exocartographer¶
exocartographer is a forward-modeling tool for constraining surface maps
orbital parameters of exoplanets from time-resolved photometry.
Example Usage¶
Draw an exoplanet map from the Gaussian Process prior, specify it’s orbital parameters, and generate synthetic light curve data.:
import numpy as np
import healpy as hp
from matplotlib import pyplot as plt
from exocartographer.gp_map import draw_map
from exocartographer import IlluminationMapPosterior
from exocartographer.util import logit, inv_logit
nside = 4 # map resolution
# Gaussian process properties
whitenoise_relative_amp = 0.02
length_scale = 30. * np.pi/180
albedo_mean = .5
albedo_std = 0.2
# Draw a valid albedo map (i.e., 0 < albedo < 1)
while True:
simulated_map = draw_map(nside, albedo_mean, albedo_std,
whitenoise_relative_amp, length_scale)
if min(simulated_map) > 0 and max(simulated_map) < 1:
break
hp.mollview(simulated_map, title='albedo', cmap='gist_gray')
plt.savefig('simulated_map.png')
# Set orbital properties
p_rotation = 23.934
p_orbit = 365.256363 * 24.0
phi_orb = np.pi
inclination = np.pi/2
obliquity = 90. * np.pi/180.0
phi_rot = np.pi
# Observation schedule
cadence = p_rotation/4.
epoch_duration = p_orbit
times = np.linspace(0, epoch_duration, epoch_duration/cadence)
# Measurement uncertainties
measurement_std = 0.001
# Use a posterior instance for easy lightcurve generation
truth = IlluminationMapPosterior(times, np.zeros_like(times),
measurement_std, nside=nside)
true_params = {
'log_orbital_period':np.log(p_orbit),
'log_rotation_period':np.log(p_rotation),
'logit_cos_inc':logit(np.cos(inclination)),
'logit_cos_obl':logit(np.cos(obliquity)),
'logit_phi_orb':logit(phi_orb, low=0, high=2*np.pi),
'logit_obl_orientation':logit(phi_rot, low=0, high=2*np.pi)}
truth.fix_params(true_params)
p = np.concatenate([np.zeros(truth.nparams), simulated_map])
lightcurve = truth.lightcurve(p)
plt.figure(figsize=(16, 3))
plt.plot(times/p_rotation, lightcurve, lw=0.5)
plt.xlim(0, p_orbit/p_rotation)
plt.ylim(ymin=0)
plt.xlabel(r'time$/P_\mathrm{rot}$')
plt.ylabel('reflectance')
plt.savefig('lightcurve.png')
