How to recover a known planet in Kepler data?¶

This tutorial demonstrates the basic steps required to recover a transiting planet candidate in the Kepler data.

We will show how you can recover the signal of Kepler-10b, the first rocky planet that was discovered by Kepler!

:

from lightkurve import search_targetpixelfile
tpf.shape

:

(4140, 10, 11)


Let’s use the plot method and pass along an aperture mask and a few plotting arguments.

:

tpf.plot(scale='log'); The target pixel file contains one bright star with approximately 50,000 counts.

Now, we will use the to_lightcurve method to create a simple aperture photometry lightcurve using the mask defined by the pipeline which is stored in tpf.pipeline_mask.

:

lc = tpf.to_lightcurve(aperture_mask=tpf.pipeline_mask)


Let’s take a look at the output lightcurve.

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lc.plot(); Now let’s use the flatten method, removes long-term variability that we are not interested in.

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flat, trend = lc.flatten(window_length=301, return_trend=True)


Let’s plot the trend estimated by the Savitzky-Golay filter:

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ax = lc.errorbar()                              # plot() returns a matplotlib axes ...
trend.plot(ax=ax, color='red', label='Trend');  # which we can pass to the next plot() to use the same axes and the flat lightcurve:

:

flat.errorbar(); Now, let’s run a period search function using the Box-Least Squares algorithm, which was added to the AstroPy package in version 3.1.

:

from astropy.stats import BoxLeastSquares
bls = BoxLeastSquares(flat.time, flat.flux, flat.flux_err)


We will use the BLS algorithm to search a pre-defined grid of transit periods and durations:

:

import numpy as np
periods = np.arange(0.3, 1.5, 0.001)
durations = np.arange(0.005, 0.15, 0.001)
periodogram = bls.power(periods, durations)

:

import matplotlib.pyplot as plt
plt.plot(periodogram.period, periodogram.power)
plt.ylabel("Power")
plt.xlabel("Period [day]"); :

best_fit = periods[np.argmax(periodogram.power)]
print('Best Fit Period: {:0.4f} days'.format(best_fit))

Best Fit Period: 0.8380 days

:

flat.fold(best_fit).errorbar(); We successfully recovered the planet!