This activity is in chapter 12 of the HOA manual and follows a discussion about variable stars and phase diagrams.

Folded Light Curve of the Variable Star SV Vul

You are now ready to construct a folded light curve, or phase diagram, using the observations of a Cepheid variable given in the following table.

 Julian Date    Magnitude  Julian Date	Magnitude
2447011.6	7.0	2447458.5	6.9
2447023.6	7.5	2447475.5	7.8
2447040.6	7.9	2447492.5	7.9
2447066.5	7.4	2447505.5	7.2
2447091.4	7.0	2447529.5	7.9
2447103.6	7.2	2447707.6	7.9
2447124.6	7.8	2447722.6	6.7
2447171.5	7.9	2447747.6	7.8
2447308.6	7.9	2447769.5	6.8
2447338.6	7.8	2447778.5	7.1
2447374.6	7.0	2447800.5	7.9
2447390.6	7.9	2447821.6	7.0
2447404.5	7.8	2447832.5	7.5
2447413.5	6.8	2447848.5	7.9
2447421.5	7.2	2447857.4	6.8
2447444.5	7.9	2447868.5	7.2

1. Construct a graph with the magnitude on the vertical axis and phase on the horizontal axis. Determine the appropriate magnitude scale from the data in Table 12.1. Since all standard phases are between 0 and 1, choose a scale for the phase axis which goes from 0 to 1.

2. We defined the phase as the decimal part of , where t₀ is the epoch and P is the period. Take the JD of the very first observation as the epoch, so t₀ = 2447011.6. Then the first observation occurs at the start of the cycle (we chose our epoch that way), so we already know the phase of the first observation: it is at phase 0 (start of the cycle). The magnitude of the first observation is 7.0, so plot a point on your graph at phase 0 and magnitude 7.0.

3. For all the other observations, we apply our formula for computing phase. First we take the time of the observation and subtract the epoch time t₀. For the 2nd data point, this gives

     2447023.6 (time of observation t)
   - 2447011.6 (time of epoch t₀)
             12.0 (time difference)

   Then we divide by the period P. For SV Vul, the period is P = 44.8 days. This gives

   12.0 / 44.8 = 0.2679

   Then we take the decimal part of what we get. Since this result is already between 0 and 1, it is already a standard phase. So for observation #2, the phase turns out to be 0.2679. For plotting purposes, we can round this off to 0.27.

   Repeat this process for every data point, computing the standard phase. When you have computed all the phases, plot each data point at the correct phase and magnitude.

4. Draw a smooth curve showing the trend of the data. Do most of the data lie near this smooth curve? This is a test of the period. Lots of scatter with no obvious trend would show that the measured period is not correct. The correct period should produce a phase diagram whose scatter is about the same as the scatter in the raw data (usually about 0.2 magnitude).