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.