We present results of 3D numerical simulations using a finite difference code featuring fixed mesh refinement (FMR), in which a subset of the computational domain is refined in space and time. We apply this code to a series of test cases including a robust stability test, a nonlinear gauge wave and an excised Schwarzschild black hole in an evolving gauge. We find that the mesh refinement results are comparable in accuracy, stability and convergence to unigrid simulations with the same effective resolution. At the same time, the use of FMR reduces the computational resources needed to obtain a given accuracy. Particular care must be taken at the interfaces between coarse and fine grids to avoid a loss of convergence at higher resolutions, and we introduce the use of "buffer zones" as one resolution of this issue. We also introduce a new method for initial data generation, which enables higher-order interpolation in time even from the initial time slice. This FMR system, "Carpet", is a driver module in the freely available Cactus computational infrastructure, and is able to endow generic existing Cactus simulation modules ("thorns") with FMR with little or no extra effort.

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In recent years, many different numerical evolution schemes for Einstein's equations have been proposed to address stability and accuracy problems that have plagued the numerical relativity community for decades. Some of these approaches have been tested on different spacetimes, and conclusions have been drawn based on these tests. However, differences in results originate from many sources, including not only formulations of the equations, but also gauges, boundary conditions, numerical methods, and so on. We propose to build up a suite of standardized testbeds for comparing approaches to the numerical evolution of Einstein's equations that are designed to both probe their strengths and weaknesses and to separate out different effects, and their causes, seen in the results. We discuss general design principles of suitable testbeds, and we present an initial round of simple tests with periodic boundary conditions. This is a pivotal first step toward building a suite of testbeds to serve the numerical relativists and researchers from related fields who wish to assess the capabilities of numerical relativity codes. We present some examples of how these tests can be quite effective in revealing various limitations of different approaches, and illustrating their differences. The tests are presently limited to vacuum spacetimes, can be run on modest computational resources, and can be used with many different approaches used in the relativity community.

We present a study of black hole threshold phenomena for a self-gravitating, massive complex scalar field in spherical symmetry. We construct Type I critical solutions dynamically by tuning a one-parameter family of initial data composed of a boson star and a massless real scalar field. The real field is used to perturb the boson star via a gravitational interaction which results in a {\em significant} transfer of energy. The resulting critical solutions, which show great similarity with unstable boson stars, persist for a finite time before dispersing or forming a black hole. We extend the stability analysis of Gleiser and Watkins [Nucl. Phys. B319, 733 (1989)], providing a method for calculating the radial dependence of boson star modes of nonzero frequency. We find good agreement between our critical solutions and boson star modes. For critical solutions less than 90% of the maximum boson star mass $M_{\rm max} \simeq 0.633 M_{Pl}^2/m$, a small halo of matter appears in the tail of the solution. This halo appears to be an artifact of the collision between the original boson star and the real field, and does not belong to the true critical solution. It seems that unstable boson stars are unstable to dispersal in addition to black hole formation. Given the similarity in macroscopic stability between boson and neutron stars, we suggest that neutron stars at or beyond the point of instability may also be unstable to explosion.Comment: 26 Pages, 16 Figures, RevTeX. Submitted to Phys. Rev.

Solar wind streams originate from low-density, magnetically open regions of the sun's torts the polar hole boundaries and the corona, known as coronal holes. The locations, areal sizes, rotation, and solar-cycle shape of the heliospheric current sheet. evolution of these regions can be reproduced and understood by applying simple ex-The resulting equatorward extensions of trapolation models to measurements of the photospheric magnetic field. The surprisingly the polar holes, rotating with the solar rigid rotation displayed by many coronal holes suggests that field-line reconnection equatorial period of -27 days, produce the occurs continually in the corona, despite the high electrical conductivity of the coronal recurrent high-speed streams and geomagplasma. The magnetic field strengths and field-line divergence rates in coronal holes can netic activity observed during the declinbe related empirically to the bulk speed and the mass and energy flux densities of the solar ing phase of the solar cycle. wind plasma. Such relations may help to illuminate the physical processes responsible At sunspot maximum, the polar holes for heating the corona and driving the solar wind.disappear and are replaced by many small ' open structures scattered over a wide range of latitudes. These holes, which generally show pronounced differential rotaCoronal holes appear as dark areas in lar regions are dominated by large holes tion, are often located near active regions x-ray and extreme-ultraviolet images of that extend down to a latitude of 60" in and are characterized by strong magnetic the sun, and as light, blurry p2tches when each hemisphere. As the Ulysses spacefields and rapidly diverging flux tubes;observed in the He

We study the fully nonlinear dynamical evolution of binary black hole data, whose orbital parameters are specified via the effective potential method for determining quasi-circular orbits. The cases studied range from the Cook-Baumgarte innermost stable circular orbit (ISCO) to significantly beyond that separation. In all cases we find the black holes to coalesce (as determined by the appearance of a common apparent horizon) in less than half an orbital period. The results of the numerical simulations indicate that the initial holes are not actually in quasi-circular orbits, but that they are in fact nearly plunging together. The dynamics of the final horizon are studied to determine physical parameters of the final black hole, such as its spin, mass, and oscillation frequency, revealing information about the inspiral process. We show that considerable resolution is required to extract accurate physical information from the final black hole formed in the merger process, and that the quasi-normal modes of the final hole are strongly excited in the merger process. For the ISCO case, by comparing physical measurements of the final black hole formed to the initial data, we estimate that less than 3% of the total energy is radiated in the merger process.

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We present a class of general relativistic solitonlike solutions composed of multiple minimally coupled, massive, real scalar fields which interact only through the gravitational field. We describe a two-parameter family of solutions we call ''phase-shifted boson stars'' ͑parametrized by central density 0 and phase ␦), which are obtained by solving the ordinary differential equations associated with boson stars and then altering the phase between the real and imaginary parts of the field. These solutions are similar to boson stars as well as the oscillating soliton stars found by Seidel and Suen ͓E. Seidel and W. M. Suen, Phys. Rev. Lett. 66, 1659 ͑1991͔͒; in particular, long-time numerical evolutions suggest that phase-shifted boson stars are stable. Our results indicate that scalar solitonlike solutions are perhaps more generic than has been previously thought.