Already with ground-based observations, the microlensing technique is sensitive to cool planets with masses down to that of the Earth orbiting 0.1-1 Mo stars, the most common stars of our Galaxy, in orbits of 1-10 AU. Currently, over 700 microlensing events towards the Galactic Bulge are alerted in real-time by the OGLE and MOA surveys each year. During these events, a source star is temporarily magnified by the gravitational potential of an intervening lens star passing near the line of sight, with an impact parameter smaller than the Einstein ring radius RE, a quantity which depends on the mass of the lens, and the geometry of the alignment. For a source star in the Bulge, with a 0.3 Mo lens, RE 2 AU, the projected angular Einstein ring radius is 1 mas, and the time to transit RE is typically 20-30 days, but can be in the range 5-100 days.
A planet orbiting the lens star generates a caustic structure in the source plane, with one small caustic around the center of mass of the system, the central caustic, and one or two larger caustics further away, the planetary caustics. If the source star happens to reach the vicinity of one of the caustics, its magnification is significantly altered as compared to a single lens, resulting in a brief peak or dip in the observed light curve.
The duration of such planetary lensing anomalies scales with the square root of the planet’s mass, lasting typically a few hours (for an Earth) to 2-3 days (for a Jupiter). These two caustics (Fig. 2) provide two modes for detection. With the central caustic approached for all events with a small impact angle between source and lens star, corresponding to a large peak magnification of the event, the detection of planets in such events becomes highly efficient (Griest & Safizadeh 1998). In contrast, planetary caustics are only approached for a specific range of orientations of the source trajectory, but the characterization of a planetary signal is much easier for such configurations.
The inverse problem, finding the properties of the lensing system is a complex nonlinear one within a wide parameter space to derive the planet/star mass ratio q, and the projected separation d in units of RE. In general, model distributions for the spatial mass density of the Milky Way, the velocities of potential lens and source stars, and a mass function of the lens stars are required in order to derive probability distributions for the masses of the planet and the lens star, their distance, as well as the orbital radius and period of the planet by means of Bayesian analysis.
The observational challenge is to monitor ongoing microlensing events detected by the OGLE and MOA survey telescopes with a fleet of telescopes to achieve round-the-clock monitoring and detect real time deviations in the photometric signal.
Tuesday 4 March 2008 by flo