BRIDGE: A Direct-tree Hybrid N-body Algorithm for Fully Self-consistent Simulations of Star Clusters and their Parent Galaxies

We developed a new direct-tree hybrid N-body algorithm for fully self-consistent N-body simulations of star clusters in their parent galaxies. In such simulations, star clusters need high accuracy, while galaxies need a fast scheme because of the large number of the particles required to model it. In our new algorithm, the internal motion of the star cluster is calculated accurately using the direct Hermite scheme with individual timesteps and all other motions are calculated using the tree code with second-order leapfrog integrator. The direct and tree schemes are combined using an extension of the mixed variable symplectic (MVS) scheme. Thus, the Hamiltonian corresponding to everything other than the internal motion of the star cluster is integrated with the leapfrog, which is symplectic. Using this algorithm, we performed fully self-consistent N-body simulations of star clusters in their parent galaxy. The internal and orbital evolutions of the star cluster agreed well with those obtained using the direct scheme. We also performed fully self-consistent N-body simulation for large-N models ($N=2\times 10^6$). In this case, the calculation speed was seven times faster than what would be if the direct scheme was used.Comment: 12 pages, 13 figures, Accepted for PAS

Evolution of Star Clusters near the Galactic Center: Fully Self-consistent N-body Simulations

We have performed fully self-consistent $N$-body simulations of star clusters near the Galactic center (GC). Such simulations have not been performed because it is difficult to perform fast and accurate simulations of such systems using conventional methods. We used the Bridge code, which integrates the parent galaxy using the tree algorithm and the star cluster using the fourth-order Hermite scheme with individual timestep. The interaction between the parent galaxy and the star cluster is calculate with the tree algorithm. Therefore, the Bridge code can handle both the orbital and internal evolutions of star clusters correctly at the same time. We investigated the evolution of star clusters using the Bridge code and compared the results with previous studies. We found that 1) the inspiral timescale of the star clusters is shorter than that obtained with "traditional" simulations, in which the orbital evolution of star clusters is calculated analytically using the dynamical friction formula and 2) the core collapse of the star cluster increases the core density and help the cluster survive. The initial conditions of star clusters is not so severe as previously suggested.Comment: 19 pages, 19 figures, accepted for publication in Ap

Evolution of Massive Black Hole Binaries

We present the result of large-scale N-body simulations of the stellar-dynamical evolution of a massive black-hole binary at the center of a spherical galaxy. We focus on the dependence of the hardening rate on the relaxation timescale of the parent galaxy. A simple theoretical argument predicts that a binary black hole creates the ``loss cone'' around it. Once the loss cone is formed, the hardening rate is determined by the rate at which field stars diffuse into the loss cone. Therefore the hardening timescale becomes proportional to the relaxation timescale. Recent N-body simulations, however, have failed to confirm this theory and various explanations have been proposed. By performing simulations with sufficiently large N (up to $10^6$) for sufficiently long time, we found that the hardening rate does depend on N. Our result is consistent with the simple theoretical prediction that the hardening timescale is proportional to the relaxation timescale. This dependence implies that most massive black hole binaries are unlikely to merge within the Hubble time through interaction with field stars and gravitational wave radiation alone.Comment: Reviced version accepted for publication in ApJ. Scheduled to appear in the February 10, 2004 issu

The Orbit, Mass, and Albedo of Transneptunian Binary 1999 RZ253

We have observed 1999 RZ253 with the Hubble Space Telescope at seven separate epochs and have fit an orbit to the observed relative positions of this binary. Two orbital solutions have been identified that differ primarily in the inclination of the orbit plane. The best fit corresponds to an orbital period, P=46.263 +0.006/-0.074 days, semimajor axis a=4,660 +/-170 km and orbital eccentricity e=0.460 +/-0.013 corresponding to a system mass m=3.7 +/-0.4 x10^18 kg. For a density of rho = 1000 kg m^-3 the albedo at 477 nm is p = 0.12 +/-0.01, significantly higher than has been commonly assumed for objects in the Kuiper Belt. Multicolor, multiepoch photometry shows this pair to have colors typical for the Kuiper belt with a spectral gradient of 0.35 per 100 nm in the range between 475 and 775 nm. Photometric variations at the four epochs we observed were as large as 12 +/-3% but the sampling is insufficient to confirm the existence of a lightcurve

On relaxation processes in collisionless mergers

We analyze N-body simulations of halo mergers to investigate the mechanisms responsible for driving mixing in phase-space and the evolution to dynamical equilibrium. We focus on mixing in energy and angular momentum and show that mixing occurs in step-like fashion following pericenter passages of the halos. This makes mixing during a merger unlike other well known mixing processes such as phase mixing and chaotic mixing whose rates scale with local dynamical time. We conclude that the mixing process that drives the system to equilibrium is primarily a response to energy and angular momentum redistribution that occurs due to impulsive tidal shocking and dynamical friction rather than a result of chaotic mixing in a continuously changing potential. We also analyze the merger remnants to determine the degree of mixing at various radii by monitoring changes in radius, energy and angular momentum of particles. We confirm previous findings that show that the majority of particles retain strong memory of their original kinetic energies and angular momenta but do experience changes in their potential energies owing to the tidal shocks they experience during pericenter passages. Finally, we show that a significant fraction of mass (~ 40%) in the merger remnant lies outside its formal virial radius and that this matter is ejected roughly uniformly from all radii outside the inner regions. This highlights the fact that mass, in its standard virial definition, is not additive in mergers. We discuss the implications of these results for our understanding of relaxation in collisionless dynamical systems.Comment: Version accepted for Publication in Astrophysical Journal, March 20, 2007, v685. Minor changes, latex, 14 figure

