Variable stars are stars which vary in brightness. Stars vary in brightness because of pulsations, because of eruptions, or because of geometric factors such as eclipses in a binary star system. Observations of this brightness variation may be used to determine the type of variable star. There are more than a dozen different types of variable stars. Some stars are periodic with periods ranging from several hours to several decades. If a variable is periodic, a precise determination of the period may be exceedingly important since the period may be directly related to the luminosity (energy output, or intrinsic brightness), or may be used to infer the masses of components of eclipsing binary systems. Some variables, however, have no well defined periods. The amplitude of the light variation can be as small as a few tenths or hundredths of a magnitude, or can be as large as 18 or 20 magnitudes. As a general rule, the greater the amplitude, the longer the period. It turns out that variable stars are often stars in very special phases of their evolution.
Estimates of the brightness of variable stars (or of non-variable stars) are always made with respect to the brightness of nearby comparison stars. A very simple method requires the availability of a bright and a faint comparison star. Ideally, the bright star should be as bright or slightly brighter than the brightest level reached by the variable while the faint star should be as faint or slightly fainter than the faint limit of the variable. Brightness estimates may be made in terms of the brightness of these two comparison stars. For example, if the brightness of the bright star is called "A" and the brightness of the faint star is called "E", then the brightness of the variable may be rated as A, B, C, D, or E. As your eye gains experience it is even possible to use intermediate ratings such as AB, CD, etc. It is exceedingly helpful if you can find examples of nearby (presumably constant) stars which have brightnesses equivalent to some of the intermediate ratings such as B, C, or CD, etc. These stars may then serve as secondary standards.
The star delta Cephei has been determined to vary in brightness. By means of visual observations we will determine the nature of this variation. We may determine the class of variable star to which delta Cephei belongs, and if its variation is periodic, we may determine the period.
Delta Cephei may be easily located by means of a small isosceles triangle between Deneb (alpha Cygnus, or alpha Cyg) and Cassiopela. The base of the triangle is formed by zeta Cephei and epsilon Cephei. The vertex, delta Cephei, points toward Cassiopeia. Zeta and epsilon represent the approximate limits within which the brightness of delta Cephei is believed to vary. Brightness ratings for delta should be estimated with respect to epsilon (as the brightest) and zeta (as the dimmest). The magnitude of epsilon is called "A" and that of zeta is called "E" so magnitude estimates for delta may range over the scale A, B, C, D, E. Intermediate estimates such as AB or DE are, of course, also possible.
Algol is normally the second brightest star in the constellation of Perseus. It was termed Algol (the daemon star) by the Arabs because it reportedly dimmed in brightness occasionally. Perseus lies between Taurus and the Pleiades and the constellation of Cassiopeia. Perseus is on the opposite side of Cassiopeia from Cepheus and may generally be seen as two chains of stars which are joined in the form of a rough "V" shape. Mirfak (alpha Per) is the brightest star in the constellation and is located near where the two chains appear to join. The "V" points toward Cassiopeia. Algol is nearly at the end of the chain which is closest to Andromeda and Pegasus. epsilon Per is roughly the third brightest star in Perseus and is nearly in the middle of the chain that points directly toward the Pleiades. For the purposes of brightness measurements we will use Mirfak as the A star and epsilon Per as the E star. Note that these three stars (Algol, Mirfak, and epsilon Per) form a triangle that is much larger than the delta Cep triangle.
Observations should be made once a night whenever the program objects and their comparison objects are visible. Observations may be made from any location. Each observation should consist of the date, time (nearest five minutes), brightness class (A-E), and the comparative certainty of the estimate in relation to the observing conditions (clear, hazy, fog, moon, etc.). Record your observations in your notebook and keep a running plot of your results.
Your goal should be to accumulate approximately forty (40) observations before the last class meeting. Note that this corresponds to an average of about three observations each week. Because of weather conditions, some weeks will need to have more observations than other weeks. Try to obtain at least one run of observations on 5-7 consecutive nights. Occasionally, you might even try to obtain more than one observation on the same night. If you detect a significant variation from one night to the next you should try to obtain a series of observations separated by about 30 minutes. This will enable you to search for short-term variations OR to document the consistancy of your observations.