The Dynamical Evolution of Stellar Black Holes in Globular Clusters

Our current understanding of the stellar initial mass function and massive star evolution suggests that young globular clusters may have formed hundreds to thousands of stellar-mass black holes, the remnants of stars with initial masses from $\sim 20 - 100\, M_\odot$. Birth kicks from supernova explosions may eject some black holes from their birth clusters, but most should be retained. Using a Monte Carlo method we investigate the long-term dynamical evolution of globular clusters containing large numbers of stellar black holes. We describe numerical results for 42 models, covering a range of realistic initial conditions, including up to $1.6\times10^6$ stars. In almost all models we find that significant numbers of black holes (up to $\sim10^3$) are retained all the way to the present. This is in contrast to previous theoretical expectations that most black holes should be ejected dynamically within a few Gyr. The main reason for this difference is that core collapse driven by black holes (through the Spitzer "mass segregation instability") is easily reverted through three-body processes, and involves only a small number of the most massive black holes, while lower-mass black holes remain well-mixed with ordinary stars far from the central cusp. Thus the rapid segregation of stellar black holes does not lead to a long-term physical separation of most black holes into a dynamically decoupled inner core, as often assumed previously. Combined with the recent detections of several black hole X-ray binary candidates in Galactic globular clusters, our results suggest that stellar black holes could still be present in large numbers in many globular clusters today, and that they may play a significant role in shaping the long-term dynamical evolution and the present-day dynamical structure of many clusters.Comment: 40 pages in preprint format, 13 figures, 4 tables, accepted for publication in Ap

Automated microorganism Sample Collection Module

Modified Gelman Sampler obtains representative sample of microorganism population. Proposed Sample Collection Module is based on direct inoculation of selected solid growth media encased in a cartridge at all times except during inoculation. Cartridge can be handled with no danger of contamination to sample or operator

Germanistische Institutspartnerschaften : Grenzen und Möglichkeiten ; Erfahrungen einer universitären Langzeit-Kooperation

Wenn wie im Falle des Instituts für Angewandte Linguistik und Translatologie der Universität Leipzig eine mehr als zehnjährige Germanistische Institutspartnerschaft mit gleich zwei russischen Partnern – den Übersetzer-Fakultäten der Linguistischen Universitäten Moskau und Pjatigorsk – nunmehr ihren Abschluss findet, so bietet es sich natürlich an zu fragen, was die GIP-Langzeitkooperation beiden Seiten an messbaren wissenschaftlichen, wissenschaftsmethodischen und curricularen Ergebnissen, an „Zuwächsen“ im Sinne der Nachwuchsförderung, des Austauschs von Dozenten und Studierenden gebracht hat. Die Bilanz – von uns dargelegt im Jubiläumsband 52 der Dokumente & Materialien des Deutschen Akademischen Austausch Dienstes – kann sich durchaus sehen lassen und rechtfertigt nicht nur die aufgewandten Mittel, sondern auch die kontinuierliche Arbeit, den nachhaltigen Einsatz und die vielfältigen Initiativen der zahlreichen Beteiligten auf beiden Seiten

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 Msun, 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 Msun 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.Comment: 30 pages, 8 figures, submitted to Ap

Retention of Stellar-Mass Black Holes in Globular Clusters

Globular clusters should be born with significant numbers of stellar-mass black holes (BHs). It has been thought for two decades that very few of these BHs could be retained through the cluster lifetime. With masses ~10 MSun, BHs are ~20 times more massive than an average cluster star. They segregate into the cluster core, where they may eventually decouple from the remainder of the cluster. The small-N core then evaporates on a short timescale. This is the so-called Spitzer instability. Here we present the results of a full dynamical simulation of a globular cluster containing many stellar-mass BHs with a realistic mass spectrum. Our Monte Carlo simulation code includes detailed treatments of all relevant stellar evolution and dynamical processes. Our main finding is that old globular clusters could still contain many BHs at present. In our simulation, we find no evidence for the Spitzer instability. Instead, most of the BHs remain well-mixed with the rest of the cluster, with only the innermost few tens of BHs segregating significantly. Over the 12 Gyr evolution, fewer than half of the BHs are dynamically ejected through strong binary interactions in the cluster core. The presence of BHs leads to long-term heating of the cluster, ultimately producing a core radius on the high end of the distribution for Milky Way globular clusters (and those of other galaxies). A crude extrapolation from our model suggests that the BH--BH merger rate from globular clusters could be comparable to the rate in the field.Comment: 5 pages, 4 figures, 1 table, published in Astrophysical Journal Letter

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 the Henon Monte 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. The implementation uses the Message Passing Interface (MPI) 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 less than 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 a saturation with the addition of more processors beyond these limits which is a characteristic of the parallel sorting algorithm. The resulting maximum speedups we achieve are approximately 60x, 100x, and 220x, respectively.Comment: 53 pages, 13 figures, accepted for publication in ApJ Supplement

Monte Carlo Simulations of Globular Cluster Evolution. VI. The Influence of an Intermediate Mass Black Hole

We present results of a series of Monte Carlo simulations investigating the imprint of a central intermediate-mass 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 Monte Carlo simulations. Significant differences exist in the number of stars that are tidally disrupted by the IMBH, which is most likely an effect of the wandering motion of the IMBH, not included in the Monte Carlo 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.Comment: 37 pages, 10 figures, Accepted for publication in ApJ Supplement. Substantial additions on modeling NGC 5694 since original versio

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 which turns out to be consistent with recent model calculations, thereby lending further support to our model.Comment: 4 pages, 1 figure, to appear in ApJ Letter

Close binary systems among very low mass stars and brown dwarfs

Using Monte Carlo simulations and published radial velocity surveys we have constrained the frequency and separation (a) distribution of very low mass star (VLM) and brown dwarf (BD) binary systems. We find that simple Gaussian extensions of the observed wide binary distribution, with a peak at 4 au and 0.6< sigma_{log(a/au)}<1.0, correctly reproduce the observed number of close binary systems, implying a close (a<2.6 au) binary frequency of 17-30 per cent and overall frequency of 32-45 per cent. N-body models of the dynamical decay of unstable protostellar multiple systems are excluded with high confidence because they do not produce enough close binary VLMs/BDs. The large number of close binaries and high overall binary frequency are also completely inconsistent with published smoothed particle hydrodynamical modelling and argue against a dynamical origin for VLMs/BDs.Comment: Proceedings of the workshop on Ultra-Low Mass Star Formation, eds. E. Martin, A. Magazzu. To appear in Astron. Nach

Restorative Justice Impact on Multinational Corporations?: A Response to Andrew Brady Spalding's Article

In response to Andrew Brady Spalding, Restorative Justice for Multinational Corporations, 76 Ohio St. L.J. 357 (2015)