385 research outputs found
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
-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
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
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 (). 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
Time-Symmetrized Kustaanheimo-Stiefel Regularization
In this paper we describe a new algorithm for the long-term numerical
integration of the two-body problem, in which two particles interact under a
Newtonian gravitational potential. Although analytical solutions exist in the
unperturbed and weakly perturbed cases, numerical integration is necessary in
situations where the perturbation is relatively strong. Kustaanheimo--Stiefel
(KS) regularization is widely used to remove the singularity in the equations
of motion, making it possible to integrate orbits having very high
eccentricity. However, even with KS regularization, long-term integration is
difficult, simply because the required accuracy is usually very high. We
present a new time-integration algorithm which has no secular error in either
the binding energy or the eccentricity, while allowing variable stepsize. The
basic approach is to take a time-symmetric algorithm, then apply an implicit
criterion for the stepsize to ensure strict time reversibility. We describe the
algorithm in detail and present the results of numerical tests involving
long-term integration of binaries and hierarchical triples. In all cases
studied, we found no systematic error in either the energy or the angular
momentum. We also found that its calculation cost does not become higher than
those of existing algorithms. By contrast, the stabilization technique, which
has been widely used in the field of collisional stellar dynamics, conserves
energy very well but does not conserve angular momentum.Comment: figures are available at http://grape.c.u-tokyo.ac.jp/~funato/; To
appear in Astronomical Journal (July, 1996
Light to Mass Variations with Environment
Large and well defined variations exist between the distribution of mass and
the light of stars on extragalactic scales. Mass concentrations in the range
10^12 - 10^13 M_sun manifest the most light per unit mass. Group halos in this
range are typically the hosts of spiral and irregular galaxies with ongoing
star formation. On average M/L_B ~ 90 M_sun/L_sun in these groups . More
massive halos have less light per unit mass. Within a given mass range, halos
that are dynamically old as measured by crossing times and galaxy morphologies
have distinctly less light per unit mass. At the other end of the mass
spectrum, below 10^12 M_sun, there is a cutoff in the manifestation of light.
Group halos in the range 10^11 - 10^12 M_sun can host dwarf galaxies but with
such low luminosities that M/L_B values can range from several hundred to
several thousand. It is suspected that there must be completely dark halos at
lower masses. Given the form of the halo mass function, it is the low relative
luminosities of the high mass halos that has the greatest cosmological
implications. Of order half the clustered mass may reside in halos with greater
than 10^14 M_sun. By contrast, only 5-10% of clustered mass would lie in
entities with less than 10^12 M_sun.Comment: 15 pages, 9 figures, 2 tables, Accepted Astrophysical Journal 619,
000, 2005 (Jan 1
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 ( 1), develops. This shallow cusp results
from the combined effects of two-body relaxation and tidal stripping. The cusp
steepness, , 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 () 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 () 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
Evolution of Star Clusters near the Galactic Center: Fully Self-consistent N-body Simulations
We have performed fully self-consistent -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
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