N-body Simulations Of Star Clusters Research Articles

MYRIAD: a newN-body code for simulations of star clusters

We present a new C++ code for collisional N-body simulations of star clusters. The code uses the Hermite fourth-order scheme with block time steps, for advancing the particles in time, while the forces and neighboring particles are computed using the GRAPE-6 board. Special treatment is used for close encounters, binary and multiple sub-systems that either form dynamically or exist in the initial configuration. The structure of the code is modular and allows the appropriate treatment of more physical phenomena, such as stellar and binary evolution, stellar collisions and evolution of close black-hole binaries. Moreover, it can be easily modified so that the part of the code that uses GRAPE-6, could be replaced by another module that uses other accelerating-hardware like the Graphics Processing Units (GPUs). Appropriate choice of the free parameters give a good accuracy and speed for simulations of star clusters up to and beyond core collapse. Simulations of Plummer models consisting of equal-mass stars reached core collapse at t~17 half-mass relaxation times, which compares very well with existing results, while the cumulative relative error in the energy remained below 0.001. Also, comparisons with published results of other codes for the time of core collapse for different initial conditions, show excellent agreement. Simulations of King models with an initial mass-function, similar to those found in the literature, reached core collapse at t~0.17, which is slightly smaller than the expected result from previous works. Finally, the code accuracy becomes comparable and even better than the accuracy of existing codes, when a number of close binary systems is dynamically created in a simulation. This is due to the high accuracy of the method that is used for close binary and multiple sub-systems.

WIDESPREAD PRESENCE OF SHALLOW CUSPS IN THE SURFACE-BRIGHTNESS PROFILE OF GLOBULAR CLUSTERS

Surface brightness profiles of globular clusters with shallow central cusps (Sigma ~ R^v with -0.3<~ v <~ -0.05) have been associated by several recent studies with the presence of a central intermediate mass black hole (IMBH). Such shallow slopes are observed in several globular clusters thanks to the high angular resolution of Hubble Space Telescope imaging. In this Letter we evaluate whether shallow cusps are a unique signature of a central IMBH by analyzing a sample of direct N-body simulations of star clusters with and without a central IMBH. We ``observe'' the simulations as if they were HST images. Shallow cusps are common in our simulation sample: star clusters without an IMBH have v >~ -0.3 in the pre-core-collapse and core-collapse phases. Post-core-collapse clusters without an IMBH transition to steeper cusps, -0.7<~ v <~ -0.4, only if the primordial binary fraction is very small, f_{bin}< 3 per cent, and if there are few stellar-mass black holes remaining. Otherwise v values overlap the range usually ascribed to the presence of an IMBH throughout the entire duration of the simulations. In addition, measuring v is intrinsically prone to significant uncertainty, therefore typical measurement errors may lead to v > -0.3 even when <v> <~ -0.4. Overall our analysis shows that a shallow cusp is not an unequivocal signature of a central IMBH and casts serious doubts on the usefulness of measuring v in the context of the hunt for IMBHs in globular clusters.

TIDAL DISRUPTION, GLOBAL MASS FUNCTION, AND STRUCTURAL PARAMETER EVOLUTION IN STAR CLUSTERS

We present a unified picture for the evolution of star clusters on the two-body relaxation timescale. We use direct N-body simulations of star clusters in a galactic tidal field starting from different multimass King models, up to 10% of primordial binaries and up to Ntot = 65, 536 particles. An additional run also includes a central Intermediate Mass Black Hole. We find that for the broad range of initial conditions we have studied the stellar mass function of these systems presents a universal evolution, which depends only on the fractional mass loss. The structure of the system, as measured by the core to half-mass radius ratio, also evolves toward a universal state, which is set by the efficiency of heating on the visible population of stars induced by dynamical interactions in the core of the system. Interactions with dark remnants (white dwarfs, neutron stars, and stellar mass black holes) are dominant over the heating induced by a moderate population of primordial binaries (3%–5%), especially under the assumption that most of the neutron stars and black holes are retained in the system. All our models without primordial binaries undergo a deep gravothermal collapse in the radial mass profile. However, their projected light distribution can be well fitted by medium concentration King models (with parameter W0 ∼ 8), even though there tends to be an excess over the best fit for the innermost points of the surface brightness. This excess is consistent with a shallow cusp in the surface brightness (μ ∼ R−ν with ν ∼ 0.4–0.7), like it has been observed for many globular clusters from high-resolution Hubble Space Telescope imaging. Generally, fitting a King profile to derive the structural parameters yields to larger fluctuations in the core size than defining the core as the radius where the surface brightness is one half of its central value. Classification of core-collapsed globular clusters based on their surface brightness profile may thus fail in systems that appear to have already bounced back to lower concentrations, particularly if the angular resolution of the observations is limited and the core is not well resolved.

Stellar-mass black holes in star clusters: implications for gravitational wave radiation

We study the dynamics of stellar-mass black holes (BH) in star clusters with particular attention to the formation of BH-BH binaries, which are interesting as sources of gravitational waves (GW). We examine the properties of these BH-BH binaries through direct N-body simulations of star clusters using the GPU-enabled NBODY6 code. We perform simulations of N <= 10^5 Plummer clusters of low-mass stars with an initial population of BHs. Additionally, we do several calculations of star clusters confined within a reflective boundary mimicking only the core of a massive cluster. We find that stellar-mass BHs with masses ~ 10 solar mass segregate rapidly into the cluster core and form a sub-cluster of BHs within typically 0.2 - 0.5 pc radius, which is dense enough to form BH-BH binaries through 3-body encounters. While most BH binaries are ejected from the cluster by recoils received during super-elastic encounters with the single BHs, few of them harden sufficiently so that they can merge via GW emission within the cluster. We find that for clusters with $N \ga 5\times 10^4$, typically 1 - 2 BH-BH mergers occur within them during the first ~ 4 Gyr of evolution. Also for each of these clusters, there are a few escaping BH binaries that can merge within a Hubble time, most of the merger times being within a few Gyr. These results indicate that intermediate-age massive clusters constitute the most important class of candidates for producing dynamical BH-BH mergers. Old globular clusters cannot contribute significantly to the present-day BH-BH merger rate since most of the mergers from them would have occurred earlier. In contrast, young massive clusters are too young to produce significant number of BH-BH mergers. Our results imply significant BH-BH merger detection rates for the proposed "Advanced LIGO" GW detector. (Abridged)

