Re-parameterisation of four limb darkening laws and their implementation into the JKTEBOP code

Limb darkening (LD) is typically parameterised using a range of functional "laws" in models of the light curves of eclipsing binary and transiting planetary systems. The two-coefficient LD laws all suffer from a strong correlation between their coefficients, preventing a reliable determination of both coefficients from high-quality light curves. We use numerical simulations to propose re-parameterisations of the quadratic, logarithmic, square-root and cubic LD laws that show much weaker correlations, and implement them into the JKTEBOP code. We recommend that these re-parameterisations are used whenever both LD coefficients are fitted. Conversely, when fitting for only one coefficient, the standard laws should be used to avoid problems with fixing coefficients at poor values. We find that these choices have little effect on the other fitted parameters of a light curve model. We also recommend that the power-2 LD law should be used as default because it provides a good fit to theoretical predictions, and that the quadratic and linear laws should be avoided because they do not.