Fast and easy-to-use tools for exoplanet transit light curve modelling using Python or Fortran.

from pytransit import Gimenez
m = Gimenez()
f = m.evaluate(t, *pv)

Transit models

• Series-expansion based transit model by A. Gimenez (A&A 450, 1231--1237, 2006).

• Quadratic limb-darkening transit model by Mandel & Agol (ApJ 580, L171–L175, 2002).

• Common features

  • Optimized and parallelized Fortran implementatios.
  • Can calculate the transit model simultaneously for several limb darkening coefficient sets.
  • Built-in model interpolation for the modelling of large datasets.
  • Built-in supersampling.

Utilities

• Routines to calculate the projected planet-to-star distance for circular and eccentric orbits.
• Routines to calculate transit durations, etc.

First clone the repository from github:

git clone https://github.com/hpparvi/PyTransit.git
cd PyTransit

and then do the normal python package build & installation. For example, building with a fairly modern gfortran and then installing the package locally (without root rights) would take:

python setup.py config_fc --fcompiler=gnu95 --opt="-Ofast" --f90flags="-cpp -fopenmp -march=native" build
python setup.py install --user

The code should compile with other compilers also, but only gfortran and Intel fortran have been tested.

Basic usage is simple:

from pytransit import Gimenez

m = Gimenez()
f = m.evaluate(t, *pv)

or

from pytransit import MandelAgol

m = MandelAgol()
f = m.evaluate(t, *pv)

Here we first initialize the model accepting the defaults (quadratic limb darkening law, no supersampling, and the use of all available cores), and then calculate the model for times in the time array t, pv being a list containing the system parameters.

For a slightly more useful example, we can do:

import numpy as np
from pytransit import Gimenez

t = np.linspace(0.8,1.2,500)
k, t0, p, a, i, e, w = 0.1, 1.01, 4, 8, 0.48*np.pi, 0.2, 0.5*np.pi
u = [0.25,0.10]

m = Gimenez()
f = m.evaluate(t, k, u, t0, p, a, i, e, w)

where k is the planet-star radius ratio, t0 the transit center, p the orbital period, a the scaled semi-major axis, i the orbital inclination, e the orbital eccentricity, w the argument of periastron, and u contains the quadratic limb darkening coefficients.

The model can also be evaluated for several limb darkening coefficient (ldc) sets simultaneously (much faster than evaluating the model several times for different coefficient sets):

...
u = [[0.25, 0.1],[0.35,0.2],[0.45,0.3],[0.55,0.4]]

m = Gimenez()
f = m.evaluate(t, k, u, t0, p, a, i, e, w)

In this case, the model returns several light curve models, each corresponding to a single ldc set.

The transit model offers built-in supersampling for transit fitting to transit photometry with poor time sampling (such as Kepler's long cadence data):

m = Gimenez(supersampling=8, exptime=0.02)
...

The model accuracy and the number of limb darkening coefficients can be set in the initialization. Finally, for fitting to large datasets, the model can be evaluated using interpolation (linear, at the moment).

Basic transit model usage with linear limb darkening law, lower accuracy, and four cores:

m = Gimenez(npol=50, nldc=1, nthr=4)
...

Transit model using linear interpolation:

m = Gimenez(lerp=True)
...

Calculate projected distance for a circular or eccentric orbit given time t, transit center time t0, period p, scaled semi-major axis a, inclination i, eccentricity e, and argument of periastron w:

import numpy as np
from pytransit.orbits_f import orbits as of

t0, p, a, i, e, w = 1.01, 4, 8, 0.48*np.pi, 0.2, 0.5*np.pi

t   = np.linspace(0.8,1.2,500)
zc  = of.z_circular( t, t0, p, a, i, nthreads=0)                  
zen = of.z_eccentric_newton(t, t0, p, a, i, e, w, nthreads=0) # Calculated using Newton's method
ze3 = of.z_eccentric_s3(t, t0, p, a, i, e, w, nthreads=0)     # Calculated using series expansion (ok for e<0.15)
ze5 = of.z_eccentric_s(t, t0, p, a, i, e, w, nthreads=0)      # Calculated using series expansion (ok for e<0.25)
zel = of.z_eccentric_ip(t, t0, p, a, i, e, w, nthreads=0, update=False) # Faster for large LCs, uses linear interpolation

Transit model using linear interpolation, two different sets of z:

m  = Gimenez(lerp=True)      # Initialize the model
I1 = m(z1,k,u)               # Evaluate the model for z1, update the interpolation table
I2 = m(z2,k,u, update=False) # Evaluate the model for z2, don't update the interpolation table

• Hannu Parviainen hpparvi@gmail.com, University of Oxford

• Gandolfi, Davide, H. Parviainen, et al. Kepler-77b: a very low albedo, Saturn-mass transiting planet around a metal-rich solar-like star. Astron. Astrophys. 557, A74 (2013).
• Parviainen, Hannu, H.J. Deeg, and J.A. Belmonte. “Secondary Eclipses in the CoRoT Light Curves: A Homogeneous Search Based in Bayesian Model Selection.” Accepted to A&A (2012)
• Rouan, D., H. Parviainen, C. Moutou, Magali Deleuil, M. Fridlund, A Ofir, M. Havel, et al. “Transiting Exoplanets from the CoRoT Space Mission.” Astronomy & Astrophysics 537 (January 9, 2012): A54.
• Murgas, F., E. Pallé, A. Cabrera-Lavers, K. D. Colón, E. L. Martín, and H. Parviainen. “Narrow Band H α Photometry of the super-Earth GJ 1214b with GTC/OSIRIS Tunable Filters.” Astronomy & Astrophysics 544 (July 24, 2012): A41.
• Tingley, Brandon, E. Palle, H. Parviainen, H. J. Deeg, M. R. Zapatero Osorio, A. Cabrera-Lavers, J. a. Belmonte, P. M. Rodriguez, F. Murgas, and I. Ribas. “Detection of Transit Timing Variations in Excess of One Hour in the Kepler Multi-planet Candidate System KOI 806 with the GTC.” Astronomy & Astrophysics 536 (December 12, 2011): L9.