Reducing orbital eccentricity in binary black hole simulations

Binary black hole simulations starting from quasi-circular (i.e., zero radial velocity) initial data have orbits with small but non-zero orbital eccentricities. In this paper the quasi-equilibrium initial-data method is extended to allow non-zero radial velocities to be specified in binary black hole initial data. New low-eccentricity initial data are obtained by adjusting the orbital frequency and radial velocities to minimize the orbital eccentricity, and the resulting ($\sim 5$ orbit) evolutions are compared with those of quasi-circular initial data. Evolutions of the quasi-circular data clearly show eccentric orbits, with eccentricity that decays over time. The precise decay rate depends on the definition of eccentricity; if defined in terms of variations in the orbital frequency, the decay rate agrees well with the prediction of Peters (1964). The gravitational waveforms, which contain $\sim 8$ cycles in the dominant l=m=2 mode, are largely unaffected by the eccentricity of the quasi-circular initial data. The overlap between the dominant mode in the quasi-circular evolution and the same mode in the low-eccentricity evolution is about 0.99.Comment: 27 pages, 9 figures; various minor clarifications; accepted to the "New Frontiers" special issue of CQ

Black Hole Mergers and Unstable Circular Orbits

We describe recent numerical simulations of the merger of a class of equal mass, non-spinning, eccentric binary black hole systems in general relativity. We show that with appropriate fine-tuning of the initial conditions to a region of parameter space we denote the threshold of immediate merger, the binary enters a phase of close interaction in a near-circular orbit, stays there for an amount of time proportional to logarithmic distance from the threshold in parameter space, then either separates or merges to form a single Kerr black hole. To gain a better understanding of this phenomena we study an analogous problem in the evolution of equatorial geodesics about a central Kerr black hole. A similar threshold of capture exists for appropriate classes of initial conditions, and tuning to threshold the geodesics approach one of the unstable circular geodesics of the Kerr spacetime. Remarkably, with a natural mapping of the parameters of the geodesic to that of the equal mass system, the scaling exponent describing the whirl phase of each system turns out to be quite similar. Armed with this lone piece of evidence that an approximate correspondence might exist between near-threshold evolution of geodesics and generic binary mergers, we illustrate how this information can be used to estimate the cross section and energy emitted in the ultra relativistic black hole scattering problem. This could eventually be of use in providing estimates for the related problem of parton collisions at the Large Hadron Collider in extra dimension scenarios where black holes are produced.Comment: 16 pages, 12 figures; updated to coincide with journal versio

Gravitational Collapse of Massless Scalar Field with Negative Cosmological Constant in (2+1) Dimensions

The 2+1-dimensional geodesic circularly symmetric solutions of Einstein-massless-scalar field equations with negative cosmological constant are found and their local and global properties are studied. It is found that one of them represents gravitational collapse where black holes are always formed.Comment: no figure

Ninja data analysis with a detection pipeline based on the Hilbert-Huang Transform

The Ninja data analysis challenge allowed the study of the sensitivity of data analysis pipelines to binary black hole numerical relativity waveforms in simulated Gaussian noise at the design level of the LIGO observatory and the VIRGO observatory. We analyzed NINJA data with a pipeline based on the Hilbert Huang Transform, utilizing a detection stage and a characterization stage: detection is performed by triggering on excess instantaneous power, characterization is performed by displaying the kernel density enhanced (KD) time-frequency trace of the signal. Using the simulated data based on the two LIGO detectors, we were able to detect 77 signals out of 126 above SNR 5 in coincidence, with 43 missed events characterized by signal to noise ratio SNR less than 10. Characterization of the detected signals revealed the merger part of the waveform in high time and frequency resolution, free from time-frequency uncertainty. We estimated the timelag of the signals between the detectors based on the optimal overlap of the individual KD time-frequency maps, yielding estimates accurate within a fraction of a millisecond for half of the events. A coherent addition of the data sets according to the estimated timelag eventually was used in a characterization of the event.Comment: Accepted for publication in CQG, special issue NRDA proceedings 200

