arXiv subjects

Jonathan R. Gair

Publications and source records attributed to Jonathan R. Gair.

At least 37 records · Page 2Linked to original sources

arXiv2021

Testing the Quasar Hubble Diagram with LISA Standard Sirens

Quasars have recently been used as an absolute distance indicator, extending the Hubble diagram to high redshift to reveal a deviation from the expansion history predicted for the standard, $Λ$CDM cosmology. Here we show that the Laser Interferometer Space Antenna (LISA) will efficiently test this claim with standard sirens at high redshift, defined by the coincident gravitational wave (GW) and electromagnetic (EM) observations of the merger of massive black hole binaries (MBHBs). Assuming a fiducial $Λ$CDM cosmology for generating mock standard siren datasets, the evidence for the $Λ$CDM model with respect to an alternative model inferred from quasar data is investigated. By simulating many realizations of possible future LISA observations, we find that for $50\%$ of these realizations (median result) 4 MBHB standard siren measurements will suffice to strongly differentiate between the two models, while 14 standard sirens will yield a similar result in $95\%$ of the realizations. In addition, we investigate the measurement precision of cosmological parameters as a function of the number of observed LISA MBHB standard sirens, finding that 15 events will on average achieve a relative precision of 5\% for $H_0$, reducing to 3\% and 2\% with 25 and 40 events, respectively. Our investigation clearly highlights the potential of LISA as a cosmological probe able to accurately map the expansion of the universe at $z\gtrsim 2$, and as a tool to cross-check and cross-validate cosmological EM measurements with complementary GW observations.

astro-ph.CO↗

arXiv2021

Assessing the impact of transient orbital resonances

One of the primary sources for the future space-based gravitational wave detector, the Laser Interferometer Space Antenna, are the inspirals of small compact objects into massive black holes in the centres of galaxies. The gravitational waveforms from such Extreme Mass Ratio Inspiral (EMRI) systems will provide measurements of their parameters with unprecedented precision, but only if the waveforms are accurately modeled. Here we explore the impact of transient orbital resonances which occur when the ratio of radial and polar frequencies is a rational number. We introduce a new Effective Resonance Model, which is an extension of the numerical kludge EMRI waveform approximation to include the effect of resonances, and use it to explore the impact of resonances on EMRI parameter estimation. For one-year inspirals, we find that the few cycle dephasings induced by 3:2 resonances can lead to systematic errors in parameter estimates, that are up to several times the typical measurement precision of the parameters. The bias is greatest for 3:2 resonances that occur closer to the central black hole. By regarding them as unknown model parameters, we further show that observations will be able to constrain the size of the changes in the orbital parameters across the resonance to a relative precision of 10% for a typical one-year EMRI observation with signal-to-noise ratio of 20. Such measurements can be regarded as tests of fundamental physics, by comparing the measured changes to those predicted in general relativity.

gr-qc↗

arXiv2020

Constraining the spin parameter of near-extremal black holes using LISA

We describe a model that generates first order adiabatic EMRI waveforms for quasi-circular equatorial inspirals of compact objects into rapidly rotating (near-extremal) black holes. Using our model, we show that LISA could measure the spin parameter of near-extremal black holes (for $a \gtrsim 0.9999$) with extraordinary precision, $\sim$ 3-4 orders of magnitude better than for moderate spins, $a \sim 0.9$. Such spin measurements would be one of the tightest measurements of an astrophysical parameter within a gravitational wave context. Our results are primarily based off a Fisher matrix analysis, but are verified using both frequentest and Bayesian techniques. We present analytical arguments that explain these high spin precision measurements. The high precision arises from the spin dependence of the radial inspiral evolution, which is dominated by geodesic properties of the secondary orbit, rather than radiation reaction. High precision measurements are only possible if we observe the exponential damping of the signal that is characteristic of the near-horizon regime of near-extremal inspirals. Our results demonstrate that, if such black holes exist, LISA would be able to successfully identify rapidly rotating black holes up to $a = 1-10^{-9}$ , far past the Thorne limit of $a = 0.998$.

gr-qc↗

arXiv2020

Cosmological Inference using Gravitational Wave Standard Sirens: A Mock Data Challenge

The observation of binary neutron star merger GW170817, along with its optical counterpart, provided the first constraint on the Hubble constant $H_0$ using gravitational wave standard sirens. When no counterpart is identified, a galaxy catalog can be used to provide the necessary redshift information. However, the true host might not be contained in a catalog which is not complete out to the limit of gravitational-wave detectability. These electromagnetic and gravitational-wave selection effects must be accounted for. We describe and implement a method to estimate $H_0$ using both the counterpart and the galaxy catalog standard siren methods. We perform a series of mock data analyses using binary neutron star mergers to confirm our ability to recover an unbiased estimate of $H_0$. Our simulations used a simplified universe with no redshift uncertainties or galaxy clustering, but with different magnitude-limited catalogs and assumed host galaxy properties, to test our treatment of both selection effects. We explore how the incompleteness of catalogs affects the final measurement of $H_0$, as well as the effect of weighting each galaxy's likelihood of being a host by its luminosity. In our most realistic simulation, where the simulated catalog is about three times denser than the density of galaxies in the local universe, we find that a 4.4\% measurement precision can be reached using galaxy catalogs with 50\% completeness and $\sim 250$ binary neutron star detections with sensitivity similar to that of Advanced LIGO's second observing run.

