The Toils of Observing an Eclipsing Binary: W Ursae Majoris
Maggie Buttermore and Anne Sweet
Macalester College
Department of Physics and Astronomy
Spring 2005
One of 18 images we took of W UMa, a bit out of focus, but including the flat field and dark image.
Introduction and Background: Eclipsing Binaries
Eclipsing binaries are an important astronomical occurrence because of the properties you can determine from them. In general, binaries are stars that orbit about a common center of mass. A visible binary occurs when the plane of rotation is perpendicular to the observer and the two stars can be individually resolved. An eclipsing binary occurs when the plane of rotation is parallel to the eye of the observer. Although the two stars of an eclipsing binary cannot be visibly distinguished from one another, they can be identified by the change in magnitude during eclipse. By observing the change in magnitude over time and using photometry to calibrate the background of each image, one can generate an accurate light curve of the system. The rigidity of the light curve will be related to the angle of inclination between the orbital plane and the observer’s eye. When the plane of eclipse is exactly parallel (i=90 degrees), the light curve will have clearly defined changes in magnitude. If the plane is not perfectly parallel (ie. a partially eclipsing binary), the light curve will have smooth and non-abrupt changes in magnitude.
Using the light curve, one can determine when one star passes behind the other star as well as the duration of the eclipse. Using this information along with the velocities obtained by spectroscopic investigation, it is possible to calculate the radius of the primary star. The same method can be used to obtain the radius of the secondary star. Once the radii have been obtained, Newton's/Kepler's Third Law becomes applicable for determining the mass. By using a system of equations, one involving the sum of the masses and one involving the ration of the masses, we can calculate the individual mass of each star.
Experimental Design
Originally, we had planed to observe the eclipsing binary Algol. We had very bad luck with the ephemeredes coinciding with cloudy nights, so we switched to W-UMa, an eclipsing binary with an ephemerid every evening, due to its 8 hour period. Because of the change in our proposal last minute, we no longer had the opportunity to combine our data with the spectroscopic data from Reid and Jim as we had originally planned, and thus had to re-work our proposal to reflect our new ambitions.
Our new goal was to create a partial light curve for W-UMa by capturing the the first half of the eclipse up to the ephemerid. We then could use to this half light curve to deduce the entire duration of the eclipse. We intended to gather approximately 15 images during the first part of the eclipse (lasting 1.5 hours), each of a duration promoting good signal to noise in the R filter (our CCD's most efficient filter). By dividing and subtracting out the twilight flats and darks taken the same evening we planned to calibrate our pictures of W-UMa with those of our check stars. Then we would calculate the magnitude in each picture to create our partial light curve which we then could use to confirm the period and change in magnitude of the star. A slightly more modest proposal, but one we thought we could handle given our luck with this project.
The information on our proposed observing objects are below:
Identifier |
Right Ascension |
Declination |
R Magnitude |
Spectral Type |
| HD 83950 A | 09 43 45.4688 | +55 57 09.075 | to be determined | F8Vp |
| HD 83950 B | 09 43 45.4688 | +55 57 09.075 | to be determined | F8Vp |
| HD 85217 | 09 50 30.0811 | +04 20 37.142 | 10.7 | F7Vn |
| GSC 03810-01196 | 09 44 08.793 | +56 00 38.69 | 10.7 | unknown |
Facilities: Macalester College Observatory
For our project, we used the Macalester College Observatory for observing. It has a 16-inch reflecting telescope, designed and built especially for Macalester by DFM Engineering. The telescope is computer controlled and linked with TheSky software for easy location of objects brighter than 20th magnitude. Our imaging was done with the SBIG ST-8 CCD camera, and we used CCDOPS to capture, reduce and analyze our images.
