Augustine Prof. Raju Mathew

Head of Department of Physics Department of Physics

St. Thomas College, Pala St. Thomas College, Pala

i

DECLARATION

I, Dinil Bose P, hereby declare that the project report, entitled “Re-estimation

Of Open Star Cluster Parameters Using 2MASS Photometry” for the award of

the Bachelor of Science in Physics is a record of original and independent work done by

me during academic year 2011 to 2014 under the supervision and guidance of Prof. Raju

Mathew, Department of Physics, St. Thomas College, Pala, Kerala.

Dinil Bose P

Department of Physics

St. Thomas College, Pala

ii

Acknowledgement

First and above all, I would like to thank and praise God, Almighty who opened door of

opputunity before me and who lead me throughout my life.

I would like to thank my parents and my family who always gave me support and courage

to fulfil my dreams. I wish to express my sincere gratitude to my guide Prof. Raju

Mathew, for his sound advice and direction over the course of this project. I express my

indebited gratitude to Ajith R, Research Scholar, Central University Kerala who walked

along with me for three years of my college life and taught me the beauty of theoretical

physics and helped me to write the programing codes for this project. I would like to

thank Lino James P, University of Sydney who provided me with necessary literature

searches for completion of the project. I wish to acknowledge Dr. Vincent Mathew,

Central University Kerala who provided access to Matlab and Mathematica program for

computations done in this project. I would like to thank Dr. Michael Augustine, Head of

Department of Physics for offering me wonderful support whenever I was in need of it. I

wish to thank Dr. Joe Jacob, Newman College Thodupuzha who helped me with valuable

suggestions during my project.. This project makes use of data products from the Two

Micron All Sky Survey 2MASS of Cutri et al. (2003), which is a joint project of the

University of Massachusetts and the Infrared Processing and Analysis Center/California

Institute of Technology, funded by the National Aeronautics and Space Administration

and the National Science Foundation. Catalogues from CDS/SIMBAD (Strasbourg), and

Digitized Sky Survey DSS images from the Space Telescope Science Institute have been

employed.

Finally, I myself realize that this project is still far from being perfect, therefore I would

appreciate and welcome some constructive advice to improve this project and I hope it

will be precious as it should be.

Dinil Bose P

iii

Contents

Certificate i

Declaration ii

Acknowledgement iii

1 Introduction 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Classification Of Open Clusters . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2.1 Shapley / Melotte Classification . . . . . . . . . . . . . . . . . . . . 21.2.2 Trumpler System . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.3 Star catalogs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.3.1 2MASS Catalog . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.4 Hertzsprung-Russell diagram . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2 Cluster Parameters 92.1 Data Extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.2 Center Determination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.3 Radius Determination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.4 Dereddening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.5 Color-Magnitude Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3 NGC 7654 153.1 Data Extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.2 Center Determination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

iv

CONTENTS CONTENTS

3.3 Radial Determination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.4 Dereddening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.5 Color Magnitude Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

4 King 18 234.1 Data Extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234.2 Center Determination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244.3 Radial Determination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274.4 Dereddening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284.5 Color Magnitude Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

5 Conclusion 31

Appendices 33

A Gnuplot 33

B Matlab 35

References 39

v

List of Figures

1.1 Classification of OCs using trumpler system. . . . . . . . . . . . . . . . . . 51.2 H-R diagram showing location of stars. . . . . . . . . . . . . . . . . . . . . 7

3.1 Picture on the left panel shows dss image of M 52 and Picture on the rightpanel shows 2MASS image of M 52 . . . . . . . . . . . . . . . . . . . . . . 16

3.2 Histogram of Declination for M 52 . . . . . . . . . . . . . . . . . . . . . . . 173.3 Histogram of Right ascension for M 52. . . . . . . . . . . . . . . . . . . . . 173.4 Star count of M 52 with Right ascension is plotted using dark lines and

corresponding Gaussian fit with dashed lines. . . . . . . . . . . . . . . . . 183.5 Star count of M 52 with declination is plotted using dark lines and corre-

sponding Gaussian fit with dashed lines. . . . . . . . . . . . . . . . . . . . 183.6 Radial Density Profile of M 52.The dotted lines indicate Kings Profile. . . 193.7 Contaminated cluster M 52 with field star. The dotted lines indicate a

isochrone. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.8 Field star of cluster M 52. The dotted lines indicate a isochrone. . . . . . . 223.9 Decontaminated cluster M 52 without field star. . . . . . . . . . . . . . . . 22

4.1 Picture on the left panel shows dss image of King 18 and Picture on theright panel shows 2MASS image of King 18. . . . . . . . . . . . . . . . . . 24

4.2 Histogram of Declination for King 18. . . . . . . . . . . . . . . . . . . . . . 254.3 Histogram of Right ascension for King 18. . . . . . . . . . . . . . . . . . . 254.4 Star count of King 18 with Right ascension is plotted using dark lines and

corresponding Gaussian fit with dashed lines. . . . . . . . . . . . . . . . . 264.5 Star count of King 18 with declination is plotted using dark lines and

corresponding Gaussian fit with dashed lines. . . . . . . . . . . . . . . . . . 264.6 Radial Density Profile of King 18. The dotted lines indicate Kings Profile. 27

vi

LIST OF FIGURES LIST OF FIGURES

4.7 Contaminated cluster King 18 with field star. The dotted lines indicate aisochrone. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