On the effectiveness of mixing in violent relaxation

Relaxation processes in collisionless dynamics lead to peculiar behavior in systems with long-range interactions such as self-gravitating systems, non-neutral plasmas and wave-particle systems. These systems, adequately described by the Vlasov equation, present quasi-stationary states (QSS), i.e. long lasting intermediate stages of the dynamics that occur after a short significant evolution called "violent relaxation". The nature of the relaxation, in the absence of collisions, is not yet fully understood. We demonstrate in this article the occurrence of stretching and folding behavior in numerical simulations of the Vlasov equation, providing a plausible relaxation mechanism that brings the system from its initial condition into the QSS regime. Area-preserving discrete-time maps with a mean-field coupling term are found to display a similar behaviour in phase space as the Vlasov system.Comment: 10 pages, 11 figure

Towards a framework for validating the matching between notifications and scents in olfactory in-car interaction

Olfactory notifications have been proven to have a positive impact on drivers. This has motivated the use of scents to convey driving-relevant information. Research has proposed the use of such scents as lemon, peppermint, lavender and rose for in-car notifications. However, there is no framework to identify which scent is the most suitable for every application scenario. In this paper, we propose an approach for validating a matching between scents and driving-relevant notifications. We suggest a study in which the olfactory modality is compared with a puff of clean air, visual, auditory, and tactile stimuli while performing the same driving task. For the data analysis, we suggest recording the lane deviation, speed, time required to recover from the error, as well as the perceived liking and comfort ratings. Our approach aims to help automotive UI designers make better decisions about choosing the most suitable scent, as well as possible alternative modalities

The Origin of the Brightest Cluster Galaxies

Most clusters and groups of galaxies contain a giant elliptical galaxy in their centres which far outshines and outweighs normal ellipticals. The origin of these brightest cluster galaxies is intimately related to the collapse and formation of the cluster. Using an N-body simulation of a cluster of galaxies in a hierarchical cosmological model, we show that galaxy merging naturally produces a massive, central galaxy with surface brightness and velocity dispersion profiles similar to observed BCG's. To enhance the resolution of the simulation, 100 dark halos at $z=2$ are replaced with self-consistent disk+bulge+halo galaxy models following a Tully-Fisher relation using 100000 particles for the 20 largest galaxies and 10000 particles for the remaining ones. This technique allows us to analyze the stellar and dark matter components independently. The central galaxy forms through the merger of several massive galaxies along a filament early in the cluster's history. Galactic cannibalism of smaller galaxies through dynamical friction over a Hubble time only accounts for a small fraction of the accreted mass. The galaxy is a flattened, triaxial object whose long axis aligns with the primordial filament and the long axis of the cluster galaxy distribution agreeing with observed trends for galaxy-cluster alignment.Comment: Revised and accepted in ApJ, 25 pages, 10 figures, online version available at http://www.cita.utoronto.ca/~dubinski/bcg

On the equilibrium morphology of systems drawn from spherical collapse experiments

We present a purely theoretical study of the morphological evolution of self-gravitating systems formed through the dissipationless collapse of N-point sources. We explore the effects of resolution in mass and length on the growth of triaxial structures formed by an instability triggered by an excess of radial orbits. We point out that as resolution increases, the equilibria shift, from mildly prolate, to oblate. A number of particles N ~= 100000 or larger is required for convergence of axial aspect ratios. An upper bound for the softening, e ~ 1/256, is also identified. We then study the properties of a set of equilibria formed from scale-free cold initial mass distributions, ro ~ r^-g with 0 <= g <= 2. Oblateness is enhanced for initially more peaked structures (larger values of g). We map the run of density in space and find no evidence for a power-law inner structure when g <= 3/2 down to a mass fraction <~0.1 per cent of the total. However, when 3/2 < g <= 2, the mass profile in equilibrium is well matched by a power law of index ~g out to a mass fraction ~ 10 per cent. We interpret this in terms of less-effective violent relaxation for more peaked profiles when more phase mixing takes place at the centre. We map out the velocity field of the equilibria and note that at small radii the velocity coarse-grained distribution function (DF) is Maxwellian to a very good approximation.Comment: 16 page

S(C)ENTINEL - monitoring automated vehicles with olfactory reliability displays

Overreliance in technology is safety-critical and it is assumed that this could have been a main cause of severe accidents with automated vehicles. To ease the complex task of per- manently monitoring vehicle behavior in the driving en- vironment, researchers have proposed to implement relia- bility/uncertainty displays. Such displays allow to estimate whether or not an upcoming intervention is likely. However, presenting uncertainty just adds more visual workload on drivers, who might also be engaged in secondary tasks. We suggest to use olfactory displays as a potential solution to communicate system uncertainty and conducted a user study (N=25) in a high-fidelity driving simulator. Results of the ex- periment (conditions: no reliability display, purely visual reliability display, and visual-olfactory reliability display) comping both objective (task performance) and subjective (technology acceptance model, trust scales, semi-structured interviews) measures suggest that olfactory notifications could become a valuable extension for calibrating trust in automated vehicles