Black-hole binaries, gravitational waves, and numerical relativity

Understanding the predictions of general relativity for the dynamical interactions of two black holes has been a long-standing unsolved problem in theoretical physics. Black-hole mergers are monumental astrophysical events, releasing tremendous amounts of energy in the form of gravitational radiation, and are key sources for both ground- and space-based gravitational-wave detectors. The black-hole merger dynamics and the resulting gravitational waveforms can only be calculated through numerical simulations of Einstein's equations of general relativity. For many years, numerical relativists attempting to model these mergers encountered a host of problems, causing their codes to crash after just a fraction of a binary orbit could be simulated. Recently, however, a series of dramatic advances in numerical relativity has allowed stable, robust black-hole merger simulations. This remarkable progress in the rapidly maturing field of numerical relativity, and the new understanding of black-hole binary dynamics that is emerging is chronicled. Important applications of these fundamental physics results to astrophysics, to gravitational-wave astronomy, and in other areas are also discussed.Comment: 54 pages, 42 figures. Some typos corrected & references updated. Essentially final published versio

Rotated Spectral Principal Component Analysis (rsPCA) for Identifying Dynamical Modes of Variability in Climate Systems.

Spectral PCA (sPCA), in contrast to classical PCA, offers the advantage of identifying organized spatiotemporal patterns within specific frequency bands and extracting dynamical modes. However, the unavoidable trade-off between frequency resolution and robustness of the PCs leads to high sensitivity to noise and overfitting, which limits the interpretation of the sPCA results. We propose herein a simple nonparametric implementation of sPCA using the continuous analytic Morlet wavelet as a robust estimator of the cross-spectral matrices with good frequency resolution. To improve the interpretability of the results, especially when several modes of similar amplitude exist within the same frequency band, we propose a rotation of the complex-valued eigenvectors to optimize their spatial regularity (smoothness). The developed method, called rotated spectral PCA (rsPCA), is tested on synthetic data simulating propagating waves and shows impressive performance even with high levels of noise in the data. Applied to global historical geopotential height (GPH) and sea surface temperature (SST) daily time series, the method accurately captures patterns of atmospheric Rossby waves at high frequencies (3-60-day periods) in both GPH and SST and El Niño-Southern Oscillation (ENSO) at low frequencies (2-7-yr periodicity) in SST. At high frequencies the rsPCA successfully unmixes the identified waves, revealing spatially coherent patterns with robust propagation dynamics

Gravitational wave astronomy of single sources with a pulsar timing array

Abbreviated: We investigate the potential of detecting the gravitational wave from individual binary black hole systems using pulsar timing arrays (PTAs) and calculate the accuracy for determining the GW properties. This is done in a consistent analysis, which at the same time accounts for the measurement of the pulsar distances via the timing parallax. We find that, at low redshift, a PTA is able to detect the nano-Hertz GW from super massive black hole binary systems with masses of \sim10^8 - 10^{10}\,M_{\sun} less than $\sim10^5$\,years before the final merger, and those with less than $\sim10^3 - 10^4$ years before merger may allow us to detect the evolution of binaries. We derive an analytical expression to describe the accuracy of a pulsar distance measurement via timing parallax. We consider five years of bi-weekly observations at a precision of 15\,ns for close-by ($\sim 0.5 - 1$\,kpc) pulsars. Timing twenty pulsars would allow us to detect a GW source with an amplitude larger than $5\times 10^{-17}$. We calculate the corresponding GW and binary orbital parameters and their measurement precision. The accuracy of measuring the binary orbital inclination angle, the sky position, and the GW frequency are calculated as functions of the GW amplitude. We note that the "pulsar term", which is commonly regarded as noise, is essential for obtaining an accurate measurement for the GW source location. We also show that utilizing the information encoded in the GW signal passing the Earth also increases the accuracy of pulsar distance measurements. If the gravitational wave is strong enough, one can achieve sub-parsec distance measurements for nearby pulsars with distance less than $\sim 0.5 - 1$\,kpc.Comment: 16 pages, 5 figure,, accepted by MNRA

Phenomenological model for the gravitational-wave signal from precessing binary black holes with two-spin effects

The properties of compact binaries, such as masses and spins, are imprinted in the gravitational-waves they emit and can be measured using parameterised waveform models. Accurately and efficiently describing the complicated precessional dynamics of the various angular momenta of the system in these waveform models is the object of active investigation. One of the key models extensively used in the analysis of LIGO and Virgo data is the single-precessing-spin waveform model IMRPhenomPv2. In this article we present a new model IMRPhenomPv3 which includes the effects of two independent spins in the precession dynamics. Whereas IMRPhenomPv2 utilizes a single-spin frequency-dependent post-Newtonian rotation to describe precession effects, the improved model, IMRPhenomPv3, employs a double-spin rotation that is based on recent developments in the description of precessional dynamics. Besides double-spin precession, the improved model benefits from a more accurate description of precessional effects. We validate our new model against a large set of precessing numerical-relativity simulations. We find that IMRPhenomPv3 has better agreement with the inspiral portion of precessing binary-black-hole simulations and is more robust across a larger region of the parameter space than IMRPhenomPv2. As a first application we analyse, for the first time, the gravitational-wave event GW151226 with a waveform model that describes two-spin precession. Within statistical uncertainty our results are consistent with published results. IMRPhenomPv3 will allow studies of the measurability of individual spins of binary black holes using GWs and can be used as a foundation upon which to build further improvements, such as modeling precession through merger, extending to higher multipoles, and including tidal effects.Comment: 15 pages, 5 figure

