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The Light Curve Viewer provides a graphical preview of user-submitted time series data before they're processed and displayed as a periodogram. This step provides the user an opportunity to view the light curve prior to sending it to the Periodogram Service. Users have the opportunity to send the light curve data to the Periodogram Service from the Light Curve Viewer results page.
There are a few controls to manipulate the scale and scope of the image on the left:
If a header row is not provided in the source file, the Light Curve Viewer Service assumes the first column is for time, and the second column is data. If this is incorrect, you can replot the light curve by selecting the correct data types from the drop-down menus above the plot, and then press Replot.
The following examples demonstrate how to use the Periodogram Service's interactive functionality to change the type of algorithm used and other parameters. Note that you can get more information about a specific parameter by clicking on its name from the periodogram results page. A detailed discussion of the parameters is also available
Occasionally, a periodogram will require a significant processing time. These periodograms will automatically go into background processing mode. If this occurs, you will see a message similar to this:
No action is required if you wish to continue. To cancel the search, click the Abort button.
Directly under the periodogram on the Periodogram Viewer page is a table of the Most Significant Periods for the submitted data. To save the table contents locally to your machine, click the Download button to view the content in IPAC ASCII Table format and then copy and paste the page into an ASCII text file.
The Constraints Range area of the Periodogram Viewer page is hidden by default. Click the Show link to display these options.
You may specify minimum and maximum constraints for the time and data columns, as well as a third constraint. For example, you may want to place a constraint on the time range, or a constraint on the flux range. Or, you may want to constrain the data to return only good-quality data as may be indicated by a status flag for each data point, or to only include data with small uncertainty values.
Previously entered values are displayed in the column on the right.
Periodogram results can be plotted in either linear or log views, depending on your preference and requirements for the specific set of data. To switch views, click the corresponding radio button directly above the plot on the results page.
The periodogram can be a very powerful tool for automating the identification of statistically significant periods of variation in time-series. However, one must exercise caution in interpreting the results table of the most significant periods. The periods and p-values (statistical likelihood of a false-positive) are sensitive to the input parameters:
Very slight modifications to the periodogram and algorithm settings can produce periodograms that qualitatively appear identical, but are quantitatively distinct with different significant periods and associated p-values. For example, changing the period step size from 0.00010 to 0.00011 days will have this effect. One could get a most significant period of 3.14159265 days in one periodogram, and 3.14160432 days in another. How can one tell if the period is significant (ie, real)? And which is the correct period?
To answer the first question, a good starting rule of thumb is to visually inspect the phased time-series, and ask if the period passes your "by eye" test. If it does, you may still have a false-positive: long-time scale slow variations can often mimic short time-scale variations at periods similar to the median time-step. These are called period aliases from red noise. One must take the overall shape of the time-series and cadence into consideration. For example, if the time-series changes in value slowly with time over the course of a year, and is sampled once per day, the periodogram may return significant periods at 0.998, 1.00001, 1.9999, and 0.4999 days, etc. These can all be false-positives.
If the phased time-series does not pass the "by eye" test despite a high statistical significance, then there may be factors in the above list that contribute to producing the misleading p-values. Unfortunately, while one can set a quantitative limit on the statistical significance of periods to accept as genuine (small p-values), this process can often be qualitative in nature and requires practiced judgment. Alternatively, time-series can be injected with synthetic signals at specific periods. These synthetic time-series can be used to test whether a particular periodogram algorithm, cadence and settings combination can recover the synthetic period.
To answer the second question, the Nyquist sampling limit helps place different periodogram results into context. There is a limit to how finely one can resolve (tell the difference between) two different periods of variability in the time-series. This is also known as the period uncertainty. For perfect, evenly sampled data with N data points, one can generally resolve ~N frequencies, where the frequency is the inverse of the period. The maximum frequency is set by the time step between sequential data values, and the minimum frequency is set by the time baseline of observations. The ~N frequencies are evenly spaced in frequency (but not period) between these two limits. In other words, one can distinguish a period of 1 day from 2 days more readily than distinguishing a period of 1001 days from 1002 days for the same set of data. Conceptually, this is analogous to the frequency spectrum in a Fourier Transform.
In practice, astronomical time-series are rarely perfectly sampled and instead have data gaps and varying cadence. This can render the analytic or even approximate determination of the period uncertainty difficult (or inversely, the frequency resolution). How does one determine the period uncertainty - e.g. 3.1416 +/- 0.0001 days in our example above? Fortunately, one can still use the periodogram to estimate the period uncertainty. First, over-sample the periodogram around the interesting period by computing the periodogram power values at lots of periods. For example, if a time-series has 100 data points, and by default the periodogram service computes power values for 100 periods between 1 and 10 days, one can "over-sample" the periodogram and recompute power values for 1000 periods or more. Using this approach, one can see that there is a small finite range of periods around a single periodogram peak where the power value remains high. The full-width half-maximum (FWHM) of this periodogram peak, relative to the baseline of power values (median, or minimum), is often a good proxy to use for the period uncertainty. In our example, if the periodogram power value is 10 at a period of 3.14160 days, and falls off to a value of 5 at periods of 3.14150 and 3.14170 days before continuing to drop to zero, then I can assign a period uncertainty of 0.0001 days. Thus, in our example, the two slightly different periodograms that yielded statistically significant periods at 3.14159265 days and 3.14160432 days are in fact giving the same result. This is because it is impossible to tell the difference between the two periods given the period uncertainty/resolution of 0.0001 days.
Finally, there is the well known issue with periodograms of determining whether the correct period is the value found by an algorithm, one-half the period, or twice the period. Oftentimes, as in the case of eclipsing binaries, one must generally invoke some physics about the object being studied to lift the degeneracies.
The Periodogram and Light Curve Viewer services work best when viewed in current versions of the Firefox Web browser, on either Mac OS X, Windows 7 or Linux systems. The following issues have been noted to occur on other browsers and operating systems, including Windows XP and Internet Explorer:
If you encounter either of the above problems, click the Reset Zoom or Replot buttons to reset the interface, and wait for the browser to catch up. For best results, avoid clicking on the zoom buttons too quickly or aggressively.
There is one additional issue that is not specific to a browser or OS:
Finally, the Periodogram service will attempt to automatically set some of the periodogram settings to optimal values in terms of filtering, computation time and period sampling. In some cases, the periodogram services can store values like the period step size with more machine precision than is displayed. Thus, when one re-enters the displayed value, slightly different results can be returned. This does not affect the validity of the returned periods. See Interpreting Results for more information.
If problems persist, please contact the Helpdesk, and include the version of your Web browser and operating sytem.