Updated: 6 March 2011

Variable Stars Project

Stars, Sight and Science
COSMOS 2004 at UC, Santa Cruz

Stars, Sight and Science is the Center for Adaptive Optics -sponsored cluster of the academic summer camp COSMOS at UC Santa Cruz. COSMOS is organized by the University of California. It takes place at the Davis, Irvine, San Diego, and Santa Cruz. Stars, Sight and Science is a merger of two subtly related fields: astronomy and vision science. The CfAO recruits staff for the astronomy and vision science projects from the UCSC Department of Astronomy & Astrophysics and Rochester University. In the four weeks that COSMOS runs, the 17 cluster students learn about astronomy and vision science in the classroom setting and in small-group research projects. The students ultimately presents their research to another cluster from the UCSC COSMOS program; this year, the partner cluster was the astrophysics cluster sponsored by the Santa Cruz Institute for Particle Physics. The project presented here is the Variable Stars Project.

Millie, Michelle, Kathy, and Christina (post-presentation)
Three beautiful, brilliant, and boisterous young women elected to participate in the Variable Stars Project:
  • Millie Alcantar is a senior from Watsonville, CA. She's also a fabulous singer.
  • Michelle Hadley is a sophomore from El Centro, CA. She's a mad volleyball player.
  • Christina Young is a junior from San Jose, CA. She's kind enough to help younger students with their science fair projects.
Kathy Cooksey was the novice project advisor for the Variable Stars Project 2004. She's finished year one in pursuit of her doctorate in astrophysics at UCSC. She's also a mad soccer player.
These students chose one of the most difficult projects of the Stars, Sight and Science cluster. They elected to solve a mystery: why does the object SZ Her vary in brightness periodically? They were presented only with this question and data that showed the variation and were subtly guided towards the answer: SZ Her is composed of two stars orbiting each other such that they regularly eclipse each other. This project is most like a complete research project in that the students learned about a curious phenomenon, developed possible explanations, experimented with those possibilities until they discover the answer, then theorized about the exact construct of the system with a program that models eclipsing binaries. From this process, Millie, Michelle, and Christina concluded that SZ Her must be an eclipsing binary system. Their data will be sent to the American Association of Variable Star Observers for use by other variable star observers; SZ Her has very little data in the AAVSO archives.
This video was created by Lick observer extraordinaire Ellie Gates. It shows four different types of variable stars. Starting in the upper right-hand corner, they are: nova, Cepheid, RR Lyrae, and eclipsing binary. The students were shown this video without being told what the objects were. They were asked to find the variable stars and to speculate as to what might be causing the variation. Then they drew rough sketches of the variation of each object over time (called a "lightcurve"). They noticed that some seemed more regular (or periodic) than others (e.g. RR Lyrae versus nova).
The students suggested that variation in stars may be due to planets, nebulae, changes in distance, and/or changes in size.
The SZ Her star chart is shown at the left. SZ Her is the bright star in the middle. The field is 5x5 arcminutes, which is about the field of view of the Nickel.
What type of name is SZ Her? Her is an abbreviation of the Latin name for the constellation The Strongman, Hercules. Astronomers often name stars after the constellation in which they're found. Stars that vary their brightness are called variable stars, and the first one to be found in a constellation was name A, the next B, and so on. When they reached the end of the alphabet with Z, they started over with AA, then AB, and so on. So the name SZ Her means that it was about the 500th variable star to be discovered in the constellation of Hercules.
The observation process for this project is described below, but More information can be found in the handy manual Observing a Variable Star-The Observations written and modified by previous Variable Stars project advisors Patrik Jonsson and Observing a Variable Star-A Recipe for Photometry.