gr-qc↗

arXiv2020

Transition from Inspiral to Plunge: A Complete Near-Extremal Trajectory and Associated Waveform

We extend the Ori and Thorne (OT) procedure to compute the transition from an adiabatic inspiral into a geodesic plunge for any spin, with emphasis on near-extremal ones. Our analysis revisits the validity of the approximations made in OT. In particular, we discuss possible effects coming from eccentricity and non-geodesic past-history of the orbital evolution. We find three different scaling regimes according to whether the mass ratio is much smaller, of the same order or much larger than the near extremal parameter describing how fast the primary black hole rotates. Eccentricity and non-geodesic past-history corrections are always sub-leading, indicating that the quasi-circular approximation applies throughout the transition regime. However, we show that the OT assumption that the energy and angular momentum evolve linearly with proper time must be modified in the near-extremal regime. Using our transition equations, we describe an algorithm to compute the full worldline in proper time for an extreme mass ratio inspiral (EMRI) and the resultant gravitational waveform in the high spin limit.

gr-qc↗

arXiv2020

2 Fast 2 Fiducial: Gaussian processes for the interpolation and marginalization of waveform error in extreme-mass-ratio-inspiral parameter estimation

A number of open problems hinder our present ability to extract scientific information from data that will be gathered by the near-future gravitational-wave mission LISA. Many of these relate to the modeling, detection and characterization of signals from binary inspirals with an extreme component-mass ratio of $\lesssim10^{-4}$. In this paper, we draw attention to the issue of systematic error in parameter estimation due to the use of fast but approximate waveform models; this is found to be relevant for extreme-mass-ratio inspirals even in the case of waveforms with $\gtrsim90\%$ overlap accuracy and moderate ($\gtrsim30$) signal-to-noise ratios. A scheme that uses Gaussian processes to interpolate and marginalize over waveform error is adapted and investigated as a possible precursor solution to this problem. Several new methodological results are obtained, and the viability of the technique is successfully demonstrated on a three-parameter example in the setting of the LISA Data Challenge.

astro-ph.IM↗

arXiv2019

Extracting distribution parameters from multiple uncertain observations with selection biases

We derive a Bayesian framework for incorporating selection effects into population analyses. We allow for both measurement uncertainty in individual measurements and, crucially, for selection biases on the population of measurements, and show how to extract the parameters of the underlying distribution based on a set of observations sampled from this distribution. We illustrate the performance of this framework with an example from gravitational-wave astrophysics, demonstrating that the mass ratio distribution of merging compact-object binaries can be extracted from Malmquist-biased observations with substantial measurement uncertainty.

physics.data-an↗

arXiv2018

Towards a framework for testing general relativity with extreme-mass-ratio-inspiral observations

Extreme-mass-ratio-inspiral observations from future space-based gravitational-wave detectors such as LISA will enable strong-field tests of general relativity with unprecedented precision, but at prohibitive computational cost if existing statistical techniques are used. In one such test that is currently employed for LIGO black-hole binary mergers, generic deviations from relativity are represented by $N$ deformation parameters in a generalised waveform model; the Bayesian evidence for each of its $2^N$ combinatorial submodels is then combined into a posterior odds ratio for modified gravity over relativity in a null-hypothesis test. We adapt and apply this test to a generalised model for extreme-mass-ratio inspirals constructed on deformed black-hole spacetimes, and focus our investigation on how computational efficiency can be increased through an evidence-free method of model selection. This method is akin to the algorithm known as product-space Markov chain Monte Carlo, but uses nested sampling and improved error estimates from a rethreading technique. We perform benchmarking and robustness checks for the method, and find order-of-magnitude computational gains over regular nested sampling in the case of synthetic data generated from the null model.

gr-qc↗

arXiv2018

Astrometric Effects of Gravitational Wave Backgrounds with non-Einsteinian Polarizations

