Using aperture photometry to study messier 67

In our study we have done photometry for open cluster M67. Photometric results are plotted in the color-magnitude 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.
Nội dung trích xuất từ tài liệu:
Using aperture photometry to study messier 67 JOURNAL OF SCIENCE OF HNUE Mathematical and Physical Sci., 2012, Vol. 57, No. 7, pp. 65-70 This paper is available online at http://stdb.hnue.edu.vn USING APERTURE PHOTOMETRY TO STUDY MESSIER 67 Doan Duc Lam and Nguyen Anh Vinh Hanoi National University of Education Abstract. Studying star clusters is a way to test 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-Russell 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 are 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-magnitude 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. Thestellar phase is indicated by parameters such as the temperature, pressure, generation andtransportation of energy within a star. Stars, having different initial masses, evolve throughdifferent stages over time. A cluster is a system of stars which were formed from a single gas cloud. There aretwo types of clusters: open cluster and global cluster. All stars in a cluster are presumedto have been born at the same time so the current phase of the stars is decided by theirinitial mass. Messier 67 (M67) or NGC 2682 is an open cluster that is located in the Crabconstellation. This is one of the oldest clusters and is of importance in the study of stellarevolution. Within it are at least 500 stars [1], and among them are about 150 white dwarfs,100 solar-type stars, some blue stragglers and some giant stars. The age of M67 is aboutReceived December 27, 2011. Accepted September 10, 2012.Physics Subject Classification: 60 44 19 .Contact Nguyen Anh Vinh, e-mail address: vinhastro@yahoo.com 65 Doan Duc Lam and Nguyen Anh Vinh4 to 5 billion years. It is located at a distance of about 800 to 900 pc from the Earth andthe distance modulus of the V filter is (m − MV ) = 9,59 [2].2. Content2.1. Aperture photometry Astronomical photometry aims to measure energy of celestial objects. Theinformation obtained helps determine the magnitude, luminosity and temperature of stars.Aperture photometry is one of the easiest of the methods available. Suppose that imageswhich are captured by CCD camera are calibrated using bias and darkness, they are on aflat field. The following are steps to be taken to carry out aperture photometry (Figure 1): Step 1. Identify the star one wishes to measure Step 2. Determine the center (xc , yc ) and radius of the aperture. Brightnessdistribution is Gaussian. The radius of the aperture must be large enough to hold entirestar but it not so large that it will reduce background noise. The radius of the annulus usedto measure brightness of background is about three to five time that of the aperture. Figure 1. Illustration of aperture photometry P i=L P j=L Ii − I xi Ji − J y j i=−L j=−L xc = ; yc = (2.1) P i=L P j=L Ii − I Ji − J i=−L j=−Lwhere i=L j=L 1 X X I= Ii , Ii = Ii,j 2.L + 1 i=−L j=−L j=L i=L 1 X X J= Jj , Ji = Ii,j 2.L + 1 j=−L i=−Land 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 Aap ).It is equal the number of electrons multiplied by Gain. Step 4. Estimate the value of background per pixel Aap using an annulus aperture. Step 5. Compute instrumental magnitude: Nap − Aap Ssky mI = −2.5 log (2.2) texpwhere texp is the time of exposure. Step 6. Correct for Earth’s atmospheric extinction and interstellar extinction todetermine apparent magnitude m0 : mI − m0 = −2.5 log(F/F0 ) = −2.5 log(e−K sec Z ) (2.3)where K is the extinction coefficient for one air m ...