4.8 Field star of cluster King 18. The dotted lines indicate a isochrone. . . . . 304.9 Decontaminated cluster King 18 without field star. . . . . . . . . . . . . . 30

vii

List of Tables

1.1 Examples for Trumpler system of classification. . . . . . . . . . . . . . . . 51.2 Magnitude Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3.1 General Data on M 52 from WEBDA. 1 . . . . . . . . . . . . . . . . . . . . 16

4.1 General Data on King 18 from WEBDA. 2 . . . . . . . . . . . . . . . . . . 24

viii

Chapter 1

Introduction

1.1 Introduction

Open star clusters (OCs) are a group of stars which are gravitationally bound self accel-

erating systems. They have various linear dimensions and morphology. The stars in OCs

are scattered, which are mostly surrounded by gas clouds, that is, they are called “open”

when compared to globular clusters which are round and compact. They contain ' 102

to 104 stars which are formed from the same gaseous material and they have evolved

in the a same time sequence. Since they are formed from same gaseous systems they

have same stellar conditions and they share the same initial conditions. The age of open

cluster varies roughly from 1 million year to 10,000 million years. The oldest accurately

determined OCs in the Milky way galaxy is NGC 6791 which is 7 billion years old. OCs

can be used as test-beds of molecular cloud fragmentation, star formation, and stellar

and dynamical evolution models. They are excellent probes of the Galactic disc structure

(Janes & Phelps, 1994; Friel, 1995). Using OCs both theoretical as well as numerical

simulations can be tested with astronomic observations. The Cluster color-magnitude di-

agrams (CMD) are the best testing grounds for stellar evolutionary models. They can be

used as models to determine the age of galaxies and nebulae. Study of OCs using N-body

1

1.2. CLASSIFICATION OF OPEN CLUSTERS CHAPTER 1. INTRODUCTION

computation posses many technical challenges regarding granularity in gravitational po-

tential, formation of binary stars in evolution (de la Fuente Marcos & de la Fuente Marcos,

2002). So astronomical observations are preferred to find out the parameters of the OCs.

But according to some estimation there are 100, 000 OCs in the galaxy, but less than

2000 of them have been discovered and cataloged (Koposov et al., 2008). Observational

parameters can be obtained using several photometric methods and its accuracy depends

upon depth of the photometry and field contamination. Old photometric systems like

Johnson system are not accurate enough. So the project reestimate the parameters of the

two OCs M52 and King 18 using new photometric method called 2MASS photometry.

OCs center, radial density profile, CMD, reddening and distance will be figured out using

JHK bands and this will be compared with the UBV bands. An isochrone will be fitted

to the CMD to analyze the stellar evolution and main sequence stars.

1.2 Classification Of Open Clusters

The study of classification OCs was taken in Harvard university by Shapley and Mellote

(Melotte, 1915; Shapley, 1916). After a few years another type of classification technique

was by Trumpler (Trumpler, 1930) and Ruprecht (Ruprecht, 1966)

1.2.1 Shapley / Melotte Classification

Shapley and Melotte set up two parameters, one related to the apparent number of stars

and the compactness of the cluster. The second parameter was dependant on the colour

(and later spectral classes) among the cluster members. Later they defined distinct classi-

fication between globular cluster and OCs (Shapley & Sawyer, 1927). They are classified

as follows:

(a) Associations containing field irregularities: These include associations which con-

tain field irregularities which are found using either by visual scanning or by statistical

2

1.2. CLASSIFICATION OF OPEN CLUSTERS CHAPTER 1. INTRODUCTION

analysis. Field irregularities vary with populations of the OCs; from several scattered

stellar members to vast congregations of stars. Classification of such a group is significant

to stellar distributions but most of them are not cataloged.

(b) Distinction only by a star count. Considered very very loose: In this category

wide spread moving clusters were considered. The stars of such group possess high proper

motion or parallel velocities. The ursa major group comes under this category. The com-

mon proper motion studies can identify such groups.With evolution the b class gradually

merges into the c class. Orion nebula represent this type of group.

(c) Very loose and irregular: In this the OCs are large and stars are scattered through-

out. These include clusters like the Pleiades and the Hyades. Some of the large clusters

like IC 4665 in Ophiuchus, χ Persei, Mel 111 in Coma Berenices.

(d) Loose and poor in number : The cluster contains a small number of stars and they

are loose and ill defined at the edges. Clusters like M21, M34, NGC 3572 in Carina, NGC

3293 and NGC 2670 in Vela are examples of such a system.

(e) Intermediate rich and concentrated : The clusters like M38 in Auriga and NGC

3114 in Carina comes under this category. They are much more concentrated and are

compact.

(f) Fairly rich and concentrated : They are almost similar to group e˝ but they contain

more stars than the above. M37 in Auriga and NGC 3532 in Carina are basic examples.

NGC 2477 and the Jewel Box (NGC 4755) in Crux comes under this category. They are

similar to the group above but they contain even more number of stars.

1.2.2 Trumpler System

The trumpler system of classification was invented by a Swiss-American astronomer R.J.

Trumpler (Trumpler, 1930). This was based on three observable parameters of open clus-

ter, the degree of concentration, the range of brightness (magnitude) of the stars in the

3

1.2. CLASSIFICATION OF OPEN CLUSTERS CHAPTER 1. INTRODUCTION

cluster, and the number of stars in the cluster.