Not as Easy as it Sounds: Experimental Method
After several frustrating evenings of cloudy nights, we headed up on the very clear night of April 14th, 2005 to observe W-UMa. After taking 5 twilight flats, we confirmed our chosen check stars to be non-variable and of the right spectral type, and waited for the sky to darken enough to begin our imaging. The eclipse was scheduled to occur at 12:30, so we targeted to begin observing at about 10:30 and finish up at about 1 am to ensure we would capture enough of the light curve. Once it became dark enough, we spent quite a bit of time focusing and by the time we finished, it was almost time to begin imaging. After taking a few preliminary images to determine which light image length would obtain relatively good signal to noise (440 seconds), we began taking images at regular (but unfortunately not at perfectly constant intervals for lack of a timer) in addition to taking images of our check stars in between the images of W-UMa. We took several dark images in the beginning as well. We took our last images at 1:15 am and called it quits for the evening, in hopes to have another chance at observing one of the more interesting binaries now that we had a bit of practice under our belt and had run into unforeseen problems during observing that we felt we were now ready to handle.
Unfortunately, the opportunity never came. Several more cloudy nights interrupted or prevented our observations of some of the other systems we were planning to observe, (always punctuated with clear nights on the nights there was no epehermid, of course!) and we were a bit discouraged. This initial W-UMa data ended up to be the best data we had for our project.
Creating our light curve: Photometry
Another troublesome endeavor! (We were running intro trouble at every turn!!) We first set out to gather our data to subtract out our flat fields and divide out our darks. However, the computer containing our data had crashed and although retrieving it was a bit of a trick we were successful in saving it. Armed with our data, we began by averaging our 5 flat field images. Afterward, we averaged our darks, but unfortunately only had two dark images of the proper length to use for our images.
(top
left) Our original image
(top right)
Our composite flat field image
(bottom left) Our composite dark image
(bottom right) Our final image with the flat field divided out and dark subtracted
Once we had divided out the flat fields and subtracted the darks for each image, we were ready to begin the photometry. Using our check stars, we had to calibrate our background in order to determine the apparent magnitudes of our star. To do this, we needed to determine the magnitude of one of our check stars using the infamous toggle box, change the magnitude to reflect the correct apparent magnitude, note the response factor we used, and apply this response factor to the image of W-UMa. Ideally, we would have had a check star within the field of view of W-UMa, but the stars in field were of a very different spectral type, so we used the two check stars nearby to calibrate the background.
The first thing we discovered was that magnitudes are rarely listed in the R magnitude. Because all of our images were taken in the R filter, we worried we were going to be unable to calibrate our stars! Fortunately, the USNOA website had a listing of many stars and their R magnitude so we were saved! For our first check star, we found the RF to be 2457, and for our second we found it to be 5039.
We began measuring the magnitudes of each star, using the different RF factors to gain a sense of the error involved. We immediately noticed that the toggle box size was not large enough to encompass the entire star (or so we thought) so we moved the toggle box systematically around within the star (measuring the magnitude at 5 different locations) to get several different magnitudes which we hoped we could average to reflect a real magnitude. However, after we discussed this with our professor, we realized this was a terrible method and wasn't telling us anything. By looking at the vertical profile, we realized that the 31 x 31 toggle box was in fact the correct size, but left out about 9% of the star. Because of this, it was necessary for us to find the exact center of the star, which we did by varying the back and range to find the center of the out of focus donut of a star.We created quite a fabulous excel spreadsheet to hold our values for observing times, coordinates, value, noise, calculated magnitude, averaged magnitude, signal to noise, and standard deviation.We averaged a signal to noise ratio of 57.4 for our photometric measurements, but the values for each measurement (we had a total of 18) ranged between 49 to 64.
We graphed average magnitude vs. time including our standard deviation to create a general light curve. We fit the curve with a high order polynomial but keep in mind our goal was only to capture the first half of the eclipse, so that is the only part of the graph we considered when calculating the change in magnitude.
A graph showing the average R mangitude vs time with standard deviation.
Results: More or Less
According to our data, the eclipse of W-UMa began at 10:50 pm April 14th 2005 with a minimum at 12:05 am April 15th. This is more of less consistent with published research, predicting an eclipse duration of 3 hours and a minima occuring at approximately at 12:30 am. We found the minimum R apparent magnitdue occured at the minima, and was 10.3+/-.39. The maximum R apparent magnitude occured immediately before the eclipse began and was 9.5+/-.39. We were unable to confirm the accuracy of these magnitudes, as we were unable to find a light curve for W UMa in the R filter, but we did find a light curve in a different filter for comparison.
