Extracting the Gravitational Recoil from Black Hole Merger Signals

Gravitational waves carry energy, angular momentum, and linear momentum. In generic binary black hole mergers, the loss of linear momentum imparts a recoil velocity, or a “kick,” to the remnant black hole. We exploit recent advances in gravitational waveform and remnant black hole modeling to extract information about the kick from the gravitational wave signal. Kick measurements such as these are astrophysically valuable, enabling independent constraints on the rate of second-generation merger. Further, we show that kicks must be factored into future ringdown tests of general relativity with third-generation gravitational wave detectors to avoid systematic biases. We find that, although little information can be gained about the kick for existing gravitational wave events, interesting measurements will soon become possible as detectors improve. We show that, once LIGO and Virgo reach their design sensitivities, we will reliably extract the kick velocity for generically precessing binaries—including the so-called superkicks, reaching up to 5000 km/s

Comparison of post-Newtonian templates for extreme mass ratio inspirals

Extreme mass ratio inspirals (EMRIs), the inspirals of compact objects into supermassive black holes, are important gravitational wave sources for the Laser Interferometer Space Antenna (LISA). We study the performance of various post-Newtonian (PN) template families relative to the high precision numerical waveforms in the context of EMRI parameter estimation with LISA. Expressions for the time domain waveforms TaylorT1, TaylorT2, TaylorT3, TaylorT4 and TaylorEt are derived up to 22PN order, i.e $\mathcal{O}(v^{44})$ ($v$ is the characteristic velocity of the binary) beyond the Newtonian term, for a test particle in a circular orbit around a Schwarzschild black hole. The phase difference between the above 22PN waveform families and numerical waveforms are evaluated during two-year inspirals for two prototypical EMRI systems with mass ratios $10^{-4}$ and $10^{-5}$. We find that the dephases (in radians) for TaylorT1 and TaylorT2, respectively, are about $10^{-9}$ ($10^{-2}$) and $10^{-9}$ ($10^{-3}$) for mass ratio $10^{-4}$ ($10^{-5}$). This suggests that using 22PN TaylorT1 or TaylorT2 waveforms for parameter estimation of EMRIs will result in accuracies comparable to numerical waveform accuracy for most of the LISA parameter space. On the other hand, from the dephase results, we find that TaylorT3, TaylorT4 and TaylorEt fare relatively poorly as one approaches the last stable orbit. This implies that, as for comparable mass binaries using the 3.5PN phase of waveforms, the 22PN TaylorT3 and TaylorEt approximants do not perform well enough for the EMRIs. The reason underlying the poor performance of TaylorT3, TaylorT4 and TaylorEt relative to TaylorT1 and TaylorT2 is finally examined.Comment: 10 page

Gravitational wave peak luminosity model for precessing binary black holes

When two black holes merge, a tremendous amount of energy is released in the form of gravitational radiation in a short span of time, making such events among the most luminous phenomenon in the universe. Models that predict the peak luminosity of black hole mergers are of interest to the gravitational wave community, with potential applications in tests of general relativity. We present a surrogate model for the peak luminosity that is directly trained on numerical relativity simulations of precessing binary black holes. Using Gaussian process regression, we interpolate the peak luminosity in the 7-dimensional parameter space of precessing binaries with mass ratios $q\leq4$, and spin magnitudes $\chi_1,\chi_2\leq0.8$. We demonstrate that our errors in estimating the peak luminosity are lower than those of existing fitting formulae by about an order of magnitude. In addition, we construct a model for the peak luminosity of aligned-spin binaries with mass ratios $q\leq8$, and spin magnitudes $|\chi_{1z}|,|\chi_{2z}|\leq0.8$. We apply our precessing model to infer the peak luminosity of the GW event GW190521, and find the results to be consistent with previous predictions.Comment: 5 pages, 4 figures; matches PRD versio

Gravitational wave peak luminosity model for precessing binary black holes

When two black holes merge, a tremendous amount of energy is released in the form of gravitational radiation in a short span of time, making such events among the most luminous phenomenon in the Universe. Models that predict the peak luminosity of black hole mergers are of interest to the gravitational wave community, with potential applications in tests of general relativity. We present a surrogate model for the peak luminosity that is directly trained on numerical relativity simulations of precessing binary black holes. Using Gaussian process regression, we interpolate the peak luminosity in the seven-dimensional parameter space of precessing binaries with mass ratios q ≤ 4 and spin magnitudes χ₁, χ₂ ≤ 0.8. We demonstrate that our errors in estimating the peak luminosity are lower than those of existing fitting formulas by about an order of magnitude. In addition, we construct a model for the peak luminosity of aligned-spin binaries with mass ratios q ≤ 8 and spin magnitudes |χ₁_z|,|χ₂_z| ≤ 0.8. We apply our precessing model to infer the peak luminosity of the GW event GW190521 and find the results to be consistent with previous predictions

