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Finding the Planets

A workshop that allows one to discover exo-planets. The workshop has an accompanying book

Trappist-1

Trappist-1 is a

planetary system, located 12 parsecs away from the Solar system (39 light years), near the ecliptic, within the constellation of Aquarius.

Trappist-1 appeared in the news because it was announced that is orbited by at least seven planets.

Workshop

During this workshop you will discover the planets around Trappist-1 on your own.

We will find the planets with data made available by NASA's K2/Kepler telescope. The mission is

search for Earth-like planets around Sun-like stars

The Trappist-1 data is publicly accessible. Geert Barentsen has made some interesting tools to analyze the data. For example, take a look at this IPython notebook.

Info

The following information is presented in the headers of the data

Long

  Binary Table
      Header Information:
          12 fields, 3599 rows of length 2932
           1:Name=TIME; Format=D; 
           2:Name=TIMECORR; Format=E; 
           3:Name=CADENCENO; Format=J; 
           4:Name=RAW_CNTS; Format=121J; Dimens=(11,11); 
           5:Name=FLUX; Format=121E; Dimens=(11,11); 
           6:Name=FLUX_ERR; Format=121E; Dimens=(11,11); 
           7:Name=FLUX_BKG; Format=121E; Dimens=(11,11); 
           8:Name=FLUX_BKG_ERR; Format=121E; Dimens=(11,11); 
           9:Name=COSMIC_RAYS; Format=121E; Dimens=(11,11); 
           10:Name=QUALITY; Format=J; 
           11:Name=POS_CORR1; Format=E; 
           12:Name=POS_CORR2; Format=E; 
      Data Information:
          Number of rows=3599
          Number of columns=12
           0:double[3599]
           1:float[3599]
           2:int[3599]
           3:int[435479]
           4:float[435479]
           5:float[435479]
           6:float[435479]
           7:float[435479]
           8:float[435479]
           9:int[3599]
           10:float[3599]
           11:float[3599]

Short

  Binary Table
      Header Information:
          12 fields, 107968 rows of length 2932
           1:Name=TIME; Format=D; 
           2:Name=TIMECORR; Format=E; 
           3:Name=CADENCENO; Format=J; 
           4:Name=RAW_CNTS; Format=121J; Dimens=(11,11); 
           5:Name=FLUX; Format=121E; Dimens=(11,11); 
           6:Name=FLUX_ERR; Format=121E; Dimens=(11,11); 
           7:Name=FLUX_BKG; Format=121E; Dimens=(11,11); 
           8:Name=FLUX_BKG_ERR; Format=121E; Dimens=(11,11); 
           9:Name=COSMIC_RAYS; Format=121E; Dimens=(11,11); 
           10:Name=QUALITY; Format=J; 
           11:Name=POS_CORR1; Format=E; 
           12:Name=POS_CORR2; Format=E; 
      Data Information:
          Number of rows=107968
          Number of columns=12
           0:double[107968]
           1:float[107968]
           2:int[107968]
           3:int[13064128]
           4:float[13064128]
           5:float[13064128]
           6:float[13064128]
           7:float[13064128]
           8:float[13064128]
           9:int[107968]
           10:float[107968]
           11:float[107968]

Table Column Formats

FITS format code         Description                     8-bit bytes

L                        logical (Boolean)               1
X                        bit                             *
B                        Unsigned byte                   1
I                        16-bit integer                  2
J                        32-bit integer                  4
K                        64-bit integer                  4
A                        character                       1
E                        single precision floating point 4
D                        double precision floating point 8
C                        single precision complex        8
M                        double precision complex        16
P                        array descriptor                8
Q                        array descriptor                16

Recreation of iPython notebook

Below you can find the preliminary results of our exploration of the data set. We got a feel for the process of extracting data, but results differed from the iPython notebook. Here we are closely following the notebook steps.

Preliminary Results

Images

First image created

Below you find the first image that I created from the long cadence FITS data. To me it is still amazing that from a series of these 11 by 11 images one can obtain so much information.

First image created

Collage

There are 3599 such images which fit nicely into a 61 times 59 rectangle. Starring at the image you could start to notice certain peculiarities. Which do you see?

Collage made the number of images is 61*59

Average

The average brightness, as can be seen from the collage, seems to steadily increase.

The average brightness

Smoothed Average

The average brightness and the exponentially smoothed average, plotted against the time.

The smoothed average brightness against time

Detrended

Detrending the light curve produces the following images

Detrended light curve

Discrete Fourier Transform

Calculating the discrete Fourier transform produces

Discrete Fourier Transform

Detrended Filtered

Removing how frequency components from the Fourier transform and inverting the transformation produces a filtered sequence.

Filtered detrended light curve

Zoomed in filtered detrended light curve

Median filter

Median filter of detrended light curve