Extrasolar Moons as Gravitational Microlenses Christine Liebig

CHAPTER 4. CHOICE OF SCENARIOS 37
by previous authors, e.g. Bennett and Rhie (1996). Our standard case will therefore
have an angular separation of moon and planet of one planetary Einstein ring radius,
dMP = 1.0 θP E . We have to refer back to figure 4.3, to stress again that the shape of
the resulting interference depends on the lunar mass as well as the separation.
4.1.5 Position angle of moon with respect to planet-star axis
The last physical parameter necessary for determining the magnification patterns is
the position angle of the moon φ, as in figure 4.1. It is the only parameter we do not
fix for our standard scenario. Instead, we vary it in steps of 30 ◦ to complete a full
circular orbit of the moon around the planet. By doing this, we are aiming at getting
complete coverage of a selected mass/separation scenario. Admittedly, it is not to be
expected that we will ever have an exactly head-on view of a perfectly circular orbit,
but it serves well as a first approximation and we will not loose much generality with
this assumption. Furthermore, an elliptical orbit would be constructed as the sum of
angular separations that vary depending on the position angle. We have simulated
variations in separation, but not yet constructed elliptical orbits.
Caustic interferences of the two caustics of moon and planet can be complex and
we have not yet succeeded in working out a thorough classification. We are considering
only orbits of the moon around its host planet which have a circular projection
centred at the planet. These orbits are symmetric along the planet-star axis, and
if we mirror the position of the moon along this axis, the resulting magnification
pattern will also be mirrored. For the axis perpendicular to the aforementioned
one and crossing the centre of the planetary caustic, this kind of symmetry only
holds approximately. As long as the planet-star separation is sufficiently large, lunar
magnification lines will have a similar appearance on either side of the planet.
Appendix chapter A contains the analysed magnification patterns and visualises
how the position of the moon affects the planetary caustic.
4.2 Parameters Relevant for Light Curve Analysis
In this section further parameters are discussed: those necessary for determining
the physical properties of the inspected lensing system, and also those required for
simulating realistic light curves. The first three parameters discussed, i.e. distance
to the source star DS, distance to the lensing system DL and the mass of the lensing
star MStar set the “big picture” of Galactic microlensing and serve to convert angular
separations (Einstein radii) to lengths (Astronomical Units). Source size RSource and
sampling rate constrain the shape and sampling density of the simulated light curves.
The observational standard error σ is needed for the final analysis of the light curves.