Dae-Il Choi

GETTING A KICK OUT OF NUMERICAL RELATIVITY

Recent developments in numerical relativity have made it possible to reliably follow the coalescence of two black holes from near the innermost stable circular orbit to final ringdown. This opens up a wide variety of exciting astrophysical applications of these simulations. Chief among these is the net kick received when two unequal mass or spinning black holes merge. The magnitude of this kick has bearing on the production and growth of supermassive black holes during the epoch of structure formation, and on the retention of black holes in stellar clusters. Here we report the first accurate numerical calculation of this kick, for two nonspinning black holes in a 1.5 : 1 mass ratio, which is expected on the basis of analytic considerations to give a significant fraction of the maximum possible recoil. We have performed multiple runs with different initial separations, orbital angular momenta, resolutions, extraction radii, and gauges. The full range of our kick speeds is 86-116 km s-1, and the most reliable runs give kicks between 86 and 97 km s-1. This is intermediate between the estimates from two recent post-Newtonian analyses and suggests that at redshifts z 10, halos with masses 109 M☉ will have difficulty retaining coalesced black holes after major mergers.

Binary black hole merger dynamics and waveforms

We study dynamics and radiation generation in the last few orbits and merger of a binary black hole system, applying recently developed techniques for simulations of moving black holes. Our analysis of the gravitational radiation waveforms and dynamical black hole trajectories produces a consistent picture for a set of simulations with black holes beginning on circular-orbit trajectories at a variety of initial separations. We find profound agreement at the level of 1% among the simulations for the last orbit, merger and ringdown. We are confident that this part of our waveform result accurately represents the predictions from Einsteins General Relativity for the final burst of gravitational radiation resulting from the merger of an astrophysical system of equal-mass nonspinning black holes. The simulations result in a final black hole with spin parameter a/m=0.69. We also find good agreement at a level of roughly 10% for the radiation generated in the preceding few orbits.

Theory of Nonlinear Landau-Zener Tunneling

We present a comprehensive analysis of the nonlinear Landau-Zener tunneling. We find characteristic scaling or power laws for the critical behavior that occurs as the nonlinear parameter equals to the gap of avoided crossing energy levels. For the nonlinear parameter larger than the energy gap, a closed-form solution is derived for the nonlinear tunneling probability, which is shown to be a good approximation to the exact solution for a wide range of the parameters. Finally, we discuss the experimental realization of the nonlinear model and possible observation of the scaling or power laws using a Bose-Einstein condensate in an accelerating optical lattice.

How to move a black hole without excision: Gauge conditions for the numerical evolution of a moving puncture

Recent demonstrations of unexcised black holes traversing across computational grids represent a significant advance in numerical relativity. Stable and accurate simulations of multiple orbits, and their radiated waves, result. This capability is critically undergirded by a careful choice of gauge. Here we present analytic considerations which suggest certain gauge choices, and numerically demonstrate their efficacy in evolving a single moving puncture black hole.

Interface conditions for wave propagation through mesh refinement boundaries

We study the propagation of waves across fixed mesh refinement boundaries in linear and nonlinear model equations in 1-D and 2-D, and in the 3-D Einstein equations of general relativity. We demonstrate that using linear interpolation to set the data in guard cells leads to the production of reflected waves at the refinement boundaries. Implementing quadratic interpolation to fill the guard cells suppresses these spurious signals.

Evolving a puncture black hole with fixed mesh refinement

We present an algorithm for treating mesh refinement interfaces in numerical relativity. We discuss the behavior of the solution near such interfaces located in the strong-field regions of dynamical black hole spacetimes, with particular attention to the convergence properties of the simulations. In our applications of this technique to the evolution of puncture initial data with vanishing shift, we demonstrate that it is possible to simultaneously maintain second order convergence near the puncture and extend the outer boundary beyond 100M, thereby approaching the asymptotically flat region in which boundary condition problems are less difficult and wave extraction is meaningful.

Wave zone extraction of gravitational radiation in three-dimensional numerical relativity

We present convergent gravitational waveforms extracted from three-dimensional, numerical simulations in the wave zone and with causally disconnected boundaries. These waveforms last for multiple periods and are very accurate, showing a peak error to peak amplitude ratio of 2% or better. Our approach includes defining the Weyl scalar {psi}{sub 4} in terms of a three-plus-one decomposition of the Einstein equations; applying, for the first time, a novel algorithm due to Misner for computing spherical harmonic components of our wave data; and using fixed mesh refinement to focus resolution on nonlinear sources while simultaneously resolving the wave zone and maintaining a causally disconnected computational boundary. We apply our techniques to a (linear) Teukolsky wave, and then to an equal-mass, head-on collision of two black holes. We argue both for the quality of our results and for the value of these problems as standard test cases for wave extraction techniques.

Three-dimensional adaptive evolution of gravitational waves in numerical relativity

Adaptive techniques are crucial for successful numerical modeling of gravitational waves from astrophysical sources such as coalescing compact binaries, since the radiation typically has wavelengths much larger than the scale of the sources. We have carried out an important step toward this goal: the evolution of weak gravitational waves using adaptive mesh refinement in the Einstein equations. The 2-level adaptive simulation is compared with unigrid runs at coarse and fine resolution, and is shown to track closely the features of the fine grid run.

To detect the looped Bloch bands of Bose-Einstein condensates in optical lattices

Abstract A loop structure was predicted to exist in the Bloch bands of Bose–Einstein condensates in optical lattices recently in [Phys. Rev. A 61 (2000) 023402]. We discuss how to detect experimentally the looped band with an accelerating optical lattice through extensive and realistic numerical simulations. We find that the loop can be detected through observing either nonlinear Landau–Zener tunneling or destruction of Bloch oscillations.

Intense field stabilization in circular polarization: Three-dimensional time-dependent dynamics

We investigate the stabilization of hydrogen atoms in a circularly polarized laser field. We use a three-dimensional, time-dependent approach to study the quantum dynamics of hydrogen atoms subject to high-intensity, short-wavelength, laser pulses. We find an enhanced survival probability as the field is increased under fixed envelope conditions. We also confirm wave packet behaviors previously seen in two-dimensional time-dependent computations.