Stefan Umbreit

MONTE CARLO SIMULATIONS OF GLOBULAR CLUSTER EVOLUTION. V. BINARY STELLAR EVOLUTION

We study the dynamical evolution of globular clusters containing primordial binaries, including full single and binary stellar evolution using our Monte Carlo cluster evolution code updated with an adaptation of the single and binary stellar evolution codes SSE and BSE from Hurley et al. We describe the modifications that we have made to the code. We present several test calculations and comparisons with existing studies to illustrate the validity of the code. We show that our code finds very good agreement with direct N-body simulations including primordial binaries and stellar evolution. We find significant differences in the evolution of the global properties of the simulated clusters using stellar evolution compared with simulations without any stellar evolution. In particular, we find that the mass loss from the stellar evolution acts as a significant energy production channel simply by reducing the total gravitational binding energy and can significantly prolong the initial core contraction phase before reaching the binary-burning quasi-steady state of the cluster evolution. We simulate a large grid of models varying the initial cluster mass, binary fraction, and concentration parameter, and we compare properties of the simulated clusters with those of the observed Galactic globular clusters (GGCs). We find that simply including stellar evolution in our simulations and assuming the typical initial cluster half-mass radius is approximately a few pc independent of mass, our simulated cluster properties agree well with the observed GGC properties such as the core radius and the ratio of the core radius to the half-mass radius. We explore in some detail qualitatively different clusters in different phases of their evolution and construct synthetic Hertzsprung-Russell diagrams for these clusters.

Quantifying the universality of the stellar initial mass function in old star clusters

We present a new technique to quantify cluster-to-cluster variations in the observed present-day stellar mass functions of a large sample of star clusters. Our method quantifies these differences as a function of both the stellar mass and the total cluster mass, and offers the advantage that it is insensitive to the precise functional form of the mass function. We applied our technique to data taken from the Advanced Camera for Surveys Survey for Globular Clusters, from which we obtained completeness-corrected stellar mass functions in the mass range 0.25-0.75 M⊙ for a sample of 27 clusters. The results of our observational analysis were then compared to Monte Carlo simulations for globular cluster evolution spanning a range of initial mass functions, total numbers of stars, concentrations, and virial radii. We show that the present-day mass functions of the clusters in our sample can be reproduced by assuming an universal initial mass function for all clusters, and that the cluster-to-cluster differences are consistent with what is expected from twobody relaxation. A more complete exploration of the initial cluster conditions will be needed in future studies to better constrain the precise functional form of the initial mass function. This study is a first step toward using our technique to constrain the dynamical histories of a large sample of old Galactic star clusters and, by extension, star formation in the early Universe.

MONTE CARLO SIMULATIONS OF GLOBULAR CLUSTER EVOLUTION. VI. THE INFLUENCE OF AN INTERMEDIATE-MASS BLACK HOLE

We present results from a series of Monte Carlo (MC) simulations investigating the imprint of a central intermediatemass black hole (IMBH) on the structure of a globular cluster. We investigate the three-dimensional and projected density profiles, and stellar disruption rates for idealized as well as realistic cluster models, taking into account a stellar mass spectrum and stellar evolution, and allowing for a larger, more realistic number of stars than was previously possible with direct N-body methods. We compare our results to other N-body and Fokker‐Planck simulations published previously. We find, in general, very good agreement for the overall cluster structure and dynamical evolution between direct N-body simulations and our MC simulations. Significant differences exist in the number of stars that are tidally disrupted by the IMBH, and this is most likely caused by the wandering motion of the IMBH, not included in the MC scheme. These differences, however, are negligible for the final IMBH masses in realistic cluster models, as the disruption rates are generally much lower than for single-mass clusters. As a direct comparison to observations we construct a detailed model for the cluster NGC 5694, which is known to possess a central surface brightness cusp consistent with the presence of an IMBH. We find that not only the inner slope but also the outer part of the surface brightness profile agree well with observations. However, there is only a slight preference for models harboring an IMBH compared to models without.

