arXiv subjects

Rainer Spurzem

Publications and source records attributed to Rainer Spurzem.

At least 109 records · Page 6Linked to original sources

arXiv2007

Comparative study between N-body and Fokker-Planck simulations for rotating star clusters: I. Equal-mass system

We have carried out N-body simulations for rotating star clusters with equal mass and compared the results with Fokker-Planck models. These two different approaches are found to produce fairly similar results, although there are some differences with regard to the detailed aspects. We confirmed the acceleration of the core collapse of a cluster due to an initial non-zero angular momentum and found a similar evolutionary trend in the central density and velocity dispersion in both simulations. The degree of acceleration depends on the initial angular momentum. Angular momentum is being lost from the cluster due to the evaporation of stars with a large angular momentum on a relaxation time scale.

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arXiv2007

NBODY meets stellar population - The HYDE-PARC Project

N-body simulations give us a rough idea of how the shape of a simulated object appears in three-dimensional space. From an observational point of view this may give us a misleading picture. The faint stars may be the most common stars in the system but the morphological information obtained by observations of an object may be dominated by the color properties of the bright stars. Due to dynamical effects, such as energy equipartition, different masses of stars may populate different regions in the object. Since stars are evolving in mass the stellar evolution may also influence the dynamics of the system. Hence, if one is interested in simulating what the morphology will look like through a telescope, one needs to simulate in addition evolving stars and weight them by their luminosity. Therefore we need to combine simulations of the dynamical evolution and a stellar population synthesis at the same time. For the dynamical evolution part we use a parallel version of a direct N-body code, NBODY6++. This code also includes stellar evolution. We link the parameters from this stellar evolution routine to the BaSeL 2.0 stellar library. For isolated clusters we found results assimilable to standard stellar population synthesis codes such as the PEGASE code. For clusters in a tidal field we found that the integrated colors become relatively bluer due to energy equipartition effects. In the time shortly before dissolution of the cluster the stellar M/L ratio becomes lower compared to isolated clusters. We compared the results of our simulations to integrated spectra of galactic globular clusters. For the cluster NGC 1851 we found good agreement between simulation and observation. For extragalactic clusters in M81 and M31 we looked at medium band spectral energy distributions and found for some clusters also a good agreement.

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arXiv2007

N-body Models of Rotating Globular Clusters

We have studied the dynamical evolution of rotating globular clusters with direct $N$-body models. Our initial models are rotating King models; we obtained results for both equal-mass systems and systems composed out of two mass components. Previous investigations using a Fokker-Planck solver have revealed that rotation has a noticeable influence on stellar systems like globular clusters, which evolve by two-body relaxation. In particular, it accelerates their dynamical evolution through the gravogyro instability. We have validated the occurence of the gravogyro instability with direct $N$-body models. In the case of systems composed out of two mass components, mass segregation takes place, which competes with the rotation in the acceleration of the core collapse. The "accelerating" effect of rotation has not been detected in our isolated two-mass $N$-body models. Last, but not least, we have looked at rotating $N$-body models in a tidal field within the tidal approximation. It turns out that rotation increases the escape rate significantly. A difference between retrograde and prograde rotating star clusters occurs with respect to the orbit of the star cluster around the Galaxy, which is due to the presence of a ``third integral'' and chaotic scattering, respectively.

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arXiv2006

A comprehensive Nbody study of mass segregation in star clusters: Energy equipartition and escape

We address the dynamical evolution of an isolated self--gravitating system with two stellar mass groups. We vary the individual ratio of the heavy to light bodies, $μ$ from 1.25 to 50 and alter also the fraction of the total heavy mass $\MH$ from 5% to 40% of the whole cluster mass. Clean-cut properties of the cluster dynamics are examined, like core collapse, the evolution of the central potential, as well as escapers. We present in this work collisional $N$-body simulations, using the high--order integrator NBODY6++ with up to ${\cal N}_{\star}=2\cdot 10^4$ particles improving the statistical significancy of the lower--${\cal N}_{\star}$ simulations by ensemble averages. Equipartition slows down the gravothermal contraction of the core slightly. Beyond a critical value of $μ\approx 2$, no equipartition can be achieved between the different masses; the heavy component decouples and collapses. For the first time the critical boundary between Spitzer--stable and --unstable systems is demonstrated in direct $N$-body models.

