JOURNAL OF SCIENCE OF HNUE
Mathematical and Physical Sci., 2012, Vol. 57, No, 7. pp. 65-70 This paper is available online at http://sldb.hnuc,edu.vn
USING APERTURE PHOTOMETRY TO STUDY MP:SSIER 67 Doan Due Lam anti Nguyen Anh Vinh
Hanoi National Univeiwnv of Education
Abstract. Studying star clusters is a way to lesl theories of stellar evolution in astronomy. Using current theories, the mass, age and components of a star are affected and decide the position of star in the Hertzsprung-Russcll color-magnitude diagram. To study the role of mass in stellar evolution, we need to look at star clusters of which all stars were formed at the same time and arc located at the same distance from planet Earth In our study we have done photometry for open cluster M67. Photometric results are plotted in the color-magnilude diagram. The number of stars in each evolutionary phase has been estimated. The existence of blue stragglers in our result requires further research about stellar evolution and interacting binary stars.
Keywords: Photometry, Messier 67, astrophysics.
1. Introduction
A star is a physical entity which evolves over time and changes in phase. The stellar phase is indicated by parameters such as the temperature, pressure, generation and transportation of energy within a star. Stars, having different initial masses, evolve through dilTerent stages over time.
A cluster is a system of stars which were formed from a single gas cloud. There are two types of clusters: open cluster and global cluster. All stars in a cluster are presumed to have been born at the same time so the current phase of the stars is decided by their initial mass. Messier 67 (M67) or NGC 2682 is an open cluster that is located in the Crab constellation. This is one of the oldest clusters and is of importance in the study of stellar evolution. Within it are at least 500 stars [1], and among them are about 150 white dwarfs, 100 solar-type stars, some blue stiagglers and some giant stars. The age of M67 is about
Received December 27, 2011. Accepted September 10,2012.
Physics Subject Classification: 60 44 19 .
Contact Nguyen Anh Vinh, e-mail address: [email protected]
65
Doan Due I .1111 and Nguyen Anh Vinh
4 to ."i billion yeiiis. Il is located at a distance of about HOO lo 900 pc from the Earth and Ihc distance modulus of the V filler is (ni ,1/1) - 9,59 [21.
2. Content
2.1. A p e r t u r e p h o t o m e t r y
Astronomical photometry aims to mc;isL!re energy of celestial objects. The information obtained helps determine the magniiudc. luminosity and temperature of stars.
Aperture phoiomelry is one (if the casicsi of the methods available. Suppose that images which are captuicti by CCD cimcra are calibrated using bias and darkness, they are on a flat field. The folh)wing arc steps It) be taken lo carry out aperture pht>lometry (Figure I):
Step L Identify the star one wishes lo measure
Step 2. Delermine the center ( ; , . y,) and radius of the aperture. Brightness distribution is Gaussian. The radius of the aperture must be large enough to hold entire star but 11 not so large that it will reduce background noise. The radius of the annulus used to measure brightness of background is about three to five time that of the aperture.
Measurement aperture - Annulus aperture of the sk\
Figure 1. Illustration of aperture photometry
^' = '-^L •• V' = '-^1 (2-1)
where
T.(i.-1) E ( . / , - 7 )
— ' • 3=-L
^ ' ' 3=L
/
2.i +'- I- ,=-L
2.L + T
7 = D ^ E ' ^ . •A = E/.o
and i, j are indexes to indicate row number and column of pixel.
66
Using aperture photometry to .study Messier 67
Step 3. Add the counts (Nap) within measurement aperture (area of aperture ,4,,^,).
It is equal the number of electrons multiplied by Gain.
Step 4. Estimate the value of background per pixel A,,,, using an annulus aperture.
Step 5. Compute instrumental magnitude:
m, = -2.5 log | ^ l V _ i V ^ ^ (2.2) where texp ^^ the time of exposure.
Step 6. Correct for Earth's atmospheric extinction and interstellar extinction to determine apparent magnitude niQ-.
m/ - mo = -2.5\og{F/Fo) - -2.51og(e-'^'^<^^) (2.3) where A' is the extinction coefficient for one air mass and Z is zenith distance.
Step 7. Convert to standard filler photometry with transformation equations.
Because all stars in the clusters are located at the same distance, so m; - A/,^,^ is the same for all stars in cluster where .U(.„,„ is the magnitude of the reference star. We have computed TU/ - M^ata for reference stars and applied this value to other stars in the cluster.
2.2. Calculation and discussion
All frames of M67 were taken by a system of telescopes and CCD cameras at an observatory in Marseille, France. We obtained two frames of M67 using a B and R filter in a Johnson-Kron-Cousins standard system. Exposure time of the CCD camera with the B and R filter was 10.04 seconds and 5.03 seconds, respectively. Data is processed with darkness, bias and flat field. The positions of reference stars are marked in a frame in Figure 2.