Degree of concentration

I Detached clusters with strong central concentration.

II Detached clusters with little central concentration.

III Detached clusters with no noticeable concentration.

IV Not well detached from surrounding star field.

Range of brightness

1. Most of the cluster stars are nearly the same in apparent brightness.

2. Moderate range in brightness.

3. Cluster is composed of bright and faint stars.

Number of stars in cluster

p. Poor (less than 50 stars).

m. Medium rich (50-100 stars).

r. Rich (more than 100 stars).

The Figure 1.1 and associated Table 1.1 show examples of trumpler classification of OCs.

4

1.2. CLASSIFICATION OF OPEN CLUSTERS CHAPTER 1. INTRODUCTION

Figure 1.1: Classification of OCs using trumpler system.1

Table 1.1: Examples for Trumpler system of classification.

I II III IV

r NGC 6791 NGC 7789 NGC 6940 NGC 1817

m NGC 436 NGC 7790 NGC 129 DoDz 9

p NGC 7788 NGC 1807 NGC 7686 Stock 12

Some open clusters may be in, or are surrounded by nebulosity. Trumpler denoted open

clusters with any type of nebulosity (including light and dark nebula) with an n at the

end of the classification. For example, the official classification for NGC 3293 is I 3 r

1www.astrophoton.com/trumpler_class.htm

5

1.3. STAR CATALOGS CHAPTER 1. INTRODUCTION

n because it is embedded in a nebula. So the trumpler system provides more accurate

classification for open clusters hence it is widely used.

1.3 Star catalogs

1.3.1 2MASS Catalog

The 2MASS catalog is based on The Two Micron All Sky Survey2 (Skrutskie et al., 2006)

The project is a collaboration between The University of Massachusetts and the Infrared

Processing and Analysis Center (JPL/ Caltech). The observations were conducted using

two telescope of 1.3 diameter located at, one at Mt. Hopkins, AZ, and one at CTIO,

Chile. Each telescope was equipped with a three-channel camera, each channel consisting

of a 256 × 256 array of HgCdTe detectors. These collected 25.4 T-bytes of raw imaging

data covering 99.99% of the celestial spheres. The 2MASS telescope scan in declination at

a rate of 1´per second. The 2MASS camera frame are 8.5´ wide and the data tiles˝ are

6° long in the declination direction. Secondary mirror was tilted opposite to the scanning

direction momentarily freezing the focal plane image while the telescope scanned in the

declination direction. When exposure exceeds 1.3 s the secondary flew back to its start

position and froze a new piece slightly displaced from the previous position. Array reset

of camera was less than 0.1-s and secondary frame was shifted during dead time. Field-

of-view of camera was shifted by ∼ 1/6 of a frame in declination from frame-to-frame.

Each image consist of six pointings on the sky for a total integration time of 7.8 s. Sub

pixel dithering improves the ultimate spatial resolution of the final Atlas Images. The

bands used in the survey and magnitude limits of the point source and extended source

are given in Table 1.2. Since the differential reliability is about 0.9995 it can be used to

spot the stars which are lower in brightness and which do not appear in other catalogs.

2http://www.ipac.caltech.edu/2mass/

6

1.4. HERTZSPRUNG-RUSSELL DIAGRAM CHAPTER 1. INTRODUCTION

Table 1.2: Magnitude Limits

Band Wavelength (µm) Point Sources (SNR=10) Extended Sources

J 1.25 15.8 15.0

H 1.65 15.1 14.3

Ks 2.17 14.3 13.5

1.4 Hertzsprung-Russell diagram

The basic ideas of stellar evolution of OC’s are studied using Hertzsprung Russell di-

agram Figure 1.2 which was developed by Danish astronomer E. Hertzsprung in 1911

(Hertzsprung, 1909) and American astronomer H. N. Russel in 1913(Russell, 1914).

Figure 1.2: H-R diagram showing location of stars.3

3http://chandra.harvard.edu/edu/formal/variable_stars/HR_student.html

7

1.4. HERTZSPRUNG-RUSSELL DIAGRAM CHAPTER 1. INTRODUCTION

It is a scatter graph of stars showing the relationship between the stars absolute magni-

tudes or luminosities versus their spectral types or classifications and effective tempera-

tures. Mostly the H-R diagram for evolutionary analysis is a plot of log(L/L�) versus

log (Teff ) and usually called theoretical H-R diagram. But in observational form Colour-

magnitude diagram (CMD) was drawn. The stars in the diagram mostly occupy along

Main sequence this can be seen in Figure 1.2. The main sequence stretches from O stars

to cool M stars and these are often called dwarfs. The next sequence is the giant branch.

The stars at the top right are extremely bright in all spectral lines, they are called super

giants. The region between the main sequence and giant branch, which is devoid of stars,

is known as the Hertzsprung gap. Using this diagram stellar evolutionary theories can

be predicted. The stellar evolutionary theories predict the location of stars in the H-R

diagram. Astronomical observations are needed for this. These diagrams depend upon

the mettalicity, reddening distance etc. So the task of producing H-R diagram difficult.

Locus of stars with different masses having the same age is called isochrone. So isochrones

define locus of stars with different masses for a particular age. So the clusters CMD is

nothing but an isochrone corresponding to the clusters age. The project tries to attain

CMD of two open star clusters and fits a isochrone to derive their age.