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arXiv2006

Performance Analysis of Direct N-Body Algorithms on Special-Purpose Supercomputers

Direct-summation N-body algorithms compute the gravitational interaction between stars in an exact way and have a computational complexity of O(N^2). Performance can be greatly enhanced via the use of special-purpose accelerator boards like the GRAPE-6A. However the memory of the GRAPE boards is limited. Here, we present a performance analysis of direct N-body codes on two parallel supercomputers that incorporate special-purpose boards, allowing as many as four million particles to be integrated. Both computers employ high-speed, Infiniband interconnects to minimize communication overhead, which can otherwise become significant due to the small number of "active" particles at each time step. We find that the computation time scales well with processor number; for 2*10^6 particles, efficiencies greater than 50% and speeds in excess of 2 TFlops are reached.

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arXiv2006

Dynamics of compact objects clusters: A post-Newtonian study

Compact object clusters are likely to exist in the centre of some galaxies because of mass segregation. The high densities and velocities reached in them deserves a better understanding. The formation of binaries and their subsequent merging by gravitational radiation emission is important to the evolution of such clusters. We address the evolution of such a system in a relativistic regime. The recurrent mergers at high velocities create an object with a mass much larger than the average. For this aim we modified the direct {\sc Nbody6}++ code to include post-Newtonian effects to the force during two-body encounters. We adjusted the equations of motion to include for the first time the effects of both periastron shift and energy loss by emission of gravitational waves and so to study the eventual decay and merger of radiating binaries. The method employed allows us to give here an accurate post-Newtonian description of the formation of a run-away compact object by successive mergers with surrounding particles, as well as the distribution of characteristic eccentricities in the events. This study should be envisaged as a first step towards a detailed, accurate study of possible gravitational waves sources thanks to the combination of the direct {\sc Nbody} numerical tool with the implementation of post-Newtonian terms on it.

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arXiv2006

Efficient Merger of Binary Supermassive Black Holes in Non-Axisymmetric Galaxies

Binary supermassive black holes form naturally in galaxy mergers, but their long-term evolution is uncertain. In spherical galaxies, N-body simulations show that binary evolution stalls at separations much too large for significant emission of gravitational waves (the "final parsec problem"). Here, we follow the long-term evolution of a massive binary in more realistic, triaxial and rotating galaxy models. We find that the binary does not stall. The binary hardening rates that we observe are sufficient to allow complete coalescence of binary SBHs in 10 Gyr or less, even in the absence of collisional loss-cone refilling or gas-dynamical torques, thus providing a potential solution to the final parsec problem.

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arXiv2005

Long-Term Evolution of Massive Black Hole Binaries. II. Binary Evolution in Low-Density Galaxies

We use direct-summation N-body integrations to follow the evolution of binary black holes at the centers of galaxy models with large, constant-density cores. Particle numbers as large as 400K are considered. The results are compared with the predictions of loss-cone theory, under the assumption that the supply of stars to the binary is limited by the rate at which they can be scattered into the binary's influence sphere by gravitational encounters. The agreement between theory and simulation is quite good; in particular, we are able to quantitatively explain the observed dependence of binary hardening rate on N. We do not verify the recent claim of Chatterjee, Hernquist & Loeb (2003) that the hardening rate of the binary stabilizes when N exceeds a particular value, or that Brownian wandering of the binary has a significant effect on its evolution. When scaled to real galaxies, our results suggest that massive black hole binaries in gas-poor nuclei would be unlikely to reach gravitational-wave coalescence in a Hubble time.

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arXiv2005

The Decay of Accreting Triple Systems as Brown Dwarf Formation Scenario

We investigate the dynamical decay of non-hierarchical accreting triple systems and its implications on the ejection model as Brown Dwarf formation scenario. A modified chain-regularization scheme is used to integrate the equations of motion, that also allows for mass changes over time as well as for momentum transfer from the accreted gas mass onto the bodies. We integrate an ensemble of triple systems within a certain volume with different accretion rates, assuming several prescriptions of how momentum is transferred onto the bodies. We follow their evolution until the systems have decayed. We analyze the end states and decay times of these systems and determine the fraction of Brown Dwarfs formed, their escape speeds as well as the semi-major axis distribution of the formed Brown Dwarf binaries. We find that the formation probability of Brown Dwarfs depends strongly on the assumed momentum transfer which is related to the motion of the gas. Due to ongoing accretion and consequent shrinkage of the systems, the median escape velocity is increased by a factor of 2 and the binary separations are decreased by a factor of 5 compared with non-accreting systems. Furthermore, the obtained semi-major axis distribution drops off sharply to either side of the median, which is also supported by observations. We conclude that accretion and momentum transfer of accreted gas during the dynamical decay of triple systems is able to produce the observed distribution of close binary Brown Dwarfs, making the ejection model a viable option as Brown Dwarf formation scenario.

