National Aeronautics and Space Administration

Educators' Corner

Power Spectrum

In the previous exercises you analyzed the light curve data of the source using the method of folding to find the best period. You then verified this period by looking at the folded light curve. Another method of finding the period of a source is to look at its power spectrum. The power spectrum is a plot of how much power there is at each frequency. It is generated using a mathematical procedure (Fourier Transform) that takes a signal (brightness as a function of time, or lightcurve) and turns it into a frequency spectrum (how much power at each frequency). This technique is like using an equalizer to find what frequencies are present in a piece of music. For a periodic source, the power spectrum will show a peak at the best frequency (the inverse of the period), and perhaps several other smaller peaks at other frequencies (there may be more than one periodicity in a source).

To find the power spectrum of GX301-2, click on the data set in the Student Hera GUI and select Power Spectrum from the list of XRONOS tools. Click on the "run" button, and you will see a parameter box with the file name and directory filled in. You will need to assign values to the parameters Newbin Time or negative rebinning, Number of Newbins/Interval and Number of Intervals/Frame. You can reuse the values you used when running File Plot or Epoch Fold for these parameters, as a first start. The resulting plot will show a peak at the strongest frequency, as well as smaller peaks at secondary frequencies.

To get rid of the error bars, type "error off" at the PLT> prompt in the powspec Output window, then "p" (to replot). For more detailed description and help with basic plotting commands, go to Plotting Basics.

Exercise E2 Generate and print out a power spectrum for the source GX301-2. Estimate the primary frequency of the source. This corresponds to the orbital period of the system. You may need to rescale the box (zoom in on the peak frequency) in order to get a good estimate. To do this, type "r x xmin xmax" (where xmin and xmax are the minimum and maximum values you want to be plotted. These can be written in exponential form as 6e-2, for 0.06, for example) at the PLT> prompt in the Output window. If the peak frequency is too wide for a good estimate, you can narrow in on it by increasing the value for the parameter Newbins/Interval and running Power Spectrum again. Then rescale the box to zoom in on the peak frequency and get a good estimated value. Print out this plot as well. How does this period compare with the one you found using Search with Fold? (To get the period, you will need to invert the frequency and then convert the result into days (from seconds)) If there are significant differences, can you explain what might cause them?

Because there may be many frequencies present in a signal, Power Spectrum can yield more complicated results than Search with Fold (notice that this tool does not output a numerical value for the "best frequency" for example). It can be very useful for producing complimentary information on a source, however.