The Gaia mission offers a new opportunity to search for the low frequency gravitational wave background using astrometric measurements. In this paper, the astrometric effect of gravitational waves is reviewed, with a particular focus on the effect of non-Einsteinian gravitational wave polarizations. A stochastic gravitational wave background generates a correlated vector field of astrometric deflections on the sky. A convenient decomposition for the correlation matrix is introduced, enabling it to be calculated for all possible gravitational wave polarizations and compared to the redshift correlations from the pulsar-timing literature; in the case of a GR background of transverse traceless gravitational waves, this also allows us to identify an astrometric analog of the famous Hellings-Downs curve. Finally, the cross-correlation between the redshift and astrometric signal is also calculated; this may form the basis for future joint pulsar-timing and astrometry searches for arbitrarily polarized gravitational wave backgrounds.

gr-qc↗

arXiv2018

Strategies for the Follow-up of Gravitational Wave Transients with the Cherenkov Telescope Array

The observation of the electromagnetic counterpart of gravitational-wave (GW) transient GW170817 demonstrated the potential in extracting astrophysical information from multimessenger discoveries. The forthcoming deployment of the first telescopes of the Cherenkov Telescope Array (CTA) observatory will coincide with Advanced LIGO/Virgo's next observing run, O3, enabling the monitoring of gamma-ray emission at E > 20 GeV, and thus particle acceleration, from GW sources. CTA will not be greatly limited by the precision of GW localization as it will be be capable of rapidly covering the GW error region with sufficient sensitivity. We examine the current status of GW searches and their follow-up effort, as well as the status of CTA, in order to identify some of the general strategies that will enhance CTA's contribution to multimessenger discoveries.

astro-ph.HE↗

arXiv2018

Eccentric, nonspinning, inspiral, Gaussian-process merger approximant for the detection and characterization of eccentric binary black hole mergers

We present $\texttt{ENIGMA}$, a time domain, inspiral-merger-ringdown waveform model that describes non-spinning binary black holes systems that evolve on moderately eccentric orbits. The inspiral evolution is described using a consistent combination of post-Newtonian theory, self-force and black hole perturbation theory. Assuming eccentric binaries that circularize prior to coalescence, we smoothly match the eccentric inspiral with a stand-alone, quasi-circular merger, which is constructed using machine learning algorithms that are trained with quasi-circular numerical relativity waveforms. We show that $\texttt{ENIGMA}$ reproduces with excellent accuracy the dynamics of quasi-circular compact binaries. We validate $\texttt{ENIGMA}$ using a set of $\texttt{Einstein Toolkit}$ eccentric numerical relativity waveforms, which describe eccentric binary black hole mergers with mass-ratios between $1 \leq q \leq 5.5$, and eccentricities $e_0 \lesssim 0.2$ ten orbits before merger. We use this model to explore in detail the physics that can be extracted with moderately eccentric, non-spinning binary black hole mergers. We use $\texttt{ENIGMA}$ to show that GW150914, GW151226, GW170104, GW170814 and GW170608 can be effectively recovered with spinning, quasi-circular templates if the eccentricity of these events at a gravitational wave frequency of 10Hz satisfies $e_0\leq \{0.175,\, 0.125,\,0.175,\,0.175,\, 0.125\}$, respectively. We show that if these systems have eccentricities $e_0\sim 0.1$ at a gravitational wave frequency of 10Hz, they can be misclassified as quasi-circular binaries due to parameter space degeneracies between eccentricity and spin corrections. Using our catalog of eccentric numerical relativity simulations, we discuss the importance of including higher-order waveform multipoles in gravitational wave searches of eccentric binary black hole mergers.

gr-qc↗

arXiv2017

Gravitational waves from extreme mass ratio inspirals around bumpy black holes

The space based interferometer LISA will be capable of detecting the gravitational waves emitted by stellar mass black holes or neutron stars slowly inspiralling into the supermassive black holes found in the centre of most galaxies. The gravitational wave signal from such an extreme mass ratio inspiral (EMRI) event will provide a unique opportunity to test whether the spacetime metric around the central black hole is well described by the Kerr solution. In this paper a well studied model for EMRIs around Kerr black holes is extended to a family of parametrically deformed bumpy black holes which preserve the basic symmetries of the Kerr metric. The new EMRI model is then used to quantify the constraints that LISA observations of EMRIs may be able to place on the deviations, or bumps, on the Kerr metric.

gr-qc↗

arXiv2017

The Fast and the Fiducial: Augmented kludge waveforms for detecting extreme-mass-ratio inspirals

The extreme-mass-ratio inspirals (EMRIs) of stellar-mass compact objects into massive black holes are an important class of source for the future space-based gravitational-wave detector LISA. Detecting signals from EMRIs will require waveform models that are both accurate and computationally efficient. In this paper, we present the latest implementation of an augmented analytic kludge (AAK) model, publicly available at github.com/alvincjk/EMRI_Kludge_Suite as part of an EMRI waveform software suite. This version of the AAK model has improved accuracy compared to its predecessors, with two-month waveform overlaps against a more accurate fiducial model exceeding 0.97 for a generic range of sources; it also generates waveforms 5-15 times faster than the fiducial model. The AAK model is well suited for scoping out data analysis issues in the upcoming round of mock LISA data challenges. A simple analytic argument shows that it might even be viable for detecting EMRIs with LISA through a semi-coherent template bank method, while the use of the original analytic kludge in the same approach will result in around 90% fewer detections.

