ld¶
Limb darkening functions
The available passband names are:
‘CHEOPS’, ‘MOST’, ‘Kepler’, ‘CoRoT’, ‘Gaia’, ‘TESS’
‘U’, ‘B’, ‘V’, ‘R’, ‘I’ (Bessell/Johnson)
‘u_’, ‘g_’, ‘r_’, ‘i_’, ‘z_’ (SDSS)
‘NGTS’
The power-2 limb-darkening law is described in Maxted (2018) 1. Uninformative sampling of the parameter space for the power-2 law is described in Short et al. (2019) 2.
Examples¶
>>> from pycheops.ld import *
>>> import matplotlib.pyplot as plt
>>> import numpy as np
>>> T_eff = 5560
>>> log_g = 4.3
>>> Fe_H = -0.3
>>> passband = 'Kepler'
>>> p2K = stagger_power2_interpolator(passband)
>>> c2,a2,h1,h2 = p2K(T_eff, log_g, Fe_H)
>>> print('h_1 = {:0.3f}, h_2 = {:0.3f}'.format(h1, h2))
>>> mu = np.linspace(0,1)
>>> plt.plot(mu, ld_power2(mu,[c2, a2]),label='power-2')
>>> plt.xlim(0,1)
>>> plt.ylim(0,1)
>>> plt.xlabel('$\mu$')
>>> plt.ylabel('$I_{\lambda}(\mu)$')
>>> plt.legend()
>>> plt.show()
References
-
pycheops.ld.
ld_power2
(mu, a)¶ Evaluate power-2 limb-darkening law
- Parameters
mu – cos of angle between surface normal and line of sight
a – array or tuple [c, alpha]
- Returns
1 - c * (1-mu**alpha)
-
pycheops.ld.
ld_claret
(mu, a)¶ Evaluate Claret 4-parameter limb-darkening law
- Parameters
mu – cos of angle between surface normal and line of sight
a – array or tuple [a_1, a_2, a_3, a_4]
- Returns
1 - Sum(i=1,4) a_i*(1-mu**(i/2))
-
class
pycheops.ld.
stagger_power2_interpolator
(passband='CHEOPS')¶ Parameters of a power-2 limb-darkening law interpolated from the Stagger grid.
- The power-2 limb darkening law is
I_X(mu) = 1 - c * (1-mu**alpha)
It is often better to use the transformed coefficients
h1 = 1 - c*(1-0.5**alpha)
and
h2 = c*0.5**alpha
as free parameters in a least-squares fit and/or for applying priors.
Returns NaN if interpolation outside the grid range is attempted
-
__call__
(T_eff, log_g, Fe_H)¶ - Parameters
T_eff – effective temperature in Kelvin
log_g – log of the surface gravity in cgs units
Fe/H – [Fe/H] in dex
- Returns
c, alpha, h_1, h_2
-
pycheops.ld.
ca_to_h1h2
(c, alpha)¶ Transform for power-2 law coefficients h1 = 1 - c*(1-0.5**alpha) h2 = c*0.5**alpha
- Parameters
c – power-2 law coefficient, c
alpha – power-2 law exponent, alpha
returns: h1, h2
-
pycheops.ld.
h1h2_to_ca
(h1, h2)¶ Inverse transform for power-2 law coefficients c = 1 - h1 + h2 alpha = log2(c/h2)
- Parameters
h1 – 1 - c*(1-0.5**alpha)
h2 – c*0.5**alpha
returns: c, alpha
-
pycheops.ld.
q1q2_to_h1h2
(q1, q2)¶ Inverse transform to h1, h2 from uninformative paramaters q1, q2
h1 = 1 - sqrt(q1) + q2*sqrt(q1) h2 = 1 - sqrt(q1)
- Parameters
q1 – (1 - h2)**2
q2 – (h1 - h2)/(1-h2)
returns: q1, q2
-
pycheops.ld.
h1h2_to_q1q2
(h1, h2)¶ Transform h1, h2 to uninformative paramaters q1, q2
q1 = (1 - h2)**2 q2 = (h1 - h2)/(1-h2)
- Parameters
h1 – 1 - c*(1-0.5**alpha)
h2 – c*0.5**alpha
returns: q1, q2