The photometric evolution of dissolving star clusters

Evolutionary synthesis models are the prime method to construct models of stellar populations, and to derive physical parameters from observations. One of the assumptions for such models so far has been the time-independence of the stellar mass function. However, dynamical simulations of star clusters in tidal fields have shown the mass function to change due to the preferential removal of low-mass stars from clusters. Here we combine the results from dynamical simulations of star clusters in tidal fields with our evolutionary synthesis code GALEV to extend the models by a new dimension: the total cluster disruption time. We reanalyse the mass function evolution found in N-body simulations of star clusters in tidal fields, parametrise it as a function of age and total cluster disruption time and use this parametrisation to compute GALEV models as a function of age, metallicity and the total cluster disruption time. We study the impact of cluster dissolution on the colour (generally, they become redder) and magnitude (they become fainter) evolution of star clusters, their mass-to-light ratios (off by a factor of ~2 -- 4 from standard predictions), and quantify the effect on the cluster age determination from integrated photometry (in most cases, clusters appear to be older than they are, between 20 and 200%). By comparing our model results with observed M/L ratios for old compact objects in the mass range 10^4.5 -- 10^8 Msun, we find a strong discrepancy for objects more massive than 10^7 Msun (higher M/L). This could be either caused by differences in the underlying stellar mass function or be an indication for the presence of dark matter in these objects. Less massive objects are well represented by the models. The models for a range of total cluster disruption times are available online. (shortened)

Fully Self-Consistent N-body Simulation of Star Cluster in the Galactic Center

AbstractWe have developed a new tree-direct hybrid algorithm, “Bridge”. It can simulate small scale systems embedded within large-N systems fully self-consistently. Using this algorithm, we have performed full N-body simulations of star clusters near the Galactic center (GC) and compared the orbital evolutions of the star cluster with those obtained by “traditional” simulations, in which the orbital evolution of the star clusters is calculated from the dynamical friction formula. We found that the inspiral timescale of the star cluster is shorter than that obtained with traditional simulations. Moreover, we investigated the eccentricities of particles escaped from the star cluster. Eccentric orbit of the star cluster can naturally explain the high eccentricities of the observed stars.

Dynamical Evolution of Star Clusters with Intermediate Mass Black Holes and Primordial Binaries

AbstractThe evolution of a star cluster is strongly influenced by the presence of primordial binaries and of a central black hole, as dynamical interactions within the core prevents a deep core collapse under these conditions. We present the results from a large set of direct N-body simulations of star clusters that include an intermediate mass black hole, single and binary stars. We highlight the structural and dynamical differences for the various cases showing in particular that on a timescale of a few relaxation times the density profile of the star cluster does no longer depend on the details of the initial conditions but only on the efficiency of the energy generation due to gravitational encounters at the center of the system.

Effects of Hardness of Primordial Binaries on Evolution of Star Clusters

AbstractWe performed N-body simulations of star clusters with primordial binaries using a new code, GORILLA. It is based on Makino and Aarseth (1992)'s integration scheme on GRAPE, and includes a special treatment for relatively isolated binaries. Using the new code, we investigated effects of hardness of primordial binaries on whole evolution of the clusters. We simulated seven N=16384 equal-mass clusters containing 10% (in mass) primordial binaries whose binding energies are 1, 3, 10, 30, 100, 300, and 1000kT, respectively. Additionally, we also simulated a cluster without primordial binaries and that in which all binaries are replaced by stars with double mass, as references of soft and hard limits, respectively. We found that, in both soft (≤ 3kT) and hard (≥ 1000kT) limits, clusters experiences deep core collapse and shows gravothermal oscillations. On the other hands, in the intermediate hardness (10-300kT), the core collapses halt halfway due an energy releases of the primordial binaries.

Core radius evolution of star clusters

We use N-body simulations of star clusters to investigate the possible dynamical origins of the observed spread in core radius among intermediate-age and old star clusters in the Large Magellanic Cloud (LMC). Two effects are considered, a time-varying external tidal field and variations in primordial hard binary fraction. Simulations of clusters orbiting a point-mass galaxy show similar core radius evolution for clusters on both circular and elliptical orbits and we therefore conclude that the tidal field of the LMC has not yet significantly influenced the evolution of the intermediate-age clusters. The presence of large numbers of hard primordial binaries in a cluster leads to core radius expansion; however, the magnitude of the effect is insufficient to explain the observations. Further, the range of binary fractions required to produce significant core radius growth is inconsistent with the observational evidence that all the LMC clusters have similar stellar luminosity functions.

Evolution of star clusters moving on elliptic orbits

We describe results of N-body simulations of star clusters moving on elliptic orbits. Our aim is to follow the evolution of these clusters and study how their dissolution times depend on particle number and eccentricity.We find that the scaling of the lifetimes is nearly independent of the eccentricity, despite the fact that the amount of tidal shocking changes with eccentricity. In addition, no leveling off of the lifetimes at the high-N end, which would indicate the influence of tidal shocking, is seen.