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(circle dot)) 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-* similar or equal to 30 - 120M(circle dot)) 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 105 to several 106). 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.