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.Comment: 9 pages, 6 figures, MNRAS in pres

Performance analysis of parallel gravitational NN-body codes on large GPU cluster

We compare the performance of two very different parallel gravitational $N$-body codes for astrophysical simulations on large GPU clusters, both pioneer in their own fields as well as in certain mutual scales - NBODY6++ and Bonsai. We carry out the benchmark of the two codes by analyzing their performance, accuracy and efficiency through the modeling of structure decomposition and timing measurements. We find that both codes are heavily optimized to leverage the computational potential of GPUs as their performance has approached half of the maximum single precision performance of the underlying GPU cards. With such performance we predict that a speed-up of $200-300$ can be achieved when up to 1k processors and GPUs are employed simultaneously. We discuss the quantitative information about comparisons of two codes, finding that in the same cases Bonsai adopts larger time steps as well as relative energy errors than NBODY6++, typically ranging from $10-50$ times larger, depending on the chosen parameters of the codes. While the two codes are built for different astrophysical applications, in specified conditions they may overlap in performance at certain physical scale, and thus allowing the user to choose from either one with finetuned parameters accordingly.Comment: 15 pages, 7 figures, 3 tables, accepted for publication in Research in Astronomy and Astrophysics (RAA

SMBH in Galactic Nuclei with Tidal Disruption of Stars

Tidal Disruption of stars by super massive central black holes from dense star clusters is modeled by high-accuracy direct $N$-body simulation. The time evolution of the stellar tidal disruption rate, the effect of tidal disruption on the stellar density profile and for the first time the detailed origin of tidally disrupted stars are carefully examined and compared with classic papers in the field. Up to 128k particles are used in simulation to model the star cluster around the super massive black hole, we use the particle number and the tidal radius of black hole as free parameters for a scaling analysis. The transition from full to empty loss-cone is analyzed in our data, the tidal disruption rate scales with the particle number $N$ in the expected way for both cases. For the first time in numerical simulations (under certain conditions) we can support the concept of a critical radius of Frank & Rees (1976), which claims that most stars are tidally accreted on highly eccentric orbits originating from regions far outside the tidal radius. Due to the consumption of stars moving on radial orbits, a velocity anisotropy is founded inside the cluster. Finally we make an estimation for the real galactic center based on our simulation results and the scaling analysis.Comment: 15 pages, 16 figures, accepted by Ap

Supermassive Black Holes in Galactic Nuclei with Tidal Disruption of Stars: Paper II - Axisymmetric Nuclei

Tidal Disruption of stars by supermassive central black holes from dense rotating star clusters is modelled by high-accuracy direct N-body simulation. As in a previous paper on spherical star clusters we study the time evolution of the stellar tidal disruption rate and the origin of tidally disrupted stars, now according to several classes of orbits which only occur in axisymmetric systems (short axis tube and saucer). Compared with that in spherical systems, we found a higher TD rate in axisymmetric systems. The enhancement can be explained by an enlarged loss-cone in phase space which is raised from the fact that total angular momentum $\bf J$ is not conserved. As in the case of spherical systems, the distribution of the last apocenter distance of tidally accreted stars peaks at the classical critical radius. However, the angular distribution of the origin of the accreted stars reveals interesting features. Inside the influence radius of the supermassive black hole the angular distribution of disrupted stars has a conspicuous bimodal structure with a local minimum near the equatorial plane. Outside the influence radius this dependence is weak. We show that the bimodal structure of orbital parameters can be explained by the presence of two families of regular orbits, namely short axis tube and saucer orbits. Also the consequences of our results for the loss cone in axisymmetric galactic nuclei are presented.Comment: 14 pages, 16 figures, accepted by Ap

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.Comment: new plots included, minor changes, 5 pages, needs mn2e.bst and mn2e.cls (included in the tar.gz file) accepted by MNRA

Hybrid methods in planetesimal dynamics: Formation of protoplanetary systems and the mill condition

The formation and evolution of protoplanetary discs remains a challenge from both a theoretical and numerical standpoint. In this work we first perform a series of tests of our new hybrid algorithm presented in Glaschke, Amaro-Seoane and Spurzem 2011 (henceforth Paper I) that combines the advantages of high accuracy of direct-summation N-body methods with a statistical description for the planetesimal disc based on Fokker-Planck techniques. We then address the formation of planets, with a focus on the formation of protoplanets out of planetesimals. We find that the evolution of the system is driven by encounters as well as direct collisions and requires a careful modelling of the evolution of the velocity dispersion and the size distribution over a large range of sizes. The simulations show no termination of the protoplanetary accretion due to gap formation, since the distribution of the planetesimals is only subjected to small fluctuations. We also show that these features are weakly correlated with the positions of the protoplanets. The exploration of different impact strengths indicates that fragmentation mainly controls the overall mass loss, which is less pronounced during the early runaway growth. We prove that the fragmentation in combination with the effective removal of collisional fragments by gas drag sets an universal upper limit of the protoplanetary mass as a function of the distance to the host star, which we refer to as the mill condition.Comment: Submitte

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).Comment: 2 pages, to appear in "Galatic Dynamics", eds. C. Boily, P. Patsis, C. Theis, S. Portegies Zwart, R. Spurzem, EDP Sciences 2003 (JENAM 2002 Conference in Porto, September 2-7, Workshop "Galactic Dynamics"). Needs eas.cls (also included