Extrasolar Moons as Gravitational Microlenses Christine Liebig

CHAPTER 2. GRAVITATIONAL LENSING 13
−∆mag
Figure 2.4: Caustics form when there are multiple lenses. The magnification map
on the left corresponds to a star-planet binary, with a mass ratio of 10 −3 . If the source
trajectory crosses caustic lines this gives rise to a characteristic deviation from the
Paczyński curve, a planetary signature.
2.3 Search for Planets via Galactic Microlensing
When we observe a Galactic lensing event, the parameters that we deal with will
have typical orders of magnitude. Imagine, that we observe an alignment of two solar
sized stars in our Milky Way. The background star will most probably lie in the
centre of the Galactic bulge at a distance of DS = 8 kpc for there we find the highest
density of stars, and indeed, that is where all Galactic lensing survey programs direct
their telescopes. The lensing star will be somewhere in the foreground, DL = 6 kpc
should be a safe assumption. We can already calculate the Einstein angle, to find
θE = 0.6 milliarcseconds.
This is far beyond the resolution abilities of real telescopes. However, even if the
individual images cannot be resolved, the magnification can still be detected if lens
and source are in relative motion to each other. This passing of the lens in front
of the source gives rise to a transient brightening as shown in figure 2.3. The
light curve that results if a point lens moves in front of a point source is often called
Paczyński curve, as it was depicted in Paczyński (1986). A magnification of µ = 1.34
corresponds to a difference in magnitude of ∆mag = 0.32 mag, which is easily
detectable. Events with a magnification of µ = 100 or more are not uncommon.
The search for massive compact halo object as potential dark matter, mentioned
it section 2.1 was not very fruitful (see e.g. Afonso et al., 2003). Microlensing
experiments carried out towards the Galactic bulge had originally been intended
as test experiments for the halo surveys, but Mao and Paczyński (1991) showed
that roughly 10% of the lensing events must have signature of a binary companion.
It was realised, that through constantly monitoring a very large number of stars
one would surely detect binary systems and possibly planets. Gould and Loeb
time