A Search for Variable Stars in Two Northern Open Clusters: NGC 381 and NGC 637

Part of the Young Naturalist Awards Curriculum Collection.

by Morgan, Grade 12, Maine - 2005 YNA Winner
A photo of a starfield, shown as specks of light and swirls of magenta color against the inky black of space.
Photo of starfield.

The goal of this expedition was to search for undiscovered variable stars using amateur astronomy equipment. A 10" telescope, CCD camera, and BVRI photometric filters were used. It was decided to search for variables in open star clusters. NGC 381 and NGC 637, both in Cassiopeia, were selected. No new variables were found in NGC 381. However, two previously undiscovered variable stars were identified in NGC 637. They are designated stars 3 and 4. Analysis of the data indicates that both are spectral class B, and star 4 is likely a Beta Cephei pulsating variable. Star 4 was found to be pulsating simultaneously in two modes.


Background:  Throughout the 20th century, variable stars have played an incredibly important role in astronomy. Variable stars allowed Edwin Hubble to prove that our universe is made up of many galaxies. Today, variable stars remain at the forefront of astronomy. There is still much to be learned about variable stars. Judging from recent studies, astronomers estimate that 2-3% of all stars are variable, but only 10% of all bright variable stars are known (Paczynski 2001). Many fundamental questions, such as why some stars vary the way they do, have yet to be answered.

Variable stars can vary for many different reasons. Most of the variable stars known today are pulsating variables (Samus, Durlevich 1998). Pulsation is when a star changes its shape or size rhythmically (Bradley 2001). All pulsating stars have fundamental frequencies at which they can oscillate, and these determine the star's period. Some stars oscillate with more than one frequency. In these stars there are several outer layers, each pulsating at its own rate.

A Hertzsprung-Russell diagram of a star's luminosity and color.
A Hertzsprung-Russel (H-R) diagram

The basic class of pulsating variables is further broken down into several different categories. These are differentiated based on several factors. The most important is the star's luminosity and its temperature. The Hertzsprung-Russel (H-R) diagram, a graph of star color (an indicator of temperature) versus luminosity, can explain in part the reasons stars pulsate (Bradley 2001). The H-R diagram contains a band from top left to bottom right called the main sequence. Most stars lie along the main sequence. Off the main sequence there are several "instability strips," or areas in which pulsation is likely to take place (Petit 1982). Also important in the classification of pulsating stars is the shape of their light curve. The light curves of stars with similar positions on the H-R diagram are often similar in appearance, and this aids classification.


The Study of Variable Stars:  Astronomers have been studying variable stars since their discovery in the early 16th century. At first, astronomers tracked changes by using the naked eye; later, they used the optical aid of telescopes (Williams 1997). For the study of variable stars, just as with all other stars, astronomers adopted the system of magnitudes. This system was developed by the ancient Greeks and designed so that the brightest stars in the sky are first magnitude and increasingly fainter stars get larger numbers (Berry, Burnell 2000). For every five magnitudes there is a 100-fold difference in brightness. A 10th magnitude star is 100 times fainter than a fifth magnitude star.

In the late 1800's and up to about 1970, astronomers used photographic film to discover many new variable stars (Wilson 2001). The photo multiplier tube (PMT) was invented in the early 1900's. This allowed astronomers to get a reading of the photons coming from a variable star quite accurately. By switching back and forth between a comparison star and the variable, very accurate measurements could be achieved. With a large enough telescope, an accuracy of /- 0.01 magnitude was sometimes possible (Budding 1993). Both methods had problems, though: Photographic measurements were inaccurate, while a PMT could only observe a single star at a time.

In the 1970's the charge-coupled device (CCD) camera was brought into use. This led to a huge advance in photometric observing. Much fainter stars could be researched, and accuracies of /- 0.001 magnitudes can be achieved occasionally by professional observatories (Berry, Burnell 2000). Recently, astronomical CCD cameras have come down sufficiently in price to make them available to amateur astronomers, creating the potential to revolutionize the study of variable stars. With a CCD camera, an amateur astronomer can collect data that rivals anything before the invention of the CCD. A CCD camera has the further advantage of being able to collect accurate data on many stars in a single image.


Introduction:  Our knowledge of variable stars is incomplete; only a small percentage of variable stars have been identified and studied. Searching for variable stars is a very time-consuming process, and professional observatories can rarely offer large blocks of time to one observing group, as the cost is too prohibitive. The availability of relatively low-cost CCD cameras has made it feasible to study variable stars using amateur astronomy equipment. Over the past two years, the author conducted several investigations into the study of variable stars with amateur telescopes and CCD cameras. First, the light curves of known variable stars were plotted using a CCD attached to various camera lenses. Then the CCD was attached to the telescope for greater photometric accuracy, and a poorly understood variable star named v377 Cas was observed in an attempt to better understand its variation. This research demonstrated that amateur equipment could be extremely effective in collecting very accurate photometric data. The progression of these experiments lead to the goal of this project, which was to set up and use a system of amateur astronomy equipment to search for new variable stars.