A PARALLEL MONTE CARLO CODE FOR SIMULATING COLLISIONAL N-BODY SYSTEMS

We present a new parallel code for computing the dynamical evolution of collisional N-body systems with up to N ∼ 10 7 particles. Our code is based on the HMonte Carlo method for solving the Fokker-Planck equation, and makes assumptions of spherical symmetry and dynamical equilibrium. The principal algorithmic developments involve optimizing data structures and the introduction of a parallel random number generation scheme as well as a parallel sorting algorithm required to find nearest neighbors for interactions and to compute the gravitational potential. The new algorithms we introduce along with our choice of decomposition scheme minimize communication costs and ensure optimal distribution of data and workload among the processing units. Our implementation uses the Message Passing Interface library for communication, which makes it portable to many different supercomputing architectures. We validate the code by calculating the evolution of clusters with initial Plummer distribution functions up to core collapse with the number of stars, N, spanning three orders of magnitude from 10 5 to 10 7 . We find that our results are in good agreement with self-similar core-collapse solutions, and the core-collapse times generally agree with expectations from the literature. Also, we observe good total energy conservation, within 0.04% throughout all simulations. We analyze the performance of the code, and demonstrate near-linear scaling of the runtime with the number of processors up to 64 processors for N = 10 5 , 128 for N = 10 6 and 256 for N = 10 7 . The runtime reaches saturation with the addition of processors beyond these limits, which is a characteristic of the parallel sorting algorithm. The resulting maximum speedups we achieve are approximately 60×, 100×, and 220×, respectively.

FORMATION OF MASSIVE BLACK HOLES IN DENSE STAR CLUSTERS. II. INITIAL MASS FUNCTION AND PRIMORDIAL MASS SEGREGATION

A promising mechanism to form intermediate-mass black holes is the runaway merger in dense star clusters, where main-sequence stars collide and form a very massive star (VMS), which then collapses to a black hole (BH). In this paper, we study the effects of primordial mass segregation and the importance of the stellar initial mass function (IMF) on the runaway growth of VMSs using a dynamical Monte Carlo code for N-body systems with N as high as 106 stars. Our code now includes an explicit treatment of all stellar collisions. We place special emphasis on the possibility of top-heavy IMFs, as observed in some very young massive clusters. We find that both primordial mass segregation and the shape of the IMF affect the rate of core collapse of star clusters and thus the time of the runaway. When we include primordial mass segregation, we generally see a decrease in core-collapse time (t cc). Although for smaller degrees of primordial mass segregation this decrease in t cc is mostly due to the change in the density profile of the cluster, for highly mass-segregated (primordial) clusters, it is the increase in the average mass in the core which reduces the central relaxation time decreasing t cc. The final mass of the VMS formed is always close to ~10–3 of the total cluster mass, in agreement with previous studies and is reminiscent of the observed correlation between the central BH mass and the bulge mass of the galaxies. As the degree of primordial mass segregation is increased, the mass of the VMS increases at most by a factor of three. Flatter IMFs generally increase the average mass in the whole cluster, which increases t cc. For the range of IMFs investigated in this paper, this increase in t cc is to some degree balanced by stellar collisions, which accelerate core collapse. Thus, there is no significant change in t cc for the somewhat flatter global IMFs observed in very young massive clusters.