8

Chapter 2

Cluster Parameters

2.1 Data Extraction

The data from the telescope were accessed using a tool of Vizier catalog1 and software

called ALADIN2. The investigated clusters have been selected from WEBDA and DIAS

catalog. WEBDA catalog provides an estimated radius and a center. Using the center

provided by WEBDA the data of cluster with primary radius 10 arcmin was extracted.

Then the Digitalized Sky Surveys DSS 3 image was extracted. Using this image the

field star decontamination and interstellar reddening were predicted. Then a cutoff of

photometric completeness limit at J < 16.5 mag was applied in order to avoid over

sampling (Bonatto et al., 2004). Then the stars which contained an observational error

more than 0.20mag were reduced. This was applied to J, H and K filters. The reduction

procedures for interstellar reddening were done later.

1http://vizier.u-strasbg.fr/viz-bin/VizieR?-source=2MASS2http://aladin.u-strasbg.fr3http://cadcwww.dao.nrc.ca/cadcbin/getdss

9

2.2. CENTER DETERMINATION CHAPTER 2. CLUSTER PARAMETERS

2.2 Center Determination

The center of the cluster is defined as the area with maximum stellar density. To find

out the center first a histogram of the OC was plotted. The histogram which contains

the information about the number of stars was made for both Right ascension and for

Declination. The bin of histogram has a width of 0.25 arc min. The histogram was

drawn using a software called TOPCAT 4. Then Star count with the coordinates were

extracted and a Gaussian fit for the profile were applied. The Gaussian fit is drawn

in GNUPLOT(Appendix A) and the fit value would give the center. But the values in

sexagesimal form should be converted it into hour angle format. For that purpose a

MATLAB (Appendix B) code was written. Using new values of center the data of the

cluster for further calculations was extracted.

2.3 Radius Determination

The cluster structure can be described using two terms called tidal radius (rt) and limiting

radius (rl) or core radius. The tidal radius gives the maximum radius where the stars

are bound to the gravitational field of the OC. The tidal radius depends both on the

effect of the Galactic tidal field on the cluster and the subsequent internal relaxation and

dynamical evolution of the cluster (Allen & Martos, 1988). After passing the tidal radius

the stars in the cluster leaves the cluster’s gravitational field and it enters the gravitational

field of the galactic plane. So it describes the stripping of stars from cluster to the galactic

plane. The core radius hereby describes the central concentration of the OC. The tidal

radius, limiting radius and concentration of cluster are related by kings formula (King,

1962), the projected density profile ∑(r) of a star cluster can be approximated by

4http://www.star.bris.ac.uk/˜mbt/topcat

10

2.4. DEREDDENING CHAPTER 2. CLUSTER PARAMETERS

∑(r) = k(X−1/2 − C−1/2)2 (2.1)

where,

X(r, rc) = 1 + (r/rc)2 (2.2)

C(rc, rt) = 1 + (rt/rc)2 (2.3)

for rt < r, with a normalization constant k.

When the equation reaches the tidal radius the projected density falls to zero. To ob-

tain radial density profile the OC was divided into concentric shells in equal incremental

steps from the cluster center. The radial stellar density distribution is performed out to

the preliminary radius. The radial density profile is calculated and plotted using MAT-

LAB program(AppendixB). Since the extracted data is in sexagesimal form, it should be

converted it into arc minute form using MATLAB code(AppendixB). The real radius of

the cluster can be defined as the point where it reaches enough stability of background

density and covers all the cluster area. The limiting and tidal radius are estimated by

fitting Kings formula to the radial density profile. The fitting is done using CFTOOL of

MATLAB.

2.4 Dereddening

It is well known that interstellar space between stars is not empty and that certain part

of the star’s radiation is scattered or absorbed by the interstellar particles before reaching

the earth. Interstellar dust non only dims stars, but also makes them redder than their

normal color. A scattering process is probably responsible for the reddening through

selective diffusion and absorption of blue light more than red light. This process is very

11

2.4. DEREDDENING CHAPTER 2. CLUSTER PARAMETERS

similar to the scattering of sunlight in our atmosphere, during sunset. Particularly, all the

stars that are more distant than 100 parsec, must be considered reddened. This situation

clearly contribute to generate a color excess. The color excess is the difference between

the observed and the intrinsic colors expressed in terms of magnitudes. For instance using

(B-V) Johnson color index, one can define the color excess as:

E(B − V ) = (B − V )observed − (B − V )intrinsic (2.4)

The combined effect of scattering and absorption is called interstellar extinction A and it

is measured in magnitude per kilo parsec. Generally extinction depends on the wavelength

of the observation: A = A(l) as well as on the environment contained in the particular

region of the galaxy under observation. Outside the galactic plane, extinction diminishes

very rapidly and can be described by the following formula:

A(r, b) = Aob(1− e(−rsin|b|/b)) (2.5)

Where Ao = extinctionconstant, b = galacticlatitude and b = thicknessofextinction

layer. However the previous formula cannot be applied to a single star because of the

very large fluctuations in the interstellar medium. So this formulas can be applied to star

clusters since they have a large number of star membership. In this project interstellar

extinction coefficient was calculated using IRSA: Galactic Reddening and Extinction Cal-

culator 5 (Schlegel et al., 1998). The color execess E(B − V ) is taken from the calculator

and then it transformed for JHK band gaps using the formulas (C. M. Dutra, 2002).

