[docs]
def linear_ld_law(mu, u1):
""" Linear limb-darkening law.
.. math::
\\frac{I(\\mu)}{I(\\mu = 1)} = 1 - u_1 (1 - \\mu),
where :math:`\\mu = \\sqrt{1 - r^2}`, and :math:`u_1` is the
limb-darkening coefficient.
"""
return 1. - u1 * (1. - mu)
[docs]
def quadratic_ld_law(mu, u1, u2):
""" Quadratic limb-darkening law.
.. math::
\\frac{I(\\mu)}{I(\\mu = 1)} = 1 - u_1 (1 - \\mu) - u_2 (1 - \\mu)^2,
where :math:`\\mu = \\sqrt{1 - r^2}`, and :math:`u_1`, :math:`u_2`
are the limb-darkening coefficients.
"""
return 1. - u1 * (1. - mu) - u2 * (1. - mu)**2
[docs]
def kipping_ld_law(mu, q1, q2):
""" Kipping limb-darkening law.
.. math::
\\frac{I(\\mu)}{I(\\mu = 1)} = 1 - u_1 (1 - \\mu) - u_2 (1 - \\mu)^2,
where,
.. math::
u_1 &= 2 \\sqrt{q_1} q_2,
u_2 &= \\sqrt{q_1} (1 - 2 q_2),
and :math:`\\mu = \\sqrt{1 - r^2}`, and :math:`q_1`, :math:`q_2`
are the limb-darkening coefficients.
"""
u1 = 2. * q1**0.5 * q2
u2 = q1**0.5 * (1. - 2. * q2)
return 1. - u1 * (1. - mu) - u2 * (1. - mu)**2
[docs]
def squareroot_ld_law(mu, u1, u2):
""" Square root limb-darkening law.
.. math::
\\frac{I(\\mu)}{I(\\mu = 1)} = 1 - u_1 (1 - \\mu) - u_2 (1 - \\sqrt{\\mu}),
where :math:`\\mu = \\sqrt{1 - r^2}`, and :math:`u_1`, :math:`u_2`
are the limb-darkening coefficients.
"""
return 1. - u1 * (1. - mu) - u2 * (1. - mu**0.5)
[docs]
def nonlinear_3param_ld_law(mu, u1, u2, u3):
""" Non-linear 3-parameter limb-darkening law.
.. math::
\\frac{I(\\mu)}{I(\\mu = 1)} = 1 - u_1 (1 - \\mu) - u_2 (1 - \\mu^{1.5}) - u_3 (1 - \\mu^2),
where :math:`\\mu = \\sqrt{1 - r^2}`, and :math:`u_1`, :math:`u_2`,
:math:`u_3` are the limb-darkening coefficients.
"""
return 1. - u1 * (1. - mu) - u2 * (1. - mu**1.5) - u3 * (1. - mu**2)
[docs]
def nonlinear_4param_ld_law(mu, u1, u2, u3, u4):
""" Non-linear 4-parameter limb-darkening law.
.. math::
\\frac{I(\\mu)}{I(\\mu = 1)} = 1 - u_1 (1 - \\mu^{0.5}) - u_2 (1 - \\mu) - u_2 (1 - \\mu^{1.5}) - u_3 (1 - \\mu^2),
where :math:`\\mu = \\sqrt{1 - r^2}`, and :math:`u_1`, :math:`u_2`,
:math:`u_3`, :math:`u_4` are the limb-darkening coefficients.
"""
return 1. - u1 * (1. - mu**0.5) - u2 * (1. - mu) \
- u3 * (1. - mu**1.5) - u4 * (1. - mu**2)