gr-qc↗

arXiv2017

Importance of transient resonances in extreme-mass-ratio inspirals

The inspiral of stellar-mass compact objects, like neutron stars or stellar-mass black holes, into supermassive black holes provides a wealth of information about the strong gravitational-field regime via the emission of gravitational waves. In order to detect and analyse these signals, accurate waveform templates which include the effects of the compact object's gravitational self-force are required. For computational efficiency, adiabatic templates are often used. These accurately reproduce orbit-averaged trajectories arising from the first-order self-force, but neglect other effects, such as transient resonances, where the radial and poloidal fundamental frequencies become commensurate. During such resonances the flux of gravitational waves can be diminished or enhanced, leading to a shift in the compact object's trajectory and the phase of the waveform. We present an evolution scheme for studying the effects of transient resonances and apply this to an astrophysically motivated population. We find that a large proportion of systems encounter a low-order resonance in the later stages of inspiral; however, the resulting effect on signal-to-noise recovery is small as a consequence of the low eccentricity of the inspirals. Neglecting the effects of transient resonances leads to a loss of 4% of detectable signals.

gr-qc↗

arXiv2016

Tunable compression of template banks for fast gravitational-wave detection and localisation

One strategy for reducing the online computational cost of matched-filter searches for gravitational waves is to introduce a compressed basis for the waveform template bank in a grid-based search. In this paper, we propose and investigate several tunable compression schemes for a general template bank. Through offline compression, such schemes are shown to yield faster detection and localisation of signals, along with moderately improved sensitivity and accuracy over coarsened banks at the same level of computational cost. This is potentially useful for any search involving template banks, and especially in the analysis of data from future space-based detectors such as eLISA, for which online grid searches are difficult due to the long-duration waveforms and large parameter spaces.

astro-ph.IM↗

arXiv2016

Fast methods for training Gaussian processes on large data sets

Gaussian process regression (GPR) is a non-parametric Bayesian technique for interpolating or fitting data. The main barrier to further uptake of this powerful tool rests in the computational costs associated with the matrices which arise when dealing with large data sets. Here, we derive some simple results which we have found useful for speeding up the learning stage in the GPR algorithm, and especially for performing Bayesian model comparison between different covariance functions. We apply our techniques to both synthetic and real data and quantify the speed-up relative to using nested sampling to numerically evaluate model evidences.

stat.ML↗

arXiv2016

Improving gravitational-wave parameter estimation using Gaussian process regression

Folding uncertainty in theoretical models into Bayesian parameter estimation is necessary in order to make reliable inferences. A general means of achieving this is by marginalizing over model uncertainty using a prior distribution constructed using Gaussian process regression (GPR). As an example, we apply this technique to the measurement of chirp mass using (simulated) gravitational-wave signals from binary black holes that could be observed using advanced-era gravitational-wave detectors. Unless properly accounted for, uncertainty in the gravitational-wave templates could be the dominant source of error in studies of these systems. We explain our approach in detail and provide proofs of various features of the method, including the limiting behavior for high signal-to-noise, where systematic model uncertainties dominate over noise errors. We find that the marginalized likelihood constructed via GPR offers a significant improvement in parameter estimation over the standard, uncorrected likelihood both in our simple one-dimensional study, and theoretically in general. We also examine the dependence of the method on the size of training set used in the GPR; on the form of covariance function adopted for the GPR, and on changes to the detector noise power spectral density.

gr-qc↗

arXiv2015

Improved analytic extreme-mass-ratio inspiral model for scoping out eLISA data analysis

The space-based gravitational-wave detector eLISA has been selected as the ESA L3 mission, and the mission design will be finalised by the end of this decade. To prepare for mission formulation over the next few years, several outstanding and urgent questions in data analysis will be addressed using mock data challenges, informed by instrument measurements from the LISA Pathfinder satellite launching at the end of 2015. These data challenges will require accurate and computationally affordable waveform models for anticipated sources such as the extreme-mass-ratio inspirals (EMRIs) of stellar-mass compact objects into massive black holes. Previous data challenges have made use of the well-known analytic EMRI waveforms of Barack and Cutler, which are extremely quick to generate but dephase relative to more accurate waveforms within hours, due to their mismatched radial, polar and azimuthal frequencies. In this paper, we describe an augmented Barack-Cutler model that uses a frequency map to the correct Kerr frequencies, along with updated evolution equations and a simple fit to a more accurate model. The augmented waveforms stay in phase for months and may be generated with virtually no additional computational cost.

gr-qc↗