Asymmetric supernova in hierarchical multiple star systems and application to J1903+0327

We develop a method to analyse the effect of an asymmetric supernova on hierarchical multiple star systems and 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 a great extent, 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 centre 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. 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 a 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 on to the neutron star to the mass lost by the secondary most likely be between 0.35 and 0.5.