Accurate inspiral-merger-ringdown gravitational waveforms for non-spinning black-hole binaries including the effect of subdominant modes

We present an analytical waveform family describing gravitational waves (GWs) from the inspiral, merger and ringdown of non-spinning black-hole binaries including the effect of several non-quadrupole modes [($\ell = 2, m = \pm 1), (\ell = 3, m = \pm 3), (\ell = 4, m = \pm 4)$ apart from $(\ell = 2, m=\pm2)$]. We first construct spin-weighted spherical harmonics modes of hybrid waveforms by matching numerical-relativity simulations (with mass ratio $1-10$) describing the late inspiral, merger and ringdown of the binary with post-Newtonian/effective-one-body waveforms describing the early inspiral. An analytical waveform family is constructed in frequency domain by modeling the Fourier transform of the hybrid waveforms making use of analytical functions inspired by perturbative calculations. The resulting highly accurate, ready-to-use waveforms are highly faithful (unfaithfulness $\simeq 10^{-4} - 10^{-2}$) for observation of GWs from non-spinning black hole binaries and are extremely inexpensive to generate.Comment: 10 pages, 5 figure

High-accuracy mass, spin, and recoil predictions of generic black-hole merger remnants

We present accurate fits for the remnant properties of generically precessing binary black holes, trained on large banks of numerical-relativity simulations. We use Gaussian process regression to interpolate the remnant mass, spin, and recoil velocity in the 7-dimensional parameter space of precessing black-hole binaries with mass ratios $q\leq2$, and spin magnitudes $\chi_1,\chi_2\leq0.8$. For precessing systems, our errors in estimating the remnant mass, spin magnitude, and kick magnitude are lower than those of existing fitting formulae by at least an order of magnitude (improvement is also reported in the extrapolated region at high mass ratios and spins). In addition, we also model the remnant spin and kick directions. Being trained directly on precessing simulations, our fits are free from ambiguities regarding the initial frequency at which precessing quantities are defined. We also construct a model for remnant properties of aligned-spin systems with mass ratios $q\leq8$, and spin magnitudes $\chi_1,\chi_2\leq0.8$. As a byproduct, we also provide error estimates for all fitted quantities, which can be consistently incorporated into current and future gravitational-wave parameter-estimation analyses. Our model(s) are made publicly available through a fast and easy-to-use Python module called surfinBH.Comment: 6+5 pages. Matches PRL version. Python implementation available at https://pypi.org/project/surfinBH

Constructing a boosted, spinning black hole in the damped harmonic gauge

The damped harmonic gauge is important for numerical relativity computations based on the generalized harmonic formulation of Einstein's equations, and is used to reduce coordinate distortions near binary black hole mergers. However, currently there is no prescription to construct quasiequilibrium binary black hole initial data in this gauge. Instead, initial data are typically constructed using a superposition of two boosted analytic single black hole solutions as free data in the solution of the constraint equations. Then, a smooth time-dependent gauge transformation is done early in the evolution to move into the damped harmonic gauge. Using this strategy to produce initial data in damped harmonic gauge would require the solution of a single black hole in this gauge, which is not known analytically. In this work we construct a single boosted, spinning, equilibrium BH in damped harmonic coordinates as a regular time-independent coordinate transformation from Kerr-Schild coordinates. To do this, we derive and solve a set of 4 coupled, nonlinear, elliptic equations for this transformation, with appropriate boundary conditions. This solution can now be used in the construction of damped harmonic initial data for binary black holes.Comment: Matches PRD version. 8 pages, 3 figure

Daily physical activity patterns during the early stage of Alzheimer’s disease

Background - Alzheimer’s disease (AD) is a neurodegenerative disease that results in severe disability. Very few studies have explored changes in daily physical activity patterns during early stages of AD when components of physical function and mobility may be preserved. Methods - Patients with mild AD and controls (n=92) recruited from the University of Kansas Alzheimer’s Disease Center Registry, wore the Actigraph GT3X+ for seven days, and provided objective physical function (VO2 max) and mobility data. Using multivariate linear regression, we explored whether individuals with mild AD had different daily average and diurnal physical activity patterns compared to controls independent of non-cognitive factors that may affect physical activity, including physical function and mobility. Results - We found that mild AD was associated with less moderate-intensity physical activity (p<0.05), lower peak activity (p<0.01), and lower physical activity complexity (p<0.05) particularly during the morning. Mild AD was not associated with greater sedentary activity or less lower-intensity physical activity across the day after adjusting for non-cognitive covariates. Conclusions - These findings suggest that factors independent of physical capacity and mobility may drive declines in moderate-intensity physical activity, and not lower-intensity or sedentary activity, during the early stage of AD. This underscores the importance of a better mechanistic understanding of how cognitive decline and AD pathology impact physical activity. Findings emphasize the potential value of designing and testing time-of-day specific physical activity interventions targeting individuals in the early stages of AD, prior to significant declines in mobility and physical function