Extrasolar Moons as Gravitational Microlenses Christine Liebig

CHAPTER 3. METHOD 19
by visualising the lensing system. Even more important is the fact that it carries
the information about observable light curves. A light curve is obtained as a onedimensional
cut through the magnification pattern. Only a few more assumptions
are necessary to simulate realistic, in principle observable, light curves – angular
source size, relative motion of lens and source, lens mass. Angular separations get
a physical meaning once the distances to the source plane and to the lens plane are
fixed.
To get the magnification of a certain source, the brightness profile of the source is
convolved with the magnification pattern. As a first approximation to the physical
brightness profiles of stars (ignoring e.g. limb-darkening effects), we use a flat surface
brightness profile. The extent of the profile is given by the radius of the source
RSource.
−∆mag
3
2
1
0
Triple Lens Light Curve
0 0.05 0.1 0.15 0.2 0.25 0.3
t/tE
Figure 3.2: The light curve resulting from the source trajectory shown in figure 3.1.
The caustic-crossing close to the cusp shows up as a distinct planetary signature.
The path of the source is described in map coordinates as a combination of a point
and a directional step vector. For each light curve, the start and the end point are
determined, while taking into account the size of the source by being limited to the
area RSource away from the map boundaries. The light curve is sampled at equidistant
intervals, the length of which is given as an input parameter in units of pixels.
See also section 4.2.5 for physical implications of the sampling parameter. At each
sampling point the brightness profile is convolved with the surrounding magnification
values and an integration over all pixels up to RSource away is performed. This is the
most computationally intensive operation in our light curve analysis programme,
the computing time scaling with R 2 Source .