Light curve for W UMa in the V filter. Source: http://faculty.rmwc.edu/tmichalik/eclpvar.htm
Results: Error Analysis
Errors are always an important part of any analysis, and although some of our methodology was less than perfect, it's nonetheless important that we discuss and try to identify all of the sources of error in our data. There are two types of error that are important to examine: random and systematic error. Sources of random error in our data could be atmopsheric disturbance, dust on the filter or telescope, as well as temperature variation in the CCD. To address the dust and temperature variation, we used flat fielding and dark subtracted prior to photometry. We were unable to address atmopsheric disturbance because we didn't take enough images of our check stars. Had we done this, we would have had several different response factors over the evening which we would have used to find a more accurate magnitude and error. Sources of systematic error in our project could be due to photometric measurements, such as an incorrect toggle box size, which would then have distorted our response factor values. To address this, we found the exact center and measured the magnitude using each response factor, and noted that our values may be off about 9%. We didn't know exactly how to quantify this diffference, as the value of each pixel drops off around the edges of the star so we couldn't use a linear relation to account for the values of the missed pixels. In addition, changes in the background over one image could also cause magnitude calculation errors. To account for this, we calibrated the toggle box background measurement in several different locations on the image. In every case, we found the background to be homogoneous, except in locations where it looked like the flat field may have been distorting the background.
In the End: Our Learning Experience
This project was an incredible frustration, but also an incredible opportunity to learn how hard observing is and how many unanticipated details are involved! If we could do this project again, the following are things we would have done differently:
First, we would have done a lot more background research before beginning. Not only on eclipsing binaries in general, but also on the binaries specific to our system. There are so many papers and commentaries out there on eclipsing binaries; both specific and general that we could have used to improve our observing techniques and approaches. If we had looked into how others had done it, we would have discovered their mistakes first and had a better sense of how to prepare ourselves.
Next, we would have entered into our project with a list of at least 3 or 4 binaries to observe with check stars prepared. That way, every clear night would have most likely been an opportunity to observe a minimum in one system, and we could have avoided the "it's cloudy" panic. We also would have planned on going up at least 3 times as well, beginning immediately, to smooth our problems out earlier in the process.
When observing, there were a lot of things we would have approached differently. First, we would have considered our filters more carefully. Although our CCD is most efficient in the R filter, it was a terrible task for us to find the R magnitudes of our check stars so that we could calibrate. The V filter would have been a much easier filter to use. Similarly, we should have considered on what type of object we focused the camera. We used Saturn to focus which was (obviously) quite a bit brighter than W-UMa. When we began imaging W-UMa, the fainter stars in the picture were out of focus, something we didn't consider until after we were done observing (which was also silly of us) and could have easily been remedied by refocusing throughout the evening (something else we recommend!) In addition, we would have taken images of our check stars at the beginning, middle and end of the night to hopes to more accurately model how the magnitudes were changing. We also would have taken more dark images of the appropriate length throughout the evening so our final dark composite would have reflected all of the internal CCD temperature changes, etc. Finally, we would have brought up a timer (or an alarm clock with the appropriate snooze time!) so that our pictures would have been taken with more regular intervals. As good as we thought our sense of timing was, it really wasn't that impressive!
We were quite disappointed with our results overall, but were quite pleased with our after-the-fact trouble shooting and with the amount we learned from this. Having to struggle so much was quite good for us! It certainly keeps us encouraged to go up and try again!
References and Useful Links: Sites That Saved Us!
1) Kim Venn, our professor, was of course extremely helpful.
2) Reid Lustig. Our very helpful classmate who taught us how to flatfield and gave us other useful tips along the way.
3) Simbad Astronomical Database. A great place to find check stars, figure out magnitudes, learn more than you ever wanted to know about any object in the sky! http://simbad.u-strasbg.fr/Simbad
4) The AAVSO website. A great place to get information on eclipsing binaries. http://www.aavso.org/ Also, a great place to find the timing of the minima of many different eclipsing binaries. http://www.aavso.org/observing/programs/eb/ebephem.shtml
5) The USNOA website. The place we FINALLY found our R magnitudes (although you can find some on Simbad if you look hard enough). http://archive.eso.org/skycat/servers/usnoa
6) Cool simulation website to see how a light curve works. http://instruct1.cit.cornell.edu/courses/astro101/java/eclipse/eclipse.htm