THE SKY AS LABORATORY – 2008/2009 1 Photometric analysis of the open cluster NGC 2420 and of the globular cluster NGC 6229 Boldrin Elena(1), Bombieri Davide(1), Ercole Luca(2) (1)Liceo “Giuseppe Berto”, sez. Scientifico, Mogliano Veneto (2) Liceo “Giordano Bruno”, sez. Scientifico, Mestre ABSTRACT under 500 Myr, and reducing to the higher spectral types. We studied the photometry of the globular cluster NGC Obviously, when the age of the cluster grows, all the 6229, and the open cluster NGC 2420, by using g, r features typical of the diagram become evident and the and i bands. By transforming g ,r, i into BVR Johnson- stars in each region have a certain mass. Cousins system and constructing CMD diagrams, we The point in the diagram where the stars go out the MS determined distance modulus (DM) by ZAMS fitting for is called turn-off (TO), and can be used to calculate the NGC 2420 and Mv(RR Lyrae) vs V(RR Lyrae) in HB age of the cluster, whether globular or open. for NGC 6229. Finally we determined the age of both Since every star of the cluster is close to the others, NGC 2420 and NGC 6229 by fitting different sets of relating to the distance of the cluster from Earth, the isochrones, for different metallicity Z, onto CMD difference between apparent and absolute magnitudes diagrams. The age of NGC 6229 has also been is called distance modulus, DM, and is constant. estimated by determining difference MV(TO)-MV(HB). Therefore a color-magnitude diagram is also a HR diagram and this allows us to estimate the distance if we have the DM. I. INTRODUCTION A star cluster is a group of stars born in the same age from the same molecular cloud with the same chemical II. OBSERVATIONAL DATA composition, kept together by gravitational force. We can distinguish between globular and open clusters. We produced the photometry of the globular cluster The first ones are generally bigger and composed of a NGC 6229 (fig.1) high number of old population II stars, and are distributed in the whole galactic halo. They have a visible spherical shape due to the strong gravity, that keeps a high stellar density in their centre. They do not have any gas or dust. Open clusters have a lower number of stars, so their gravitational bound is weaker. They are generally very bright, because they contain young stars at a high temperature. Analysing the light coming from an open cluster we can estimate its age. An abundance of blue stars means that the cluster is young. The stellar density can be extremely variable, sometimes similar to that of the field stars, making the cluster hard to recognize; anyway it is always lower than the density of the central areas of a globular cluster. Open clusters can be found only in the galactic disk of spiral galaxies and in irregular ones. Generally, since all the stars in a cluster have about the same age, chemical composition and distance, every difference in the stellar parameters is caused just by the initial mass of each star, that determines a different Fig. 1 NGC 6229 evolution. When we create a CMD or a H-R diagram of the stars and of the open cluster NGC 2420 (fig. 2) in a cluster, its shape depends on the age of the cluster, showing an almost complete MS for the young ones, THE SKY AS LABORATORY – 2008/2009 2 subtracting off an average sky count, determined in a circle ring around the object, to obtain the effective flux. In this case this technique was not suitable because of the high stellar density, that made inaccurate, or even impossible for the globular cluster, the average sky count determination. Therefore we applied the PSF photometry (Point Spread Function). This is a mathematical model of the stellar profile which describes the average distribution on the CCD surface of the photons coming from a single star. Because of the Earth atmosphere effect (seeing), this distribution has a Gaussian shape, whose typical width (FWHM). To calculate the PSF we chose some stars which showed a regular distribution of light and presented the characteristic trend of the cluster stars. These stars ought to be quite isolated, in order Fig. 2 NGC 2420 not to have the tail end of the profiles overlapping. Besides, they had to be regularly distributed throughout The globular cluster NGC 6229, situated in the the whole image. IRAF determines, by applying the psf Hercules constellation at RA = 16h 