The Impact of Stellar Clustering on the Observed Multiplicity of
  Super-Earth systems: Outside-in Cascade of Orbital Misalignments Initiated by
  Stellar Flybys
  A recent study suggests that the observed multiplicity of super-Earth (SE)
systems is correlated with stellar overdensities: field stars in high
phase-space density environments have an excess of single-planet systems
compared to stars in low density fields. This correlation is puzzling as
stellar clustering is expected to influence mostly the outer part of planetary
systems. Here we examine the possibility that stellar flybys indirectly excite
the mutual inclinations of initially coplanar SEs, breaking their co-transiting
geometry. We propose that flybys excite the inclinations of exterior substellar
companions, which then propagate the perturbation to the inner SEs. Using
analytical calculations of the secular coupling between SEs and companions,
together with numerical simulations of stellar encounters, we estimate the
expected number of "effective" flybys per planetary system that lead to the
destruction of the SE co-transiting geometry. Our analytical results can be
rescaled easily for various SE and companion properties (masses and semi-major
axes) and stellar cluster parameters (density, velocity dispersion and
lifetime). We show that for a given SE system, there exists an optimal
companion architecture that leads to the maximum number of effective flybys;
this results from the trade-off between the flyby cross section and the
companion's impact on the inner system. Subject to uncertainties in the cluster
parameters, we conclude that this mechanism is inefficient if the SE system has
a single exterior companion, but may play an important role in "SE + two
companions" systems that were born in dense stellar clusters. Whether this
effect causes the observed correlation between planet multiplicity and stellar
overdensities remains to be confirmed.