AV /EB−V = 3.1 (2.6)

AJ/AV = 0.276 (2.7)

EJ−H/EB − V = 0.33 (2.8)

5http://irsa.ipac.caltech.edu/applications/DUST/

12

2.5. COLOR-MAGNITUDE DIAGRAM CHAPTER 2. CLUSTER PARAMETERS

2.5 Color-Magnitude Diagram

The CMD of star cluster shows relationship between absolute magnitude, luminosity, age

and metallicity. In UBV photometry to produce CMD (B−V) versus B was plotted. But

in 2MASS photometry (J−H) versus J was ploted. To plot CMD reddening corrected

data of stars in the cluster were required. Then field stars present in the diagram should

be eliminated. There are four methods to do field star decontamination. Since stars in

the cluster are born together, they are supposed to have the same motion. Their veloc-

ities perpendicular to the line of sight are given by the proper motion and the velocity

in line of sight by the radial velocity. So, using kinematics study of the cluster the field

stars can be eliminated but the proper motion data is available only for few stars and

it is difficult to identify the binary stars. The other method is to use the photometric

criterion. Since the stars belonging to the clusters lie in same evolutionary sequence in

the CMD. The field stars have different age than the stars at the cluster, they move away

from the main sequence thus it can be eliminated. The clusters which have a large age

above 10Myr have a wide main sequence in the CMD so it is difficult to evaluate field

stars from the other stars. The other method is to use spectroscopic methods to eliminate

field stars. This method determines the spectral types and luminosity class of individual

star cluster from their spectra. The comparison between the spectral information and the

photometric information will give an idea about the evolutionary status of the star and

the distance. The stars which have different spectra and photometry have different evo-

lutionary sequence at the expected position of CMD and can be considered as field star.

But spectra is available for bright stars only so it is impossible to use it for entire clusters.

The other method is the use of statistical methods. In this method, CMD of the cluster

with the CMD of field star were compared. A combination of statistical criteria and pho-

tometric methods were used to attain field star decontamination (Tadross, 2011). Cluster

data with limiting radius were extracted and stars with one degree away from the cluster

center was extracted to attain field stars. Then field stars were compared according to the

13

2.5. COLOR-MAGNITUDE DIAGRAM CHAPTER 2. CLUSTER PARAMETERS

cluster data. The cluster data was divided into cells and the same cells with the field star

was compared and stars were reduced. After field star decontamination padova isochrone

was fitted to the cluster (Bertelli et al., 2008). The isochrones of different metallicity and

age are downloaded from the website 6. Different isochrones were computed to fit the

CMD. From the fitting isochrone the age and metallicity of the cluster was derived.

6http://pleiadi.pd.astro.it/

14

Chapter 3

NGC 7654

NGC 7654, also known as M 52, is a prominent cluster which lies in the Cassiopeia

constellation. It was discovered by Charles messier in 1774 (Messier, 1781). One of the

earliest studies was done by Pesch (1960). He used UBV photometry and found out

a reddening of E(B-V)=0.51 − 0.81. The age of the cluster was determined but Lindoff

(1968). He calculated the age about 35 Myr. Using empirical calculation Bruch & Sanders

(1983) found the cluster mass to be approximately 518 M�. The angular diameter of

D′ = 12 is calculated by the Lynga & Palous (1987) and he classified M 52 as Trumpler

type II2r. Main sequence turn off age of approximately 50 Myr was found by Lotkin.

Nilakshi et al. (2002) found the Rcore = 1.59±0.08 and core stellar density ρc = 22.4±1.7

starspc−2.

3.1 Data Extraction

At first the data is extracted using ALADIN selecting the center from WEBDA catalog. In

WEBDA the central coordinates of M 52 are (J200) α = 23h24m48s and δ = +61◦35◦36◦.

The other parameters provided by WEBDA is in given Table 3.1 . The primary radius

of 10 arc is selected for extraction of 2MASS data. The selection procedures discussed in

15

3.2. CENTER DETERMINATION CHAPTER 3. NGC 7654

section 2.1 were applied. The DSS and 2MASS images are in given Figure 3.1 .

Table 3.1: General Data on M 52 from WEBDA. 1

α δ Age d E(B-V) Metallicity

(hms) (◦) (Myr) (kpc)

23h24m48s +61◦35◦36◦ 58 1.444 0.65 -

Figure 3.1: Picture on the left panel shows dss image of M 52 and Picture on the rightpanel shows 2MASS image of M 52

3.2 Center Determination

The extracted data using center from the WEBDA was taken to TOPCAT. Using the

software the stars for one arc minute bins were counted for both right ascension and

declination. The histogram for both declination Figure 3.2 and right ascension Figure 3.3

are given.1http://www.univie.ac.at/webda/cgi-bin/ocl_page.cgi?dirname=ngc7654

16

3.2. CENTER DETERMINATION CHAPTER 3. NGC 7654

Figure 3.2: Histogram of Declination for M 52

Figure 3.3: Histogram of Right ascension for M 52.

Then the number of stars in each bin to Right ascension Figure 3.4 and Declination Fig-

ure 3.5 were plotted. Then a Gaussian curve to find the center of the cluster was fitted

since center of the cluster is defines as the center where it has maximum density. The

Gaussian curve is fitted using the codes written in Gnuplot.

