Most known extrasolar planets (exoplanets) have been discovered using the radial velocity$^{bf 1,2}$ or transit$^{bf 3}$ methods. Both are biased towards planets that are relatively close to their parent stars, and studies find that around 17--30% (r
efs 4, 5) of solar-like stars host a planet. Gravitational microlensing$^{bf 6rm{bf -}bf 9}$, on the other hand, probes planets that are further away from their stars. Recently, a population of planets that are unbound or very far from their stars was discovered by microlensing$^{bf 10}$. These planets are at least as numerous as the stars in the Milky Way$^{bf 10}$. Here we report a statistical analysis of microlensing data (gathered in 2002--07) that reveals the fraction of bound planets 0.5--10 AU (Sun--Earth distance) from their stars. We find that 17$_{bf -9}^{bf +6}$% of stars host Jupiter-mass planets (0.3--10 $MJ$, where $MJ {bf = 318}$ $Mearth$ and $Mearth$ is Earths mass). Cool Neptunes (10--30 $Mearth$) and super-Earths (5--10 $Mearth$) are even more common: their respective abundances per star are 52$_{bf -29}^{bf +22}$% and 62$_{bf -37}^{bf +35}$%. We conclude that stars are orbited by planets as a rule, rather than the exception.
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 (2008) 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.
