Dynamical Evolution Of Globular Clusters Research Articles

The evolution of globular clusters

Taking a wide range of the initial conditions, including spatial density distribution and mass function etc, the dynamical evolution of globular clusters in the Milky Way is investigated in detail by means of Monte Carlo simulations. Four dynamic mechanisms are considered: stellar evaporation, stellar evolution, tidal shocks due to both the disk and bulge, and dynamical friction. It is found that stellar evaporation dominates the evolution of low-mass clusters and all four are important for massive ones. For both the power-law and lognormal initial clusters mass functions, we can find the best-fit models which can match the present-day observations with their main features of the mass function almost unchanged after evolution of several Gyr. This implies that it is not possible to determine the initial mass function only based on the observed ones today. Moreover, the dispersion of the modelled mass functions mainly depends on the potential wells of host galaxies with the almost constant peaks, which is consistent with current observations.

Observational Constraints on the Formation and Evolution of Globular Cluster Systems

AbstractThis paper reviews some of the observational properties of globular cluster systems, with a particular focus on those that constrain and inform models of the formation and dynamical evolution of globular cluster systems. I first discuss the observational determination of the globular cluster luminosity and mass function. I show results from new very deep HST data on the M87 globular cluster system, and discuss how these constrain models of evaporation and the dynamical evolution of globular clusters. The second subject of this review is the question of how to account for the observed constancy of the globular cluster mass function with distance from the center of the host galaxy. The problem is that a radial trend is expected for isotropic cluster orbits, and while the orbits are observed to be roughly isotropic, no radial trend in the globular cluster system is observed. I review three extant proposals to account for this, and discuss observations and calculations that might determine which of these is most correct. The final subject is the origin of the very weak mass-radius relation observed for globular clusters. I discuss how this strongly constrains how globular clusters form and evolve. I also note that the only viable current proposal to account for the observed weak mass-radius relation naturally effects the globular cluster mass function, and that these two problems may be closely related.

Monte Carlo Simulations of Globular Cluster Evolution. IV. Direct Integration of Strong Interactions

We study the dynamical evolution of globular clusters containing populations of primordial binaries, using our newly updated Monte Carlo cluster evolution code with the inclusion of direct integration of binary scattering interactions. We describe the modifications we have made to the code, as well as improvements we have made to the core Monte Carlo method. We present several test calculations to verify the validity of the new code, and perform many comparisons with previous analytical and numerical work in the literature. We simulate the evolution of a large grid of models, with a wide range of initial cluster profiles, and with binary fractions ranging from 0 to 1, and compare with observations of Galactic globular clusters. We find that our code yields very good agreement with direct N-body simulations of clusters with primordial binaries, but yields some results that differ significantly from other approximate methods. Notably, the direct integration of binary interactions reduces their energy generation rate relative to the simple recipes used in Paper III, and yields smaller core radii. Our results for the structural parameters of clusters during the binary-burning phase are now in the tail of the range of parameters for observed clusters, implying that either clusters are born significantly more or less centrally concentrated than has been previously considered, or that there are additional physical processes beyond two-body relaxation and binary interactions that affect the structural characteristics of clusters.

On the Probability of Stellar Encounters in Globular Clusters

The number of stellar encounters in a globular cluster per unit time, with given changes in energy and direction of motion relative to the cluster center, has been determined assuming an anisotropic field star distribution function. An exact expression for the integrated probability of such encounters is derived for the case of equal-mass stars, and ranges of physical variables are analyzed. The distributions of the probability and number of encounters in a globular cluster with and without a black hole in the Plummer and King models are also studied. It is shown that the influence of the black hole on the probability distribution almost vanishes at the distance r0 ≈ 1.55rc, where rc is the core radius of the cluster. Moreover, in the area of radius (2–3)r0 strong encounters are significant and the Fokker-Planck approximation cannot be used for modeling the dynamical evolution of globular clusters. The method is developed for determining the probability of distant (weak), as well as close, encounters and for studying the dynamical evolution of globular clusters in the space of the energy integral (E) and angular momentum per unit mass (J) under close encounters.