17

3.2. CENTER DETERMINATION CHAPTER 3. NGC 7654

0

20

40

60

80

100

120

140

160

180

200

350.8 350.9 351 351.1 351.2 351.3 351.4 351.5 351.6

Sta

r C

ount

α°(J2000)

Figure 3.4: Star count of M 52 with Right ascension is plotted using dark lines andcorresponding Gaussian fit with dashed lines.

0

50

100

150

200

250

300

61.4 61.45 61.5 61.55 61.6 61.65 61.7 61.75

Sta

r C

ount

δ°(J2000)

Figure 3.5: Star count of M 52 with declination is plotted using dark lines and corre-sponding Gaussian fit with dashed lines.

The Gaussian fit for right ascension gives a value of about 351.2 and a declination of

about 61.58. Converting it into hour angle format, value for right ascension is 23h24m48s

and for declination is +61◦34◦48◦.

18

3.3. RADIAL DETERMINATION CHAPTER 3. NGC 7654

3.3 Radial Determination

The radius of the cluster can be found out using Kings formula Equation 2.1. In order

to determine the radius of the cluster the radial density profile of the cluster was drawn.

It is plot of number of stars per radius around the center. The radial density profile

drawn using written MATLAB code and fitting of kings profile is done using CFTOOL

of MATLAB. The radial density profile is shown in the Figure 3.6.

From the profile fit the star density was calculated and it is about 3.6 starspc−2. The core

radius is about 0.88 par second and the limiting radius is about 8.0 par second. The tidal

radius is about 15 par second. The radial density profile indicates that the inner core of

the cluster has reached energy equipartition. Since there exist high density of stars at

the center the radial density profile is not much clear in that region and it indicates that

there is a post-core collapse has occurred to the cluster M 52.

Figure 3.6: Radial Density Profile of M 52.The dotted lines indicate Kings Profile.

19

3.4. DEREDDENING CHAPTER 3. NGC 7654

3.4 Dereddening

Since the cluster lies in the lower galactic latitudes, it suffers from reddening. Using the

Extinction Calculator the color excess E(B − V ) = .9681± 0.0496 was found.

AV /EB−V = 3.1 (3.1)

AV = 2.9950 (3.2)

EJ−H/EB−V = 0.33 (3.3)

EJ−H = EB−V × 0.33 (3.4)

EJ−H = 0.3171 (3.5)

AJ = 0.276× AV (3.6)

AJ = 0.825 (3.7)

Then the color excess was subtracted from the data of the star cluster and was it is used

for further process.

3.5 Color Magnitude Diagram

To draw the CMD the reddening of the cluster should be reduced. For this calculated

reddening value was used. This reddening value for each bands was subtracted. The

Figure 3.7 shows the reddened clusters color magnitude diagram. The dashed lines shows

the isochrone fitting done to the cluster. The isochrones used in the process were padova

isochrones. Since cluster lies in lower latitudes it suffers from high field star decontami-

nation. Since the field star contamination can largely affect the isochrone fitting the field

star has to be reduced. The field star was selected in such a way that it was selected away

from the center. The field stars are shown in the Figure 3.8

20

3.5. COLOR MAGNITUDE DIAGRAM CHAPTER 3. NGC 7654

Figure 3.7: Contaminated cluster M 52 with field star. The dotted lines indicate aisochrone.

The field star decontamination was carried out using statistical methods. In this the

number of stars per each cell was counted and it was subtracted from the cluster stars.

The density of the stars for each cell was considered in the process. The decontaminated

cluster is given in the Figure 3.9 From the fitting of the cluster it had been found that

the cluster has an age of 7.35Gyr and it had about a metalicity of about 1.15.

21

3.5. COLOR MAGNITUDE DIAGRAM CHAPTER 3. NGC 7654

Figure 3.8: Field star of cluster M 52. The dotted lines indicate a isochrone.

Figure 3.9: Decontaminated cluster M 52 without field star.

22

Chapter 4

King 18

The open cluster King 18 was found out by King (1949). It has a poor stellar ensemble

of diameter 4′. This cluster was not properly recognised for many years. According to

Dias et al. (2002) the cluster has an angular diameter of 5′. Using UBV photometry

Maciejewski (2008) found the linear diameter to be 9.5± 0.4pc. Using JHKs photometry,

Glushkova et al. (2010) calculated the distance to the cluster as 1860 ± 85 pc. Koposov

et al. (2008) found (m−M)0 to be about 12.59.

4.1 Data Extraction

At first, the data was extracted using ALADIN selecting the center from WEBDA cat-

alog. In WEBDA the central coordinates of King 18 were (J200) α = 22h52m06s and

δ = +58◦17◦00◦. The other parameters provided by WEBDA is given in Table 4.1. The

primary radius of 10 arc was selected for extraction of 2MASS data. The selection pro-

cedures discussed in section 2.1 were applied. The DSS and 2MASS images are given in

Figure 4.1.

1http://www.univie.ac.at/webda/cgi-bin/ocl_page.cgi?dirname=ki18

23

4.2. CENTER DETERMINATION CHAPTER 4. KING 18

Table 4.1: General Data on King 18 from WEBDA. 1

α δ Age d E(B-V) Metallicity

(hms) (◦) (Myr) (kpc)

22h52m06s δ = +58◦17◦00◦ 25 0.63 - -

Figure 4.1: Picture on the left panel shows dss image of King 18 and Picture on the rightpanel shows 2MASS image of King 18.

