Bayesian analysis of caustic-crossing microlensing events

¹ Institut d'Astrophysique de Paris, UMR 7095 CNRS, 98 bis boulevard Arago, 75014 Paris, France e-mail: cassan@iap.fr
² Université Pierre & Marie Curie, Paris, France
³ Scottish Universities Physics Alliance, School of Physics & Astronomy, University of St Andrews, North Haugh, KY169SS, UK
⁴ Las Cumbres Observatory, 6740B Cortona Dr, suite 102, Goleta, CA 93117, USA
⁵ School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS, UK

Received: 27 November 2009
Accepted: 23 February 2010

Abstract

Aims. Caustic-crossing binary-lens microlensing events are important anomalous events because they are capable of detecting an extrasolar planet companion orbiting the lens star. Fast and robust modelling methods are thus of prime interest in helping to decide whether a planet is detected by an event. Cassan introduced a new set of parameters to model binary-lens events, which are closely related to properties of the light curve. In this work, we explain how Bayesian priors can be added to this framework, and investigate on interesting options.

Methods. We develop a mathematical formulation that allows us to compute analytically the priors on the new parameters, given some previous knowledge about other physical quantities. We explicitly compute the priors for a number of interesting cases, and show how this can be implemented in a fully Bayesian, Markov chain Monte Carlo algorithm.

Results. Using Bayesian priors can accelerate microlens fitting codes by reducing the time spent considering physically implausible models, and helps us to discriminate between alternative models based on the physical plausibility of their parameters.