arXiv subjects

Mark Hannam

Publications and source records attributed to Mark Hannam.

At least 55 records · Page 3Linked to original sources

arXiv2015

Frequency-domain gravitational waves from non-precessing black-hole binaries. II. A phenomenological model for the advanced detector era

We present a new frequency-domain phenomenological model of the gravitational-wave signal from the inspiral, merger and ringdown of non-precessing (aligned-spin) black-hole binaries. The model is calibrated to 19 hybrid effective-one-body--numerical-relativity waveforms up to mass ratios of 1:18 and black-hole spins of $|a/m| \sim 0.85$ ($0.98$ for equal-mass systems). The inspiral part of the model consists of an extension of frequency-domain post-Newtonian expressions, using higher-order terms fit to the hybrids. The merger-ringdown is based on a phenomenological ansatz that has been significantly improved over previous models. The model exhibits mismatches of typically less than 1\% against all 19 calibration hybrids, and an additional 29 verification hybrids, which provide strong evidence that, over the calibration region, the model is sufficiently accurate for all relevant gravitational-wave astronomy applications with the Advanced LIGO and Virgo detectors. Beyond the calibration region the model produces physically reasonable results, although we recommend caution in assuming that \emph{any} merger-ringdown waveform model is accurate outside its calibration region. As an example, we note that an alternative non-precessing model, SEOBNRv2 (calibrated up to spins of only 0.5 for unequal-mass systems), exhibits mismatch errors of up to 10\% for high spins outside its calibration region. We conclude that waveform models would benefit most from a larger number of numerical-relativity simulations of high-aligned-spin unequal-mass binaries.

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arXiv2015

Comparison of subdominant gravitational wave harmonics between post-Newtonian and numerical relativity calculations and construction of multi-mode hybrids

Gravitational waveforms which describe the inspiral, merger and ringdown of coalescing binaries are usually constructed by synthesising information from perturbative descriptions, in particular post-Newtonian theory and black-hole perturbation theory, with numerical solutions of the full Einstein equations. In this paper we discuss the "glueing" of numerical and post-Newtonian waveforms to produce hybrid waveforms which include subdominant spherical harmonics ("higher order modes"), and focus in particular on the process of consistently aligning the waveforms, which requires a comparison of both descriptions and a discussion of their imprecisions. We restrict to the non-precessing case, and illustrate the process using numerical waveforms of up to mass ratio $q=18$ produced with the BAM code, and publicly available waveforms from the SXS catalogue. The results also suggest new ways of analysing finite radius errors in numerical simulations.

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arXiv2014

A simple model of complete precessing black-hole-binary gravitational waveforms

The construction of a model of the gravitational-wave (GW) signal from generic configurations of spinning-black-hole binaries, through inspiral, merger and ringdown, is one of the most pressing theoretical problems in the build-up to the era of GW astronomy. We present the first such model in the frequency domain, "PhenomP", which captures the basic phenomenology of the seven-dimensional parameter space of binary configurations with only three key physical parameters. Two of these (the binary's mass ratio and an effective total spin parallel to the orbital angular momentum, which determines the inspiral rate) define an underlying non-precessing-binary model. The non-precessing-binary waveforms are then "twisted up" with approximate expressions for the precessional motion, which require only one additional physical parameter, an effective precession spin, $χ_p$. All other parameters (total mass, sky location, orientation and polarisation, and initial phase) can be specified trivially. The model is constructed in the frequency domain, which will be essential for efficient GW searches and source measurements. We have tested the model's fidelity for GW applications by comparison against hybrid post-Newtonian-numerical-relativity waveforms at a variety of configurations --although we did not use these numerical simulations in the construction of the model. Our model can be used to develop GW searches, to study the implications for astrophysical measurements, and as a simple conceptual framework to form the basis of generic-binary waveform modelling in the advanced-detector era.

