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Equipment Description
Eclipsing Binaries
The study and measurement of Eclipsing Binaries is another area where
amateurs with CCD equipment can make useful contributions. Eclipsing
binaries are variable stars that dim and brighten on more-or-less regular
schedules due to one star passing in front of another as the two orbit
one another. A famous, but somewhat difficult to observe (due to its slow decline and
subsequent rise) eclipsing binary is the "A" star in Orion's Trapezium. The
'movie' below shows the change that occurs in this popular asterism between
full-light and light at mid-eclipse (about one magnitude change).
An amateur can do very good work with eclipsing binaries without all the fuss and bother of
filters and complex calibrations. You can do good work even with a bright moon
or light clouds in the sky! A very good tutorial is available at the USNO. You are mostly doing
differential photometry where you compare the brightness of the variable
star to two others within the same CCD frame. The CCDOPS camera control software
that comes with the SBIG cameras has a function that allows the user to
measure the relative brightnesses of stars in an image and I assume other
camera control software is similar or you can get one of the commercial products
that will allow you to do so. JIMSAIP is a free DOS
download that will permit you measure many types of images if your video card is
VESA compliant.
To get a good TOM (time of minimum), you need to measure a good portion of both the descending
and the ascending legs of the light curve on either side of the minimum. Some
eclipses are longer than others, so you need to do a little planning to be sure
you start soon enough. Hopefully, you can monitor your data as you go along so
you can tell if you have gotten enough data on the ascending side. This is important
as TOMs can be both earlier and later than predicted. Of course, this is really
what you are looking for, as large O-Cs (observed - calculated times) indicate that
the epoch and/or period of the eclipsing binary need to be adjusted. I've just started
as of this writing (July 1998) and have already encountered a TOM 1hr 16m late.
It helps a great deal if you have some idea of the predicted minimum of your selected
binary star. The American Association of Variable Star Observers
(AAVSO) can provide you with lists of variables they are monitoring which will
include the epoch (a particular TOM) and the period, both in Julian Days. It is a simple
matter to add an integer number of periods to the epoch to get a predicted minimum
near your current calendar date. It is a little more difficult to decide if the eclipse
will be visible from your location at the indicated time. I have written a free utility
(DOS) which can be downloaded here (36 kB) that will read data for as
many variables as you like from an ascii file, calculate the TOMs, decide which are visible
from your location (based upon your criteria of sun angle (presumably negative) and elevation
of the variable at the TOM), then sort the results by increasing date. Thus, you get
a calendar of dates that show you which of your program stars are undergoing visible eclipses
and when. A short sample is
--------CDT-------------
JD Name DATE TIME ELEV
50995.793 SW CYG 1JUL 1998 2: 1: 53 58.7
50999.75 V346 CYG 5JUL 1998 1: 0: 10 58.3
50999.772 RW CAP 5JUL 1998 1: 31: 25 49.8
51001.602 SX OPH 6JUL 1998 21: 26: 28 59.2
51001.634 SS LIB 6JUL 1998 22: 13: 28 57.3
51003.665 SX OPH 8JUL 1998 22: 57: 37 65.6
To take the data, you decide when to start and then take images every 5 minutes or so for as
long as it takes to get both sides of the eclipse. You also must decide how long an exposure
to use. It is a good idea to expose sufficiently such that the variable and the comparison stars
are about half-way up the full-well depth of your CCD pixels to keep the S/N high for better
accuracy. Allow a few minutes before your planned start of data collection to determine a good
exposure level. With the ST-7, I use the auto-grab feature with auto-dark subtraction. This
will take the pre-determined exposure (typically 10-30 seconds) at the intervals selected
(typically 5 or 6 minutes) for as long as desired, automatically saving the images to disk.
I find enough time between images to measure each image and to record the values in my observing
log along with the time of the exposure (it is a good idea to set your computer clock precisely
to a correct time signal before you start - I find that my computer clock will maintain at least
a second accuracy over three or four hours, but you should check your computer in case you have to
work in a correction factor). I just run another copy of CCDOPS in another Win95
window to do the processing while the copy that is running the camera keeps the timer going to
get the images at the right time. I (naturally enough) measure the
brightness of the variable and two nearby comparison stars that are about the same brightness as
the variable, remembering that the variable will dim during the eclipse. It is simple and quick
to use a handheld calculator to calculate .5*(comp1 + comp2) - variable to follow the progress of
the eclipse. Using the formula this way (the negative of the formula in the tutorial mentioned
above) will cause the data points to get smaller as the eclipse progresses which is a more natural
way (for me, at least) to view the data. This can be important if the TOM is significantly
different from the predicted value. It can be very frustrating to miss a relatively rare eclipse
because you quit too soon!
Post-processing consists of entering the data points in a spreadsheet set up to convert the date,
hour, minute, and second to JD (adding 1/2 the exposure time to the time of the exposure which, for
the SBIG cameras is recorded for the START of the exposure), the above-mentioned
.5*(comp1 + comp2) - variable, and (comp1 - comp2). This last gives you an idea of your overall
quality as the average value of (comp1-comp2) for the session can easily be .01 mags. Using the
plot functions of the spreadsheet gives you a nice pictorial representation of the data. See
the example curves for SZ HER, SZ HER(2),
V836 CYG, V346 CYG, ER ORI.
Getting the TOM from such curves is relatively easy as there is a program circulating among
AAVSO participants based upon a method described by Kwee and Van Woerden. You can
download (32k) here a program I am told is freeware (I didn't write
it) which you can use at your own risk. I have been using it to get the TOMs I send in
to the AAVSO though with no apparent problems. You can send your timings to Marvin Baldwin
of the AAVSO at mbald00@hsonline.net. Be sure to include your name, email or snail mail address,
that your measurements are CCD-based, the TOM and number of data points (from the Kwee program
output), how you determined the TOM (Kwee or other), and whether your TOM is heliocentric
or geocentric (recommended). You can get more info from the American Association of Variable Star Observers
(AAVSO).