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Extrasolar Moons as Gravitational Microlenses Christine Liebig

Extrasolar Moons as Gravitational Microlenses Christine Liebig

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CHAPTER 4. CHOICE OF SCENARIOS 37<br />

by previous authors, e.g. Bennett and Rhie (1996). Our standard c<strong>as</strong>e will therefore<br />

have an angular separation of moon and planet of one planetary Einstein ring radius,<br />

dMP = 1.0 θP E . We have to refer back to figure 4.3, to stress again that the shape of<br />

the resulting interference depends on the lunar m<strong>as</strong>s <strong>as</strong> well <strong>as</strong> the separation.<br />

4.1.5 Position angle of moon with respect to planet-star axis<br />

The l<strong>as</strong>t physical parameter necessary for determining the magnification patterns is<br />

the position angle of the moon φ, <strong>as</strong> in figure 4.1. It is the only parameter we do not<br />

fix for our standard scenario. Instead, we vary it in steps of 30 ◦ to complete a full<br />

circular orbit of the moon around the planet. By doing this, we are aiming at getting<br />

complete coverage of a selected m<strong>as</strong>s/separation scenario. Admittedly, it is not to be<br />

expected that we will ever have an exactly head-on view of a perfectly circular orbit,<br />

but it serves well <strong>as</strong> a first approximation and we will not loose much generality with<br />

this <strong>as</strong>sumption. Furthermore, an elliptical orbit would be constructed <strong>as</strong> the sum of<br />

angular separations that vary depending on the position angle. We have simulated<br />

variations in separation, but not yet constructed elliptical orbits.<br />

Caustic interferences of the two caustics of moon and planet can be complex and<br />

we have not yet succeeded in working out a thorough cl<strong>as</strong>sification. We are considering<br />

only orbits of the moon around its host planet which have a circular projection<br />

centred at the planet. These orbits are symmetric along the planet-star axis, and<br />

if we mirror the position of the moon along this axis, the resulting magnification<br />

pattern will also be mirrored. For the axis perpendicular to the aforementioned<br />

one and crossing the centre of the planetary caustic, this kind of symmetry only<br />

holds approximately. As long <strong>as</strong> the planet-star separation is sufficiently large, lunar<br />

magnification lines will have a similar appearance on either side of the planet.<br />

Appendix chapter A contains the analysed magnification patterns and visualises<br />

how the position of the moon affects the planetary caustic.<br />

4.2 Parameters Relevant for Light Curve Analysis<br />

In this section further parameters are discussed: those necessary for determining<br />

the physical properties of the inspected lensing system, and also those required for<br />

simulating realistic light curves. The first three parameters discussed, i.e. distance<br />

to the source star DS, distance to the lensing system DL and the m<strong>as</strong>s of the lensing<br />

star MStar set the “big picture” of Galactic microlensing and serve to convert angular<br />

separations (Einstein radii) to lengths (Astronomical Units). Source size RSource and<br />

sampling rate constrain the shape and sampling density of the simulated light curves.<br />

The observational standard error σ is needed for the final analysis of the light curves.

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