Radiation from low-momentum zoom-whirl orbits

We study zoom-whirl behaviour of equal mass, non-spinning black hole binaries in full general relativity. The magnitude of the linear momentum of the initial data is fixed to that of a quasi-circular orbit, and its direction is varied. We find a global maximum in radiated energy for a configuration which completes roughly one orbit. The radiated energy in this case exceeds the value of a quasi-circular binary with the same momentum by 15%. The direction parameter only requires minor tuning for the localization of the maximum. There is non-trivial dependence of the energy radiated on eccentricity (several local maxima and minima). Correlations with orbital dynamics shortly before merger are discussed. While being strongly gauge dependent, these findings are intuitive from a physical point of view and support basic ideas about the efficiency of gravitational radiation from a binary system.Comment: 9 pages, 6 figures, Amaldi8 conference proceedings as publishe

Simulation of Binary Black Hole Spacetimes with a Harmonic Evolution Scheme

A numerical solution scheme for the Einstein field equations based on generalized harmonic coordinates is described, focusing on details not provided before in the literature and that are of particular relevance to the binary black hole problem. This includes demonstrations of the effectiveness of constraint damping, and how the time slicing can be controlled through the use of a source function evolution equation. In addition, some results from an ongoing study of binary black hole coalescence, where the black holes are formed via scalar field collapse, are shown. Scalar fields offer a convenient route to exploring certain aspects of black hole interactions, and one interesting, though tentative suggestion from this early study is that behavior reminiscent of "zoom-whirl" orbits in particle trajectories is also present in the merger of equal mass, non-spinning binaries, with appropriately fine-tuned initial conditions.Comment: 16 pages, 14 figures; replaced with published versio

An exact solution for 2+1 dimensional critical collapse

We find an exact solution in closed form for the critical collapse of a scalar field with cosmological constant in 2+1 dimensions. This solution agrees with the numerical simulation done by Pretorius and Choptuik of this system.Comment: 5 pages, 5 figures, Revtex. New comparison of analytic and numerical solutions beyond the past light cone of the singularity added. Two new references added. Error in equation (21) correcte

DEFROST: A New Code for Simulating Preheating after Inflation

At the end of inflation, dynamical instability can rapidly deposit the energy of homogeneous cold inflaton into excitations of other fields. This process, known as preheating, is rather violent, inhomogeneous and non-linear, and has to be studied numerically. This paper presents a new code for simulating scalar field dynamics in expanding universe written for that purpose. Compared to available alternatives, it significantly improves both the speed and the accuracy of calculations, and is fully instrumented for 3D visualization. We reproduce previously published results on preheating in simple chaotic inflation models, and further investigate non-linear dynamics of the inflaton decay. Surprisingly, we find that the fields do not want to thermalize quite the way one would think. Instead of directly reaching equilibrium, the evolution appears to be stuck in a rather simple but quite inhomogeneous state. In particular, one-point distribution function of total energy density appears to be universal among various two-field preheating models, and is exceedingly well described by a lognormal distribution. It is tempting to attribute this state to scalar field turbulence.Comment: RevTeX 4.0; 16 pages, 9 figure

Unequal Mass Binary Black Hole Plunges and Gravitational Recoil

We present results from fully nonlinear simulations of unequal mass binary black holes plunging from close separations well inside the innermost stable circular orbit with mass ratios q = M_1/M_2 = {1,0.85,0.78,0.55,0.32}, or equivalently, with reduced mass parameters $\eta=M_1M_2/(M_1+M_2)^2 = {0.25, 0.248, 0.246, 0.229, 0.183}$. For each case, the initial binary orbital parameters are chosen from the Cook-Baumgarte equal-mass ISCO configuration. We show waveforms of the dominant l=2,3 modes and compute estimates of energy and angular momentum radiated. For the plunges from the close separations considered, we measure kick velocities from gravitational radiation recoil in the range 25-82 km/s. Due to the initial close separations our kick velocity estimates should be understood as a lower bound. The close configurations considered are also likely to contain significant eccentricities influencing the recoil velocity.Comment: 12 pages, 5 figures, to appear in "New Frontiers" special issue of CQ