PHYS 3154 Observational Astrophysics J. H. Simonetti jsimonetti@vt.edu

Simple "How To" for Period04

Period04 is the Delta Scuti Network's free program for analyzing variable star light curves that will run in Windows. Specifically, Period04 enables searching for periods in your light curves. Since Period04 will run in Windows you can print out spectra, etc., as in most such programs, which can be handy (e.g., for papers!).

The tutorial (tutorial1.pdf) that comes with the software is an excellent guide for using Period04. The tutorial is simple to follow.

For those unfamiliar with Fourier analysis, the following comments might be useful:

• Fourier analysis is a search for the sinsusoidal functions that, when combined, approximate the observed light curve. One can specify the functions by specifying their period, amplitude, and phase (or starting point). Instead of period, one can use frequency (frequency = 1 over the period). The Fourier spectrum shows the "power" (squared amplitude) at each frequency for each possible sinusoidal component in the light curve. The spectrum can be messy, but a simple approach to interpreting it is to determine and remove one dominant component at a time from the light curve, then repeating the Fourier analysis, until you think you understand how many "important" frequencies (periods) are present.
• You need to prepare a two column data file containing times (or decimal dates, or JD) in one column, and magnitude in the other.
• Start Period04, and load your data. The tutorial suggests that a quick visual look at your light curve is useful before you actually run the Fourier part of Period04. This is indeed true, otherwise you might be misled by the Fourier results. Try estimating the dominant period of oscillation in the light curve (is it 0.5 days, or 2.3 hours, or what?). Make your estimate in the units of time (hours, or days, or...) that you use in your data file. Say that period is T. Calculate 1/T, the frequency corresponding to this dominant period. You should expect a peak in the Fourier spectrum near or at this frequency.
• Also estimate the time between samples in your light curve. Did you obtain a data point every 5 minutes, or 2.3 days, or what? The smallest period sin wave that you can successfully measure in your light curve will have a period of twice your sampling timescale. If you obtained data points every 5 minutes, the shortest period sin wave you can accurately determine is 10 minutes. Shorter period oscillations will not be well determined. (This is the so-called Nyquist Theorem.) If this time between data points is t, then the Nyquist frequency is 1/2t. The tutorial mentions the Nyquist frequency, and Period04 determines the Nyquist frequency for your light curve. Period04 suggests you cut off the Fourier analysis calculation at the Nyquist frequency --- a good suggestion.
• With your estimate of the dominant period present in your data, and your Nyquist frequency, you should be able to understand how to apply Period04 to your data, as you follow tutorial1.pdf.
• Note that the "Sampling Window" result first obtained in the tutorial is NOT the true Fourier spectrum result for the star. Instead this result is meant to indicate how you might be misled by the uneven sampling present in your data (e.g., missing days). If you have estimated the dominant period as discussed above, you will not be misled. Furthermore, the Sampling Window result can be useful in indicating to you what peaks in the Fourier spectrum for your data are artifacts of your sampling. For example, if you have data for only every other day, then a period of 2 days (frequency of 0.5 cycles per day) will have a relatively high peak in the spectrum, but this is not a result of the star varying on a 2 day period! Instead, it's comes about because a sine wave with a 2-day period will have a maximum landing on the existing data points taken every other day, and a minimum landing on the days when there are no data! Furthermore, these observations will also produce peaks in the spectrum at frequencies of 2*0.5, 3*0.5, 4*0.5, etc., cycles per day, since sine waves with those frequencies will also have maxima on the existing data points and minima on the moments when there are no data points. (The appearance of more than one peak for such a situation is called "aliasing" and is also mentioned in the tutorial.)

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