I was traveling with past PAS president Don Ware to a photometry symposium at Yerkes Observatory. During the drive, he made a comment that has always stuck with me. He said, "Astronomy is the only science where amateurs can make a contribution in many different areas." Examples include astrometry of solar system objects, occultations, meteor observations, solar observations, comet hunting, searching for novae, and variable star astronomy.

Amateurs can and do make useful observations of variable stars. It is easy for amateurs to maintain an observation program which can last many years. Observations of binary systems are used to detect period changes and used to update ephemeris. Ground-based data is also needed to support orbiting satellites. Amateurs are often solicited to participate in campaigns to monitor a star’s behavior. Once it changes, the satellite will slew to the star and begin its observing run.

A VERY SHORT HISTORY OF BRIGHTNESS

The history of magnitude estimation originates with Hipparchus of Greece. About 200 BC, he catalogued the positions and proposed a brightness scale for more than 1,000 stars. Nearly 400 years later, Ptolemy incorporated that scale, six for the faintest star and one for the brightest star, in his model of the universe. The brightness scale continued well after the Ptolemaic model of the universe was replaced by the Copernican Theory.

In the 1800s, natural philosophy of the period proposed that all human senses reacted logarithmically in their response to stimuli. In 1856, Norman Pogson proposed the brightness scale we used today. He proposed that a difference of five magnitudes equal a ratio of 100 to one. One magnitude difference is the fifth root of 100 (or 2.512) and the log of this number is 0.4, which was convenient, as all data reduction used logarithms.

NAMING CONVENTION

In 1844, there were 14 stars known to be variable. Argelander believed that variability was a rare phenomenon. He believed that no one would ever discover more than nine variables in any constellation. He proposed the naming convention of assigning the capital letters R through Z to variables within a respective constellation. This was the first list.

As more variables were discovered, the list was expanded by doubling the capital letters; RR...RZ, SS...SZ, etc. Once this series was filled, the list resumed at the beginning of the alphabet, AA...AZ, and so on. The letter J was excluded and there could be no inversion of letters, i.e., AB but no BA. This convention covered the first 334 variables in a constellation. Sagittarius was the first constellation to exceed this number. The convention then continued with variable V335.

THE MEANING OF VARIABILITY

Stars evolve over very long periods of time and can exhibit variability at extreme wavelengths. The general definition of variability is; the period of variability is within a period of decades, variability is observed in the optical region of the spectrum (later extended to the near infrared), and the variability should have an amplitude perceptible to the human eye, 0.2-0.3 magnitudes.

The light that is measured is a function of the receptor. The magnitude seen with the eye, designated as M_V, is the brightness estimate at about 540 nanometers. This same star can have a different magnitude derived using photographic plates, M_PG, which are sensitive to light at 430 nanometers, i.e., toward the blue end of the spectrum. The difference between these two measures of brightness, M_PG - M_V, is referred to as the color index.

OBSERVING

When making a brightness estimate, the recommendation is to use a telescope with just enough aperture. Generally, estimates are more accurate when within two to four magnitudes of the limit of the telescope. The telescope threshold can be calculated using the simple equation, M = 8.8 + 5 Log D. A pair of 50 mm binoculars (D is almost two inches) should see stars to magnitude 10.3. Simple binoculars can be used for many bright variable stars.

Begin the evening with charts in hand. After finding the program star, place it and the comparison stars into the center of the field of view. When identification is made, take the stars out of focus. This is done because it is easier to estimate the brightness of disks. The estimate can be made using common and easy "fractional technique."

This method simply involves selecting two comparison stars, one brighter and one fainter than the program star. The program star is estimated as a fractional difference between the two stars. The trick is to keep your eyes moving back and forth constantly reviewing the estimates. The resulting fractional amount can be applied to the difference in the known magnitude of the two stars to derive the brightness of the program star.

Recorded observations generally include; 1) the date, 2) the time, 3) name of the variable star, 4) the estimate, brighter comparison star with fractional difference of the variable and the fainter comparison star, 5) the reduced magnitude estimates of the variable, 6) the instrument used, and 7) a note of the observing conditions.

The date and time need to be transposed to the Julian Calendar for data reduction. After several months or a season of observing the data can be reduced. A scatter plot of the data, magnitude plotted against time, should begin to form a "light curve." Ideally, there should be a dense number of data points during the observation period. With a large amplitude star, two and more magnitudes, the estimated observation errors should be small in proportion to the total variation.

Much more has been written about variable stars. There are numerous resources on the Internet. Charts and other information can be found at the American Association of Variable Star Observers. Their address is   <www.aavso.org>. VSNET, <www.kuastro.kyoto-u.ac.ip/vsnet>, is a site maintained by the University of Kyoto in Japan. In Europe, <thola.de/bav.html> is a German Variable Star site with many other informative links.

Lesson Two: Star Trail Photography by Eric Clifton