AAVSO: Photoelectric Photometry Newsletter Volume 20, No. 1

(O-C) analysis is used to refine the periods of variable stars, or to detect and measure period changes in these stars. It uses times of maximum or minimum brightness, obtained over long periods of time. The observed time (O) is compared with the calculated (C) time, using the assumed constant known period. If the actual period is constant, and equal to the assumed period, then (O-C) will always be zero --- give or take the error of measuring the time of maximum. If the actual period is constant, but greater or less than the assumed period, then a plot of (O-C) against time will be a straight line. The correction to the assumed period can be found from the slope of the line. If the actual period is changing linearly with time, then a plot of (O-C) against time will be a parabola. The magnitude and direction of the period change can be found from the coefficient of t² of the parabola.

A good analogy is with a clock. Imagine three clocks: #1 keeps perfect time; #2 ticks at a constant rate, but is one second slow; #3 is running slower by 1 second a day. The analogy is with a star (#1) which has a constant period which is known correctly, a star (#2) which has a constant period but which is not known correctly, and a star (#3) whose period is gradually slowing down.

If we compare clock #2 with clock #1, it will be wrong by 1 second on day 1, by 1 + 1 = 2 seconds on day 2, by 2 + 1 = 3 seconds on day 3, by 3 + 1 = 4 seconds on day 4 etc. The error ("O-C") increases linearly with time.

If we compare clock #3 with clock #1, it will be right on day 1, wrong by 1 second on day 2, by 1 + 2 = 3 seconds on day 3, by 3 + 3 = 6 seconds on day 4, by 6 + 4 = 10 seconds on day 5, by 10 + 5 = 15 seconds on day 6 etc. The error ("O-C") increases as the square of the elapsed time. Because of this, small changes in the period of a variable star can be measured if the star is observed over a long period of time. Astronomers' ability to measure these period changes is proportional to the square of the time over which we measure it. The period change may reflect the evolution of the star, and (especially in the case of eclipsing variables) mass loss from the star.

Since AAVSO observers have monitored stars over many years, or decades, they have played an important part in understanding period changes in variable stars.

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