Dynamical Evolution of Globular Clusters in the Galaxy

Given the initial conditions of spatial density distribution, velocitydistribution and mass function, the dynamical evolution of globularclusters in the Milky Way is investigated in details by means of Monte Carlo simulations. Four dynamic mechanisms are considered: stellarevaporation, stellar evolution, tidal shocks due to both the disc andbulge, and dynamical friction. It is found that stellar evaporationdominates the evolution of low-mass clusters and all four are importantfor massive ones. For both the power-law and lognormal initial clustersmass functions, we can find the best-fitting models which can match thepresent-day observations with their main features of the mass functionalmost unchanged after evolution of several Gyr. This implies that it isnot possible to determine the initial mass function only based on theobserved mass function today. The dispersion of the modelled massfunctions mainly depends on the potential wells of host galaxies withthe almost constant peaks, which is consistent with current observations

Monte Carlo Simulations of Globular Cluster Evolution. III. Primordial Binary Interactions

We study the dynamical evolution of globular clusters using our two-dimensional Monte Carlo code with the inclusion of primordial interactions for equal-mass stars. We use approximate analytical cross sections for energy generation from binary-binary and binary-single interactions. After a brief period of slight contraction or expansion of the core over the first few relaxation times, all clusters enter a much longer phase of stable binary burning lasting many tens of relaxation times. The structural parameters of our models during this phase match well those of most observed globular clusters. At the end of this phase, clusters that have survived tidal disruption undergo deep core collapse, followed by gravothermal oscillations. Our results clearly show that the presence of even a small fraction of binaries in a cluster is sufficient to support the core against collapse significantly beyond the normal core-collapse time predicted without the presence of binaries. For tidally truncated systems, collapse is easily delayed sufficiently that the cluster will undergo complete tidal disruption before core collapse. As a first step toward the eventual goal of computing all interactions exactly using dynamical three- and four-body integration, we have incorporated an exact treatment of binary-single interactions in our code. We show that results using analytical cross sections are in good agreement with those using exact three-body integration, even for small fractions, where binary-single interactions are energetically most important.

The Main-Sequence Luminosity Function of Palomar 5 from THE [ITAL]HUBBLE SPACE TELESCOPE[/ITAL

A low mass, large core radius, low central concentration, and strong tidal tails suggest that the globular cluster Palomar 5 has lost a large fraction of its initial mass over time. If the dynamical evolution of Pal 5 has been dominated by the effects of mass loss, then theoretical arguments suggest that the luminosity function should be deficient in low-mass stars. Using deep WFPC2 F555W and F814W photometry, we determine the main-sequence luminosity functions both near the cluster center and in a field near the half-light radius. A comparison of these luminosity functions yields no compelling evidence of mass segregation within the cluster, in accord with expectations for low-concentration clusters. On the other hand, a comparison of the global mass function of Pal 5 with that of ω Cen and M55 indicates an increasing deficiency of stars with progressively lower masses. A fit of the observed luminosity function to theoretical models indicates a mass function for Pal 5 of dN/dm ∝ m-0.5, which is notably more deficient in low-mass stars than other globular clusters that have been studied with the Hubble Space Telescope. The flatness of the mass function is consistent with models of the dynamical evolution of globular clusters that have lost ~90% of their original stellar mass. We suggest that, like NGC 6712, Pal 5 has lost a large percentage of its original stellar content as a result of tidal shocking.

Tidal shocking and destruction of globular clusters

Abstract Dynamical evolution of globular clusters is strongly influenced and often driven by tidal interactions with the Galaxy. Passing through the Galactic disk or near the bulge, globular clusters experience fast gravitational perturbations, the compressive tidal shocks. A succession of tidal shocks leads to kinematic heating of the clusters and their ultimate destruction. I present the latest Fokker-Planck models including the first and second order tidal diffusion coefficients. In the limit of strong shocks, the typical value of the core collapse time t cc decreases from 10 to 3 half-mass relaxation times, while the destruction time is just 2, t cc. The effects of tidal shocks are rapidly self-limiting: as clusters lose mass and become more compact, the importance of the shocks diminishes. This implies that tidal shocks were more important in the past.