Constraining intermediate-mass black holes in globular clusters

Decades after the first predictions of intermediate-mass black holes (IMBHs) in globular clusters (GCs) there is still no unambiguous observational evidence for their existence. The most promising signatures for IMBHs are found in the cores of GCs, where the evidence now comes from the stellar velocity distribution, the surface density profile, and, for very deep observations, the mass-segregation profile near the cluster center. However, interpretation of the data, and, in particular, constraints on central IMBH masses, require the use of detailed cluster dynamical models. Here we present results from Monte Carlo cluster simulations of GCs that harbor IMBHs. As an example of application, we compare velocity dispersion, surface brightness and mass-segregation profiles with observations of the GC M10, and constrain the mass of a possible central IMBH in this cluster. We find that, although M10 does not seem to possess a cuspy surface density profile, the presence of an IMBH with a mass up to 0.75% of the total cluster mass, corresponding to about 600 M ☉, cannot be excluded. This is also in agreement with the surface brightness profile, although we find it to be less constraining, as it is dominated by the light of giants, causing it to fluctuate significantly. We also find that the mass-segregation profile cannot be used to discriminate between models with and without IMBH. The reason is that M10 is not yet dynamically evolved enough for the quenching of mass segregation to take effect. Finally, detecting a velocity dispersion cusp in clusters with central densities as low as in M10 is extremely challenging, and has to rely on only 20-40 bright stars. It is only when stars with masses down to 0.3 M ☉ are included that the velocity cusp is sampled close enough to the IMBH for a significant increase above the core velocity dispersion to become detectable.

CLEARING THE DUST FROM GLOBULAR CLUSTERS

Recent Spitzer observations of the globular cluster M15 detected dust associated with its intracluster medium. Surprisingly, these observations imply that the dust must be very short-lived compared to the time since the last Galactic plane crossing of the cluster. Here we propose a simple mechanism to explain this short lifetime. We argue that the kinetic energy of the material ejected during a stellar collision may be sufficient to remove the gas and dust entirely from a cluster, or to remove the gas as a wind, in addition to partially destroying the dust. By calculating the rate of stellar collisions using an N-body model for the cluster, we find remarkable agreement between the average time between collisions and the inferred dust lifetime in this cluster, suggesting a possible close relation between the two phenomena. Furthermore, we also obtain the birthrate of blue stragglers formed through collisions in M15. By comparing with the observed number of blue stragglers, we derive an upper limit for their average lifetime that turns out to be consistent with recent model calculations, thereby lending further support to our model.

DISKS AROUND BROWN DWARFS IN THE EJECTION SCENARIO. I. DISK COLLISIONS IN TRIPLE SYSTEMS

We investigate the fate of disks around brown dwarfs in the ejection scenario and the implications on their observable properties. For that purpose, a parameter study of close triple approaches leading to escape is carried out where the ejected body is surrounded by a low-mass disk. We analyze the recircularized radial surface density profile of the post-encounter disk in dependence of the minimum two-body distances between the escaper and the perturbing bodies. Our results show that the general appearance of the disks is rather similar to disks after two-body encounters in as much as there is also an exponential drop in surface density for the outer disk regions as well as an enhancement of surface density for the innermost region relative to the initial disk profile. However, the disks after close triple approaches are mostly less massive, have generally flatter recircularized surface density disk profiles, and have radii that are similar or larger compared to disks after two-body encounters. From our results, we construct a simple scale-free model only depending on the minimum encounter distances of the two perturbers. Such a model is especially useful for statistical studies of disk collisions in triple systems that must cover a large range of encounter distances.

The imprints of IMBHs on the structure of globular clusters: Monte-Carlo simulations

We present the first results of a series of Monte-Carlo simulations investigating the imprints of a central black hole on the core structure of globular clusters. We investigate the three-dimensional and the projected density profile of the inner regions of idealized as well as more realistic globular cluster models, taking into account a stellar mass spectrum, stellar evolution and allowing for a larger, more realistic, number of stars than was previously possible with direct N-body methods. We compare our results to other N-body simulations published previously in the literature.

Neutron Stars and Binary Pulsars in Globular Clusters

Dense stellar systems such as globular clusters are known to produce many more millisecond pulsars per mass than galaxies. We have begun investigations, theoretically, into the formation and evolution of binary pulsars, and in particular millisecond pulsars. We present preliminary results of eight simulations with the aim of highlighting some interesting comparisons to observations which we are now able to make.