Extrasolar Moons as Gravitational Microlenses Christine Liebig

CHAPTER 3. METHOD 17
approximate a three-dimensional mass distribution as many successive lens planes.
Combining all this, the programme is very well equipped for simulating quasar
microlensing (where the background light of a quasar is microlensed by individual
stars of the strongly lensing foreground galaxy), as well as simulating strong lensing
on the cosmological scale. Wambsganß (1999) provides a discussion of the algorithm
and further references to its applications.
3.1.2 The moonlens code
The original microlens code is optimised for a huge number (∼ 10 6 ) of lenses
(Wambsganß, 1999). Features like the underlying cell structure of the hierarchical
tree code and the random lens generator are redundant for the simulation of planetary
systems. On the other hand, it is fundamental to be able to choose the lens
positions and masses to match realistic systems.
These modification have been implemented and from then on this simplified
version was used, referred to as moonlens from now on. moonlens is capable of
handling a chosen number of lenses (currently up to 10 2 ) at fixed positions. The
primary lens has unit mass, whereas all other lens masses are given in mass ratios
relative to this. By assigning a physical mass to the primary lens, the physical
mass scale is determined for the set of lenses. The lenses are described in three
parameters (relative mass, x- and y-position in units of θE of the primary lens). So
it is easily possible to simulate a given planetary system, for example our own (see
figure 1.1). But we concentrate on the ternary lens case with extreme mass ratios
of 0.3 M⊙ : 10 −3 : 10 −5 , i.e. a subsolar mass star, a Saturn-mass companion and a
satellite with 10 −2 Saturn masses.
moonlens is written in Fortran77 and can be compiled with any standard Fortran
compiler, for example g77 and gfortran. It consists of one main routine and several
subroutines. Parameters are read in from an input file, so that no recompiling is
necessary for changing the physical parameters. Processing time is of the order of a
few CPU hours on a PC for a reasonable resolution (1000 × 1000 pixels, 2000 rays
shot per pixel), when zoomed in on a planetary caustic. Output is currently given in
two formats: FITS files are printed using the CFITSIO library and standard routines
from the cookbook 2 . For alternative processing (and useful for control purposes) an
ASCII matrix is written out. We used it with Gnuplot to create the colour plots in
this thesis.
3.2 Light Curves
To investigate the effects that satellites of extrasolar planets have on microlensing,
we must examine how the changed gravitational potential influences the light curves,
because this is what we will eventually detect through observations. We analyse a
2 heasarc.gsfc.nasa.gov/fitsio/