Jonathan R. Gair

Intermediate and extreme mass-ratio inspirals — astrophysics, science applications and detection using LISA

Black hole binaries with extreme (gtrsim104:1) or intermediate (~102–104:1) mass ratios are among the most interesting gravitational wave sources that are expected to be detected by the proposed laser interferometer space antenna (LISA). These sources have the potential to tell us much about astrophysics, but are also of unique importance for testing aspects of the general theory of relativity in the strong field regime. Here we discuss these sources from the perspectives of astrophysics, data analysis and applications to testing general relativity, providing both a description of the current state of knowledge and an outline of some of the outstanding questions that still need to be addressed. This review grew out of discussions at a workshop in September 2006 hosted by the Albert Einstein Institute in Golm, Germany.

Massive black-hole binary inspirals: results from the LISA parameter estimation taskforce

The LISA Parameter Estimation Taskforce was formed in September 2007 to provide the LISA Project with vetted codes, source distribution models and results related to parameter estimation. The Taskforces goal is to be able to quickly calculate the impact of any mission design changes on LISAs science capabilities, based on reasonable estimates of the distribution of astrophysical sources in the universe. This paper describes our Taskforces work on massive black-hole binaries (MBHBs). Given present uncertainties in the formation history of MBHBs, we adopt four different population models, based on (i) whether the initial black-hole seeds are small or large and (ii) whether accretion is efficient or inefficient at spinning up the holes. We compare four largely independent codes for calculating LISAs parameter-estimation capabilities. All codes are based on the Fisher-matrix approximation, but in the past they used somewhat different signal models, source parametrizations and noise curves. We show that once these differences are removed, the four codes give results in extremely close agreement with each other. Using a code that includes both spin precession and higher harmonics in the gravitational-wave signal, we carry out Monte Carlo simulations and determine the number of events that can be detected and accurately localized in our four population models.

Observable properties of orbits in exact bumpy spacetimes

We explore the properties of test-particle orbits in bumpy spacetimes—stationary, reflection-symmetric, asymptotically flat solutions of Einstein equations that have a non-Kerr (anomalous) higher-order multipole-moment structure but can be tuned arbitrarily close to the Kerr metric. Future detectors should observe gravitational waves generated during inspirals of compact objects into supermassive central bodies. If the central body deviates from the Kerr metric, this will manifest itself in the emitted waves. Here, we explore some of the features of orbits in non-Kerr spacetimes that might lead to observable signatures. As a basis for this analysis, we use a family of exact solutions proposed by Manko and Novikov which deviate from the Kerr metric in the quadrupole and higher moments, but we also compare our results to other work in the literature. We examine isolating integrals of the orbits and find that the majority of geodesic orbits have an approximate fourth constant of the motion (in addition to the energy, angular momentum, and rest mass) and the resulting orbits are triperiodic to high precision. We also find that this fourth integral can be lost for certain orbits in some oblately deformed Manko-Novikov spacetimes, leading to ergodic motion. However, compact objects will probably not end up on these chaotic orbits in nature. We compute the location of the innermost stable circular orbit (ISCO) and find that the behavior of an orbit in the approach to the ISCO can be qualitatively different depending on whether the location of the ISCO is determined by the onset of an instability in the radial or vertical direction. Finally, we compute periapsis and orbital-plane precessions for nearly circular and nearly equatorial orbits in both the strong and weak field, and discuss weak-field precessions for eccentric equatorial orbits.

Testing General Relativity with Low-Frequency, Space-Based Gravitational-Wave Detectors

We review the tests of general relativity that will become possible with space-based gravitational-wave detectors operating in the ∼ 10−5 − 1 Hz low-frequency band. The fundamental aspects of gravitation that can be tested include the presence of additional gravitational fields other than the metric; the number and tensorial nature of gravitational-wave polarization states; the velocity of propagation of gravitational waves; the binding energy and gravitational-wave radiation of binaries, and therefore the time evolution of binary inspirals; the strength and shape of the waves emitted from binary mergers and ringdowns; the true nature of astrophysical black holes; and much more. The strength of this science alone calls for the swift implementation of a space-based detector; the remarkable richness of astrophysics, astronomy, and cosmology in the low-frequency gravitational-wave band make the case even stronger.

Use of the MULTINEST algorithm for gravitational wave data analysis

We describe an application of the MultiNest algorithm to gravitational wave data analysis. MultiNest is a multimodal nested sampling algorithm designed to efficiently evaluate the Bayesian evidence and return posterior probability densities for likelihood surfaces containing multiple secondary modes. The algorithm employs a set of live points which are updated by partitioning the set into multiple overlapping ellipsoids and sampling uniformly from within them. This set of live points climbs up the likelihood surface through nested iso-likelihood contours and the evidence and posterior distributions can be recovered from the point set evolution. The algorithm is model-independent in the sense that the specific problem being tackled enters only through the likelihood computation, and does not change how the live point set is updated. In this paper, we consider the use of the algorithm for gravitational wave data analysis by searching a simulated LISA data set containing two non-spinning supermassive black hole binary signals. The algorithm is able to rapidly identify all the modes of the solution and recover the true parameters of the sources to high precision.

