Did a stellar fly-by shape the planetary system around Pr 0211 in the
  cluster M 44?
  Out of the $\sim$ 3000 exoplanets detected so far, only fourteen planets are
members of open clusters: among them an exoplanet system around Pr 0211 in the
cluster M44 which consists of at least two planets with the outer planet moving
on a highly eccentric orbit at 5.5 AU. One hypothesis is that a close fly-by of
a neighbouring star was responsible for the eccentric orbit. We test this
hypothesis. First we determine the type of fly-by that would lead to the
observed parameters and then use this result to determine the history of such
fly-bys in simulations of the early dynamics in an M44-like environment. We
find that although very close fly-bys are required to obtain the observed
properties of Pr 0211c, such fly-bys are relatively common due to the high
stellar density and longevity of the cluster. Such close fly-bys are most
frequent during the first 1-2 Myr after cluster formation, corresponding to a
cluster age $\leq$ 3 Myr. During the first 2 to 3 Myr about 6.5% of stars
actually experience a fly-by that would lead to such a small system-size as
observed for Pr0211 or even smaller. It is unclear whether planets generally
form on such short timescales. However, afterwards the close fly-by rate is
still 0.2-0.5 Myr$^{-1}$, which means extrapolating this to the age of M44
12%-20% of stars would experience such close fly-bys over this timespan. Our
simulations show that the fly-by scenario is a realistic option for the
formation of eccentricity orbits of the planets in M44. The occurrence of such
events is relatively high leading to the expectation that similar systems are
likely common in open clusters in general.
