Monte-Carlo simulations of globular cluster dynamics

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Physics, 2000.Includes bibliographical references (leaves 156-163).We present the results of theoretical calculations for the dynamical evolution of dense globular star clusters. Our new study was motivated in part by the wealth of new data made available from the latest optical, radio, and X-ray observations of globular clusters by various satellites and ground-based observatories, and in part by recent advances in computer hardware. New parallel supercomputers, combined with improved computational methods, now allow us to perform dynamical simulations of globular cluster evolution using a realistic number of stars (N - 10 - 106) and taking into account the full range of relevant stellar dynamical and stellar evolutionary processes. These processes include two-body gravitational scattering, strong interactions and physical collisions involving both single and binary stars, stellar evolution of single stars, and stellar evolution and interactions in close binary stars. We have developed a new numerical code for computing the dynamical evolution of a dense star cluster. Our code is based on a Monte Carlo technique for integrating numerically the Fokker-Planck equation. We have used this new code to study a number of important problems. In particular, we have studied the evolution of globular clusters in our Galaxy, including the effects of a mass spectrum, mass loss due to the tidal field of the Galaxy, and stellar evolution. Our results show that the direct mass loss from stellar evolution can significantly accelerate the total mass loss from a globular cluster, causing most clusters with low initial central concentrations to disrupt completely. Only clusters born with high central concentrations, or with relatively few massive stars, are likely to survive until the present and remain observable. Our study of mass segregation in clusters shows that it is possible to retain significant numbers of very-low-mass (m < 0.1M.) objects, such as brown dwarfs or planets, in the outer halos of globular clusters, even though they are quickly lost from the central, denser regions. This is contrary to the common belief that globular clusters are devoid of such low-mass objects. We have also performed, for the first time, dynamical simulations of clusters containing a realistic number of stars and a significant fraction of binaries. We find that the energy generated through binarybinary and binary-single-star interactions in the cluster core can support the system against gravothermal collapse on timescales exceeding the age of the Universe, explaining naturally the properties of the majority of observed globular clusters with resolved cores.by Kriten J. Joshi.Ph.D

Thermal and Dynamical Equilibrium in Two-Component Star Clusters

We present the results of Monte Carlo simulations for the dynamical evolution of star clusters containing two stellar populations with individual masses m1 and m2 > m1, and total masses M1 and M2 < M1. We use both King and Plummer model initial conditions and we perform simulations for a wide range of individual and total mass ratios, m2/m1 and M2/M1. We ignore the effects of binaries, stellar evolution, and the galactic tidal field. The simulations use N = 10^5 stars and follow the evolution of the clusters until core collapse. We find that the departure from energy equipartition in the core follows approximately the theoretical predictions of Spitzer (1969) and Lightman & Fall (1978), and we suggest a more exact condition that is based on our results. We find good agreement with previous results obtained by other methods regarding several important features of the evolution, including the pre-collapse distribution of heavier stars, the time scale on which equipartition is approached, and the extent to which core collapse is accelerated by a small subpopulation of heavier stars. We briefly discuss the possible implications of our results for the dynamical evolution of primordial black holes and neutron stars in globular clusters.Comment: 31 pages, including 13 figures, to appear in Ap

Monte Carlo Simulations of Globular Cluster Evolution - II. Mass Spectra, Stellar Evolution and Lifetimes in the Galaxy

We study the dynamical evolution of globular clusters using our new 2-D 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 - 3x10^5 stars, and follow the evolution up to core collapse, or disruption, whichever occurs first. We find that the lifetimes of our models are significantly longer than those obtained using 1-D Fokker-Planck (F-P) methods. We also find that our results are in very good agreement with recent 2-D F-P calculations, for a wide range of initial conditions. Our results show that the direct mass loss due to stellar evolution can significantly accelerate the mass loss through the tidal boundary, causing most clusters with a low initial central concentration (Wo <~ 3) to disrupt quickly in the Galactic tidal field. Only clusters born with high initial central concentrations (Wo >~ 7) or steep initial mass functions are likely to survive to the present and undergo core collapse. We also study the orbital characteristics of escaping stars, and find that the velocity distribution of escaping stars in collapsing clusters looks significantly different from the distribution in disrupting clusters. We calculate 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 lifetime by at most a factor of a few compared to a circular orbit in which the cluster fills its Roche lobe at all times.Comment: 32 pages, including 10 figures, to appear in ApJ, minor corrections onl

Distant Companions and Planets around Millisecond Pulsars

We present a general method for determining the masses and orbital parameters of binary millisecond pulsars with long orbital periods (P_orb >> 1 yr), using timing data in the form of pulse frequency derivatives. We apply our method to analyze the properties of the second companion in the PSR B1620-26 triple system. We use the latest timing data for this system to constrain the mass and orbital parameters of the second companion. We find that all possible solutions have a mass m_2 in the range 2.4 10^-4 M_sun <= m_2 sin i_2 <= 1.2 10^-2 M_sun, i.e., almost certainly excluding a second companion of stellar mass and suggesting instead that the system contains a planet or a brown dwarf. Using Monte-Carlo realizations of the triple configuration in three dimensions we find the most probable value of m_2 to be 0.010(5) M_sun, corresponding to a distance of 38(6) AU from the center of mass of the inner binary (the errors indicate 80% confidence intervals). We also apply our method to analyze the planetary system around PSR B1257+12, where a distant, giant planet may be present in addition to the three well-established Earth-mass planets. We find that the simplest interpretation of the frequency derivatives implies the presence of a fourth planet with a mass of ~100 M_earth in a circular orbit of radius ~40 AU.Comment: 30 pages, Latex, 10 Postscript figures, uses aaspp4.sty. ApJ submitted. Also available at http://ensor.mit.edu/~rasi

Monte-Carlo Simulations of Globular Cluster Evolution - I. Method and Test Calculations

We present a new parallel supercomputer implementation of the Monte-Carlo method for simulating the dynamical evolution of globular star clusters. Our method is based on a modified version of Henon's Monte-Carlo algorithm for solving the Fokker-Planck equation. Our code allows us to follow the evolution of a cluster containing up to 5x10^5 stars to core collapse in < 40 hours of computing time. In this paper we present the results of test calculations for clusters with equal-mass stars, starting from both Plummer and King model initial conditions. We consider isolated as well as tidally truncated clusters. Our results are compared to those obtained from approximate, self-similar analytic solutions, from direct numerical integrations of the Fokker-Planck equation, and from direct N-body integrations performed on a GRAPE-4 special-purpose computer with N=16384. In all cases we find excellent agreement with other methods, establishing our new code as a robust tool for the numerical study of globular cluster dynamics using a realistic number of stars.Comment: 35 pages, including 8 figures, submitted to ApJ. Revised versio