Contamination example 2b

M star slightly contaminated by a G star and informative priors on orbital parameters

Hannu Parviainen
Instituto de Astrofísica de Canarias

Last modified: 15.7.2019

Here we use the pytransit.contamination module to estimate the true planet to star radius ratio robustly using multicolour photometry in the presence of possible flux contamination from an unresolved source in the photometry aperture, as detailed in Parviainen et al. 2019 (submitted). This can be used in the validation of transiting planet candidates, where, e.g., blended eclipsing binaries are a significant source of false positives.

This notebook runs the simulation for a light curve without contamination and informative priors on the impact parameter and stellar density, while the previous notebook (1a) did the same with uninformative priors on the orbital parameters.

Light curves: We don't use real data here, but create simulated multicolour photometry lightcurves using the MockLC class found in src.mocklc. The code is the same that was used for the simulations in Parviainen et al. (2019).

Log posterior function: The log posterior function is defined by MockLPF class found in src.blendlpf.MockLPF. The class inherits pytransit.lpf.PhysContLPF and overrides the _init_instrument method to define the instrument and the contamination model (amongst other things to make running a variety of simulations smooth).

Parametrisation: As discussed in the paper, the contamination is parametrised by the apparent area ratio ($k_\mathrm{True}^2$), true area ratio ($k_\mathrm{App}^2$), and the effective temperatures of the host and contaminant stars. The apparent area ratio defines how deep the transit is in a single single passband and can be wavelength dependent (if the host and contaminant are of different spectral type), while the true area ratio stands for the unblended true geometric planet-star area ratio.

The true radius ratio ($k_\mathrm{True}$) is the main quantity of interest in transiting planet candidate validation), since it together with a stellar radius estimate gives the true absolute planetary radius.



In [1]:

    
%pylab inline









    



Populating the interactive namespace from numpy and matplotlib



In [2]:

    
import sys
from corner import corner
sys.path.append('.')



In [14]:

    
from pytransit.contamination import true_radius_ratio
from src.mocklc import MockLC, SimulationSetup
from src.blendlpf import MockLPF
import src.plotting as pl

Create a mock light curve



In [4]:

    
lc = MockLC(SimulationSetup('M', 0.1, 0.0, 0.15, 'short_transit', cteff=5500, know_orbit=True))
lc.create(wnsigma=[0.001, 0.001, 0.001, 0.001], rnsigma=0.00001, rntscale=0.5, nights=1);
lc.plot();

Initialize the log posterior function



In [5]:

    
lpf = MockLPF('Example_1', lc)



In [6]:

    
lpf.print_parameters(columns=2)









    



  0 |G| tc         [-inf ..  inf]	  1 |G| pr         [0.00 ..  inf]
  2 |G| rho        [0.00 ..  inf]	  3 |G| b          [0.00 .. 1.00]
  4 |P| k2_app     [0.00 .. 0.06]	  5 |G| k2_true    [0.00 ..  inf]
  6 |G| teff_h     [2500.00 .. 12000.00]	  7 |G| teff_c     [2500.00 .. 12000.00]
  8 |P| q1_0       [0.00 .. 1.00]	  9 |P| q2_0       [0.00 .. 1.00]
 10 |P| q1_1       [0.00 .. 1.00]	 11 |P| q2_1       [0.00 .. 1.00]
 12 |P| q1_2       [0.00 .. 1.00]	 13 |P| q2_2       [0.00 .. 1.00]
 14 |P| q1_3       [0.00 .. 1.00]	 15 |P| q2_3       [0.00 .. 1.00]
 16 |L| loge_0     [-4.00 .. 0.00]	 17 |L| loge_1     [-4.00 .. 0.00]
 18 |L| loge_2     [-4.00 .. 0.00]	 19 |L| loge_3     [-4.00 .. 0.00]

Optimize



In [7]:

    
lpf.optimize_global(1000)



In [8]:

    
lpf.plot_light_curves()

Estimate the posterior

The contamination parameter space is a bit difficult to sample (especially if the signal to noise ratio is low), so the sampling should be continued at least for 10000 iterations.



In [9]:

    
lpf.sample_mcmc(5000, reset=True, repeats=2)

Analysis

We plot the main results below. It is clear that a single good-quality four-colour light curve still allows for contamination from a source of similar spectral type as the host star. However, in this example, the maximum allowed level of contamination is not sufficient to take the transiting object out of the planetary regime.

Also, the joint posterior plots clearly show that any significant contamination must come from a source of a similar spectral type as the host. Combining this information with prior knowledge about the probability of having such a system without colour variations can be used in probabilistic planet candidate validation.

Plot the basic joint posterior



In [10]:

    
df = lpf.posterior_samples()



In [11]:

    
pl.joint_radius_ratio_plot(df, fw=13, clim=(0.099, 0.12), htelim=(3570, 3630), ctelim=(4000,7500), blim=(0, 0.5), rlim=(3.8, 5.2));



In [12]:

    
pl.joint_contamination_plot(df, fw=13, clim=(0, 0.4), htelim=(3570, 3630), ctelim=(4000,7500), blim=(0, 0.5), rlim=(3.8, 5.2));

Plot the apparent and true radius ratio posteriors



In [18]:

    
pl.marginal_radius_ratio_plot(df, bins=60, klim=(0.097, 0.12), figsize=(7,5));
axhline(true_radius_ratio(0.1, 0.15), lw=1, ls='--')









    Out[18]:





<matplotlib.lines.Line2D at 0x1c212cfac8>

Make a corner plot to have a good overview to the posterior space



In [17]:

    
corner(df.iloc[:,2:-3]);