4.2 Center Determination

The extracted data using center from the WEBDA was taken to TOPCAT. Using the

software the stars for one arc minute bins were counted for both right ascension and

declination. The histogram for both declination Figure 4.2 and right ascension Figure 4.3

are given.

24

4.2. CENTER DETERMINATION CHAPTER 4. KING 18

Figure 4.2: Histogram of Declination for King 18.

Figure 4.3: Histogram of Right ascension for King 18.

Then the number of stars in each bin to Right ascension Figure 4.4 and Declination Fig-

ure 4.5 were plotted. Then a Gaussian curve was fitted to find the center of the cluster

since center of the cluster is defined as the center where it have maximum density. The

Gaussian curve was fitted using the codes written in Gnuplot.

25

4.2. CENTER DETERMINATION CHAPTER 4. KING 18

0

20

40

60

80

100

120

140

160

180

342.6 342.7 342.8 342.9 343 343.1 343.2 343.3 343.4

Sta

r C

ount

α°(J2000)

Figure 4.4: Star count of King 18 with Right ascension is plotted using dark lines andcorresponding Gaussian fit with dashed lines.

0

50

100

150

200

250

58.1 58.15 58.2 58.25 58.3 58.35 58.4 58.45

Sta

r C

ount

δ°(J2000)

Figure 4.5: Star count of King 18 with declination is plotted using dark lines and corre-sponding Gaussian fit with dashed lines.

The Gaussian fit for right ascension gave a value about 343.2 and a declination value

about 58.28. Converting it in to hour angle format valu for right ascension is 22h52m00s

and declination is +58◦16◦00◦

26

4.3. RADIAL DETERMINATION CHAPTER 4. KING 18

4.3 Radial Determination

The radius of the cluster can be found out using Kings formula Equation 2.1. In order

to determine the radius of the cluster the radial density profile of the cluster was drawn.

It is a plot of number of stars per radius around the center. The radial density profile

was drawn using MATLAB code and fitting of kings profile was done using CFTOOL of

MATLAB. The radial density profile es shown in the Figure 4.6.

From the profile the star density was calculated and it is about 2.5 starspc−2. The core

radius was about 0.5996 par second and the limiting radius was about 1.077 par second.

The tidal radius was about 5.9 par second. The radial distribution of the stellar density

followed the King’s profile in a satisfactory way.

0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

20

40

60

80

100

120

140

160

180

R arcmin

De

ns

ity

(s

tars

/arc

min

2)

0.5 1 1.50

50

100

150

R arcmin

De

ns

ity

(s

tars

/arc

min

2)

Figure 4.6: Radial Density Profile of King 18. The dotted lines indicate Kings Profile.

27

4.4. DEREDDENING CHAPTER 4. KING 18

4.4 Dereddening

Since the cluster King 18 was in a lower galactic latitude than M 52 it has more reddening.

Using the Extinction Calculator the color excess E(B−V ) = 1.04681±0.0408 was found.

AV /EB−V = 3.1 (4.1)

AV = 3.1604 (4.2)

EJ−H/EB−V = 0.33 (4.3)

EJ−H = EB−V × 0.33 (4.4)

EJ−H = 0.344 (4.5)

AJ = 0.276× AV (4.6)

AJ = 0.8722 (4.7)

(4.8)

Then the color excess was subtracted from the data of the star cluster and then was used

for further process.

4.5 Color Magnitude Diagram

To draw the CMD the reddening of the cluster should be reduced. For this calculated

reddening value was used. This reddening value for each bands was subtracted. The

Figure 4.7 shows the reddened cluster’s color magnitude diagram. The dashed lines shows

the isochrone fitting done to the cluster. The isochrones used in the process were padova

isochrones. Since the cluster lies in the lower latitudes, it suffered from high field star

decontamination. Since the field star contamination can largely effect the isochrone fitting

the field star has to be reduced. The field star was selected in a such a way that it was

selected away from the center. The field stars are shown in the Figure 4.8.

28

4.5. COLOR MAGNITUDE DIAGRAM CHAPTER 4. KING 18

Figure 4.7: Contaminated cluster King 18 with field star. The dotted lines indicate aisochrone.

The field star decontamination was done using statistical methods. In this the number of

stars per each cell was counted and it was subtracted from the cluster stars. The density

of the stars for each cell was considered in the process. The decontaminated cluster was

given in the Figure 4.9. From the fitting of the cluster it had been found that the cluster

had an age of 0.35Gyr and it had about a metalicity of about 0.01615.

29

4.5. COLOR MAGNITUDE DIAGRAM CHAPTER 4. KING 18

Figure 4.8: Field star of cluster King 18. The dotted lines indicate a isochrone.

Figure 4.9: Decontaminated cluster King 18 without field star.

30

Chapter 5

Conclusion

The photometric study of two open clusters, M 52 and King 18 was carried out us-

ing 2MASS photometry. The parameters of both cluster were re-estimated using JHK

bands. Both clusters had some variations in the cluster parameters from the current

litrature. Open cluster M 52 had a center in right ascension 23h24m48s and in declination

+61◦34◦48◦. Since it has lower galactic latitudes it suffered from reddening and the color

excess was about EJ−H = 0.3171. The study using radial density profile showed that the

cluster M 52 had a radius of about 0.88 par second and a tidal radius of about 15 par

second. From the radial density profile it can be noted that the cluster had suffered from

post-core collapse. Using the isochrone fitting to the cluster the age is about 7.35Gyr and

metallicity is about 1.15. Since WEBDA catalog did not contain metallicity a new value

was computed through the project. Open cluster King 18 seems to be a cluster which was

studied poorly. It had center in right ascension 22h52m00s and declination +58◦16◦00◦.