46m 58s.9 DEC = instruction, an average profile model which, once +47° 31’ 40” (J2000), has a size of about 4,5’ and is of applied to every star of the image, allows to define the class 4, while the open cluster NGC 2420, in the exact position of the star and the quantity of received Gemini constellation at RA = 07h 38m 23.9s DEC= photons, subtracting at the same time the light intensity +21° 34′ 27″ (J2000), has a size of about 10’ and is of of the background sky and dividing the stellar flux by class I 1 r. the exposition time. As a result, we obtained the stellar The photometry has been realized with the data instrumental magnitudes. We applied this procedure for extracted from the SDSS (Sloan Digital Sky Survey) the images in g, r and i band of both clusters. Data Release 6, whose photometric survey has been made with a 120 Mpx CCD (Charge Coupled Device) Since the instrumental magnitude is only an indication of the 2.5-meters telescope in Apache Point (New of the photon flux coming to the stars, we had to bring Mexico, USA). back to a calibrated magnitude, which can be We have done the photometry in the three photometric determined with the following equation: bands g, r and i, and then we have converted them into the more common BVR bands of Johnson-Cousins m=m0+(ms-25)-kx system. Characteristic wavelengths of the photometric ugriz m0 = constant depending on the considered filter bands are: ms = instrumental magnitude u 3551 Ǻ k = atmospheric extinction coefficient x = airmass g 4686 Ǻ 25 = constant applied by the program to the r 6165 Ǻ instrumental magnitude values, to make them positive. i 7481 Ǻ z 8931 Ǻ The parameters values, acquired by the SDSS catalogue for our fields, are: NGC 2420 G r i III. DESCRIPTION OF THE WORK m0 24,45 24,07 23,74 k 0,14 0,09 0,03 To perform the photometric analysis of the FITS files we used IRAF software (Image Reduction and x 1,06 1,06 1,06 Analysis Facility), in particular DAOPHOT and IMAGES packages and their daofind, phot, psf, allstar NGC 6229 g r i and tv mark, imexamine tasks. The data are divided into m0 24,58 24,12 23,75 rectangular fields, partially overlapping to allow a k 0,20 0,11 0,06 precise combination, based on the common elements of x 1,18 1,18 1,18 two or more adjacent fields. One of the two clusters we studied was entirely contained in just one field, while We obtained the g, r and i magnitudes of 915 stars in for the other one we matched the images of two the open cluster NGC 2420 and 1970 in the globular adjacent fields within the three studied bands, by using cluster NGC 6229, and then we converted them in B, V the imcombine function. and R by using the transformation equations elaborated The techniques we used to make the photometric by Jordi et al. (2006) [1]. analysis were the aperture photometry and the PSF We used these values to elaborate the color-magnitude fitting. The first one consists of adding up the pixel diagrams (B-V vs V), from which we determined the counts within circles centred on each object and THE SKY AS LABORATORY – 2008/2009 3 distance, the color-absolute magnitude (B-V vs Mv) diagrams and the age of the two clusters. To determine the age of NGC 2420 we fitted In case of NGC 2420 we corrected the B-V color isochrones with different metallicity Z obtained from indices on the basis of a mean color excess <E(B- CMD 2.1 input form at http://stev.oapd.inaf.it/cgi- V)>=0.05, published in scientific literature for this bin/cmd_2.1 getting the best result with ages between cluster [2][3][4] , according to the relation: 1,26 Gyr and 1,59 Gyr and metallicity Z=0,01, as fig. 4 shows. (B-V) = (B-V)0 + <E(B-V)> The correction process of the B-V and V values has not and the V magnitudes for the interstellar extinction been done for the globular cluster NGC 6229 since its according to the relation: E(B-V) proves to be equal to 0 or at most 0,01 from literature. V=V0+R<E(B-V)> We built up the (B-V)0 vs V diagram (fig. 5), where we put R=3.1. (B-V)0 - V 15,0 (B-V)0 - V0 E(B-V)=0,05 R=3,1 16,0 13,60 17,0 AGB HB 18,0 15,60 RR Lyrae 19,0 V RGB Mv+13,3 20,0 17,60 0 V 21,0 TO 22,0 19,60 Mv+13 Mv+13,6 23,0 -0,3 -0,2 -0,1 0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0 1,1 1,2 1,3 1,4 1,5 21,60 (B-V)0 Fig.5 (B-V)0 vs V diagram 0,10 0,30 0,50 0,70 0,90 1,10 1,30 1,50 (B-V)0 and we deduced the DM by using the mean HB visual Fig.