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arXiv2004

N-Body Growth of a Bahcall-Wolf Cusp Around a Black Hole

We present a clear N-body realization of the growth of a Bahcall-Wolf f ~ E^0.25 (rho ~ 1/r^1.75) density cusp around a massive object ("black hole") at the center of a stellar system. Our N-body algorithm incorporates a novel implementation of Mikkola-Aarseth chain regularization to handle close interactions between star and black hole particles. Forces outside the chain were integrated on a GRAPE-6A/8 special-purpose computer with particle numbers up to N=0.25 x 10^6. We compare our N-body results with predictions of the isotropic Fokker-Planck equation and verify that the time dependence of the density (both configuration and phase-space) predicted by the Fokker-Planck equation is well reproduced by the N-body algorithm, for various choices of N and of the black hole mass. Our results demonstrate the feasibility of direct-force integration techniques for simulating the evolution of galactic nuclei on relaxation time scales.

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arXiv2004

Accretion of stars on to a massive black hole: A realistic diffusion model and numerical studies

To be presented is a study of the secular evolution of a spherical stellar system with a central star-accreting black hole (BH) using the anisotropic gaseous model. This method solves numerically moment equations of the full Fokker-Planck equation, with Boltzmann-Vlasov terms on the left- and collisional terms on the right-hand sides. We study the growth of the central BH due to star accretion at its tidal radius and the feedback of this process on to the core collapse as well as the post-collapse evolution of the surrounding stellar cluster in a self-consistent manner. Diffusion in velocity space into the loss-cone is approximated by a simple model. The results show that the self-regulated growth of the BH reaches a certain fraction of the total mass cluster and agree with other methods. Our approach is much faster than competing ones (Monte Carlo, $N$--body) and provides detailed informations about the time and space dependent evolution of all relevant properties of the system. In this work we present the method and study simple models (equal stellar masses, no stellar evolution or collisions). Nonetheless, a generalisation to include such effects is conceptually simple and under way.

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arXiv2004

Dynamical Evolution of Rotating Stellar Systems: III. The Effect of Mass Spectrum

We have studied the dynamical evolution of rotating star clusters with mass spectrum using a Fokker-Planck code. As a simplest multi-mass model, we first investigated the two-component clusters. Rotation is found to accelerate the dynamical evolution through the transfer of angular momentum outward, as well as from the high masses to the low masses. However, the degree of acceleration depends sensitively on the assumed initial mass function since dynamical friction, which generates mass segregation, also tends to accelerate the evolution, and the combined effect of both is not linear or multiplicative. As long as dynamical friction dominates in the competition with angular momentum exchange the heavy masses lose random energy and angular momentum, sink towards the centre, but their remaining angular momentum is sufficient to speed them up rotationally. This is gravo-gyro instability. As a consequence, we find that the high mass stars in the central parts rotate faster than low mass stars. This leads to the suppression of mass segregation compared to the non-rotating clusters. From the study of multi-component models, we observe similar trends to the two-component models in almost all aspects. The mass function changes less drastically for clusters with rotation. Unlike non-rotating clusters, the mass function depends on $R$ and $z$. Our models are the only ones that can predict mass function and other quantities to be compared with new observations.

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arXiv2003

Dense gas-star systems: Super-massive stars evolution

In the 60s and 70s super-massive central objects (from now onwards SMOs) were thought to be the main source of active galactic nuclei (AGNs) characteristics (luminosities of $L \approx 10^{12} L_{\odot}$). The release of gravitational binding energy by the accretion of material on to an SMO in the range of $10^7 - 10^9 M_{\odot}$ has been suggested to be the primary powerhouse (Lynden-Bell 1969). That rather exotic idea in early time has become common sense nowadays. Not only our own galaxy harbours a few million-solar mass black hole (Genzel 2001) but also many of other non-active galaxies show kinematic and gas-dynamic evidence of these objects (Magorrian et al. 1998) The concept of central super-massive stars (SMSs henceforth) (${\cal M} \ge 5 \times 10^4 M_{\odot}$, where ${\cal M}$ is the mass of the SMS) embedded in dense stellar systems was suggested as a possible explanation for high- energy emissions phenomena occurring in AGNs and quasars (Vilkoviski 1976, Hara 1978), such as X-ray emissions (Bahcall and Ostriker, 1975). SMSs and super-massive black holes (SMBHs) are two possibilities to explain the nature of SMOs, and SMSs may be an intermediate step towards the formation of SMBHs (Rees 1984). In this paper we give the equations that describe the dynamics of such a dense star-gas system which are the basis for the code that will be used in a prochain future to simulate this scenario. We also briefly draw the mathematical fundamentals of the code