Using radial density profile a core radius of about 0.5996 par second was found, limiting

radius was about 1.077 par second and tidal radius was about 5.9 par second. The cluster

had color excess EJ−H = 0.344. Fitting isochrone to Color Magnitude Diagram yielded

the cluster had an age of about 0.35Gyr and metallicity of about 0.01615. A new metal-

licity value was computed to the cluster in addition to WEBDA catalog. The 2MASS

31

CHAPTER 5. CONCLUSION

photometry provided a more accurate description of stars and it included faint stars than

UBV photometry. Since the field star decontamination process used in the study had

many defects in future a new technique will be obtained using metallicity gradient of

stars. In future evolution of these clusters will be studied and it will be extended to new

clusters.

32

Appendix A

Gnuplot

Gnuplot is a command-line program that can generate two- and three-dimensional plots

of functions, data, and data fits. The graphs generated for center determination were

computed using this program1. The program also provides a Gaussian fits for center

determination. The program is given below,

# Define initial parameters

PI=3.14; s=60 ; m=10.5 ; a=2;

# Define function we want to fit

gauss(x) = a/(2*PI*s**2)**0.5*exp(-(x-m)**2/(2*s**2))

# do the fitting

fit gauss(x) "Input.txt" using 2:3 via s, m, a

# Finally plot theory and the points

set key off

set terminal postscript portrait enhanced color lw 2"Helvetica"14

set xlabel "{/Symbol d}{/Symbol \260}(J2000)"

set ylabel "Star Count"

1http://www.mathworks.in/products/matlab/

33

APPENDIX A. GNUPLOT

plot "Input.txt" using 1:3 with lines, gauss(x) with lines

set output "Output.eps"

set size 1.0,.4

set terminal postscript portrait enhanced monochrome lw 2"Helvetica"14

replot

set terminal x11

set size 1,1

34

Appendix B

Matlab

MATLAB is a high-level language and interactive environment for numerical computation,

visualization, and programming. MATLAB codes for radial density profile is given below.

It provides a function where the first input should be text file with stars co-ordinates and

second input should be center of Right ascension and third should be center of Declination.

The fourth input provides the number bins it should create.

%Program for Radial Density

function [pp]=plotit(in1,in2,in3,in4)

a=dlmread(in1);

x=a(:,1)

y=a(:,2);

xmin=min(x);

xmax=max(x);

ymin=min(y);

ymax=max(y);

x0=in3;%(xmin+xmax)/2;

y0=in4;%(ymin+ymax)/2;

r=sqrt((x-x0).ˆ2+(y-y0).ˆ2);

% rr=sqrt((x-x0).ˆ2+(y-y0).ˆ2);

0http://www.mathworks.in/products/matlab/

35

APPENDIX B. MATLAB

rmin=min(r);

rmax=max(r);

dx=in2;

pp=[rmin:rmax/dx:rmax+rmax/dx];

c=zeros(1,length(pp));

l=1;

t=0;

rr=0;

cc=0;

%pp=[rmin:rmax/dx:rmax+rmax/dx];

for p=rmin:rmax/dx:rmax+rmax/dx

for q=1:length(r)

% ccccc=[rr,p,r(q)]

if (p>rr&&p<r(q))

c(l)=c(l)+1;

end

rr=r(q);

end

% if (c(l)==0)

% c(l)=t;

% end

% t=c(l);

cc(l)=c(l)/(((2*3.14*p)ˆ2)*10ˆ2);

l=l+1;

end

size(cc)

size(r)

%cc=c’ ./r.ˆ2;

x=pp*31.4

y=cc

plot(pp*31.4,cc,’-’);

dlmwrite(’x.txt’,x,’\n’)

dlmwrite(’y.txt’,y,’\n’)

end

36

APPENDIX B. MATLAB

There are many types of co-ordinate systems sometimes it should be converted into one an-

other. This a another MATLAB program which converted the given decimal co-ordinates

from ALADIN software into hour angle format and radian format. The code is given

below. The data file contains co-ordinate in decimal format

clear all

load data.txt

x=data(:,1);

xh=x/15;

h=floor(xh);

xm=xh-h;

mi=xm*60;

xs=mi-floor(mi);

s=xs*60;

m=floor(mi);

Re=[h,m,s];

C=h+m/100+s/10000

r=3.819719;

Rx=(h/r)+(m/(400))+(s/(400));

clear x xh Re s m xs mi xm h

x=data(:,2);

xh=x/15;

h=ceil(xh);

xm=xh-h;

mi=xm*60;

xs=mi-ceil(mi);

s=xs*60;

m=ceil(mi);

37

APPENDIX B. MATLAB

Re=[h,m,s];

P=h+m/100+s/10000

Ry=(h/r)+(m/(400))+(s/(400));

Z=[C,P]

H=[Rx,Ry]

dlmwrite (’convhour.txt’,Z,’ ’)

dlmwrite (’convradian.txt’,H,’ ’)

38

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Document was created using LATEX language.

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