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arXiv2014

Gravitational-wave observations of binary black holes: Effect of non-quadrupole modes

We study the effect of non-quadrupolar modes in the detection and parameter estimation of gravitational waves (GWs) from non-spinning black-hole binaries. We evaluate the loss of signal-to-noise ratio and the systematic errors in the estimated parameters when one uses a quadrupole-mode template family to detect GW signals with all the relevant modes, for target signals with total masses $20 M_\odot \leq M \leq 250 M_\odot$ and mass ratios $1 \leq q \leq 18$. Target signals are constructed by matching numerical-relativity simulations describing the late inspiral, merger and ringdown of the binary with post-Newtonian/effective-one-body waveforms describing the early inspiral. We find that waveform templates modeling only the quadrupolar modes of the GW signal are sufficient (loss of detection rate $< 10\%$) for the detection of GWs with mass ratios $q\leq4$ using advanced GW observatories. Neglecting the effect of non-quadrupole modes will introduce systematic errors in the estimated parameters. The systematic errors are larger than the expected $1\,σ$ statistical errors for binaries with large, unequal masses ($q\gtrsim4, M \gtrsim 150 M_\odot$), for sky-averaged signal-to-noise ratios larger than $8$. We provide a summary of the regions in the parameter space where neglecting non-quadrupole modes will cause unacceptable loss of detection rates and unacceptably large systematic biases in the estimated parameters.

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arXiv2014

Towards models of gravitational waveforms from generic binaries II: Modelling precession effects with a single effective precession parameter

Gravitational waves (GWs) emitted by generic black-hole binaries show a rich structure that directly reflects the complex dynamics introduced by the precession of the orbital plane, which poses a real challenge to the development of generic waveform models. Recent progress in modelling these signals relies on an approximate decoupling between the non-precessing secular inspiral and a precession-induced rotation. However, the latter depends in general on all physical parameters of the binary which makes modelling efforts as well as understanding parameter-estimation prospects prohibitively complex. Here we show that the dominant precession effects can be captured by a reduced set of spin parameters. Specifically, we introduce a single \emph{effective precession spin} parameter, $χ_p$, which is defined from the spin components that lie in the orbital plane at some (arbitrary) instant during the inspiral. We test the efficacy of this parameter by considering binary inspiral configurations specified by the physical parameters of a corresponding non-precessing-binary configuration (total mass, mass ratio, and spin components (anti-)parallel to the orbital angular momentum), plus the effective precession spin applied to the larger black hole. We show that for an overwhelming majority of random precessing configurations, the precession dynamics during the inspiral are well approximated by our equivalent configurations. Our results suggest that in the comparable-mass regime waveform models with only three spin parameters faithfully represent generic waveforms, which has practical implications for the prospects of GW searches, parameter estimation and the numerical exploration of the precessing-binary parameter space.

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arXiv2013

Modelling gravitational waves from precessing black-hole binaries: Progress, challenges and prospects

The inspiral and merger of two orbiting black holes is among the most promising sources for the first (hopefully imminent) direct detection of gravitational waves (GWs), and measurements of these signals could provide a wealth of information about astrophysics, fundamental physics and cosmology. Detection and measurement require a theoretical description of the GW signals from all possible black-hole-binary configurations, which can include complicated precession effects due to the black-hole spins. Modelling the GW signal from generic precessing binaries is therefore one of the most urgent theoretical challenges facing GW astronomy. This article briefly reviews the phenomenology of generic-binary dynamics and waveforms, and recent advances in modelling them.

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arXiv2013

Error-analysis and comparison to analytical models of numerical waveforms produced by the NRAR Collaboration

The Numerical-Relativity-Analytical-Relativity (NRAR) collaboration is a joint effort between members of the numerical relativity, analytical relativity and gravitational-wave data analysis communities. The goal of the NRAR collaboration is to produce numerical-relativity simulations of compact binaries and use them to develop accurate analytical templates for the LIGO/Virgo Collaboration to use in detecting gravitational-wave signals and extracting astrophysical information from them. We describe the results of the first stage of the NRAR project, which focused on producing an initial set of numerical waveforms from binary black holes with moderate mass ratios and spins, as well as one non-spinning binary configuration which has a mass ratio of 10. All of the numerical waveforms are analysed in a uniform and consistent manner, with numerical errors evaluated using an analysis code created by members of the NRAR collaboration. We compare previously-calibrated, non-precessing analytical waveforms, notably the effective-one-body (EOB) and phenomenological template families, to the newly-produced numerical waveforms. We find that when the binary's total mass is ~100-200 solar masses, current EOB and phenomenological models of spinning, non-precessing binary waveforms have overlaps above 99% (for advanced LIGO) with all of the non-precessing-binary numerical waveforms with mass ratios <= 4, when maximizing over binary parameters. This implies that the loss of event rate due to modelling error is below 3%. Moreover, the non-spinning EOB waveforms previously calibrated to five non-spinning waveforms with mass ratio smaller than 6 have overlaps above 99.7% with the numerical waveform with a mass ratio of 10, without even maximizing on the binary parameters.

