rodluger
commented
6 years ago I like the approach that is consistent with quadratic limb darkening, which is the one people are most familiar with in general. Currently starry allows the user to either set the m=0 sph harm coefficients or the polynomial coefficients u_n. I think these two options should be enough.
On Mon, Apr 23, 2018, 5:41 PM Eric Agol notifications@github.com wrote:
The quadratic limb-darkening function is parameterized as:
I(\mu)/I(1) = 1-u_1 (1-\mu) - u_2 (1-\mu)^2
while Gimenez (2006) parameterizes it as:
I(\mu)/I(1) = 1- \sum_{n=1}^\infty a_n (1-\mu^n)
i.e. the exponent applies to the \mu, not the (1-\mu), which I think originates with Kopal. The latter is more akin to the non-linear law, although the n in that case takes on half-integer values.
Alternatively, we could simply parameterize these as sums of spherical harmonics, which avoids needing to convert between coefficients of limb-darkening and coefficients of the spherical harmonics.
Which approach makes the most sense?
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The quadratic limb-darkening function is parameterized as:
I(\mu)/I(1) = 1-u_1 (1-\mu) - u_2 (1-\mu)^2
while Gimenez (2006) parameterizes it as:
I(\mu)/I(1) = 1- \sum_{n=1}^\infty a_n (1-\mu^n)
i.e. the exponent applies to the \mu, not the (1-\mu), which I think originates with Kopal. The latter is more akin to the non-linear law, although the n in that case takes on half-integer values.
Alternatively, we could simply parameterize these as sums of spherical harmonics, which avoids needing to convert between coefficients of limb-darkening and coefficients of the spherical harmonics.
Which approach makes the most sense?