Extrasolar Moons as Gravitational Microlenses Christine Liebig

CHAPTER 4. CHOICE OF SCENARIOS 33
Both examples are singular in the solar system, but we argue that more massive
moons are the more interesting ones anyway. A more massive moon can effectively
stabilise the obliquity of a planet, which is thought to be favouring the habitability
of the planet (Benn, 2001). The next highest mass ratio found in the solar system
is two orders of magnitude smaller: qMP = MTriton
MNeptune = 2 × 10−4 . At the low mass
end of our analysis we examine qMP = 10 −3 . See figure 4.3 for the three mass ratios
that we adopt.
There are analogies to the planet-star mass ratio. A higher value of the lunar
mass ratio leads to a higher deflection of light rays by the moon, and will produce a
larger sized lunar caustic. Consequently, the lunar caustic will cover a larger fraction
of the planetary caustic and be noticeable in a larger fraction of source trajectories.
One of our requirements is that the planet has already been detected with a caustic
crossing. It is just spelling out common sense to state that the probability to discover
a massive moon next to an already discovered planet is higher than to find a less
massive natural satellite of the planet.
(a) qMP = 10 −3 (b) qMP = 10 −2 (c) qMP = 10 −1
Figure 4.3: The moon mass determines the size and strength of the lunar caustic,
on which we have zoomed in. From left to right the lunar mass ratio is increased
from qMP = 10 −3 to 10 −1 , all other parameters remain constant. Distinctly different
caustic topologies are induced by the interference of lunar and planetary caustic.
4.1.3 Angular separation of planet and star
The angular separation dP S of a binary of star and planet will evoke a certain
topology of caustics, see figure 4.4. They gradually evolve from the close separation
case with two small triangular caustics on the far side of the star and a small central
caustic at the star position, to a large central caustic for the intermediate case, when
the planet is situated near the stellar Einstein ring, dP S = θE. If the planet is moved
further out, one obtains a small central caustic and a larger isolated, diamond-shaped
planetary caustic (figure 4.5(b)) that is very asymmetric and elongated towards the
primary mass in the beginning, but becomes more and more symmetric if the planet
is placed further outwards (figure 4.5(c)).