Asymmetric supernova in hierarchical multiple star systems and
  application to J1903+0327
  We develop a method to analyze the effect of an asymmetric supernova on
hierarchical multiple star systems and we present analytical formulas to
calculate orbital parameters for surviving binaries or hierarchical triples and
runaway velocities for their dissociating equivalents. The effect of an
asymmetric supernova on the orbital parameters of a binary system has been
studied to great extent (e.g. Hills 1983; Kalogera 1996; Tauris & Takens 1998),
but this effect on higher multiplicity hierarchical systems has not been
explored before. With our method, the supernova effect can be computed by
reducing the hierarchical multiple to an effective binary by means of
recursively replacing the inner binary by an effective star at the center of
mass of that binary. We apply our method to a hierarchical triple system
similar to the progenitor of PSR J1903+0327 suggested by Portegies Zwart et al.
(2011). We confirm their earlier finding that PSR J1903+0327 could have evolved
from a hierarchical triple that became unstable and ejected the secondary star
of the inner binary. Furthermore, if such as system did evolve via this
mechanism the most probable configuration would be a small supernova kick
velocity, an inner binary with a large semi-major axis, and the fraction of
mass accreted onto the neutron star to the mass lost by the secondary would
most likely be between 0.35 and 0.5