Several wide field surveys for variable stars are currently being conducted using camera lenses and CCD cameras, such as the Hungarian Automated Telescope and the All Sky Automated Survey (Bakos et al 2002; Pojmanski 2000). These surveys cover huge portions of sky but without much resolution. It was decided to use a telescope to observe a smaller area of sky, but with more detail, and to a fainter limiting magnitude. The system was designed using only hardware that is readily available commercially, so that this setup could serve as a prototype for other variable star searches operated by amateur astronomers. Many amateur astronomers already have all of the hardware needed to set up a system similar to that described here; the hope was that if the system proved effective, it could lead other amateurs to put their equipment to use searching for variable stars.

The target fields were selected so as to contain an open cluster. An open cluster is a loose grouping of stars that is held together by their mutual gravity. There are several good reasons to search for variable stars in open clusters. First, there will generally be more stars in an image of an open cluster than in a random star field. Second, and more importantly, the distance and age of open clusters can be calculated from their color-magnitude diagram. This information is very interesting because astronomers normally have no way of knowing the ages of, or the distances to, most stars. These extra pieces of information make the discovery of a variable star in an open cluster far more exciting than the finding of a randomly placed star. For example, if one knows a star's distance from Earth, the absolute magnitude, or true brightness, of a star may be calculated. This gives the star's exact placement on the Hertzsprung-Russel diagram. Furthermore, if one knows a star's age, it is possible to tell what phase of its life cycle a star is in, which is yet another piece of information explaining why the star varies the way it does.

The clusters to be observed were selected based on three criteria. First, they had to be well placed for viewing during the fall. Second, only clusters in which there had never been any searches for variable stars were considered. And, finally, the clusters needed to be located so that there was a bright star in the cluster that could be used to guide the telescope during the exposures. Much care was taken in this process to ensure that this research would not duplicate any previous studies.


The massive 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.

A line graph titled "Extinction."
Graph showing the extinction of the standard star.

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.

Two dot plot graphs.
Figure 1: NGC 637 and NGC 381 data

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.

A star chart appearing as many black dots of varying sizes against a white background. Two dots in the middle of the area and very close to one another are labeled 3 and 4.
Figure 2: NGC 637.

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.

A dot graph showing differential magnitude for Star 4.
Figure 3: Star 4.

Star 4 is a short-period pulsating star with a V-magnitude of 11.1. The BVRI measurements show that the star has an absolute magnitude of -2.58 magnitude and a B-V color index of -0.18 magnitude, indicating star 4 is an early B-type star (Pickles 1998). The star was found to be pulsating simultaneously in two modes. Its main frequency has an amplitude of 0.14 magnitudes and a period of 4.55 hours (0.19 days). A secondary frequency with a 3.85-day period and an amplitude of 0.04 magnitude also exists. This analysis was done with the Period 98 software. The star's light curve has a fairly sinusoidal shape. From its light curve and its colors, star 4 is most likely a Beta Cephei (BCEP) type variable. Figure 3 shows a light curve for Star 4 phased on the star's primary period.

A dot chart concerning Stars 3 and 4.
Figure 4: NGC 637 stars 3 and 4

Star 3's variability can be seen in Figure 4, which shows the light curves of the stars in the I-band over five nights of study. It is 10.7 magnitude in V, with an absolute brightness of -2.91 magnitude. The color index of the star (-0.22 magnitude) indicates an early B spectral type. The star's amplitude is approximately 0.1 magnitude. The data collected suggest a 0.8-day period. While star 3 appears to be a pulsating variable, more data is needed to truly understand its variation.


Conclusions:  A search was conducted for new variable stars in two northern open clusters, NGC 637 and NGC 381. Photometric measurements of more than 1,100 stars down to a limiting magnitude of about I = 15 were collected between the two target fields. Two new variables were identified in NGC 637. Because the stars are both members of NGC 637, their distance moduli, in magnitudes and reddening coefficients, are known. Both are fairly bright, approximately magnitude 11.1 and 10.7 in V. The extinction and transformation equations of the site and the equipment setup were defined, allowing absolute photometry of any star in the BVRI wavelengths. This allowed the stars' colors to be measured, showing that they are both spectral type B. Star 4 is most likely a Beta Cephei-type pulsating variable. More data is needed to fully understand the variation of star 3, but it lies within the pulsational instability regions of the upper main sequence of the HR diagram, and is very likely a pulsating variable (Pamyatnykh 1999). Star 3 offers an opportunity for further research; with more information it should be possible to identify the cause of this star's variation. Table 2 summarizes the information collected on the two new stars found in NGC 637.

Table 2:
  Period Amplitude Spectral type
Star 2 0.8d? 0.1m B
Star 4 0.19d, 3.85d 0.15m, 0.04 B

This research once again demonstrates the potential that amateur astronomy equipment has in the study of variable stars. Many amateurs own equipment similar to that which was used to conduct this research. The system described in this paper will hopefully motivate some amateurs to put their equipment to use in a similar manner.



Acknowledgements:  I would like to thank my teacher, Mr. TK O'Neill, and my parents for making this project possible. I would also like to thank Diffraction Limited Software for a generous discount on their program MaxIM DL. I would like to thank Paul Howell, my neighbor and an astronomy graduate student at Boston University, for his helpful suggestions.