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.

The Formation and Evolution of Candidate Young Globular Clusters in NGC 3256

We present images of the recent galaxy merger NGC 3256 obtained with the Wide Field Planetary Camera 2 of the Hubble Space Telescope in B and I filters. We show that there is a large population of more than 1000 compact, bright, blue objects in this galaxy within the 7 kpc × 7 kpc region studied. These objects have sizes, colors, and luminosities like those expected for young Galactic globular clusters, with ages ranging from a few to several hundred megayears. On this basis, we identify at least some fraction of the compact, bright, blue objects in NGC 3256 as young globular clusters. The young cluster system makes up a significant fraction of the total luminosity of the galaxy within the region studied—15%–20% in B and half that in I, indicating a high efficiency of cluster formation on a galaxy-wide scale. In order to determine the properties of this young cluster system, the selection effects in size, color, and luminosity are carefully modeled. We find that the intrinsic color distribution is broad and there is no significant trend of color with magnitude. The combination of the broad range of observed colors and the lack of a trend of redder colors at fainter magnitudes cannot be fitted solely by a broad age distribution and/or differential reddening, although the latter is clearly present. The observations can be accounted for by either the preferential depletion/destruction of lower mass clusters as they age or a very young age (≲20 Myr) for the cluster population, comparable to or less than the dynamical time of the region in which the clusters are observed. We also find that the luminosity function of the young cluster system can be roughly fitted by a power law with an exponent of -1.8, with tentative evidence that it flattens at faint magnitudes. The clusters are compact in size, with typical estimated half-light radii of 5–10 pc, but there is no obvious cutoff for larger radii and only a shallow trend of size with luminosity. We discuss the implications of these results for models of the formation and dynamical evolution of globular clusters, as well as for interpretation of the properties of older globular cluster systems.

Dynamical Evolution of Rotating Globular Clusters

We have computed simplified globular cluster evolutionary tracks which take into account the effects of internal relaxation, of the cluster rotation, of the galactic tidal field, and, in a cruder way, of stellar evolution and of gravitational shocking. The objectives are first to quantify the influence of rotation in the dynamical evolution of globular clusters; and second, to investigate the evolution of globular cluster angular momentum and flattening (Lagoute and Longaretti 1995a, Longaretti and Lagoute 1995b,c).

Pulsars as probes of newtonian dynamical systems

As clocks, pulsars rival the best atomic clocks on Earth. Though the rest-frame ‘tick’ rate (period P ) of any given pulsar is unknown, the rest-frame rates of change of the periods are known to be very small. Therefore when they are observed to be large, one is quite certain that the rate of changes must be due to changing Doppler shifts: Ṗ to acceleration, P̈ to jerk, and periodic shifts to orbiting companion stars or planets. The first two give otherwise unobtainable information on the density and masses of the stellar remnants in the cores of globular clusters. The orbits of binary pulsars provide a test of the theory of the evolution of red giant stars, and in globular clusters provide the first direct evidence for the three- and four-body encounters which are believed to determine the dynamical evolution of globular clusters. The orbits of binary pulsars in our own Galaxy also show evidence for the fluctuations which the fluctuation-dissipation theorem implies should occur during the dissipative tidal circularization of orbits. And newtonian dynamical effects may soon add irrefutable confirmation to recent observations suggesting that some pulsars are surrounded by planetary systems similar to our own. There may not be life on their planets, but pulsars certainly breathe new life into the study of newtonian dynamical systems.

The core collapse of globular clusters with stellar evolution

The orbit averaged Fokker-Planck equation is used to study the dynamical evolution of globular clusters. Stellar evolutions according to their masses are incorporated in the model. The initial density distribution is chosen by Plummer's model with the initial mass function index α=0.65, 1.35, 2.35, and 3.35. The mass-loss rate is given by the model of Fusi-Pecci and Renzini. It is found that the stellar mass loss acts as an energy source, and thereby affects the dynamical evolution of globular clusters by slowing down the evolution rate and extending the core collapse time. Also, the dynamical length scale is extended.

