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Project 9: "Variable Star Studies--Keys to the Universe"
by Barrett Duff
Level: Advanced
Requirements: Filter Wheel, Photometry Software, Light Curves
Objective
Students will become familiar with three types of stars that vary in light: pulsating variables, eruptive variables and eclipsing variables. These stars tell us much about the size and structure of the universe and about stellar dynamics and evolution. At least one star each of the pulsating and eruptive variables and one eclipsing binary class will be selected for study. Light curves for the selected stars will be plotted and the periods calculated. An optional secondary objective would be to determine the color index and spectral class for each variable.
Background
Pulsating variable stars include Cepheids I and II, RR Lyrae, Mira, RV Tauri and other types. Cepheids are perhaps the easiest to study as they are bright (0 to -5 absolute magnitude) F to G supergiants with regular periods of 3 to 50 days and amplitudes up to 2 magnitudes. RR Lyrae variables are found in the galactic halo and in globular clusters in our galaxy and can be seen in other nearby galaxies. RR Lyrae are bright (around 0 absolute magnitude) A to F blue giants and are interesting to study because they have a short (0.3 to 0.7- day) regular period with an amplitude of 1 to 2 magnitudes. They reveal much about the structure of the galaxy and stellar evolution.
R Coronae, T Tauri and RW Aurigae are examples of eruptive variables that can be studied by imaging over a long period of time using the same method as for the Lyrae and Cepheids. These stars, however, undergo sudden, rapid and erratic changes and consequently are not as easy to plot. Catching one changing several magnitudes in brightness over a few days time is a dramatic event.
Eclipsing binaries and cataclysmic variables represent other interesting stars of varying light. As the name implies, eclipsing binaries are two associated stars rotating about each other such that they eclipse each other during each cycle. There are more than two hundred eclipsing binaries with well determined orbits with periods of a few days. beta-Persei (Algol) is the classic example with a period of 2.87 days. Others are U Cephei, lambda-Tauri, and beta-Lyrae. In addition, there are several thousand eclipsing binaries that could be studied to refine the orbital information. Cataclysmic variables are degenerate hot dwarfs, the end products of evolution of moderate to small-mass stars paired in a close binary system with a mass-losing cooler red star. The mass of the red star is transferred to the blue dwarf with variable rates of interaction leading to instabilities and eruptive events in some cases so violent as to constitute a nova. T Coronae Borealis is one example of a red giant companion that results in a recurring nova.
Discussion of Work
Select an example Cepheid variable star above 30° in the east. Delta-Cephei, the namesake star, has a period of 5 days and is a good start for variable observation from July to October. Take images using the V filter at the beginning and end of each session over an interval of twice the star's period in days. For example, take as many nights as possible during 10 days in the case of delta-Cephei. Record the precise mid-exposure time (see Note 1). Plot the resulting magnitudes versus days. Determine two or more maximums. The time between two adjacent maximums is the period of the variable. If the time between two observed maximums is greater than one period, the measured time interval must be divided by the number of included cycles. This can be accomplished by dividing the observed time interval by the period found in the literature and rounding the resulting number to the nearest whole number, i.e. number of included cycles. Compare your measured result with the published value. Note that if your calculated number of cycles turns out to be 1.5, 2.5 or 3.5, for example, you have an aliasing problem. You can try rounding the number to the higher and lower values and see which more closely matches the literature value, but a better way would be to repeat the observations at more frequent intervals to catch two adjacent maximums.
Next, select an example of an RR Lyrae star. The period of an RR Lyrae can be determined best by scheduling two consecutive nights and taking an image of the selected star(s) every half hour through a V filter. Record the precise time of the mid-exposure ( Note 1). Plot the resulting magnitudes versus time in days.
Students should select at least one of the R Coronae, T Tauri or RW Auriga examples of eruptive variable stars in the eastern part of the sky to follow during a semester of observing. If a change of magnitude is noted, try to increase the frequency of observations. Plot the data obtained and determine the period if possible. Of course, novae and supernovae are the most dramatic examples of eruptive variables but these cannot be predicted. If the student is so fortunate to discover a new one, he or she will achieve immediate fame.
Finally, students can select various eclipsing binaries and cataclysmic variables. As above, determine the light curve for each and report any anomalous behavior.
Note 1. Accurate time is essential for good astronomy. One method of obtaining precise time is to tune a short wave radio to WWV at 5, 10 or 15 kHz and record the time the light frame starts. To that time add one-half of the exposure time to obtain the mid-exposure time. Try to get this point to within one or two seconds accuracy. Record the results in Universal Time (UT) or convert to Julian Days which is used by astronomers. Another method of obtaining accurate time is to set the computer clock at the beginning of each session by dialing the NIST number in TheSky under Tools, Date and Time, Time Service. The program will automatically dial the number and reset the clock. Finally, Seiko makes an inexpensive wrist watch that updates itself 36 times a day to "atomic clock accuracy" via FM sub-carrier frequencies. This may not be available in all locations. In any event, try not to rely on the local telephone time service which in some areas can be several seconds off.
References
Any
good textbook of astronomy
AAVSO publications
The Astronomical Almanac, pub. annually by Naval Observatory and Royal Greenwich
Obs.
Observer's Handbook, pub. annually by the Royal Astronomical Society of Canada
General Catalog of Variable Stars and the New Catalog of Suspected Variable
Stars; the best source for these two works is via the Internet at:
http://adc.gsfc.nasa.gov
(look for catalogs 2139B & 2140 within this site)
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