Journal Article

Investigations of approximate expressions for the transit duration

David M. Kipping

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 407, issue 1, pages 301-313
Published in print September 2010 | ISSN: 0035-8711
Published online August 2010 | e-ISSN: 1365-2966 | DOI:
Investigations of approximate expressions for the transit duration

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In this work, we investigate the accuracy of various approximate expressions for the transit duration of a detached binary against the exact solution, found through solving a quartic equation. Additionally, a new concise approximation is derived, which offers more accurate results than those currently in the literature. Numerical simulations are performed to test the accuracy of the various expressions. We find that our proposed expression yields a >200 per cent improvement in accuracy relative to the most previously employed expression.

We derive a new set of equations for retrieving the light-curve parameters and consider the effect of falsely using circular expressions for eccentric orbits, with particularly important consequences for transit surveys. The new expression also allows us to propose a new light-curve fitting parameter set, which minimizes the mutual correlations and thus improves computational efficiency. The equation is also readily differentiated to provide analytic expressions for the transit duration variation due to secular variations in the system parameters, for example due to apsidal precession induced by perturbing planets.

Keywords: methods: analytical; techniques: photometric; celestial mechanics; eclipses; planetary systems

Journal Article.  8928 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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