Morgan       A Search for Variable Stars in Two Northern Open Clusters: NGC 381 and NGC 637
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A Meade 10 inch LX 200 Schmidt Cassegrain telescope.
A Meade 10" LX 200 Schmidt Cassegrain telescope
Equipment and Procedure: A Meade 10" LX 200 Schmidt Cassegrain telescope was used with an SBIG ST-7xe CCD. The CCD consists of two chips; the main imager is a Kodak KAF401e array of 750 x 510 9 nm pixels. A separate guiding chip is positioned beside the main chip. An f3.3 focal reducer was placed in front of the camera to create a focal length of 825 mm @ f3.3 for the system. The resulting field of view with the ST-7xe camera was 20 x 30 arc minutes. The CCD was equipped with a filter wheel holding Bessel BVRI standardized photometric filters, with the majority of the data collected in the I-band. The software Maxim DL was used for camera control, image calibration, and photometry. The open-source software Munidos (Hroch 2001) was used with the additional open-source programs Readall and Varfind to search the images for variable stars (Kral 2003). The programs were grouped using MS DOS batch files, allowing the data-reduction process to be somewhat automated. Period 98 was used to perform Fourier analysis on the data (Sperl 1998).

Images were collected using the following method. The telescope was pointed at a bright star, and the CCD was focused. Then the telescope was pointed at the target field and a guide star was acquired. The guide chip was set up with Maxim DL to image once a second and issue tracking corrections to the telescope. The main CCD chip was set to take a series of exposures of 1-2 minutes separated by one minute. This allowed for 20-30 images per hour. Images of the twilight sky were also taken. These "flat frames" were used later when calibrating the raw images to correct for uneven illumination of the CCD chip. Dark frames, or images of the camera's internal noise, were also taken. These were later subtracted out of the raw images to reduce noise in the final image.

These images were analyzed in two steps, using the Munidos suite (comprised of Munidos, Readall, and Varfind) and Maxim DL. The series of images of one cluster were all placed into one folder. They were then calibrated using flat and dark frames. Next, the images were fed into an MS DOS batch file that was created to use Munidos to measure the brightness of all of the stars in each frame. The Readall routine was then recruited to sort the data and match the star names between images. Finally, Varfind was employed to compute the average magnitude of each star, and the standard deviation of that star's data. The magnitude vs. standard deviation data was then exported into Excel, where it was plotted. The resulting graph forms a well-defined "error curve" based on the signal-to-noise ratio of the stars in the image (Data Section, Figure 1). Outliers from this curve were identified as potential variable stars.

Once the candidate stars were identified, they were investigated further with Maxim DL. The light curve of each star was plotted using differential photometry, a technique in which the brightness of the variable star is compared to the brightness of several constant comparison stars in each image. Most of the stars with high data scatter are not truly variable but only appear to vary because of interference from nearby stars. These can be sorted out by inspecting the images and the light curves. The data for the stars that are truly variable were then saved and plotted in Excel.

Graph showing the extinction of the standard star.
Graph showing the extinction of the standard star (Click to enlarge)
The extinction characteristics of the system were also calculated. This allowed the measurement of the stars' colors. As a star's light travels through the atmosphere, some of it is scattered. Shorter wavelengths of light are scattered more than longer wavelengths. To correct for this, two equations are formed, the transformation equation, which converts instrumental to standard magnitudes, and the extinction equation, which corrects for the fact that the measurement was taken through the atmosphere (Berry, Burnell 2000).

In order to form these correction equations, a standard star whose magnitude and colors are well defined was followed from low on the horizon until it was near the zenith. The intensity of the star and the air mass (volume of air) in each image were measured. A graph showing the extinction of the standard star is shown at left.

With the transformation and extinction equations, the standard BVRI magnitude of any star may be calculated by transforming its intensity to standard magnitudes, then correcting for the effects of the atmosphere. These magnitudes are then subtracted to form B-V, V-R, and V-I colors. Finally, a correction must be applied for light scatter due to interstellar dust along the galactic disc. These values were obtained from the WEBDA open-cluster database and were specific to the cluster being observed (Mermilliod 2003). This allowed the stars' true colors and absolute brightness to be obtained.

Data: During this study, two open clusters were observed: NGC 381 and NGC 637. Both clusters are located in the constellation Cassiopeia. A total of 30 hours of observations of NGC 381 and 42 hours of NGC 637 were collected in the I-band.


Figure 1: NGC 637 and NGC 381 data (Click to enlarge)
The graphs in Figure 1 show the relation between the magnitude and the error margin of the data for the two open clusters. Differential magnitude (comparison star minus measured star) is on the X-axis, while the standard deviation of each star's data is plotted on the Y. In the graphs a fair number of stars appear to be variables, but most of these objects are in fact stars whose light is being contaminated by the light of another star that is close by (or touching) it in the images, leading to poor photometric accuracy for these stars. For this reason, all of the objects off of the curve were examined manually with MaxIM DL.

Figure 2: NGC 637.
Figure 2: NGC 637 (Click to enlarge)
Two of the outliers in the magnitude-variance graph of NGC 637 (Figure 1) were found to be undiscovered variable stars. Neither star was previously known to be variable. Their location is shown on the labeled image in Figure 2. They are named star 3 and 4, after the names given to the stars in NGC 637 by Grubissich in 1975; this naming system has also been adopted by the WEBDA online open-cluster database (Mermilliod 2003). The coordinates of star 3 are: 01:43:32, +64:02:06; for star 4, they are: 01:43:32, +64:02:14.



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