Mirek Giersz

Monte Carlo simulations of star clusters – VII. The globular cluster 47 Tuc

We describe Monte Carlo models for the dynamical evolution of the massive globular cluster 47 Tuc (NGC 104). The code includes treatments of two-body relaxation, most kinds of threeand four-body interactions involving primordial binaries and those formed dynamically, the Galactic tide, and the internal evolution of both single and binary stars. We arrive at a set of initial parameters for the cluster which, after 12Gyr of evo lution, gives a model with a fairly satisfactory match to surface brightness and density profil es, the velocity dispersion profile, the luminosity function in two fields, and the acceleration o f pulsars. Our models appear to require a relatively steep initial mass function for stars a bove about turnoff, with an index of about 2.8 (where the Salpeter mass function has an index of 2.35), and a relatively flat initial mass function (index about 0.4) for the lower main sequence. According to the model, the current mass is estimated at 0.9 million solar masses, of which about 34% consists of remnants. We find that primordial binaries are gradually tak ing over from mass loss by stellar evolution as the main dynamical driver of the core. Despite the high concentration of the cluster, core collapse will take at least another 20Gyr.

Compact binaries in star clusters – I. Black hole binaries inside globular clusters

We study the compact binary population in star clusters, focusing on binaries containing black holes, using a self-consistent Monte Carlo treatment of dynamics and full stellar evolution. We find that the black holes experience strong mass segregation and become centrally concentrated. In the core the black holes interact strongly with each other and black hole–black hole binaries are formed very efficiently. The strong interactions, however, also destroy or eject the black hole–black hole binaries. We find no black hole–black hole mergers within our simulations but produce many hard escapers that will merge in the Galactic field within a Hubble time. We also find several highly eccentric black hole–black hole binaries that are potential Laser Interferometer Space Antenna (LISA) sources, suggesting that star clusters are interesting targets for space-based detectors. We conclude that star clusters must be taken into account when predicting compact binary population statistics.

The dragon simulations: globular cluster evolution with a million stars

Introducing the dragon simulation project, we present direct N-body simulations of four massive globular clusters (GCs) with 106 stars and 5 per cent primordial binaries at a high level of accuracy and realism. The GC evolution is computed with nbody6++gpu and follows the dynamical and stellar evolution of individual stars and binaries, kicks of neutron stars and black holes (BHs), and the effect of a tidal field. We investigate the evolution of the luminous (stellar) and dark (faint stars and stellar remnants) GC components and create mock observations of the simulations (i.e. photometry, colour–magnitude diagrams, surface brightness and velocity dispersion profiles). By connecting internal processes to observable features, we highlight the formation of a long-lived ‘dark’ nuclear subsystem made of BHs, which results in a two-component structure. The inner core is dominated by the BH subsystem and experiences a core-collapse phase within the first Gyr. It can be detected in the stellar (luminous) line-of-sight velocity dispersion profiles. The outer extended core – commonly observed in the (luminous) surface brightness profiles – shows no collapse features and is continuously expanding. We demonstrate how a King model fit to observed clusters might help identify the presence of post core-collapse BH subsystems. For global observables like core and half-mass radii, the direct simulations agree well with Monte Carlo models. Variations in the initial mass function can result in significantly different GC properties (e.g. density distributions) driven by varying amounts of early mass-loss and the number of forming BHs. (Less)

