The secular evolution of the Kuiper belt after a close stellar encounter

We show the effects of the perturbation caused by a passing by star on the Kuiper belt objects (KBOs) of our Solar System. The dynamics of the Kuiper belt (KB) is followed by direct $N$-body simulations. The sampling of the KB has been done with $N$ up to $131,062$, setting the KBOs on initially nearly circular orbits distributed in a ring of surface density $\Sigma \sim r^{-2}$. This modelization allowed us to investigate the secular evolution of the KB upon the encounter with the perturbing star. Actually, the encounter itself usually leads toward eccentricity and inclination distributions similar to observed ones, but tends also to excite the low-eccentricity population ($e < 0.1$ around $a\sim 40$\,$\mathrm{AU}$ from the Sun), depleting this region of low eccentricities. The following long-term evolution shows a "cooling" of the eccentricities repopulating the low-eccentricity area. In dependence on the assumed KBO mass spectrum and sampled number of bodies, this repopulation takes place in a time that goes from 0.5 Myr to 100 Myr. Due to the unavoidable limitation in the number of objects in our long-term simulations ($N \leq 16384$), we could not consider a detailed KBO mass spectrum, accounting for low mass objects, thus our present simulations are not reliable in constraining correlations among inclination distribution of the KBOs and other properties, such as their size distribution. However, our high precision long term simulations are a starting point for future larger studies on massively parallel computational platforms which will provide a deeper investigation of the secular evolution ($\sim 100\,$Myr) of the KB over its whole mass spectrum.Comment: 13 pages, 12 figures, 5 table

Selection of the SIM Astrometric Grid

We investigate the choice of stellar population for use as the Astrometric Grid for the Space Interferometry Mission (SIM). SIM depends on the astrometric stability of about 2000 stars, the so called Grid, against which the science measures are referenced. Low metallicity, and thus relatively high luminosity K giants are shown to be the population of choice, when available. The alternative, nearby G dwarfs, are shown to be suseptable to unmodeled motions induced by gas-giant planetary companions, should there be a significant population of such companions. Radial velocity filtering is quite efficient in selecting Grid members from the K giants with yields exceeding 50% if filtering at 30m/s (1-sigma) is available. However if the binary fraction of the G dwarfs approaches 100% as some studies suggest, the yield of stable systems would be in the range of 15% at best (with 10m/s filtering). Use of the initial SIM measurement as a final filter is shown not to be critical in either case, although it could improve the yield of stable grid members. For a Grid composed of weak-lined K giants, the residual contamination by large unmodeled motions will amount to about 3% (and rises to about 6% if a 60m/s radial velocity criterion is used). The selective introduction of quadratic terms in the proper motion solutions during the post-mission phase of data reduction can reduce contamination to a remarkable 1% or better in either case. Analytic estimates based on circular orbits are developed which show how these results come about.Comment: 42 pages including 13 eps figures. To be published Sept 2002 in PAS

Black hole mergers in the universe

Mergers of black-hole binaries are expected to release large amounts of energy in the form of gravitational radiation. However, binary evolution models predict merger rates too low to be of observational interest. In this paper we explore the possibility that black holes become members of close binaries via dynamical interactions with other stars in dense stellar systems. In star clusters, black holes become the most massive objects within a few tens of millions of years; dynamical relaxation then causes them to sink to the cluster core, where they form binaries. These black-hole binaries become more tightly bound by superelastic encounters with other cluster members, and are ultimately ejected from the cluster. The majority of escaping black-hole binaries have orbital periods short enough and eccentricities high enough that the emission of gravitational radiation causes them to coalesce within a few billion years. We predict a black-hole merger rate of about $1.6 \times 10^{-7}$ per year per cubic megaparsec, implying gravity wave detection rates substantially greater than the corresponding rates from neutron star mergers. For the first generation Laser Interferometer Gravitational-Wave Observatory (LIGO-I), we expect about one detection during the first two years of operation. For its successor LIGO-II, the rate rises to roughly one detection per day. The uncertainties in these numbers are large. Event rates may drop by about an order of magnitude if the most massive clusters eject their black hole binaries early in their evolution.Comment: 12 pages, ApJL in pres

