1,892 research outputs found
Particle-Particle Particle-Tree: A Direct-Tree Hybrid Scheme for Collisional N-Body Simulations
In this paper, we present a new hybrid algorithm for the time integration of
collisional N-body systems. In this algorithm, gravitational force between two
particles is divided into short-range and long-range terms, using a
distance-dependent cutoff function. The long-range interaction is calculated
using the tree algorithm and integrated with the constant-timestep leapfrog
integrator. The short-range term is calculated directly and integrated with the
high-order Hermite scheme. We can reduce the calculation cost per orbital
period from O(N^2) to O(N log N), without significantly increasing the
long-term integration error. The results of our test simulations show that
close encounters are integrated accurately. Long-term errors of the total
energy shows random-walk behaviour, because it is dominated by the error caused
by tree approximation.Comment: 22 pages, 15 figure
Dynamical friction on satellite galaxies
For a rigid model satellite, Chandrasekhar's dynamical friction formula
describes the orbital evolution quite accurately, when the Coulomb logarithm is
chosen appropriately. However, it is not known if the orbital evolution of a
real satellite with the internal degree of freedom can be described by the
dynamical friction formula. We performed N-body simulation of the orbital
evolution of a self-consistent satellite galaxy within a self-consistent parent
galaxy. We found that the orbital decay of the simulated satellite is
significantly faster than the estimate from the dynamical friction formula. The
main cause of this discrepancy is that the stars stripped out of the satellite
are still close to the satellite, and increase the drag force on the satellite
through two mechanisms. One is the direct drag force from particles in the
trailing tidal arm, a non-axisymmetric force that slows the satellite down. The
other is the indirect effect that is caused by the particles remaining close to
the satellite after escape. The force from them enhances the wake caused in the
parent galaxy by dynamical friction, and this larger wake in turn slows the
satellite down more than expected from the contribution of its bound mass. We
found these two have comparable effects, and the combined effect can be as
large as 20% of the total drag force on the satellite.Comment: 15 pages, 10 figures, submitted to PASJ; v2: 14 pages, 13 figures,
accepted by PAS
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
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