Forward Modeling Exoplanet Detection Code
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README.md

ExoMult

This is a forward modeling program that will simulate the detected transiting exoplanet population around the Kepler sample of "solar-like" stars. You can import your own multi-planet system parameters to determine the probability of being detected or you can use an underlying power-law distribution to determine what population would be expected empirically. Multiplicity and its effects on detection efficiency are also considered here.

Getting Started

These instructions will get you a copy of the project up and running on your local machine for research, development, and testing purposes. ExoMult was orginally written in R, but we provide a wrapper to run the program in Python as well.

Prerequisites

To run the software begin by installing R. The latest version of R can be downloaded from:

https://www.r-project.org

When running ExoMult in Python, it is still necessary to download and install R.

Running ExoMult in R

Before starting, make sure that "kepler_solar-like_stellar_parameters.csv" and "ExoMult.R" are located in the same directory. Start by opening R in this directory.

$ R

Now load ExoMult into R

> source("ExoMult.R")

Now you can execute the ExoMult function

> ExoMult()

ExoMult will return a data frame of the detected planets and export the results to a csv file "simulated_detect_pop.csv"

Alternatively, the ExoMult.Prob function will produce a detection probabilty for a given system of planets.

> ExoMult.Prob(radius=c(1,2,3,4), period=c(10,20,30,40), eccentricity=c(0,0.05,0.1,0.15))

ExoMult.Prob will produce a data frame corresponding to the input planetary system. This data frame will be sorted by decending detection probability.

Output Description
Probability_Detection The probabilty each planet transits and is detected.
Frequency_Detection The frequency in which this planet was found, given that any planet was detected.
Probability_Detection_m_Planets The probability that a mulitplicity of at least m will be detected for this system, where m is an integer value corresponding to the data frame index.

Running ExoMult in Python

For improved speed and easy we recommend using ExoMult in R, however, a Python wrapper is also available. Before starting, make sure that "kepler_solar-like_stellar_parameters.csv", "ExoMult.R", and "ExoMult.py" are located in the same directory.

Other required modules include : numpy, rpy2, pandas2ri, and their associated dependencies.

Begin by opening Python in the appropriate directory.

$ python

Now load ExoMult (for Python3):

>>> exec(open("./ExoMult.py").read())

Now load ExoMult (for Python2):

>>> execfile("ExoMult.py")

Now you can execute the ExoMult function

>>> ExoMult()

ExoMult will return a Pandas data frame of the detected planets and export the results to a csv file "simulated_detect_pop.csv"

Alternatively, the ExoMult_Prob function will produce a detection probabilty for a given system of planets.

>>> ExoMult_Prob(radius=np.array[(1,2,3,4)], period=np.array[(10,20,30,40)], eccentricity=np.array[(0,0.05,0.1,0.15)])

ExoMult_Prob will produce a Pandas data frame corresponding to the input planetary system. This data frame will be sorted by decending detection probability.

Output Description
Probability_Detection The probabilty each planet transits and is detected.
Frequency_Detection The frequency in which this planet was found, given that any planet was detected.
Probability_Detection_m_Planets The probability that a mulitplicity of at least m will be detected for this system, where m is an integer value corresponding to the data frame index.

The ExoMult Function

The above opperation will run ExoMult with the default setting.

ExoMult(rMin=0.5, rMax=16, alpha_1=-1.65, rad_break=2.66, alpha_2=-4.35, pMin=0.5, pMax=500, 
  beta_1=0.76, per_break=7.09, beta_2=-0.64, mut_Ray=1, ecc_alpha=0, ecc_beta=1, frac_m1=0.72,
  frac_m2=0.68, frac_m3=0.66, frac_m4=0.63, frac_m5=0.60, frac_m6=0.55, frac_m7=0.40, export_csv=TRUE)

Arguments

  • rMin, rMax = The minimum/maximum values of radius considered in this population simulation. The units are provided in Earth radii.

  • pMin, pMax = The minimum/maximum values of period considered in this population simulation. The units are provided in days.

  • alpha_1, alpha_2 = The population parameter for the planet radius distribution. The values correspond to exponent of the power-law.

  • beta_1, beta_2 = The population parameter for the planet period distribution. The values correspond to exponent of the power-law.

  • rad_break = The radius value where the power-law distribution changes exponents.

  • per_break = The period value where the power-law distribution changes exponents.

  • mut_Ray = The Rayleigh distribution parameter used to determine the expected mutual inclination dispersion for each system. This values is given in units of degrees. Putting a zero in this parameter will produce flat disks.

  • ecc_alpha, ecc_beta = The Beta distribution parameters used to determine the eccentricty of each planet. The default settings will produce zero eccentricity for each planet.

  • frac_m1, frac_m2, frac_m3, frac_m4, frac_m5, frac_m6, frac_m7 = the fraction of the stellar population with at least m planets.

  • export_csv = Tell ExoMult whether it should or should not print the results to a csv file. A Boolean value is expected.

The ExoMult.Prob (or ExoMult_Prob) Function

ExoMult.Prob(radius, period, eccentricity, mut_Ray=0)

Arguments

  • radius = A user provided vector of planet radii within the system of interest. The units are provided in Earth radii. Currently, ExoMult can accept systems with up to 7 planets.

  • period = A user provided vector of planet periods, ordered to correspond with the planet radii given. The units are provided in days.

  • eccentricity = A user provided vector of planet eccentricities, odered to correspond with the planet radii given. These values should range from [0,1].

  • mut_Ray = The Rayleigh distribution parameter used to determine the expected mutual inclination dispersion for each system. This values is given in units of degrees. Putting a zero in this parameter will produce flat disks.

Recommendations

To utilize this code for an alternative stellar population, be sure that your stellar sample file has the same format as "kepler_solar-like_stellar_parameters.csv". For improved speed and easy we recommend using ExoMult in R.

Attribution

Please cite as Zink, Christiansen, & Hansen (2019).

@article{ExoMult,
author = {{Zink}, J. K. and {Christiansen}, J. L. and {Hansen}, B. M. S.},
title = {Accounting for incompleteness due to transit multiplicity in Kepler planet occurrence rates},
journal = {MNRAS},
volume = {483},
number = {4},
pages = {4479-4494},
year = {2019},
doi = {10.1093/mnras/sty3463}
}