Because of limited exposure time, each frame of M67 contains only 60 of the brightest stars. We have calculated instrument magnitude of all stars, "zero points" of reference stars and applied these values for all stars in the cluster:
(m/ - M,ata)B = 26.32 ± 0.05 (2.4) The color index for the B and R filter is {B — R) = 0.068. Extinction coefficients are
K{B) = 0.154 for B filter and K{R) = 0.088 for R filter.
After obtaining absolute magnitude of all stars in the cluster we have plotted them in the color-magnitude diagram (Figure 3). The horizontal axis is the color index for B — R and tbe vertical axis is the B magnitude. Our result shows that 40% of the stars in the main sequence are low to intermediate mass stars of A or B spectial type while 30% of the stars are leaving the main sequence and are concentrated near the 'turn-off point'. So 67
Doiin Due I -iiin and Nguyen Anh Vinh
Figure 2. Image of Messier M67. The reference stars are marked
Figure 3. Color-magnitude diagram of open cluster M67
we can say that about one third of stars in the cluster have approximately the same mass.
The 'turn-off point' is at 13 of B magnitude and 0.9 of color index B - R.
68
Using aperture photometry lo .study Messier 67
Table I. Magnitude of stars in M67, Mn and Mu are the magnitude of stars using the B and R filter
Star#
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
J\/„
16.16 13.86 11.22 14.24 16.01 14.65 1473 12.54 15.13 11.62 13.24 16,81 15.09 13.3 13.38 14.07 11.08 13.87 13.77 15.97 13.28 16.59 15.15 13.4 14.89 15.23 11.52 12.61 13.37 13.8
M,) 14.96 12.94 10.84 13.39 14.79 13.73 13.77 12.12 13.86 9.988 12.32 15.15 1402 12.36 12.62 13.13 10.17 12.93 13.01 14.79 12.38 15.16 13.82 12.46 13.77 14.05 9.901 11.84 12.14 12.88
B- R 1.192 0.917 0 382 0.854 1.223 0.92 0.953 0.415 1.269 1.628 0.919 1.669 1.068 0.94 0.761 0.947 0.918 0.94 0.759 1.185 0.901 1.434 1.331 0.94 1.125 1.185 1.622 0.77 1.237 0.919
Slar#
31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Mil 13..35 13.38 12.48 13.79 12.86 13.76 14.56 13.33 14.87 14.72 13.99 12.01 15.95 13.36 16.26 13.84 15.25 14.02 15.9 10.02 16.68 11.5 14.91 14.29 13.21 13.43 13.73 15.96 11.45 14.86
Mil 12.46
12.6 10.89 12.83 11.92 12.81 13.6 12.4 13.71 13.63 13.06 11.3 14 75 11.88 1495 12.87 1419 13.11 14.56 10.04 15.45 9.641 13.99 13.37 12.38 12.5 12.75 15.01 11.22 13.8
B~ II 0.895 0.772 1.588 0.966 0.943 0.948 0.962 0.929 1.164 1.095 0.924 0.71 1.202 1.476 1.305 0.974 1.063 0.914 1.344 -0.02 1 226 1 854 0.92 0.925 0.827 0.93 0.981 0.946 0.231 1.062 Note. B — Ris the color index for the B
the margin of' and R filter, error is 0.05 Giant stars which have already left the main sequence appear above the main sequence in the upper right corner of Figure 3. They represent about 10% of the total number of stars in M67. White dwarfs should be located below the main sequence but they are not visible in our data and thus not present in the color-magnitude diagram. In previous studies, M67 is believed to be one of the oldest clusters so that the number of 69
Doan Due Lam iind Nguyen Anh Vinh
while dwarfs and giant slurs constitutes a considerable fraction of tbe total number of stars 11 l.The lack of while dwarfs in our data could be due lo equipment limitation and limited observation lime.
Blue stragglers, the brightest stars in the B filler, are located at the upper left corner of the color-magnilude diagram as shown in Figure 3. Their initial mass is a few times that of the solar masses. However, they doii'l appear lo be a part of the cluster's evolution. The presence of blue stragglers in many clusters is still in question regarding stellar evolution.
It has been suggested that blue stragglers came about as a result of interaction of binary stars. Almost all of the blue siiagglcrs arc found near the center of the cluster, a region crowded with many sttirs This hypothesis agrees wilh many previous studies and does not support the idea that blue stragglers are in front of or behind clusters and not in a cluster 3. Conclusion
Using aperture photometry, we have measured magnitude and made color-magnitude diagrams for Messier 67. Suppose all of the stars in M67 were formed at the same time and located at the same distance from Earth. We estimate the number of stars in deferent phases of evolution. The result shows that the current phase of each star is dependent on its initial mass. This is in agreement with theories about stellar evolution. It is thought that the existance of Blue stragglers in the cluster is not a random coincidence.
Acknowledgements. We are grateful to Georges Comte who provided the images of M67 for this research.
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