In May 2013 the second paper from the series of papers about the MOCCA code was published in the Montly Notices of the Royal Astronomical Society (Giersz et al. 2013).
We describe a major upgrade of the Monte Carlo code that has previously been used for many studies of dense star clusters. We outline the steps needed in order to calibrate the results of the new Monte Carlo code against N-body simulations for large-N systems, up to N = 200 000. The new version of the Monte Carlo code (called MOCCA), in addition to features of the old version, incorporates the direct Fewbody integrator for three- and four-body interactions, and a new treatment of the escape process based on work of Fukushige & Heggie. Now stars that fulfill the escape criterion are not removed immediately, but can stay in the system for a certain time that depends on the excess of the energy of the star above the escape energy. These stars are termed potential escapers.
With the addition of the Fewbody integrator the code can follow all interaction channels that are important for the rate of creation of various types of objects observed in star clusters, and it is ensured that the energy generation by binaries is treated in a manner similar to in the N-body model.
There are at most three new parameters that have to be adjusted against N-body simulations for large N: two (or one, depending on the chosen approach) connected with the escape process, and one responsible for the determination of the interaction probabilities. The values adopted for the free parameters have at most a weak dependence on N. They allow MOCCA to reproduce N-body results with reasonable precision, not only for the rate of cluster evolution and the cluster mass distribution, but also for the detailed distributions of mass and binding energy of binaries. In addition, the code can follow the rate of formation of blue stragglers and black hole-black hole binaries. The code computes interactions between binaries and single stars up to a maximum separation r pmax , and it is found that MOCCA needs a large value of r pmax to obtain agreement with N-body simulations.
In spite of some limitations, such as its spherical symmetry, a Monte Carlo code such as MOCCA is at present the most advanced code for simulations of real star clusters. It can follow the cluster evolution at a level of detail comparable to that in an N-body code, but orders of magnitude faster.