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Primary eclipse of AB And

Best Observing Season: any Level: Advanced Learning Goals: The student will find observe the minimum of an eclipsing binary star. Terminology: contact binary, egress, ingress, photometry, polarimetry, spectroscopy Software: MaxIm, Megastar, Photom, a graphing program Archive Image Directory: varstars/eclbin  Archive Image List: ab-and*.fts, ww_cyg*.fts References: Levy, David. 1989, Observing Variable Stars (University Press, Cambridge); the AAVSO homepage (http://www.aavso.org ); The Astronomical Almanac

 

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Background and Theory

One of the most useful scientific research projects suitable for small telescopes equipped with CCD cameras or high quality photometers is monitoring period changes in short-period binaries. Many such binaries are bright (V<12), have orbital periods less than one day and have deep eclipse minima (DV>0.1), making them easy targets for modestly equipped observatories. The scientific goals of eclipse timing observations are (a) to determine the period with high accuracy so that observers using non-photometric instruments (e.g. radio, spectroscopic, polarimetric) can predict eclipses with high accuracy, and (b) to detect changes in the period which might be caused by physical changes in the system, e.g. mass transfer.

A particularly interesting class of eclipsing binaries is the W Ursa-Majoris or contact binary. Contact binaries are so close that they are ‘touching’, i.e. there is a common mass envelope [1] which looks like a distended egg. These systems typically have orbital periods of a few hours and have light curves which are continuously variable. The periods tend to be stable, but because there can be significant mass transfer between the components, there are often small period changes. By carefully measuring the time of primary eclipse and comparing with previously observations over several decades, fractional period changes as small as ~10^-8 can be measured. Many of the known systems are bright (V<12) so that it is easy to make accurate photometric measurements with a modest telescope.

Note: Portions of this lab will require Photom, which you may not be familiar with.  Consult Appendix C and with your instructor for details on using this program.

Procedure

Observing

1.      Determine an appropriate range of right ascensions and declinations for the observing date(s) available to you using a sky display program.  Choose a suitable contact binary system either from the AAVSO table included here or from a literature reference.

2.      Use a sky display program (e.g. Megastar or Starry Night) to find a bright (V<10) reference star and at least one check star in the same field of view [2] as the contact binary.

3.      Determine the expected time of primary eclipse using the following formula.

where JD_min is the expected Julian date of primary eclipse, JD₀ is the reference Julian date from the Table, P is the period, and E is the number of cycles from the reference date. To find the approximate number of cycles, determine the Julian dates (including time of day) for the start of the desired observing period [3] and solve for E (which will not be an integer). Then set E to the next largest integer and solve for  JD_min

Here’s an example of the above calculation. Let’s suppose we want to plan an observation of the binary AB And on the night of Oct 28/29, 1995. The beginning of the evening (6pm CST) corresponds to 0^h UT on 29 Oct or JD 2,450,019.5 (Julian date starts at 12 noon UT). The JD reference date for AB And is JD = 2,436,109.5793 and the period is  0.33189215^d. Hence E=41,910.967 at 0^h UT so we round up to 41,911. This predicts a minimum at JD 2,450,019.511 (0^h16^m UT) which is still dusk. The next minimum occurs one period later at E=41,912 or JD 2,450,019.843 (8^h14^m UT) which is 2^h14^m CST - nicely dark.

4.      Observe the field containing the target, calibration, and check stars once every 2 minutes for about three hours centered on the expected time of eclipse. Be careful that the exposure time and filter are chosen so that all three stars have good signal-to-noise ratios but that none are saturated. The filter choice is not important (the time of minimum does not depend on color) but filter R will probably give the best signal-to-noise ratio. The way to schedule this type of observation is to use a repeat keyword and a beginning local sidereal time.  Use the Observing Schedule Input Form on the web.

Image Analysis

1.      Run Megastar.  Create a finding chart of the field around the variable star that you observed.  Locate the variable star.  Print this finding chart for future reference.  This chart will be easier to use if you change the field size to be the same as the field of view of the telescope (about 21 arcminutes for the IRO), and make the magnitude range equal to the magnitude range that you can observe with the telescope you are using (Consult Appendix A to check brightness versus exposure time for the IRO). Do this for all of the stars you observed (including the standard stars).

2.      Run MaxIm.  Locate the calibrator star and check stars that you chose in the image by comparing the field of the image to your finding chart.  Record the R.A.’s and Dec’s of all your stars.

3.      Start the program ATFTools, and enter the names of the working copies of your images in the image list.  To do this, click on File, then Set Input Images..., then choose your working files.  To choose multiple files, click on the name of one file, then hold down the Ctrl key and click on each of the others.

4.      The easiest way to perform photometry on a large set of images is to use Photom (part of ATFTools).  This program performs differential photometry on all of the images, comparing the variable and check stars to a calibrator star, whose magnitude is arbitrarily set to zero.  Differential photometry is done by first making a circle around a star (or asteroid or other (small) bright object) and adding up all of the ADU counts within that circle.  The sky background brightness is subtracted from this total, and the resulting ADU counts are set equal to a magnitude (in this case zero).  The magnitudes of other stars in the field are determined relative to this star by comparing ADU counts.  One problem with this method is that it is possible to choose a variable star as your comparison star.  If this is the case, then the calibrator star’s variability will contaminate the results.  To eliminate this possibility, at least two check stars are chosen, and analyzed in the same way as the variable star.  These check stars should show zero variability with time.  If these stars show variability, a new set of calibrator and check stars are chosen, and the photometry repeated.  Fortunately, in Photom, the whole process is automated, and you do not need to do all of the arithmetic by hand.

5.      Click on the Photom icon, or choose it from the menu.  (Note: Photom and Fphotom are not the same thing!)  Fill in the target object boxes, and the calibrator and check star boxes.  Pick aperture photometry parameters (the defaults are usually fine).  Make sure that the Run Now option is enabled.  Click on Ok when you are finished.  This runs Photom on your image list.

6.      After running Photom, the resulting text file can be imported into a scientific spreadsheet program (e.g. Axum, Graphical Analysis) and the data plotted.  You may need to strip out excess information from the file. Make a plot of your target (variable) star’s magnitude versus Julian Date.  Also make a plot of each of your check stars versus Julian Date.  All of the plots of your check stars should be very constant with time.  Be sure to include the error bars.  The magnitudes of the errors are given in the Photom output file.  A sample plot of an eclipsing binary is shown below.

7.      Finally, to form an accurate estimate of the time of minimum, you can ‘fold’ the ingress portion of the light curve on the egress portion to find the bisector which minimizes the difference. This can be (crudely) done by folding the graph paper over and reading the JD of the fold, but more elegantly by using MathCAD. Ask the lab instructor for details.

 Table1: AAVSO list of eclipsing binaries