CONAN.utils.ellipsoidal_variation_coefficients

CONAN.utils.ellipsoidal_variation_coefficients#

CONAN.utils.ellipsoidal_variation_coefficients(coeffs, y, input_LDlaw='quad', mu_min=0.05, n_powers=4, show_plot=False)#

calculate alpha1 and alpha2, the ellisoidal varation coefficients. The value of alpha2 is usually close to unity.

see eqn 12 and 13 of Esteves2013 https://doi.org/10.1088/0004-637X/772/1/51. This is expanded for the case of quadratic and claret 4-parameter limb darkening laws (using eqn 9 and 10 of Deline2025 https://arxiv.org/pdf/2505.01544). where alpha_ev=alpha2 and beta_ev=alpha1.

  • Kopal LD law –> 1 - κ1(1-μ) - κ2(1-μ^2) - κ3(1-μ^3) - κ4(1-μ^4).

  • power-2 law –> 1 - c*(1-μ^α).

  • claret 4-parameter law –> 1 - u1(1-μ^0.5) - u2(1-μ) - u3(1-μ^1.5) - u4(1-μ^2).

Parameters:

  • coeffs (list, array) – limb darkening coefficients. length 1 for linear limb darkening law (u1), length 2 for quad (u1, u2) and power-2 (c, alpha) limb darkening law, and length 4 for claret (“non-linear”: u1, u2, u3, u4) limb darkening law. Note that the power-2 and claret coefficients are transformed to Kopal LD law before being used in EV equations, since Kopal LD laws are different from these.

  • y (float,UFloat) – gravity darkening coefficient

  • input_LDlaw (str, optional) – limb darkening law of the input coefficients. either “quad”, “power-2” or “claret”. default is “quad”.

  • mu_min (float, optional) – minimum mu value to consider when fitting the Kopal limb darkening law to the input law. default is 0.05, but can be set to a higher value to exclude the steep drop in intensity near the limb which is often poorly captured by the input LD laws.

  • n_powers (int, optional) – number of powers (of μ) of the Kopal limb darkening law to match the input (power-2 or Claret) LD. Default is 4, since the Kopal limb darkening law has 4 powers of μ at maximum.

  • show_plot (bool, optional) – if True, shows a plot of the limb darkening profile and the Kopal fit. default is False.

Returns:

alpha – alpha1 - float, UFloat: ellipsoidal variation coefficient 1 used in the fractional constants f1 and f2 alpha2 - float, UFloat: ellipsoidal variation coefficient 2 used in the main amplitude Aev

Return type:

SimpleNamespace

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