Digitized Sky Survey

On July 8th, the students observed SZ Her with the Nickel 40'' Reflector of Lick Observatory, Mt. Hamilton, CA. They observed remotely from the CfAO conference room with the help of Ellie.
Observing is a hectic affair, but Millie, Michelle, and Christina made it through relatively unscathed. And with good data; as shown by the lightcurve on the left, the students managed to observe the minimum in the the "visual" (V) or green-colored band at 11:13:24 PST (6:13:24 UT). Data reduction and photometry were performed with IRAF (Image Reduction and Analysis Facility), which is standard astronomer fair. The Nickel software already accounts for the noise due to the electronics of the telescope and CCD (i.e. camera). The images were divided by the appropriate flat field image, which removes the dust artifacts of the filters and effectively normalizes the sensitivity of the CCD. Next, the images were registered, or aligned, so that the objects of interest (namely, SZ Her and the comparison stars) would be located at the same pixel location in each image. Aperture photometry was performed with the IRAF package qphot ("quick photometry"). The magnitudes given are differential magnitudes, meaning the brightness of SZ Her was measured relative to surrounding, presumably non-varying stars.
The students' data was supplemented with observations taken by Kathy on June 29-30, 2004, and Lynne Raschke on July 1-2, 2004, also on the Nickel.
Kathy observed the primary minimum at 11:17:21 PST, and Lynne observed the secondary at 00:10:15 PST. Kathy and Lynne knew when to observe SZ Her by examining the AAVSO charts of Eclipsing Binary Ephemeris and the Rolling Hills Observatory Ephemeris Calculator. In fact, SZ Her was chosen specifically because it would be eclipsing on the scheduled observation run with the students. Fortunately, the Nickel was free these other nights to flesh out the lightcurve.
To the right is the folded lightcurve of SZ Her with data from all three nights of observation. A folded lightcurve neatly and clearly displays all the data of an eclipsing binary system; it requires knowledge of the ephemeris, which is an equation of the form:
T = To + P*E
where T is the time of the primary minimum, To the known time of a primary ecplise, P the period of the system (time from primary to primary minima), and E the number of periods since To. The data is then folded to span phases 0 to 1, with primary minima landing on 0 or 1 and secondary on 0.5.
The students were charged with producing a lightcurve like SZ Her's with the help of the following simple equipment: foam balls of various sizes and colors, scarves, light bulbs of various sizes and wattages, a variometer, a TV turn table, and photodetector. These objects represented the different possible mechanisms and/or processes that the students had suggested for why stars might vary. The foam balls represented planets, scarves clouds of dust, and light bulbs stars. The turn table enabled them to simulate the orbit of objects about each other, and the variometer allowed the students to vary the brightness (which is the same as changing the size). They set up some configuration of the above elements, then generated lightcurves like the one below for each case. By examining the lightcurve (e.g. relative difference of minima) and debating the physics, the students determined that the case where there are two lightbulbs produce the most realistic approximation of the SZ Her Lightcurve.
These lightcurves are replicas of the students'. The first configuration of two bulbs they tried was a large 25W bulb orbiting a large 60W bulb (pink curve). This setup produces a deep primary minimum when the 25W bulb blocked the light from the 60W and a shallow minimum when the 60W bulb eclipsed the 25W bulb. Next the students replaced the large 25W bulb with a small 25W bulb (blue curve). They observed that the primary minimum was not as deep as in the first configuration because the small 25W bulb did not cover as much of the large 60W bulb as when they had a large 25W bulb. Then they tried changing the relative sizes; they setup a large 25W bulb orbiting a small 40W bulb (yellow curve). Unfortunately, a small 60W bulb was not available, which makes comparison with the other setups tricky; in the lightcurve to the left, the Small 40W/Large 25W data was scaled to the continua of the other two configurations. Actually, this last configuration is the one that produces the largest difference between the primary and secondary minima because when the 25W bulb is in front of the 40W bulb, the latter is completely obscured. Alternatively, when the 40W bulb is in front, it only blocks a small part of the 25W bulb.
Nightfall is a terrific program that models eclipsing binary systems. A detailed description of how to use Nightfall is given in Observing a Variable Star-Interpreting the Data. Nightfall uses the convention whereby the primary minimum occurs at phase 0.5 and secondary at 0 and 1.
The lightcurve of SZ Her was loaded into Nightfall (green points), and the students adjusted six parameters until the model lightcurve (red curve) fit the data. The parameters and their meaning are as follows: mass ratio is the mass of secondary star over mass of primary star; inclination is the angle at which the system is viewed, with 90° being edge on; primary and secondary fill factors, which relates to the size of the stars and their mass; and temperature of the primary and secondary stars, which relates to their brightness.
In order to find the best fit with reasonable values for the six parameters, the students were given a short lesson on stellar classification and the spectral type of the two SZ Her stars (but not which was which). According to Guiuricin et al. 1981, the primary star in SZ Her is an A5 or A0 star and the secondary star is a F4V star. A stars are usually white stars with temperature in the range 6900-9400K; F stars are white or yellowish-white and 5800-6900K. A0 means that the primary star is toward the hotter limit of the A-type temperature range; and F4V means the secondary is a main sequence or dwarf star. SZ Her is classified as an EA/SD eclipsing binary by VizieR, which means that the secondary minimum is very shallow and that the system is semi-detached (one star is reaching the point where its material will be accreted by the other star).
Basically, for SZ Her, the primary star is a brighter, hotter, smaller star than the secondary star, and one star has a distended, tear-drop shape because its self-gravity is barely greater than the gravity of its companion. The students figured this out by fitting their data with the Nightfall model lightcurve. The following numbers produced the best fit were as follows: mass ratio = 2.365; inclination = 96.005° primary fill factor = 0.849; secondary fill factor = 0.672; primary temperature = 9628K; and secondary temperature = 5548K. The literature give the period of SZ Her as 19.6 hours. Millie, Michelle, and Christina presented on their project to another cluster of COSMOS. Their presentation can be downloaded here. In addition, their data will be sent to AAVSO for use by other variable star observers- amateur and professional. Eclipsing binary systems are a very important type of variable star. For one, systems of two or more stars appears to be the norm in the Universe. Since the stars in eclipsing binaries are very close, they interact strongly gravitationally, and this allows astronomers to measure, at least, the mass ratio; there are not many ways to measure the mass of stars.
Thus, Millie, Michelle, and Christina studied a very useful system, worked with very important data, and learned much about a common stellar system. They worked with typical astronomy tools such as the Nickel telescope and the IRAF package. In addition, they ran the gambit of the scientific process in answering the question: Why does SZ Her vary in brightness periodically?