MOCCA code for star cluster simulations II: comparison with n-body simulations

We describe a major upgrade of a Monte Carlo code which has previously been used for many studies of dense star clusters. We outline the steps needed in order to calibrate the results of the new Monte Carlo code against N -body simulations for large N systems, up to N = 200000. The new version of the Monte Carlo code (called MOCCA), in addition to the old version, incorporates direct FewBody integrator for three- and four-body interactions, and new treatment of the escape process based on Fokushige & Heggie (2000). Now stars which fulfil the escape criterion are not removed immediately, but can stay in the system for a certain time which depends on the excess of the energy of a star above the critical energy. They are called potential escapers. FewBody integrator allows to follow all interaction channels, which are important for the rate of creation of various types of obj ects observed in star clusters, and assures that the energy generation by binaries is treated in a meaner similar to the N-body model. There are at most three parameters which have to be adjusted against N-body simulations for large N . Two (or one, depends on the chosen approach) connected with the escape process and one responsible for determination of the interaction probabilities. The adopted free parameters are independent on N . They allow MOCCA code to reproduce N-body results, in a reasonably precision, not only for the rate of clu ster evolution and the cluster mass distribution, but also for the detailed distributions of ma ss and binding energy of binaries. Additionally, the code can follow the rate of formation of blue stragglers and black hole black hole binaries. The code computes interactions between binaries and single stars up to a maximum separationrpmax, and it is found that the MOCCA code needs rather large value of rpmax to get agreement with the N-body simulations. The MOCCA code is at present the most advanced code for simulations of real star clusters. It can follow the cluster evolution in details compara ble to N-body code, but orders of magnitude faster.

MOCCA code for star cluster simulations – IV. A new scenario for intermediate mass black hole formation in globular clusters

We discuss a new scenario for the formation of intermediate mass black holes (IMBHs) in dense star clusters. In this scenario, IMBHs are formed as a result of dynamical interactions of hard binaries containing a stellar-mass black hole (BH), with other stars and binaries. We discuss the necessary conditions to initiate the process of intermediate mass BH formation and the influence of an IMBH on the host global globular cluster (GC) properties. We discuss two scenarios for IMBH formation. The SLOW and FAST scenarios. They occur later or earlier in the cluster evolution and require smaller or extremely large central densities, respectively. In our simulations, the formation of IMBHs is highly stochastic. In general, higher formation probabilities follow from larger cluster concentrations (i.e. central densities). We further discuss possible observational signatures of the presence of IMBHs in GCs that follow from our simulations. These include the spatial and kinematic structure of the host cluster, possible radio, X-ray and gravitational wave emissions due to dynamical collisions or mass transfer and the creation of hypervelocity main-sequence escapers during strong dynamical interactions between binaries and an IMBH. All simulations discussed in this paper were performed with the MOCCA (MOnte Carlo Cluster simulAtor) Monte Carlo code. MOCCA accurately follows most of the important physical processes that occur during the dynamical evolution of star clusters but, as with other dynamical codes, it approximates the dissipative processes connected with stellar collisions and binary mergers.

Monte Carlo simulations of star clusters – II. Tidally limited, multimass systems with stellar evolution

A revision of Stodo lkiewiczs Monte Carlo code is used to simulate evolution of large star clusters. The new method treats each superstar as a single star and follows the evolution and motion of all individual stellar objects. A survey of the evolution of N-body systems influenced by the tidal field of a parent galaxy and by stellar evolution is presented. The process of energy generation is realised by means of ap- propriately modified versions of Spitzers and Mikkolas formulae for the interaction cross section between binaries and field stars and binaries themselves. The results pre- sented are in good agreement with theoretical expectations and the results of other methods (Fokker-Planck, Monte Carlo and N-body). The initial rapid mass loss, due to stellar evolution of the most massive stars, causes expansion of the whole cluster and eventually leads to the disruption of less bound systems (W0 = 3). Models with larger W0 survive this phase of evolution and then undergo core collapse and subse- quent post-collapse expansion, like isolated models. The expansion phase is eventually reversed when tidal limitation becomes important. The results presented are the first major step in the direction of simulating evolution of real globular clusters by means of the Monte Carlo method.

