TANGO

Animate exoplanet transits!

Written by Oscar Barragán

email: [email protected]

October, 2018

Updated: March, 2021

Introduction

Planets perform a gravitational TANGO around their host stars which is called orbit. If the orbit inclination is close to 90°, the presence of a planet orbiting its host star can be inferred by detecting the periodic drops of stellar flux caused by the planet partly occulting the stellar disc. This phenomenon is called transit. If we observe the transits caused by planets in stellar light curves (flux vs time), we are able to decode the gravitational coreography and obtain planetary and orbital properties of the system. This code helps you to visualise how the planet's motion was looking when they were transiting the stellar disc.

Dependencies

• numpy
• matplotlib
• seaborn
• glob
• moviepy
• pytransit (optional, if you want to plot the models)

Animate K2 data of GJ 9827

The system GJ 9827 contains (at least) three transiting planets. They were discovered by K2 on its Campaign 12 ( see Niraula et al., 2017, Prieto-Arranz et al., 2018, and Rodriguez et al., 2017 for more details). The brightness of this star combined with the exquisite photometry of Kepler, give us a marvelous light curve where the three transiting planets are visible. During February 12, 2017, planets b, c and d transited the star consecutively, and this was observed by Kepler. We will animate this now!

First, just clone TANGO.

git clone https://github.com/oscaribv/tango

The next step is to enter the tango directory and see what we can find inside it

cd tango
ls
  gj9827  README.md src tango.py

You can see that there is a directory called gj9827. This directory contains the light curve and input file needed to create your animation. The file lc_gj9827.dat contains K2 long cadence data collected between 2963.5 and 2964.3 (BJD - 2454833) days. In this window there are three consecutive transits of GJ 9827 b, c and d (I used the light curve provided by EVEREST to create this file).

So now we have the light curve that we want to animate. The next step is to create the input file that will be used to pass the orbit solutions to the code. If you open the input file you will see something like this

#Input file for tango
#system: GJ 9827
#Created by O. Barragan, October 2018.
#Modified by O. Barragan, March 2021

#Data file with the flattened light curve
lcname = 'lc_gj9827.dat'

#--------------------------------------------------------------------
#                 Planet and orbit parameters
# Each parameter is a list in which each element
# correspond to a planet. For this case, there are three
# planets. But you can create animations with 1, 2, 3, and more planets.
#--------------------------------------------------------------------

#This file was creating using the values reported in Prieto-Arranz et al., (2018)
#Orbital period (days)
P =[1.2089662,3.6482269,6.2014190]
#time of mid-transit (days) Be sure that you are using the same units that in your data file
T0 = [2905.8264631,2905.5496113,2907.9619764]
#Orbit eccentricity
e = [0.,0.,0.]
#Angle of periastron
w = [np.pi/2,np.pi/2,np.pi/2]
#Scaled semi-major axis
a = [7.229235,15.096,21.5019118]
#orbit inclination (degrees)
inclination = [88.330714*np.pi/180,89.06*np.pi/180,87.702*np.pi/180]
#Scaled planet radius (Rp/R*)
rp = [0.0232259,0.0181983,0.0299279]
#Limb darkening coefficients following a quadratic law
u1 =  0.58
u2 =  0.15
#Next two variables are used to control the cadence of the light curve data
#Integration time of the data
t_cad = 30./60./24.
#Number of steps to integrate the data
n_cad = 30
#These values are useful now to integrate Kepler long cadence data

#The code can estimate the stellar colour based on Halle & Heller 2021
#Assuming is a black body given a stellar temperature T_star in Kelvin
T_star = 4200 #K


#--------------------------------------------------------------------
#              Animation controls
#--------------------------------------------------------------------
#Window size to show the data (days)
size_time = 0.5 
#1./(photograms per day) in this case the code will create a photogram each 7.2 min
vel_time  = 1./500.
#Animation minimum time (Be sure that you are using the same units as in your data file)
tmin =  2963.3
#Animation maximum time (Be sure that you are using the same units as in your data file)
tmax =  2964.3
#frame rate
frate = 1./24.

#--------------------------------------------------------------------
#                     Plot controls
#--------------------------------------------------------------------

#Control if we overplot the light curve model
#You need to have installed pyaneti in your computer to use it
is_plot_model = False

#-----------------------------------------------------------------
#                         END
#-----------------------------------------------------------------

Now that we have our input file ready, it is time to run TANGO to create our first animation. Just type (the process takes some time)

$ python tango.py gj9827
  Creating png files
  png files have been created
  Creating animation
  MoviePy - Building file gj9827/gj9827.gif with imageio.
  Moviepy - Building video gj9827/gj9827.mp4.
  Moviepy - Writing video gj9827/gj9827.mp4

  Moviepy - Done !
  Your animation is ready at gj9827/gj9827.gif

If you see something like this appearing in your terminal, now you have created your animation of GJ 9827. Open the file gj9827/gj9827.gif and you will see this

What is this?

The upper panel of the animation shows the K2 photometric time-series. Each point represent the integrated flux received at the Kepler detector at different times. There are some clear flux drops, which we know are caused by transiting planets. The lower panel shows the reconstructed planets' paths in the sky. The position of the planets represent the data acquired at the time marked with a vertical dashed line in the upper panel. We can see how the three planets cross the stellar disk one after the other causing a whimsical flux variation. The planet and star sizes are to scale!

Animate K2 data and model of GJ 9827

Now that we have learned how to create an animation with TANGO, maybe we wan to to over-plot the inferred light curve model to to show how our parameters can explain the observations. This can be easily done by changing only one line in the input file for GJ 9827.

TANGO uses the code pytransit to create the model that will be over-plotted on the animation. This tutorial assumes that you do not have pytransit installed in your computer. To install pytransit you just need to type in your terminal

pip install pytransit

and this will install pytransit in your machine. For more details visit pytransit website. Now you are ready to plot the model in your animation! Just have to change the variable is_plot_model to True inside gj9827/input.py file.

#--------------------------------------------------------------------
#                     Plot controls
#--------------------------------------------------------------------

#Control if we overplot the light curve model
#You need to have installed pyaneti in your computer to use it
is_plot_model = True

and re-run TANGO

$ python tango.py gj9827
  Creating png files
  png files have been created
  Creating animation
  Your animation is ready at gj9827/gj9827.gif

Now your gj9827/gj9827.gif animation should look like this

The animation shows the same features as the previous example, but this time we can see the inferred model of the stellar flux caused by the transiting planets. Note how the model (upper panel) appears according to the position of the planets (lower panel).

Have Fun!

If you have any comments, requests, suggestions or just need any help, please don't think twice, just contact me!