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.

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We investigate the effect of different initial virial temperatures, Q, on the dynamics of star clusters. We find that the virial temperature has a strong effect on many aspects of the resulting system, including among others: the fraction of bodies escaping from the system, the depth of the collapse of the system, and the strength of the mass segregation. These differences deem the practice of using "cold" initial conditions no longer a simple choice of convenience. The choice of initial virial temperature must be carefully considered as its impact on the remainder of the simulation can be profound. We discuss the pitfalls and aim to describe the general behavior of the collapse and the resultant system as a function of the virial temperature so that a well reasoned choice of initial virial temperature can be made. We make a correction to the previous theoretical estimate for the minimum radius, R min , of the cluster at the deepest moment of collapse to include a Q dependency, R min ≈ Q+N (−1/3) , where N is the number of particles.We use our numerical results to infer more about the initial conditions of the young cluster R136. Based on our analysis, we find that R136 was likely formed with a rather cool, but not cold, initial virial temperature (Q ≈ 0.13). Using the same analysis method, we examined 15 other young clusters and found the most common initial virial temperature to be between 0.18 and 0.25.

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