Compact Binaries in Star Clusters II - Escapers and Detection Rates

We use a self-consistent Monte Carlo treatment of stellar dynamics to investigate black hole binaries that are dynamically ejected from globular clusters to determine if they will be gravitational wave sources. We find that many of the ejected binaries have initially short periods and will merge within a Hubble time due to gravitational wave radiation. Thus they are potential sources for ground-based gravitational wave detectors. We estimate the yearly detection rate for current and advanced groundbased detectors and find a modest enhancement over the rate predicted for binaries produced by pure stellar evolution in galactic fields. We also find that many of the ejected binaries will pass through the longer wavelength Laser Interferometer Space Antenna (LISA) band and may be individually resolvable. We find a low probability that the Galaxy will contain a binary in the LISA band during its three-year mission. Some such binaries may, however, be detectable at Mpc distances implying that there may be resolvable stellar-mass LISA sources beyond our Galaxy. We conclude that globular clusters have a significant effect on the detection rate of ground-based detectors and may produce interesting LISA sources in local group galaxies.

Monte Carlo simulations of star clusters – VI. The globular cluster NGC 6397

We describe Monte Carlo models for the dynamical evolution of the nearby globular cluster NGC 6397. The code includes treatments of two-body relaxation, most kinds of three- and four-body interactions involving primordial binaries and those formed dynamically, the Galactic tide and the internal evolution of both single and binary stars. We arrive at a set of initial parameters for the cluster which, after 12 Gyr of evolution, gives a model with a fairly satisfactory match to the surface brightness profile, the velocity dispersion profile and the luminosity function in two fields. We describe in particular those aspects of the evolution which distinguish this cluster from M4, which has a roughly similar mass and Galactocentric distance, but a qualitatively different surface brightness profile. Within the limitations of our modelling, we conclude that the most plausible explanation for the difference is fluctuations: both clusters are post-collapse objects, but sometimes have resolvable cores and sometimes not.

mocca code for star cluster simulations – I. Blue stragglers, first results

We introduce an improved code for simulations of star clusters, called MOCCA. It combines the Monte Carlo method for star cluster evolution and the Fewbody code to perform scattering experiments. The Fewbody was added in order to track more precisely dynamical interactions between objects which can lead to creations of various exotic objects observed in the star clusters, like Blue Stragglers Stars (BSS). The MOCCA code is currently one of the most advanced codes for simulating real size star clusters. It follows the star cluster evolution closely to N-body codes but is much faster. We show that the MOCCA code is able to follow the evolution of BSS with details. It is a suitable tool to perform full scale evolution of real star clusters and detail comparison with observations of exotic star cluster objects like BSS. This paper is the first one of the series of papers about properties of BSS in star clusters. This type of stars is particularly interesting today, because by studying them one can get important constrains on a link between the stellar and dynamical evolution of star clusters. We discuss here first results concerning BSS for an arbitrary chosen test model. We investigate properties of BSS which characterize different channels of formation like masses, semi-major axes, eccentricities, and orbital periods. We show how BSS from different channels change their types, and discuss initial and final positions of BSS, their bimodal distribution in the star cluster, lifetimes and more.

A stochastic Monte Carlo approach to model real star cluster evolution—II. Self-consistent models and primordial binaries

ABSTRA C T The new approach outlined in Paper I to follow the individual formation and evolution of binaries in an evolving, equal point-mass star cluster is extended for the self-consistent treatment of relaxation and close three- and four-body encounters for many binaries (typically a few per cent of the initial number of stars in the cluster mass). The distribution of single stars is treated as a conducting gas sphere with a standard anisotropic gaseous model. A Monte Carlo technique is used to model the motion of binaries, their formation and subsequent hardening by close encounters, and their relaxation (dynamical friction) with single stars and other binaries. The results are a further approach towards a realistic model of globular clusters with primordial binaries without using special hardware. We present, as our main result, the self-consistent evolution of a cluster consisting of 300 000 equal point-mass stars, plus 30 000 equal-mass binaries over several hundred half-mass relaxation times, well into the phase where most of the binaries have been dissolved and evacuated from the core. The cluster evolution is about three times slower than found by Gao et al. Other features are rather comparable. At every moment we are able to show the individual distribution of binaries in the cluster.