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rodluger / Limbdark.jl

Analytical transit light curves for limb darkened stars
MIT License
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Non-linear limb-darkening? Power-2 limb-darkening? #13

Closed ericagol closed 6 years ago

ericagol commented 6 years ago

Limb-darkening with a z^{n/2} behavior (what Claret refers to as "non-linear" limb-darkening) can also probably be computed analytically in terms of hypergeometric functions and series expansions. This might be a faster alternative to using Batman or the Mandel/Agol routines in this case. The power-law limb-darkening, z^\alpha, proposed by Hestroffer, Morello and Maxted is (perhaps) the most accurate two-parameter limb-darkening. It would be nice if we could come up with an analytic expression for this limb-darkening model.

Alternatively, we can Taylor expand these limb-darkening laws at the location of the planet, and then use the polynomial series expansion in z^n to approximate over the disk of the planet.

ericagol commented 6 years ago

I can't find an analytic expression for either of these cases, so closing this for now. The polynomial expansion idea may still be worth pursuing.