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arXiv2003

Super-massive stars: Radiative transfer

The concept of central super-massive stars (${\cal M} \ge 5 \times 10^4 M_{\odot}$, where ${\cal M}$ is the mass of the super-massive star) embedded in dense stellar systems was suggested as a possible explanation for high- energy emissions phenomena occurring in active galactic nuclei and quasars (Vilkoviski 1976, Hara 1978), such as X-ray emissions (Bahcall and Ostriker, 1975). SMSs and super-massive black holes are two possibilities to explain the nature of super-massive central objects, and super-massive stars may be an intermediate step towards the formation of super-massive black holes (Rees 1984). Therefore it is important to study such a dense gas-star system in detail. We address here the implementation of radiative transfer in a model which was presented in former work (Amaro-Seoane and Spurzem 2001, Amaro-Seoane et al. 2002). In this sense, we extend here and improve the work done by Langbein et al. (1990) by describing the radiative transfer in super-massive stars using previous work on this subject (Castor 1972).

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arXiv2002

Collisional dynamics around binary black holes in galactic centers

We follow the sinking of two massive black holes in a spherical stellar system where the black holes become bound under the influence of dynamical friction. Once bound, the binary hardens by three-body encounters with surrounding stars. We find that the binary wanders inside the core, providing an enhanced supply of reaction partners for the hardening. The binary evolves into a highly eccentric orbit leading to coalescence well beyond a Hubble time. These are the first results from a hybrid ``self consistent field'' (SCF) and direct Aarseth N-body integrator (NBODY6), which combines the advantages of the direct force calculation with the efficiency of the field method. The code is designed for use on parallel architectures and is therefore applicable to collisional N-body integrations with extraordinarily large particle numbers (> 10^5). This creates the possibility of simulating the dynamics of both globular clusters with realistic collisional relaxation and stellar systems surrounding supermassive black holes in galactic nuclei.

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arXiv2001

Super-massive stars: Dense star-gas systems

We use a gaseous model and a semi-analytical approach to study the evolution of a super-massive central gaseous object (a super-massive star, (SMS from now on) in an AGN and its evolution by interactions with the surrounding stellar system. Our future work in this field is outlined, which aims at a more detailed study of energy flows in the interstellar medium, stellar evolution and the relation between QSOs and galaxy formation.

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arXiv2001

Dynamical evolution of rotating stellar systems - II. Post-collapse, equal mass system

We present the first post core collapse models of initially rotating star clusters, using the numerical solution of an orbit-averaged 2D Fokker-Planck equation. Based on the code developed by Einsel & Spurzem (1999), we have improved the speed and the stability and included the steady three-body binary heating source. We have confirmed that rotating clusters, whether they are in a tidal field or not, evolve significantly faster than non-rotating ones. Consequences for observed shapes, density distribution, and kinematic properties of young and old star clusters are discussed. The results are compared with gaseous and 1D Fokker-Planck models in the non-rotating case.

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arXiv2001

The loss-cone problem in dense nuclei

We address the classical problem of star accretion onto a supermassive central gaseous object in a galactic nucleus. The resulting supermassive central gas-star object is assumed to be located at the centre of a dense stellar system for which we use a simplified model consisting of a Plummer model with an embedded density cusp using stellar point masses. From the number of stars belonging to the loss-cone, which plunge onto the central object on elongated orbits from outside, we estimate the accretion rate taking into account a possible anisotropy of the surrounding stellar distribution. The total heating rate in the supermassive star due to the loss-cone stars plunging onto it is estimated. This semi-analytical study, revisiting and expanding classical paper's work, is a starting point of future work on a more detailed study of early evolutionary phases of galactic nuclei. It merits closer examination, because it is one of the key features for the link between cosmology and galaxy formation.

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