Related papers: A universal approach to the calculation of the tra…
We derive analytic, closed-form solutions for the light curve of a planet transiting a star with a limb darkening profile which is a polynomial function of the stellar elevation, up to arbitrary integer order. We provide improved analytic…
In this paper a set of analytic formulae are presented with which the partial derivatives of the flux obscuration function can be evaluated -- for planetary transits and eclipsing binaries -- under the assumption of quadratic limb…
We present exact analytic formulae for the eclipse of a star described by quadratic or nonlinear limb darkening. In the limit that the planet radius is less than a tenth of the stellar radius, we show that the exact lightcurve can be well…
In this paper we describe an algorithm and deduce the related mathematical formulae that allows the computation of observed fluxes in stellar and planetary systems with arbitrary number of bodies being part of a transit or occultation…
We present here an efficient method for computing the visible flux for each body during a multi-body eclipsing event for all commonly used limb darkening laws. Our approach follows the idea put forth by Pal (2012) to apply Green's Theorem…
Limb darkening laws are convenient parameterizations of the stellar intensity center-to-limb variation, and their use is ubiquitous in eclipse and transit modeling. But they are not "laws" in any sense -- they are simple approximations of…
Very precise measurements of exoplanet transit lightcurves both from ground and space based observatories make it now possible to fit the limb-darkening coefficients in the transit-fitting procedure rather than fix them to theoretical…
The light curve of an exoplanetary transit can be used to estimate the planetary radius and other parameters of interest. Because accurate parameter estimation is a non-analytic and computationally intensive problem, it is often useful to…
We carried out numerical experiments on the evaluation of the possibilities of obtaining the information about brightness distributions for the components of eclipsing variables from the data of high-precision photometry expected for…
The light curve of an exoplanetary transit can be used to estimate the planetary radius and other parameters of interest. Because accurate parameter estimation is a non-analytic and computationally intensive problem, it is often useful to…
The transit method, employed by MOST, \emph{Kepler}, and various ground-based surveys has enabled the characterization of extrasolar planets to unprecedented precision. These results are precise enough to begin to measure planet atmosphere…
Limb-darkening is fundamental in determining transit lightcurve shapes, and is typically modeled by a variety of laws that parametrize the intensity profile of the star that is being transited. Confronted with a transit lightcurve, some…
Inaccurate limb-darkening models can be a significant source of error in the analysis of the light curves for transiting exoplanet and eclipsing binary star systems, particularly for high-precision light curves at optical wavelengths. The…
We present a solution for the light curve of two bodies mutually transiting a star with polynomial limb darkening. The term "mutual transit" in this work refers to a transit of the star during which overlap occurs between the two transiting…
We present the first exact analytical solutions for exoplanet transit light curves under arbitrary real power-law limb darkening, $I(\mu) = I_0\mu^\alpha$ with $\alpha > -2$, removing the two-decade restriction to integer-polynomial forms.…
The depth of an exoplanetary transit in the light curve of a distant star is commonly approximated as the squared planet-to-star radius ratio, (R_p/R_s)^2. Stellar limb darkening, however, results in significantly deeper transits. Here we…
Extended source effects can be seen in gravitational lensing events when sources cross critical lines. Those events probe the stellar intensity profile and could be used to measure limb darkening coefficients to test stellar model…
The power-2 law, $I_{\lambda}(\mu)=1- c (1 - \mu^{\alpha})$, accurately represents the limb-darkening profile for cool stars. It has been implemented in a few transit models to-date using numerical integration but there is as-yet no…
The ability to observe extrasolar planets transiting their stars has profoundly changed our understanding of these planetary systems. However, these measurements depend on how well we understand the properties of the host star, such as…
Stellar limb darkening must be properly accounted for to accurately determine the radii of exoplanets at various wavelengths. The standard approach to address limb darkening involves either using laws with coefficients from modelled stellar…