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What is the Periodogram class?

lightkurve has a class specifically for dealing with periodograms of time series data. This can be useful for finding the periods of variable stars. Below is a quick example of how to find the period of an eclipsing binary star using lightkurve.

Firstly lets grab a light curve file from mast. We’ll use KIC 10030943, which is an eclipsing binary observed by the original Kepler mission. We’re just going to use one quarter for this demo.

[1]:
import astropy.units as u  # We'll need this later.
[2]:
# Obtain the data
from lightkurve import search_lightcurvefile
lc = search_lightcurvefile('10264202', quarter=10).download().PDCSAP_FLUX.remove_nans()

Let’s plot the light curve to see what we’re working with.

[3]:
lc.scatter();
../_images/tutorials_01-using-the-periodogram-class_5_0.png

This light curve looks like it has some structure in it! Let’s use the periodogram class to find the rotation period. You can create a periodogram from the KeplerLightCurve object by using the periodogram method.

[4]:
pg = lc.to_periodogram()

Now we can plot the periodogram in the same way that we plot the original light curve.

[5]:
pg.plot();
../_images/tutorials_01-using-the-periodogram-class_9_0.png

This looks like there is a huge signal at a certain frequency! Let’s plot it in period space, so that we can see what period the oscillation is occurring at.

[6]:
pg.plot(format='period', scale='log');
../_images/tutorials_01-using-the-periodogram-class_11_0.png

This looks like a very fast period. Let’s find the period with the highest power and fold out light curve.

[7]:
period = pg.period_at_max_power
print('Best period: {}'.format(period))
lc.fold(period.value).scatter();
Best period: 0.2587311606278735 d
../_images/tutorials_01-using-the-periodogram-class_13_1.png

As is quite common for eclipsing binaries with deep secondary eclipses, we have found a harmonic of the period of the eclipsing binary. Let’s plot it again with quadruple the period.

[8]:
period = pg.period_at_max_power * 4
print('Best period: {}'.format(period))
lc.fold(period.value).scatter();
Best period: 1.034924642511494 d
../_images/tutorials_01-using-the-periodogram-class_15_1.png

It looks like we could probably get a better fit than this. Let’s try increasing the number of points in our periodogram.

[9]:
# I've set min_period and max_period to slightly reduce the computational time
pg = lc.to_periodogram(min_period=0.9*u.day, max_period=1.2*u.day, oversample_factor=10)
[10]:
period = pg.period_at_max_power
print('Best period: {}'.format(period))
lc.fold(period.value).scatter();
Best period: 1.0350971683913832 d
../_images/tutorials_01-using-the-periodogram-class_18_1.png

That’s improved our fit! It looks like this eclipsing binary has a period of approximately 1 day.


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