Session Q16: Numerical Modeling of Binary Black Holes

On Demand

We present high accuracy, fully nonlinear, numerical simulations of binary black holes up to a mass ratio of $q=30$. Using improved methods, we extend the capabilities of the numerical relativity code, SpEC, to simulate binary black holes with mass ratios beyond its previous limit of $q=10$. Such systems are potential sources for current gravitational wave detectors (i.e. LIGO) and are expected to be even more promising for future space-based detectors (e.g. LISA). The binaries are evolved through a minimum of $14$ orbits, providing a sufficient number of gravitational wave cycles to compare with predictions from approximate models. We present comparisons of our numerical waveforms with self-force predictions, the most promising perturbative scheme for extreme mass ratio inspirals. Additionally, we compare our waveforms with effective-one-body (EOB) approximants, which model the full waveform and are presumed to be valid at any mass ratio.   

Not Participating

Binary black hole systems with constituents that have very different masses are a subset of the binary population that, from a computational perspective, are more challenging to simulate than equal or near equal mass binaries. Their resource demands are significant and it is broadly understood that their successful evolution will require particular approaches and methods that are tuned to this region of the parameter space. We combine two such approaches, namely a parallel octree-refined adaptive mesh and a wavelet adaptive multiresolution method to produce the mesh. This highly scalable framework permits the efficient and rapid simulation of such intermediate mass ratio inspirals (IMRIs). We present some results from these efforts that have proven successful in simulating binaries with large mass ratios.   

On Demand

We present a method of constructing rotation parameters $a$ and $b$ for performing Type I and Type II transformations of Weyl scalars $\Psi_a$ into the quasi-Kinnersley frame. This frame is transverse ($\Psi_1=\Psi_3=0$) and should have $\Psi_2 \to -\sqrt{\mathcal{I}/3}$ asymptotically, where $\mathcal{I}$ is a spacetime invariant. This frame better represents physical properties of the spacetime, such as outgoing gravitational radiation. Using the quasi-Kinnersley frame, we study an index $\mathcal{D}$ that, in conjuction with the $\mathcal{S}$ invariant, measures the deviations from Petrov Type D of a BBH system in the strong-field region. $\mathcal{D}$ is invariant under Type II and III rotations, but not under Type I. Studying this index will tell us more accurately how far a BBH spacetime deviates from Type D. This index is used in numerical simulations of BBH systems to investigate the Petrov Type in the Strong Field region during the final inspiral and merger phases. This talk will also discuss how the gravitational wave scalar $\Psi_4$ in the quasi-Kinnersley frame can be used to extract gravitational radiation. Since the QK $\Psi_4$ is an accurate representation of outgoing radiation, waveforms can be extracted close to the BBH system, reducing computational expense.   

Not Participating

Although gravitational memory was realized in the 1970s, numerical simulations of binary black hole mergers have been unable to resolve this phenomenon until now. We show that by using Cauchy-characteristic extraction (CCE) to extract waveforms in simulations produced by SXS's Spectral Einstein Code, we can accurately resolve the gravitational memory. We present results for memory in simulations with a variety of mass ratios and spins. We also discuss the measurability of memory for both LIGO and LISA.   

Not Participating

Scalar spherical harmonics form the backbone of analysis of radiating fields in elementary physics. Extending such analyses to describe radiating tensor fields, gravitational-wave and CMB astronomers typically use ``spin-weighted'' spherical harmonics, which account more completely for the properties of those tensors under rotation. I will describe the appropriate framework for understanding these harmonics, as well as generalizations that will allow us to account for the properties under more general Lorentz transformations, and how this can lead to more efficient representations of the gravitational and electromagnetic fields.   

On Demand

High-spin binary black hole (BBH) simulations are computationally expensive. As the spin increases, the region where an excision surface can be placed becomes narrower. This makes the evolutions even more demanding because of the accuracy required to be able to find a suitable excision surface. We explore a new gauge condition for generalized harmonic systems to broaden the region where the excision surface is placed, and present preliminary results from evolutions of a single high-spin black hole. Our objective is the application of this new gauge condition to high-spin BBH evolutions.   

Not Participating

The electric charge is a parameter often neglected in general-relativistic simulations of black holes. As a result, little is known about the dynamics of charged binary black holes in the latest stages of their inspiral. In this talk, we present our first numerical-relativity simulations of quasi-circular mergers of these systems. Using a $3+1$ formalism, we obtained fully self-consistent solutions of Einstein-Maxwell's equations, and extracted the electromagnetic and gravitational output. We will discuss what LIGO-Virgo observations of mergers of binary black holes and the (non-)detections of electromagnetic counterparts can teach us about the charge of astrophysical black holes.   

Not Participating

In this talk, we address the computationally intense task of numerical modeling of black hole (BH) binaries by focusing on simple geometries that are static and, therefore, never merge. Two different binary models are used to investigate null closed orbits and their response to external perturbations. The first system is the Majumdar-Papapetrou (MP) solution, which describes a static configuration of an arbitrary number of maximally charged black holes. We focus on the special case of two MP black holes and investigate some of its properties, such as the different types of closed photon orbits and the instability scale of unstable circular orbits. The second system comes from Analogue Models of Gravity, which rely on the mathematical relationship between perturbations in fluids and scalar perturbations in curved spacetimes. In this work, we use a double-sink solution of the fluid equations and explore an analogy with the MP geometry. We show that the ergoregion of the double-sink geometry does not coincide with the event horizon, which raises the possibility of superradiant scattering and Penrose-like processes in more realistic astrophysical systems.   

On Demand

Binary black holes emit gravitational radiation with net linear momentum leading to a retreat of the final remnant black hole that can reach up to $\sim5,000$ km/s. Full numerical relativity simulations are the only tool to accurately compute these recoils since they are largely produced when the black hole horizons are about to merge and they are strongly dependent on their spin orientations at that moment. We present eight new numerical simulations of BBH in the hangup-kick configuration family, leading to the maximum recoil. Black holes are equal mass and near maximally spinning ($|\vec{S}_{1,2}|/m_{1,2}^2=0.97$). Depending on their phase at merger, this family leads to $\sim\pm4,700$ km/s and all intermediate values of the recoil along the orbital angular momentum of the binary system. We introduce a new invariant method to evaluate the recoil dependence on the merger phase via the waveform peak amplitude used as a reference phase angle and compare it with previous definitions. We also compute the mismatch between these hangup-kick waveforms to infer their observable differentiability by gravitational wave detectors, such as advanced LIGO, finding currently reachable signal-to-noise ratios, hence allowing for the identification of highly recoiling black holes.