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arXiv2013

Testing the validity of the single-spin approximation in inspiral-merger-ringdown waveforms

Gravitational-wave signals from black-hole binaries with non-precessing spins are described by four parameters -- each black hole's mass and spin. It has been shown that the dominant spin effects can be modeled by a \emph{single} spin parameter, leading to the development of several \emph{three-parameter} waveform models. Previous studies indicate that these models should be adequate for gravitational-wave detection. In this paper we focus on the systematic biases that would result from using them to estimate binary parameters, and consider a one-parameter family of configurations at one choice of mass ratio and effective single spin. We find that for low-mass binaries within that family of configurations, where the observable waveform is dominated by the inspiral, the systematic bias in all physical parameters is smaller than the parameter uncertainty due to degeneracies between the mass ratio and the spins, at least up to signal-to-noise ratios (SNRs) of 50. For higher-mass binaries, where the merger and ringdown make a greater contribution to the observed signal, the bias in the mass ratio is comparable to its uncertainty at SNRs of only $\sim$30, and the bias in the measurement of the total spin is \emph{larger} than the uncertainty defined by the 90% confidence region even at an SNR of only 10. Although this bias may be mitigated in future models by a better choice of single-effective-spin parameter, these results suggest that it may be possible to accurately measure \emph{both} black-hole spins in intermediate-mass binaries.

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arXiv2013

Towards models of gravitational waveforms from generic binaries: A simple approximate mapping between precessing and non-precessing inspiral signals

One of the greatest theoretical challenges in the build-up to the era of second-generation gravitational-wave detectors is the modeling of generic binary waveforms. We introduce an approximation that has the potential to significantly simplify this problem. We show that generic precessing-binary inspiral waveforms (covering a seven-dimensional space of intrinsic parameters) can be mapped to a two-dimensional space of non-precessing binaries, characterized by the mass ratio and a single effective total spin. The mapping consists of a time-dependent rotation of the waveforms into the quadrupole-aligned frame, and is extremely accurate (matches $> 0.99$ with parameter biases in the total spin of $Δχ\leq 0.04$), even in the case of transitional precession. In addition, we demonstrate a simple method to construct hybrid post-Newtonian--numerical-relativity precessing-binary waveforms in the quadrupole-aligned frame, and provide evidence that our approximate mapping can be used all the way to the merger. Finally, based on these results, we outline a general proposal for the construction of generic waveform models, which will be the focus of future work.

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arXiv2013

When can gravitational-wave observations distinguish between black holes and neutron stars?

Gravitational-wave observations of compact binaries have the potential to uncover the distribution of masses and angular momenta of black holes and neutron stars in the universe. The binary components' physical parameters can be inferred from their effect on the phasing of the gravitational-wave signal, but a partial degeneracy between the components' mass ratio and their angular momenta limits our ability to measure the individual component masses. At the typical signal amplitudes expected by the Advanced Laser Interferometer Gravitational-wave Observatory (signal-to-noise ratios between 10 and 20), we show that it will in many cases be difficult to distinguish whether the components are neutron stars or black holes. We identify when the masses of the binary components could be unambiguously measured outside the range of current observations: a system with a chirp mass $\mathcal{M} \le 0.871 $ M$_\odot$ would unambiguously contain the smallest-mass neutron star observed, and a system with $\mathcal{M} \ge 2.786 \Msun$ must contain a black hole. However, additional information would be needed to distinguish between a binary containing two 1.35 M$_\odot$ neutron stars and an exotic neutron-star--black-hole binary. We also identify those configurations that could be unambiguously identified as black-hole binaries, and show how the observation of an electromagnetic counterpart to a neutron-star--black-hole binary could be used to constrain the black-hole spin.

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arXiv2012

Degeneracy between mass and spin in black-hole-binary waveforms

We explore the degeneracy between mass and spin in gravitational waveforms emitted by black-hole binary coalescences. We focus on spin-aligned waveforms and obtain our results using phenomenological models that were tuned to numerical-relativity simulations. A degeneracy is known for low-mass binaries (particularly neutron-star binaries), where gravitational-wave detectors are sensitive to only the inspiral phase, and the waveform can be modelled by post-Newtonian theory. Here, we consider black-hole binaries, where detectors will also be sensitive to the merger and ringdown, and demonstrate that the degeneracy persists across a broad mass range. At low masses, the degeneracy is between mass ratio and total spin, with chirp mass accurately determined. At higher masses, the degeneracy persists but is not so clearly characterised by constant chirp mass as the merger and ringdown become more significant. We consider the importance of this degeneracy both for performing searches (including searches where only non-spinning templates are used) and in parameter extraction from observed systems. We compare observational capabilities between the early (~2015) and final (2018 onwards) versions of the Advanced LIGO detector.

