MOCCA Code for Star Cluster Simulations - II. Comparison with N-body Simulations

📝 Abstract

We describe a major upgrade of a Monte Carlo code which 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=200000 $. The new version of the Monte Carlo code (called MOCCA), in addition to the features of the old version, incorporates the direct Fewbody integrator (Fregeau et al. 2004) for three- and four-body interactions, and a new treatment of the escape process based on Fukushige & Heggie (2000). Now stars which fulfil the escape criterion are not removed immediately, but can stay in the system for a certain time which depends on the excess of the energy of a star above the escape energy. They are called potential escapers. With the addition of the Fewbody integrator the code can follow all interaction channels which are important for the rate of creation of various types of objects observed in star clusters, and ensures that the energy generation by binaries is treated in a manner similar to the $N $-body model. There are at most three new parameters which 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. Additionally, the code can follow the rate of formation of blue stragglers and black hole - black hole binaries.

💡 Analysis

We describe a major upgrade of a Monte Carlo code which 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=200000 $. The new version of the Monte Carlo code (called MOCCA), in addition to the features of the old version, incorporates the direct Fewbody integrator (Fregeau et al. 2004) for three- and four-body interactions, and a new treatment of the escape process based on Fukushige & Heggie (2000). Now stars which fulfil the escape criterion are not removed immediately, but can stay in the system for a certain time which depends on the excess of the energy of a star above the escape energy. They are called potential escapers. With the addition of the Fewbody integrator the code can follow all interaction channels which are important for the rate of creation of various types of objects observed in star clusters, and ensures that the energy generation by binaries is treated in a manner similar to the $N $-body model. There are at most three new parameters which 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. Additionally, the code can follow the rate of formation of blue stragglers and black hole - black hole binaries.

📄 Content

arXiv:1112.6246v2 [astro-ph.GA] 17 Dec 2013 Mon. Not. R. Astron. Soc. 000, 1–16 (2002) Printed 21 August 2018 (MN LATEX style file v2.2) MOCCA Code for Star Cluster Simulations - II. Comparison with N-body Simulations Mirek Giersz1⋆, Douglas C. Heggie2, Jarrod R. Hurley3 and Arkadiusz Hypki1 1Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, ul. Bartycka 18, 00-716 Warsaw, Poland 2University of Edinburgh, School of Mathematics and Maxwell Institute for Mathematical Sciences, King’s Buildings, Edinburgh EH9 3JZ, UK 3Centre for Astrophysics & Supercomputing, Swinburne University of Technology, Hawthorn VIC 3122, Australia Accepted . . . . Received . . . ; in original form . . . ABSTRACT We describe a major upgrade of a Monte Carlo code which 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 = 200000. The new version of the Monte Carlo code (called MOCCA), in addition to the features of the old version, incorporates the direct Fewbody integrator (Fregeau et al. 2004) for three- and four-body interactions, and a new treatment of the escape process based on Fukushige & Heggie (2000). Now stars which fulfil the escape criterion are not removed immediately, but can stay in the system for a certain time which depends on the excess of the energy of a star above the escape energy. They are called potential escapers. With the addition of the Fewbody integrator the code can follow all interaction channels which are important for the rate of creation of various types of objects observed in star clusters, and ensures that the energy generation by binaries is treated in a manner similar to the N-body model. There are at most three new parameters which have to be adjusted against N-body sim- ulations 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 clus- ter evolution and the cluster mass distribution, but also for the detailed distributions of mass and binding energy of binaries. Additionally, the code can follow the rate of formation of blue stragglers and black hole - black hole binaries. The code computes interactions between bina- ries and single stars up to a maximum separation rpmax, and it is found that MOCCA needs a rather large value of rpmax to get agreement with the N-body simulations. Except for some limitations such as 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 in detail comparable to an N-body code, but orders of magnitude faster. Key words: stellar dynamics – methods: numerical – globular clusters: evolution 1 INTRODUCTION This is the second paper in a new series of papers in which we attempt to describe the development of MOCCA (MOnte Carlo Cluster simulAtor) and its application to the simulations of star cluster evolution. The first in the series (Hypki & Giersz 2012) de- scribed in detail recent developments of the previous version of the Monte Carlo code (Giersz, Heggie, & Hurley (2008), and ref- erences therein) and the first results of simulations concerning blue stragglers (BSS) in an evolving star cluster environment. In this pa- per, we further develop the code and perform a very detailed com- ⋆E-mail: mig@camk.edu.pl (MG) parison with N-body simulations of large N stellar systems up to N = 2 × 105. MOCCA (Hypki & Giersz 2012) is at present one of the most advanced numerical codes for stellar dynamical simulations, and is capable of following the evolution of real star clusters in detail comparable to that of N-body simulations, but orders of magnitude faster (several hours for N = 2 × 106). The dynamical ingredients of the Monte Carlo code are essentially the same as those described in Giersz (1998, 2001, 2006) and Giersz, Heggie, & Hurley (2008), whose code embodies several features introduced by Stod´ołkiewicz (1986), whose code was in turn based on that originally devised by H´enon (1971). Two main features distinguish MOCCA from the previous version of the Monte Carlo code: (i) it now incor- c⃝2002 RAS 2 M. Giersz, D.C. Heggie, J.R. Hurley & A. Hypki porates dynamical interactions between binary and single stars and between pairs of binaries based on the Fewbody integra- tor developed by Fregeau et al. (2004); (ii) it replaces the treat- ment of the escape process in the static tidal field based on Baumgardt (2001) by one in accordance with the theory proposed by Fukushige & Heggie (2000). The escape process is not instan- taneous any more; an object needs time to find its way around the Lagrangian point L1

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