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Two Recent Developments Concerning the Monte Carlo Method

Published online by Cambridge University Press:  14 August 2015

M. Hénon
M. Hénon*
Affiliation:
Observatoire de Nice, Nice, France

Abstract

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This paper consists of two independent parts.

  1. (1) The Monte Carlo method for computing the evolution of spherical stellar systems has been modified so that the computation can be continued after the time of formation of the central singularity. Results are presented for systems with equal and unequal star masses. The initial core-halo formation is followed by a general expansion of the cluster, while the central singularity absorbs a growing fraction of the total negative energy.

  2. (2) Theoretical expressions of the ‘diffusion coefficients’, which describe the effect of encounters in a stellar system, contain a factor In(γN) where N is the number of stars and γ is a constant usually taken to be of the order of 0.4. A reconsideration of the ‘non-dominant terms’ leads to a substantially lower value, of the order of 0.15 for equal masses and 0.075 for unequal masses with a typical distribution. This correction improves the agreement between N-body and Monte Carlo simulations of spherical systems.

Type
Part I/Spherical Systems
Information
Symposium - International Astronomical Union , Volume 69: Dynamics of Stellar Systems , 1975 , pp. 133 - 149
Copyright
Copyright © Reidel 1975 

References

Aarseth, S. J.: 1971, Astrophys. Space Sci. 13, 324.Google Scholar
Aarseth, S. J.: 1973, Vistas in Astronomy 15, 13.Google Scholar
Aarseth, S. J.: 1974, Astron. Astrophys. 35, 237.Google Scholar
Aarseth, S. J.: 1975, this volume, p. 57.CrossRefGoogle Scholar
Aarseth, S. J., Hénon, M., and Wielen, R.: 1975, Astron. Astrophys. 37, 183.Google Scholar
Abramowitz, M. and Stegun, I. A.: 1965, Handbook of Mathematical Functions, Dover, New York, p. 1004.Google Scholar
Chandrasekhar, S.: 1941, Astrophys. J. 93, 285.Google Scholar
Chandrasekhar, S.: 1942, Principles of Stellar Dynamics, Chicago University Press, Chicago.Google Scholar
Hénon, M.: 1961, Ann. Astrophys. 24, 369.Google Scholar
Hénon, M.: 1971, Astrophys. Space Sci. 13, 284 and 14, 151.CrossRefGoogle Scholar
Hénon, M.: 1973, in Martinet, L. and Mayor, M. (eds.), Dynamical Structure and Evolution of Stellar Systems, Swiss Society of Astronomy and Astrophysics Third Advanced Course, Geneva Observatory, p. 224.Google Scholar
King, I.: 1975, this volume, p. 99.Google Scholar
Larson, R. B.: 1970, Monthly Notices Roy. Astron. Soc. 147, 323; 150, 93.CrossRefGoogle Scholar
Liboff, R. L.: 1959, Phys. Fluids 2, 40.CrossRefGoogle Scholar
Lynden-Bell, D. and Wood, R.: 1968, Monthly Notices Roy. Astron. Soc. 138, 495.CrossRefGoogle Scholar
Spitzer, L. Jr.: 1969, Astrophys. J. 158, L139.Google Scholar
Spitzer, L. Jr.: 1975, this volume, p. 3.Google Scholar
Spitzer, L. Jr. and Hart, M. H.: 1971, Astrophys. J. 164, 399.Google Scholar
Spitzer, L. Jr. and Thuan, T. X.: 1972, Astrophys. J. 175, 31.Google Scholar
Von Hoerner, S.: 1968, Bull. Astron., Sér. 3, 3, 147.Google Scholar
Wielen, R.: 1967, Veröffentl. Astron. Rechen-Inst. Heidelberg, Nr. 19.Google Scholar
Wielen, R.: 1971, Astrophys. Space Sci. 13, 300.Google Scholar
Wielen, R.: 1974, in Mavridis, L. N. (ed.), Proceedings of the First European Astronomical Meeting (Athens 1972), Springer-Verlag, Berlin-Heidelberg-New York, Vol. 2, p. 326.CrossRefGoogle Scholar
Wielen, R.: 1975, this volume, p. 119.CrossRefGoogle Scholar