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arXiv2012

Is black-hole ringdown a memory of its progenitor?

We have performed an extensive numerical study of coalescing black-hole binaries to understand the gravitational-wave spectrum of quasi-normal modes excited in the merged black hole. Remarkably, we find that the masses and spins of the progenitor are clearly encoded in the mode spectrum of the ringdown signal. Some of the mode amplitudes carry the signature of the binary's mass ratio, while others depend critically on the spins. Simulations of precessing binaries suggest that our results carry over to generic systems. Using Bayesian inference, we demonstrate that it is possible to accurately measure the mass ratio and a proper combination of spins even when the binary is itself invisible to a detector. Using a mapping of the binary masses and spins to the final black hole spin, allows us to further extract the spin components of the progenitor. Our results could have tremendous implications for gravitational astronomy by facilitating novel tests of general relativity using merging black holes.

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arXiv2012

An efficient iterative method to reduce eccentricity in numerical-relativity simulations of compact binary inspiral

We present a new iterative method to reduce eccentricity in black-hole-binary simulations. Given a good first estimate of low-eccentricity starting momenta, we evolve puncture initial data for ~4 orbits and construct improved initial parameters by comparing the inspiral with post-Newtonian calculations. Our method is the first to be applied directly to the gravitational-wave (GW) signal, rather than the orbital motion. The GW signal is in general less contaminated by gauge effects, which, in moving-puncture simulations, limit orbital-motion-based measurements of the eccentricity to an uncertainty of $Δe \sim 0.002$, making it difficult to reduce the eccentricity below this value. Our new method can reach eccentricities below $10^{-3}$ in one or two iteration steps; we find that this is well below the requirements for GW astronomy in the advanced detector era. Our method can be readily adapted to any compact-binary simulation with GW emission, including black-hole-binary simulations that use alternative approaches, and neutron-star-binary simulations. We also comment on the differences in eccentricity estimates based on the strain $h$, and the Newman-Penrose scalar $Ψ_4$.

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arXiv2012

The NINJA-2 catalog of hybrid post-Newtonian/numerical-relativity waveforms for non-precessing black-hole binaries

The Numerical INJection Analysis (NINJA) project is a collaborative effort between members of the numerical relativity and gravitational wave data analysis communities. The purpose of NINJA is to study the sensitivity of existing gravitational-wave search and parameter-estimation algorithms using numerically generated waveforms, and to foster closer collaboration between the numerical relativity and data analysis communities. The first NINJA project used only a small number of injections of short numerical-relativity waveforms, which limited its ability to draw quantitative conclusions. The goal of the NINJA-2 project is to overcome these limitations with long post-Newtonian - numerical relativity hybrid waveforms, large numbers of injections, and the use of real detector data. We report on the submission requirements for the NINJA-2 project and the construction of the waveform catalog. Eight numerical relativity groups have contributed 63 hybrid waveforms consisting of a numerical portion modelling the late inspiral, merger, and ringdown stitched to a post-Newtonian portion modelling the early inspiral. We summarize the techniques used by each group in constructing their submissions. We also report on the procedures used to validate these submissions, including examination in the time and frequency domains and comparisons of waveforms from different groups against each other. These procedures have so far considered only the $(\ell,m)=(2,2)$ mode. Based on these studies we judge that the hybrid waveforms are suitable for NINJA-2 studies. We note some of the plans for these investigations.

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arXiv2012

Black-hole hair loss: learning about binary progenitors from ringdown signals

Perturbed Kerr black holes emit gravitational radiation, which (for the practical purposes of gravitational-wave astronomy) consists of a superposition of damped sinusoids termed quasi-normal modes. The frequencies and time-constants of the modes depend only on the mass and spin of the black hole - a consequence of the no-hair theorem. It has been proposed that a measurement of two or more quasi-normal modes could be used to confirm that the source is a black hole and to test if general relativity continues to hold in ultra-strong gravitational fields. In this paper we propose a practical approach to testing general relativity with quasi-normal modes. We will also argue that the relative amplitudes of the various quasi-normal modes encode important information about the origin of the perturbation that caused them. This helps in inferring the nature of the perturbation from an observation of the emitted quasi-normal modes. In particular, we will show that the relative amplitudes of the different quasi-normal modes emitted in the process of the merger of a pair of nonspinning black holes can be used to measure the component masses of the progenitor binary.