Dynamics of the spin-half Heisenberg chain at intermediate temperatures

Combining high-temperature expansions with the recursion method and quantum Monte Carlo simulations with the maximum entropy method, we study the dynamics of the spin-1/2 Heisenberg chain at temperatures above and below the coupling J. By comparing the two sets of calculations, their relative strengths are assessed. At high temperatures, we find that there is a low-frequency peak in the momentum integrated dynamic structure factor, due to diffusive long-wavelength modes. This peak is rapidly suppressed as the temperature is lowered below J. Calculation of the complete dynamic structure factor S(k,w) shows how the spectral features associated with the two-spinon continuum develop at low temperatures. We extract the nuclear spin-lattice relaxation rate 1/T1 from the w-->0 limit, and compare with recent experimental results for Sr2CuO3 and CuGeO3. We also discuss the scaling behavior of the dynamic susceptibility, and of the static structure factor S(k) and the static susceptibility X(k). We confirm the asymptotic low-temperature forms S(pi)~[ln(T)]^(3/2) and X(pi)~T^(-1)[ln(T)]^(1/2), expected from previous theoretical studies.Comment: 15 pages, Revtex, 14 PostScript figures. 2 new figures and related discussion of the recursion method at finite temperature adde

Extreme Mass-Ratio Inspirals in the Effective-One-Body Approach: Quasi-Circular, Equatorial Orbits around a Spinning Black Hole

We construct effective-one-body waveform models suitable for data analysis with LISA for extreme-mass ratio inspirals in quasi-circular, equatorial orbits about a spinning supermassive black hole. The accuracy of our model is established through comparisons against frequency-domain, Teukolsky-based waveforms in the radiative approximation. The calibration of eight high-order post-Newtonian parameters in the energy flux suffices to obtain a phase and fractional amplitude agreement of better than 1 radian and 1 % respectively over a period between 2 and 6 months depending on the system considered. This agreement translates into matches higher than 97 % over a period between 4 and 9 months, depending on the system. Better agreements can be obtained if a larger number of calibration parameters are included. Higher-order mass ratio terms in the effective-one-body Hamiltonian and radiation-reaction introduce phase corrections of at most 30 radians in a one year evolution. These corrections are usually one order of magnitude larger than those introduced by the spin of the small object in a one year evolution. These results suggest that the effective-one-body approach for extreme mass ratio inspirals is a good compromise between accuracy and computational price for LISA data analysis purposes.Comment: 21 pages, 8 figures, submitted to Phys. Rev.

State-of-the art of acousto-optic sensing and imaging of turbid media

Acousto-optic (AO) is an emerging hybrid technique for measuring optical contrast in turbid media using coherent light and ultrasound (US). A turbid object is illuminated with a coherent light source leading to speckle formation in the remitted light. With the use of US, a small volume is selected,which is commonly referred to as the “tagging” volume. This volume acts as a source of modulated light, where modulation might involve phase and intensity change. The tagging volume is created by focusing ultrasound for good lateral resolution; the axial resolution is accomplished by making either the US frequency, amplitude, or phase time-dependent. Typical resolutions are in the order of 1 mm. We will concentrate on the progress in the field since 2003. Different schemes will be discussed to detect the modulated photons based on speckle detection, heterodyne detection, photorefractive crystal (PRC) assisted detection, and spectral hole burning (SHB) as well as Fabry-Perot interferometers. The SHB and Fabry-Perot interferometer techniques are insensitive to speckle decorrelation and therefore suitable for in vivo imaging. However, heterodyne and PRC methods also have potential for in vivo measurements. Besides measuring optical properties such as scattering and absorption, AO can be applied in fluorescence and elastography applications

Analytic Spectra of CMB Anisotropies and Polarization Generated by Scalar Perturbations in Synchronous Gauge

We present a detailed analytical calculation of CMB temperature anisotropies \alpha_k and polarization \beta_k generated by scalar metric perturbations in synchronous gauge, parallel to our previous work with RGW as a generating source. This is realized primarily by an analytic time-integration of Boltzmann's equation, yielding the closed forms of \alpha_k and \beta_k. Approximations, such as the tight-coupling approximation for photons a prior to the recombination and the long wavelength limit for scalar perturbations are used. The residual gauge modes in scalar perturbations are analyzed and a proper joining condition of scalar perturbations at the radiation-matter equality is chosen, ensuring the continuity of energy perturbation. The resulting analytic expressions of the multipole moments of polarization a^E_l, and of temperature anisotropies a^T_l are explicit functions of the scalar perturbations, recombination time, recombination width, photon free streaming damping factor, baryon fraction, initial amplitude, primordial scalar spectral index, and the running index. These results show that a longer recombination width yields higher amplitudes of polarization on large scales and more damping on small scales, and that a late recombination time shifts the peaks of C^{XX'}_l to larger angular scales. The analytic spectra C^{XX'}_l agree with the numerical ones and with those observed by WMAP on large scales (l \lesssim 500), but deviate considerably from the numerical results on smaller scales, showing the limitations of our approximate analytic calculations. Several possible improvements are pointed out for further studies.Comment: Accepted by Classical and Quantum Gravity. 43 pages, 15 figure