Extrasolar Moons as Gravitational Microlenses Christine Liebig

CHAPTER 4. CHOICE OF SCENARIOS 39
whole lensing system. All other masses enter the equation in units of the primary
mass. The Einstein radius, see equation (2.3), is the natural measure for angular
separations in our system and is proportional to the square root of this mass. A
given magnification pattern is produced with a unit mass and scales with the mass
of the primary lens (while lengths scale with √ MStar as the Einstein radius).
It is not at all straightforward to obtain the mass of the lensing star through
microlensing observations. It has been achieved in individual cases through a combined
measurement of parallax and the Einstein radius θE , summarised in Gould
(2008b), but lens mass determination is not an easy task. For our simulations we
rely on statistic drawn from Galactic models (figure 4.8). We assume our primary
mass to be an M-dwarf star with a mass of MStar = 0.3M⊙, because that is the
most abundant type of star to be found toward the Galactic bulge. We derive the
corresponding Einstein radius θE(DS, DL, MStar) = 0.32 milliarcseconds.
4.2.4 Source size
−∆mag
3
2
1
0
Triple Lens Binary Lens Figure 4.9: For this pair of
light curves a source size of one
solar radius has been chosen:
Rsource = R⊙. The triple-lens
0 0.1 0.2 0.3 0.4
t/tE
0.5 0.6 0.7
light curve is obtained from the
magnification pattern in figure
4.10. There is a noticeable difference
between the triple-lens light
curve and the binary-lens light
curve and the planetary causticcrossing
features are pronounced
in both.
The source size influences the “time resolution” of a light curve. For every light
curve point we have to integrate over the projected size of the source. Finer caustic
structures can easily get lost in this process. Unfortunately, for our source star
assumptions we have to take into account not only the abundance function of the
Galactic stellar population, but also the luminosity of a given stellar type. M-dwarfs
are in all probability too faint to be seen at a large distance by our telescopes – even
if they are lensed and magnified. Therefore giant stars are more probable as source
stars in our gravitational lensing setting. But the finite source size constitutes
a serious limitation to the discovery of extrasolar moons. In fact, Han and Han
(2002) stated that detecting satellite signals in the lensing light curves will be close
to impossible, because the signals are seriously smeared out by the severe finitesource
effect. They tested various source sizes (and planet-moon separations) for an
Earth-mass planet with a Moon-mass satellite. They find that even for a K0-type
source star any light curve modifications caused by the moon are washed out. Those