## Phase Diagrams

When the same cycle repeats over and over, it is referred to as periodic behavior but not all variable stars are periodic. If the variable star is periodic and you want to know what is happening at any moment during a cycle, it doesn't matter which cycle you're observing because every cycle is exactly the same. What does matter is which part of the cycle you're observing. So if a star is strictly periodic, then its variation depends only on where it is in its cycle, a quantity called phase.

Phase is measured in cycles and because phase is measured in cycles, a single cycle starts at 0 and ends at 1. A phase of 0.5 corresponds to 50% through the cycle. A phase of 0.2 corresponds to 20% through the cycle and a phase of 1 corresponds to 100% through the cycle. After a cycle has reached 100% of its phase it begins anew.

To compute the phase in terms of cycles, you need to know the length of each cycle in seconds, minutes, hours, or days. In other words you need to know the period. In this book, to compute the period of a variable you'll use the computer program TS11. We'll discuss TS11 in a few moments. I'll tell you were to get a free copy and you can begin using it immediately.

To compute the phase in terms of cycles you also need to know the starting time of the cycle, called the epoch. These may be new terms to you but don't let them intimidate you. You'll be using them often so they will become familiar in a short time.

These two quantities, the period and the epoch, will enable you to compute the phase at any given time.

Suppose the epoch is at f0 (time at zero) and the period is P and you wish to calculate the phase at some time t. First we find how far we are into the cycle, by simply subtracting the starting time:

For example, if t0 is JD 4500 and t is JD 4600, you are 100 days into the cycle. To calculate the phase in units of cycles, you simply divide this quantity (f - t0) by the period:

The symbol <j> is the Greek letter phi and it is used to represent the phase, in cycles. Let's say the period is 500 days. If you divide 100 by 500 you will see that we are 20% into the cycle or at phase 0.2. When you compute a phase, you're interested in what is called a standard phase. To calculate the standard phase, you're going to need to know the period of the variable star.

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