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How to recover a known planet in Kepler data?

This tutorial will demonstrate the basic steps required to recover the signal of Kepler-10b, the first rocky planet that was discovered by Kepler!

Let’s start by downloading the pixel data for this target for one of Kepler’s observing quarters:

import lightkurve as lk
tpf = lk.search_targetpixelfile("Kepler-10", author="Kepler", quarter=3, cadence="long").download()

Let’s use the plot method to show the pixel data at one point in time (frame index 100). We’ll also pass along a few plotting arguments.

tpf.plot(frame=100, scale='log', show_colorbar=True);
<AxesSubplot:title={'center':'Target ID: 11904151, Cadence: 7505'}, xlabel='Pixel Column Number', ylabel='Pixel Row Number'>

The target pixel file appears to show one bright star with a core brightness of approximately 50,000 electrons/seconds.

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.

<AxesSubplot:xlabel='Time - 2454833 [BKJD days]', ylabel='Flux [$\\mathrm{e^{-}\\,s^{-1}}$]'>

Now let’s use the .flatten() method, which removes long-term variability that we are not interested in using a high-pass filter called Savitzky-Golay.

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

Let’s plot the trend estimated in red:

ax = lc.errorbar(label="Kepler-10")                   # plot() returns a matplotlib axes ...
trend.plot(ax=ax, color='red', lw=2, label='Trend');  # which we can pass to the next plot() to use the same axes
<AxesSubplot:xlabel='Time - 2454833 [BKJD days]', ylabel='Flux [$\\mathrm{e^{-}\\,s^{-1}}$]'>

and the flat lightcurve:

<AxesSubplot:xlabel='Time - 2454833 [BKJD days]', ylabel='Flux [$\\mathrm{e^{-}\\,s^{-1}}$]'>

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

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

import numpy as np
periodogram = flat.to_periodogram(method="bls", period=np.arange(0.5, 1.5, 0.001))
<AxesSubplot:xlabel='Period [$\\mathrm{d}$]', ylabel='BLS Power'>

It looks like we found a strong signal with a periodicity near 0.8 days!

best_fit_period = periodogram.period_at_max_power
print('Best fit period: {:.3f}'.format(best_fit_period))
Best fit period: 0.838 d
flat.fold(period=best_fit_period, epoch_time=periodogram.transit_time_at_max_power).errorbar();
<AxesSubplot:xlabel='Phase [JD]', ylabel='Flux [$\\mathrm{e^{-}\\,s^{-1}}$]'>

We successfully recovered the planet!