De Toekomst van Waterkwaliteitsmonitoring, Deel 3: Biomonitoring

In general terms the problems with the existing water quality monitoring approach concern effective and efficient monitoring strategies. In 1993 the project "Monitoring water quality in the future" started in order to address these problems which will only increase in the future. In the framework of this project five reports have been produced, focussing on: Chemical Monitoring (Volume 1) ; Mixture toxicity parameters (Volume 2) ; Biomonitoring (Volume 3) ; Monitoring strategies for complex mixtures (Volume 4); and Organizational aspects (Volume 5). The specific objectives were to produce concise reviews of methods to signal changes in and control water quality (Volumes 1-3), to give a review of testing strategies for complex mixtures of chemical substances which can give more complete information at less costs (Volume 4) and to review existing practices and make recommendations concerning standardization, optimization and organization of monitoring activities in the European Union, with a focus on effectiveness and efficiency (Volume 5). In an executive summary overall recommendations are also made by drawing these together from the individual studies. The present report (Volume 3) includes a short description of existing biomonitoring methodologies and measurement strategies, as well as a discussion on possibilities, developments, limitations and financial consequences

Monte-Carlo Simulations of Globular Cluster Evolution - I. Method and Test Calculations

We present a new parallel supercomputer implementation of the Monte-Carlo method for simulating the dynamical evolution of globular star clusters. Our method is based on a modified version of Henon's Monte-Carlo algorithm for solving the Fokker-Planck equation. Our code allows us to follow the evolution of a cluster containing up to 5x10^5 stars to core collapse in < 40 hours of computing time. In this paper we present the results of test calculations for clusters with equal-mass stars, starting from both Plummer and King model initial conditions. We consider isolated as well as tidally truncated clusters. Our results are compared to those obtained from approximate, self-similar analytic solutions, from direct numerical integrations of the Fokker-Planck equation, and from direct N-body integrations performed on a GRAPE-4 special-purpose computer with N=16384. In all cases we find excellent agreement with other methods, establishing our new code as a robust tool for the numerical study of globular cluster dynamics using a realistic number of stars.Comment: 35 pages, including 8 figures, submitted to ApJ. Revised versio

MYRIAD: A new N-body code for simulations of Star Clusters

We present a new C++ code for collisional N-body simulations of star clusters. The code uses the Hermite fourth-order scheme with block time steps, for advancing the particles in time, while the forces and neighboring particles are computed using the GRAPE-6 board. Special treatment is used for close encounters, binary and multiple sub-systems that either form dynamically or exist in the initial configuration. The structure of the code is modular and allows the appropriate treatment of more physical phenomena, such as stellar and binary evolution, stellar collisions and evolution of close black-hole binaries. Moreover, it can be easily modified so that the part of the code that uses GRAPE-6, could be replaced by another module that uses other accelerating-hardware like the Graphics Processing Units (GPUs). Appropriate choice of the free parameters give a good accuracy and speed for simulations of star clusters up to and beyond core collapse. Simulations of Plummer models consisting of equal-mass stars reached core collapse at t~17 half-mass relaxation times, which compares very well with existing results, while the cumulative relative error in the energy remained below 0.001. Also, comparisons with published results of other codes for the time of core collapse for different initial conditions, show excellent agreement. Simulations of King models with an initial mass-function, similar to those found in the literature, reached core collapse at t~0.17, which is slightly smaller than the expected result from previous works. Finally, the code accuracy becomes comparable and even better than the accuracy of existing codes, when a number of close binary systems is dynamically created in a simulation. This is due to the high accuracy of the method that is used for close binary and multiple sub-systems.Comment: 24 pages, 29 figures, accepted for publication to Astronomy & Astrophysic

How many young star clusters exist in the Galactic center?

We study the evolution and observability of young compact star clusters within about 200pc of the Galactic center. Calculations are performed using direct N-body integration on the GRAPE-4, including the effects of both stellar and binary evolution and the external influence of the Galaxy. The results of these detailed calculations are used to calibrate a simplified model applicable over a wider range of cluster initial conditions. We find that clusters within 200 pc from the Galactic center dissolve within about 70 Myr. However, their projected densities drop below the background density in the direction of the Galactic center within 20 Myr, effectively making these clusters undetectable after that time. Clusters farther from the Galactic center but at the same projected distance are more strongly affected by this selection effect, and may go undetected for their entire lifetimes. Based on these findings, we conclude that the region within 200 pc of the Galactic center could easily harbor some 50 clusters with properties similar to those of the Arches or the Quintuplet systems.Comment: ApJ Letters in pres