# 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!

[1]:

import lightkurve as lk


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.

[2]:

tpf.plot(frame=100, scale='log', show_colorbar=True);

[2]:

<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.

[3]:

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


Let’s take a look at the output lightcurve.

[4]:

lc.plot();

[4]:

<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.

[5]:

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


Let’s plot the trend estimated in red:

[6]:

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

[6]:

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


and the flat lightcurve:

[7]:

flat.errorbar(label="Kepler-10");

[7]:

<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:

[8]:

import numpy as np
periodogram = flat.to_periodogram(method="bls", period=np.arange(0.5, 1.5, 0.001))
periodogram.plot();

[8]:

<AxesSubplot:xlabel='Period [$\\mathrm{d}$]', ylabel='BLS Power'>


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

[9]:

best_fit_period = periodogram.period_at_max_power
print('Best fit period: {:.3f}'.format(best_fit_period))

Best fit period: 0.838 d

[10]:

flat.fold(period=best_fit_period, epoch_time=periodogram.transit_time_at_max_power).errorbar();

[10]:

<AxesSubplot:xlabel='Phase [JD]', ylabel='Flux [$\\mathrm{e^{-}\\,s^{-1}}$]'>


We successfully recovered the planet!