Hénon-like Monte Carlo simulations of spherical clusters: references

We sort the references according to the 5 Monte Carlo codes that use the algorithm invented by Michel Hénon and have led to published work. This list is not complete. Instead, we try to mention all key papers for the development and use of each code.

Hénon code

Hénon 71a, 71b, 73: Detailed description of the method and simulations.
Aarseth, Hénon & Wielen 74: Comparison with N-body models.
Hénon 75: late developments of the MC code.

Stodolkiewicz code

Stodolkiewicz 82: Description of the code and first simulations (single- and multi-mass clusters)
Stodolkiewicz 85: Proceeding paper showing first results with binaries
Stodolkiewicz 86: First introduction of binaries in a MC code.

Giersz code

Giersz 98: Presentation of code and first results. Single-mass clusters with dynamically formed binaries.
Giersz 01: Tidally limited, multimass systems with stellar evolution.
Giersz & Spurzem 00, 03: Hybrid code treating single stars with the gaseous approach and binaries with the Monte Carlo representation.
Giersz & Heggie 03: MC models of omega Cen

MIT/NU code

Joshi et al. 00: Presentation of the code and single-mass models.
Watters et al. 00: Investigations about conditions for equilibrium in clusters with 2 mass components.
Joshi, Nave & Rasio 01:
Tidally limited, multimass systems with stellar evolution.
Fregeau et al. 02: Study of mass segregation in 2-component clusters.
Fregeau et al. 03: Models with primordial binaries.
Gürkan, Freitag & Rasio 04: Study of core collapse for clusters with broad mass spectrum (to form massive black holes through run-away collisions, see also Rasio, Freitag & Gürkan 03)

Freitag code

Freitag & Benz 01: Presentation of the code and test computations for pure relaxation (single- and multi-mass clusters).
Freitag & Benz 02: Introduction of stellar evolution, collisions and central black hole. Galactic nucleus models.
Freitag 01, 03a, 03b: Monte Carlo simulations to determine the rate of capture of stars by a massive black hole through emission of gravitational waves.
Rasio, Freitag & Gürkan 03: Run-away formation of very massive stars in dense clusters.

Other Monte Carlo schemes for cluster dynamics

In the 70's, Spitzer and collaborators have developed a Monte Carlo code which was in many aspects similar to Hénon's. The main difference is that the orbital motions of particles (i.e. spherical shells, like in Hénon's code) was explicitely integrated, a feature that allowed to follow dynamical phases of the cluster's evolution.

In the late 70's early 80's, Shapiro and collaborators wrote a code whose principles are a combination of the Monte Carlo code à la Hénon and of Fokker-Plank codes. This scheme uses particles whose orbital properties are slowly changed according to energy (E) ang angular momentum (J) diffusion coefficients. After a fraction of the relaxation time, the new distribution function is computed by binning the particles in the (E,J) space (use is made of adiabatic invariants to account for the potential change). From this, the new diffusion coefficients are tabulated in (E,J) space and a new step starts. This method offers the advantage that particles need not represent the same number of stars because the never directly interact with each other. In particular, one may increase the resolution at the centre of the cluster by splitting particles. But this scheme is more complex than Hénon's and seems difficult to apply to clusters with a mass spectrum.
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