Evolution of Clusters of Galaxies: Mass Stripping from Galaxies and Growth of Common Halos

We investigated the evolution of clusters of galaxies using self-consistent $N$-body simulations in which each galaxy was modeled by many particles. We carried out simulations for about 20 cases using different initial conditions. In all simulations, clusters were initially in virial equilibrium. We found that more than half of the total mass escaped from individual galaxies within a few crossing times of the cluster, and that a diffuse halo was formed. The growth rate of the common halo depended on the size of individual galaxies only weakly. The stripping of the mass from galaxies was mainly due to the interaction of galaxies, not due to the effect of the tidal field of the cluster potential. The amount of stripped mass was larger for galaxies in the central region than for those in the outer region, since the interactions were more frequent in the central region. As a result, a positive correlation between the distance from the center and the mass of the galaxy developed. The volume-density profile of the common halo is expressed as $\rho\propto r^{-1}$ in the central region. This mass distribution is consistent with the mass distribution in clusters estimated using X-ray observations.Comment: 12 pages with 12 figures; accepted for publication in PAS

Collisional Evolution of Galaxy Clusters and the Growth of Common Halos

We investigated the dynamical evolution of clusters of galaxies in virial equilibrium using Fokker-Planck models and self-consistent N-body models. In particular, we focused on the growth of a common halo, which is a cluster-wide halo formed by matter stripped from galaxies, and the development of a central density cusp. The Fokker-Planck models include the effects of two-body gravitational encounters both between galaxies and between galaxies and common halo particles. The effects of tidal mass stripping from the galaxies due to close galaxy-galaxy encounters and accompanying dissipation of the orbital kinetic energies of the galaxies were also taken into account in the Fokker-Planck models. We find that the results of the Fokker-Planck models are in excellent agreement with those of the N-body models regarding the growth of the common halo mass and the evolution of the cluster density profiles. In the central region of the cluster, a shallow density cusp, approximated by $\rho (r) \propto r^{-\alpha}$ ($\alpha \sim$ 1), develops. This shallow cusp results from the combined effects of two-body relaxation and tidal stripping. The cusp steepness, $\alpha$, weakly depends on the relative importance of the tidal stripping. When the effect of stripping is important, the central velocity dispersion decreases as the central density increases and, consequently, a shallow ($\alpha <2$) cusp is formed. In the limit of no stripping, usual gravothermal core collapse occurs, i.e. the central velocity dispersion increases as the central density increases with a steep ($\alpha >2$) cusp left. We conclude from our consideration of the origin of the cusp demonstrated here that shallow cusps should develop in real galaxy clusters.Comment: revised, 21 pages, 16 figures, to appear in PASJ, 54, No.1 (2002

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

Missing Link Found? The "Runaway" Path to Supermassive Black Holes

Observations of stellar kinematics, gas dynamics and masers around galactic nuclei have now firmly established that many galaxies host central supermassive black holes (SMBHs) with masses in the range $10^6 \sim 10^9$M$_{\odot}$. However, how these SMBHs formed is not well understood. One reason for this situation is the lack of observations of intermediate-mass BHs (IMBHs), which could bridge the gap between stellar-mass BHs and SMBHs. Recently, this missing link (i.e., an IMBH) has been found in observations made by the ASCA and the Chandra of the central region of the starburst galaxy M82 \citep{MT99, PG99, MT01, Ka01}. Subsequent observations by SUBARU have revealed that this IMBH apparently coincides with a young compact star cluster. Based on these findings, we suggest a new formation scenario for SMBHs. In this scenario, IMBHs first form in young compact star clusters through runaway merging of massive stars. While these IMBHs are forming, the host star clusters sink toward the galactic nucleus through dynamical friction, and upon evaporation deposit their IMBHs near the galactic center. The IMBHs then form binaries and eventually merge via gravitational radiation, forming an SMBH.Comment: 12 pages 2 figuresm submitted to Astrophysical Journal, Letter

Relaxation of a Collisionless System and the Transition to a New Equilibrium Velocity Distribution

In this paper, we present our conclusions from the numerical study of the collapse of a destabilized collisionless stellar system. We use both direct integration of the Vlasov-Poisson equations and an N-body tree code to obtain our results, which are mutually confirmed. We find that spherical and moderately nonspherical collapse configurations evolve to new equilibrium configurations in which the velocity distribution approaches a Gaussian form, at least in the central regions. The evolution to this state has long been an open question, and in this work we are able to clarify the process responsible and to support predictions made from statistical considerations (Lynden-Bell 1967; Nakamura 2000). The simulations of merging N-body systems show a transition to a Gaussian velocity distribution that is increasingly suppressed as the initial separation of centres is increased. Possible reasons for this are discussed.Comment: 25 pages, LaTeX. Accepted for publication in Ap

A dynamical origin for early mass segregation in young star clusters

Some young star clusters show a degree of mass segregation that is inconsistent with the effects of standard two-body relaxation from an initially unsegregated system without substructure, in virial equilibrium, and it is unclear whether current cluster formation models can account for this degree of initial segregation in clusters of significant mass. In this Letter we demonstrate that mergers of small clumps that are either initially mass segregated, or in which mass segregation can be produced by two-body relaxation before they merge, generically lead to larger systems which inherit the progenitor clumps' segregation. We conclude that clusters formed in this way are naturally mass segregated, accounting for the anomalous observations and suggesting that this process of prompt mass segregation due to initial clumping should be taken fully into account in constructing cluster dynamical models.Comment: 13 pages, 4 figures, submitted to ApJ

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