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arXiv2011

Reliability of complete gravitational waveform models for compact binary coalescences

With recent advances in post-Newtonian (PN) theory and numerical relativity (NR) it has become possible to construct inspiral-merger-ringdown waveforms by combining both descriptions into one hybrid signal. While addressing the reliability of such waveforms, previous studies have identified the PN contribution as the dominant source of error, which can be reduced by incorporating longer NR simulations. Here we overcome the two outstanding issues that make it difficult to determine the minimum NR simulation length necessary to produce suitably accurate hybrids: (1) the criteria for a GW search is the mismatch between the true waveform and a set of model waveforms, optimized over all waveforms in the model, but for discrete hybrids this optimization was not yet possible. (2) these calculations typically require that numerical waveforms already exist, while we develop an algorithm to estimate hybrid mismatches errors without numerical data. Our procedure relies on combining supposedly equivalent PN models at highest available order with common data in the NR regime, and their difference serves as a measure of the uncertainty assumed in each waveform. Contrary to some earlier studies, we estimate that ~10 NR orbits before merger should allow for the construction of waveform families that are accurate enough for detection in a broad range of parameters, only excluding highly spinning, unequal-mass systems. Nonspinning systems, even with high mass-ratio (q>=20) are well modeled for astrophysically reasonable component masses. The parameter bias is only of the order of 1% for total mass and symmetric mass-ratio and less than 0.1 for the dimensionless spin magnitude. We take the view that similar NR waveform lengths will remain the state of the art in the advanced detector era, and begin to assess the limits of the science that can be done with them.

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arXiv2010

Tracking the precession of compact binaries from their gravitational-wave signal

We present a simple method to track the precession of a black-hole-binary system, using only information from the gravitational-wave (GW) signal. Our method consists of locating the frame from which the magnitude of the $(\ell=2,|m|=2)$ modes is maximized, which we denote the "quadrupole-aligned" frame. We demonstrate the efficacy of this method when applied to waveforms from numerical simulations. In the test case of an equal-mass nonspinning binary, our method locates the direction of the orbital angular momentum to within $(Δθ, Δϕ) = (0.05^{\circ},0.2^{\circ})$. We then apply the method to a $q = M_2/M_1 = 3$ binary that exhibits significant precession. In general a spinning binary's orbital angular momentum $\mathbf{L}$ is \emph{not} orthogonal to the orbital plane. Evidence that our method locates the direction of $\mathbf{L}$ rather than the normal of the orbital plane is provided by comparison with post-Newtonian (PN) results. Also, we observe that it accurately reproduces similar higher-mode amplitudes to a comparable non-spinning (and therefore non-precessing) binary, and that the frequency of the $(\ell=2,|m|=2)$ modes is consistent with the "total frequency" of the binary's motion. The simple form of the quadrupole-aligned waveform will be useful in attempts to analytically model the inspiral-merger-ringdown (IMR) signal of precessing binaries, and in standardizing the representation of waveforms for studies of accuracy and consistency of source modelling efforts, both numerical and analytical.

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arXiv2010

Simulations of black-hole binaries with unequal masses or non-precessing spins: accuracy, physical properties, and comparison with post-Newtonian results

We present gravitational waveforms for the last orbits and merger of black-hole-binary (BBH) systems along two branches of the BBH parameter space: equal-mass binaries with equal non-precessing spins, and nonspinning unequal-mass binaries. The waveforms are calculated from numerical solutions of Einstein's equations for black-hole binaries that complete between six and ten orbits before merger. Along the equal-mass spinning branch, the spin parameter of each BH is $χ_i = S_i/M_i^2 \in [-0.85,0.85]$, and along the unequal-mass branch the mass ratio is $q =M_2/M_1 \in [1,4]$. We discuss the construction of low-eccentricity puncture initial data for these cases, the properties of the final merged BH, and compare the last 8-10 GW cycles up to $Mω= 0.1$ with the phase and amplitude predicted by standard post-Newtonian (PN) approximants. As in previous studies, we find that the phase from the 3.5PN TaylorT4 approximant is most accurate for nonspinning binaries. For equal-mass spinning binaries the 3.5PN TaylorT1 approximant (including spin terms up to only 2.5PN order) gives the most robust performance, but it is possible to treat TaylorT4 in such a way that it gives the best accuracy for spins $χ_i > -0.75$. When high-order amplitude corrections are included, the PN amplitude of the $(\ell=2,m=\pm2)$ modes is larger than the NR amplitude by between 2-4%.

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