Runaway collisions in young star clusters. I. Methods and tests

We present the methods and preparatory work for our study of the collisional runaway scenario to form a very massive star (VMS, M∗ > 400M⊙) at the centre of a young, compact stellar cluster. In the first phase of the process, a very dense central core of massive stars (M∗ ≃ 30− 120M⊙) forms through mass segregation and gravothermal collapse. This leads to a collisional stage, likely to result in the formation of a VMS (itself a possible progenitor for an intermediate-mass black hole) through a runaway sequence of mergers between the massive stars. In this paper we present the runaway scenario in a general astrophysical context. We then explain the numerical method used to investigate it. Our approach is based on a Monte Carlo code to simulate the stellar dynamics of spherical star clusters using a very large number of particles (a few 10 to several 10). Finally, we report on test computations carried out to ensure that our implementation of the important physics is sound. In a second paper, we present results from more than 100 cluster simulations realized to determine the conditions leading to the collisional formation of a VMS and the characteristics of the runaway sequences.