rodluger / Limbdark.jl

Analytical transit light curves for limb darkened stars
MIT License
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Missing notation in the paper: #88

Open ericagol opened 4 years ago

ericagol commented 4 years ago

Here is some notation missing from the table at the end of the paper:

1). In equation (7), dS indicates an integral over the projected area of the star (also in eqn 20-22).

2). The variable u in equation 26 is an integration variable, defined just before the equation.

3). A, B & C in equation 31 are defined just after that equation.

4). x_0 = cos(kappa_0) and x_1 = cos(kappa_1).

5). epsilon is a small parameter used in testing the code near boundaries in figures 4 & 14.

6). In equations (53) and (54), eta is a variable defined in Mandel & Agol 2002.

7). In Figure 15 the lower case f is the same as the upper case F.

8). In Figure 7, the calligraphy F is the same as F.

9). \Delta t is the exposure time; t' is an integration variable in equation 101.

10). q_1 & q_2 are the quadratic limb-darkening coefficients used in Kipping (2015).

11). In Appendix A the notation is taken from the Mandel & Agol (2002) paper.

12). In equation (40) and equations (102-106), a, b & p are variables used in defining these equations. Note that the b in these equations is not the impact parameter variable used throughout the paper; these equations are the only time that b is used in this way.

13). In section 7, D_max is the maximum number of depths in the adaptive Simpson integration, and \epsilon_tol is the tolerance specified in the adaptive Simpson integration.

14). j_max is an upper index for the sum in equation 81.