### Abstract

We study the dynamical evolution of globular clusters using our new two-dimensional Monte Carlo code, and we calculate the lifetimes of clusters in the Galactic environment. We include the effects of a mass spectrum, mass loss in the Galactic tidal field, and stellar evolution. We consider initial King models containing N = 10^{5}-3 × 10^{5} stars, with the dimensionless central potential W_{0} = 1, 3, and 7, and with power-law mass functions m^{-α}, with α = 1.5, 2.5, and 3.5. The evolution is followed up to core collapse or disruption, whichever occurs first. We compare our results with those from similar calculations using Fokker-Planck methods. The disruption and core collapse times of our models are significantly longer than those of one-dimensional Fokker-Planck models. This is consistent with recent comparisons with direct N-body simulations, which have also shown that the one-dimensional Fokker-Planck models can significantly overestimate the escape rate from tidally truncated clusters. However, we find that our results are in very good agreement with recent two-dimensional Fokker-Planck calculations, for a wide range of initial conditions, although our Monte Carlo models have a slightly lower mass-loss rate. We find even closer agreement of our results with modified Fokker-Planck calculations that take into account the finite nature of the system. In agreement with previous studies, our results show that the direct mass loss due to stellar evolution can significantly accelerate the mass-loss rate through the tidal boundary, by reducing the binding energy of the cluster and making it expand. This effect causes most clusters with a low initial central concentration (W_{0} ≲ 3) to disrupt quickly in the Galactic tidal field. The disruption is particularly rapid in clusters with a relatively flat mass spectrum. Only clusters born with high central concentrations (W_{0} ≳ 7) or with very steep initial mass functions (α ≳ 3.5) are likely to survive to the present and undergo core collapse. We identify the mechanism by which clusters disrupt as a dynamical instability in which the rate of mass loss increases catastrophically as the tidal boundary moves inward on the crossing timescale. To understand the various processes that lead to the escape of stars, we study the velocity distribution and orbital characteristics of escaping stars. We also compute the lifetime of a cluster on an eccentric orbit in the Galaxy, such that it fills its Roche lobe only at perigalacticon. We find that such an orbit can extend the disruption time by at most a factor of a few compared to a circular orbit in which the cluster fills its Roche lobe at all times.

Original language | English (US) |
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Pages (from-to) | 691-702 |

Number of pages | 12 |

Journal | Astrophysical Journal |

Volume | 550 |

Issue number | 2 PART 1 |

State | Published - Apr 1 2001 |

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### Keywords

- Celestial mechanics, stellar dynamics
- Globular clusters: general
- Methods: numerical

### ASJC Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science

### Cite this

*Astrophysical Journal*,

*550*(2 PART 1), 691-702.