Expected properties of the first gravitational wave signal detected with pulsar timing arrays

In this paper we attempt to investigate the nature of the first gravitational wave (GW) signal to be detected by pulsar timing arrays (PTAs): will it be an individual, resolved supermassive black hole binary (SBHB), or a stochastic background made by the superposition of GWs produced by an ensemble of SBHBs? To address this issue, we analyse a broad set of simulations of the cosmological population of SBHBs, that cover the entire parameter space allowed by current electromagnetic observations in an unbiased way. For each simulation, we construct the expected GW signal and identify the loudest individual sources. We then employ appropriate detection statistics to evaluate the relative probability of detecting each type of source as a function of time for a variety of PTAs; we consider the current International PTA, and speculate into the era of the Square Kilometre Array. The main properties of the first detectable individual SBHBs are also investigated. Contrary to previous work, we cast our results in terms of the detection probability (DP), since the commonly adopted criterion based on a signal-to-noise ratio threshold is statistic-dependent and may result in misleading conclusions for the statistics adopted here. Our results confirm quantitatively that a stochastic signal is more likely to be detected first (with between 75 to 93 per cent probability, depending on the array), but the DP of single-sources is not negligible. Our framework is very flexible and can be easily extended to more realistic arrays and to signal models including environmental coupling and SBHB eccentricity.

From spin noise to systematics: stochastic processes in the first International Pulsar Timing Array data release

We analyse the stochastic properties of the 49 pulsars that comprise the first International Pulsar Timing Array (IPTA) data release. We use Bayesian methodology, performing model selection to determine the optimal description of the stochastic signals present in each pulsar. In addition to spin-noise and dispersion-measure (DM) variations, these models can include timing noise unique to a single observing system, or frequency band. We show the improved radio-frequency coverage and presence of overlapping data from different observing systems in the IPTA data set enables us to separate both system and band-dependent effects with much greater efficacy than in the individual PTA data sets. For example, we show that PSR J1643−1224 has, in addition to DM variations, significant band-dependent noise that is coherent between PTAs which we interpret as coming from time-variable scattering or refraction in the ionised interstellar medium. Failing to model these different contributions appropriately can dramatically alter the astrophysical interpretation of the stochastic signals observed in the residuals. In some cases, the spectral exponent of the spin noise signal can vary from 1.6 to 4 depending upon the model, which has direct implications for the long-term sensitivity of the pulsar to a stochastic gravitational-wave (GW) background. By using a more appropriate model, however, we can greatly improve a pulsars sensitivity to GWs. For example, including system and band-dependent signals in the PSR J0437−4715 data set improves the upper limit on a fiducial GW background by ∼ 60% compared to a model that includes DM variations and spin-noise only.

Hubble without the Hubble: Cosmology using advanced gravitational-wave detectors alone

We investigate a novel approach to measuring the Hubble constant using gravitational-wave (GW) signals from compact binaries by exploiting the narrowness of the distribution of masses of the underlying neutron-star population. Gravitational-wave observations with a network of detectors will permit a direct, independent measurement of the distance to the source systems. If the redshift of the source is known, these inspiraling double-neutron-star binary systems can be used as standard sirens to extract cosmological information. Unfortunately, the redshift and the system chirp mass are degenerate in GW observations. Thus, most previous work has assumed that the source redshift is obtained from electromagnetic counterparts. In this paper, we explore what we can learn about the background cosmology and the mass distribution of neutron stars from the set of neutron-star (NS) mergers detected by such a network. We use a Bayesian formalism to analyze catalogs of NS-NS inspiral detections. We find that it is possible to constrain the Hubble constant, H_0, and the parameters of the NS mass function using gravitational-wave data alone, without relying on electromagnetic counterparts. Under reasonable assumptions, we will be able to determine H_0 to +/- 10% using ~100 observations, provided the Gaussian half-width of the underlying double NS mass distribution is less than 0.04 solar masses. The expected precision depends linearly on the intrinsic width of the NS mass function, but has only a weak dependence on H_0 near the default parameter values. Finally, we consider what happens if, for some fraction of our data catalog, we have an electromagnetically measured redshift. The detection, and cataloging, of these compact-object mergers will allow precision astronomy, and provide a determination of H_0 which is independent of the local distance scale.

Searching for anisotropic gravitational-wave backgrounds using pulsar timing arrays

We present the results of simulated injections testing the first Bayesian search-pipeline capable of investigating the angular-structure of a gravitational-wave (GW) background influencing pulsar signals. A stochastic background of GWs from the incoherent superposition of many inspiraling supermassive black hole binaries at nHz frequencies is likely to be the dominant GW signal detectable by pulsar timing arrays (PTAs). Even though one might expect a background composed of a high-redshift cosmological population of sources to be fairly isotropic, deviations from isotropy may be indicative of local GW hotspots or some form of continuous anisotropy in the angular-distribution of GW-power. A GWB induces time-of-arrival deviations in pulsar signals which are correlated between separated pulsars. In an isotropic background this cross-correlation follows a distinctive relationship, known as the Hellings and Downs curve, that depends only on the angular separation of the pulsars. If the background is anisotropic, the cross-correlation is different, but predictable, and also depends on the absolute position of the pulsars. By simulating datasets containing GWBs with various anisotropic configurations, we have explored the prospects for constraining anisotropy using near future data. We find that at moderate to high signal to noise ratio the assumption of isotropy is no longer an appropriate description of the simulated background. Furthermore, we can recover the nature of the injected anisotropy in a Bayesian parameter-estimation search, and propose a prior on the anisotropy search-space motivated by the physicality of the implied distribution of sources.

Graviton mass bounds from space-based gravitational-wave observations of massive black hole populations

Max-Planck Institut fu¨r Gravitationasphysik (Albert-Einstein-Institut),Am Mu¨hlenberg 1, D-14476, Potsdam, Germany(Dated: July 19, 2011)Space-based gravitational-wave (GW) detectors, such as LISA or a similar ESA-led mission, willoffer unique opportunities to test general relativity. We study the bounds that space-based detectorscould place on the graviton Compton wavelength λ