American Association of Variable Star Observers.  http://www.aavso.org , 2004

Bakos, G.A., et al. "System description and first light-curves of HAT, an autonomous observatory for variability search." The Publications of the Astronomical Society of the Pacific 114.799 (2002): 974-987.

Berry, Richard, and James Burnell. The Handbook of Astronomical Image Processing. Richmond, VA: Wilmann-Bell, 2000.

Birney, D. Scott. Observational Astronomy. New York: Cambridge University Press, 1991.

Blake, Cullen. "The Princeton Variability Survey." The Publications of the Astronomical Society of the Pacific 115.803 (2003): 104-112.

Bohm-Vitense, Erika. Introduction to Stellar Astrophysics: Volume I: Stellar Observations and Data. New York: Cambridge University Press, 1989.

Bradley, P.A. "Stellar Pulsation." Encyclopedia of Astronomy and Astrophysics. Paul Murdin, ed. New York: Groves Dictionaries, 2001.

Budding, Edwin. An Introduction to Astronomical Photometry. New York: Cambridge University Press, 1993.

Carroll, Bradley W. and Dale A. Ostlie. An Introduction to Modern Astrophysics. Reading, MA: Addison-Wesley Publishing, 1996.

Crinklaw, G. Etzel. "A Photometric Analysis of the Eclipsing Binary OX Cassiopeiae." Astronomical Journal 98 (October 1989): 1,418-1,426.

Grubissich, C. "Three-Colour Photometry of the Two Galactic Star Clusters NGC 559 and NGC 637." Astronomy and Astrophysics Supplement Series 21 (July 1975): 99-107.

Howell, Steve B., ed. Astronomical CCD Observing and Reduction Techniques.  San Francisco, CA: Astronomical Society of the Pacific, 1992.

Howell, Steve B. Handbook of CCD Astronomy. Cambridge, England: Cambridge University Press, 2000.

Hroch, Philip. "Munipack Homepage."  http://munipack.astronomy.cz/ , 2001

Huestamendia, G., G. del Rio, and J.-C. Mermilliod. "UBV Photometry of Open Clusters in the Cassiopeia Region I — Photoelectric observations of NGC 436 and 637." Astronomy and Astrophysics Supplement Series 87.1 (January 1991): 153-158.

Jaschek, Carlos, and Mercedes Jaschek. The Classification of Stars. New York: Cambridge University Press, 1987.

Karttunen, H., P. Kroger, H. Oja, M. Poutanen, and K.J. Donner, eds. Fundamental Astronomy. New York: Springer-Verlag, 1987.

Kholopov, P.N., et al. Combined General Catalog of Variable Stars (GCVS).

Vizier Online Data Service at the Centre des Données Astronomiques de Strasbourg, France. 2004. http://vizier.u-strasbg.fr

Kral, Lukas. "Varfind Homepage." 2003.  http://kral.astronomy.cz/soft/varfind/

Mermilliod, J.-C., and E. Paunzen. "Analysing the Database for Stars in Open Clusters. I. General methods and description of the data." Astronomy and Astrophysics 410 (2003): 511-518.

"NASA ADS Home Page."  http://adswww.harvard.edu/, 2004

Paczynski, Bohdan. "Monitoring All Sky for Variability."  ArXiv  2 (2001).

Pamyatnykh, A. "Pulsational Instability Domains in the Upper Main Sequence . " Acta Astronomica 49 (1999): 119-148.

Petit, M. Variable Stars. New York: John Wiley and Sons, 1982.

Petry, C.E. and K. Degioia-Eastwood. "New Color Magnitude Diagrams for NGC 637 and NGC 7245." Bulletin of the American Astronomical Society 24 (1992): 1,235.

Pickles, A.J. "A Stellar Spectral Flux Library: 1150-25000 A." The Publications of the Astronomical Society of the Pacific 110.749 (1998): 863-878.

Pilkington, Garry. "The Location of Cephieds in the Galaxy and on the H-R Diagram." 2001.http://www.astro.livjm.ac.uk/courses/one/NOTES/Garry%20Pilkington/loc.htm

Pojmanski, G. "The All Sky Automated Survey Catalog of About 3,800 Variable Stars." Acta Astronomica 50 (2000): 177-190.

Pojmanski, G. "The All Sky Automated Survey Catalog of Variable Stars. I. 0 h - 6 h Quarter of the Southern Hemisphere." Acta Astronomica 52 (2002): 397-427.

Sperl, M. "Manual for Period 98, Version 1.0.4: A period search-program for Windows and Unix." Communications in Asteroseismology 111 (1998): 1-100.

Sterken, C. and C. Jaschek, eds. Light Curves of Variable Stars. Cambridge, England: Cambridge University Press, 1996.

Unsold, A., and B. Baschek. The New Cosmos: An Introduction to Astronomy and Astrophysics. New York: Springer-Verlag, 2002.

Wilson, R.E. "Variable Stars" and "Eclipsing Binaries." Encyclopedia of Astronomy and Astrophysics. Paul Murdin, ed. New York: Groves Dictionaries, 2001.