Young Star Clusters in the LMC

The young globular star clusters in the LMC offer us insights into the formation and early dynamical evolution of globular clusters which are unobtainable from the old globular clusters in our Galaxy. Because these young clusters are so young and populous, they provide an opportunity to measure the upper end of the initial mass function by direct means and also through the dynamical effects of stellar mass loss on the structure of the clusters.

Time variation of ellipticity of globular clusters in the Large Magellanic Cloud

Dynamical evolution of globular clusters in the Large Magellanic Cloud (LMC) is investigated by means of N-body simulations; particular attention is paid to time evolution in the ellipticitical figure of globular clusters. The simulations were started with a binary globular cluster. It merged into a single cluster with ellipticity of about 0.3. The simulations were continued until the cluster became rounder due to the effects of two body relaxation and of tidal field of LMC. It is found that the outward angular momentum transport due to the gravothermal contraction makes the inner region rounder; the ellipticity at about the initial half-mass radius (rh) decreases with the e-folding time of 20 relaxation times. On the other hand, the outer region becomes rounder due to the stripping of stars by the tidal field; the ellipticity at about 3rh decreases with the e-folding time of 80 crossing times therein, though the time scale depends on the direction of the tidal field relative to the spin of the cluster. These two effects are comparable at about the half-mass radius. Taking account of such theoretical results we reanalyzed observed data for the ellipticity at about the half-mass radius of LMC clusters. We estimated the relaxation time and crossing time for each of the observed clusters, from which we calculated the effective time of getting round of the cluster. We plotted the observed ellipticity of the clusters against their non-dimensional age — i.e., the age normalized by the effective time. We found that observed ellipticity distribution is consistent with our picture.

Young star clusters in the LMC

We discuss the integrated colours, kinematics, formation, dynamical evolution and initial mass functions of the young globular star clusters in the Large Magellanic Cloud (LMC). Because these clusters are so young, they offer us insights, unobtainable from the old globular clusters in our Galaxy, into the formation and early dynamical evolution of globular clusters.

Dynamical Evolution of Globular Clusters with Mass Spectrum

AbstractWe present a series of numerical models describing the dynamical evolution of globular clusters with a mass spectrum, based on integration of the Fokker-Planck equation. We include three-body binary heating and a steady galactic tidal field. A wide range of initial mass functions is adopted and the evolution of the mass function is examined. The mass function begins to change appreciably during the post-collapse expansion phase due to the selective evaporation of low mass stars through the tidal boundary. One signature of highly evolved clusters is thus the significant flattening of the mass function. The age (in units of the half-mass relaxation time) increases very rapidly beyond about 100 signifying the final stage of cluster disruption. This appears to be consistent with the sharp cut-off of half-mass relaxation times at near 108 years for the Galactic globular clusters.

Multicomponent models for the dynamic evolution of globular clusters

The Fokker-Planck equation has been integrated to produce a series of numerical models describing the dynamical evolution of globular clusters with a mass spectrum. Three-body binary heating is included to obtain postcollapse evolution and a steady Galactic tidal field is imposed. Since no direct interactions between stars are considered, the models are appropriate for globular clusters with a relatively low mass (M ≤ 10 5 M ○. ). A wide range of initial mass functions is considered and the evolution of the mass function is examined.

Dynamical Evolution of Globular Clusters

One of the world's most distinguished astrophysicists presents a comprehensive theoretical treatment of the dynamical evolution of globular clusters. Lyman Spitzer's research in this field established the framework for decades of investigation. Now he summarizes in a unified, systematic way this branch of theoretical astrophysics with its still challenging problems.Originally published in 1988.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

After Core Collapse. What?

As our understanding of core collapse in globular clusters has improved through detailed computer simulations, attention has naturally turned to dynamical evolution of globular clusters after core collapse. The results of recent simulations of post-collapse cluster evolution are reviewed. An assessment is given of progress towards the goal of developing astrophysically realistic models that cover all phases of globular cluster evolution. A focus of this review is the stability of the post-collapse expansion phase to the large amplitude core oscillations first observed in the simulations of Sugimoto and Bettwieser and now confirmed by several other studies. The implications of core oscillations for the observation of post-collapse clusters are discussed.