Gravitational Waves from Mergin Compact Binaries: How Accurately Can One Extract the Binary's Parameters from the Inspiral Waveform?

The most promising source of gravitational waves for the planned detectors LIGO and VIRGO are merging compact binaries, i.e., neutron star/neutron star (NS/NS), neutron star/black hole (NS/BH), and black hole/black-hole (BH/BH) binaries. We investigate how accurately the distance to the source and the masses and spins of the two bodies will be measured from the gravitational wave signals by the three detector LIGO/VIRGO network using ``advanced detectors'' (those present a few years after initial operation). The combination ${\cal M} \equiv (M_1 M_2)^{3/5}(M_1 +M_2)^{-1/5}$ of the masses of the two bodies is measurable with an accuracy $\approx 0.1\%-1\%$. The reduced mass is measurable to $\sim 10\%-15\%$ for NS/NS and NS/BH binaries, and $\sim 50\%$ for BH/BH binaries (assuming $10M_\odot$ BH's). Measurements of the masses and spins are strongly correlated; there is a combination of $\mu$ and the spin angular momenta that is measured to within $\sim 1\%$. We also estimate that distance measurement accuracies will be $\le 15\%$ for $\sim 8\%$ of the detected signals, and $\le 30\%$ for $\sim 60\%$ of the signals, for the LIGO/VIRGO 3-detector network.Comment: 103 pages, 20 figures, submitted to Phys Rev D, uses revtex macros, Caltech preprint GRP-36

Gravitational waves from eccentric compact binaries: Reduction in signal-to-noise ratio due to nonoptimal signal processing

Inspiraling compact binaries have been identified as one of the most promising sources of gravitational waves for interferometric detectors. Most of these binaries are expected to have circularized by the time their gravitational waves enter the instrument's frequency band. However, the possibility that some of the binaries might still possess a significant eccentricity is not excluded. We imagine a situation in which eccentric signals are received by the detector but not explicitly searched for in the data analysis, which uses exclusively circular waveforms as matched filters. We ascertain the likelihood that these filters, though not optimal, will nevertheless be successful at capturing the eccentric signals. We do this by computing the loss in signal-to-noise ratio incurred when searching for eccentric signals with those nonoptimal filters. We show that for a binary system of a given total mass, this loss increases with increasing eccentricity. We show also that for a given eccentricity, the loss decreases as the total mass is increased.Comment: 14 pages, 4 figures, ReVTeX; minor changes made after referee's comment

Measuring gravitational waves from binary black hole coalescences: I. Signal to noise for inspiral, merger, and ringdown

We estimate the expected signal-to-noise ratios (SNRs) from the three phases (inspiral,merger,ringdown) of coalescing binary black holes (BBHs) for initial and advanced ground-based interferometers (LIGO/VIRGO) and for space-based interferometers (LISA). LIGO/VIRGO can do moderate SNR (a few tens), moderate accuracy studies of BBH coalescences in the mass range of a few to about 2000 solar masses; LISA can do high SNR (of order 10^4) high accuracy studies in the mass range of about 10^5 to 10^8 solar masses. BBHs might well be the first sources detected by LIGO/VIRGO: they are visible to much larger distances (up to 500 Mpc by initial interferometers) than coalescing neutron star binaries (heretofore regarded as the "bread and butter" workhorse source for LIGO/VIRGO, visible to about 30 Mpc by initial interferometers). Low-mass BBHs (up to 50 solar masses for initial LIGO interferometers; 100 for advanced; 10^6 for LISA) are best searched for via their well-understood inspiral waves; higher mass BBHs must be searched for via their poorly understood merger waves and/or their well-understood ringdown waves. A matched filtering search for massive BBHs based on ringdown waves should be capable of finding BBHs in the mass range of about 100 to 700 solar masses out to 200 Mpc (initial LIGO interferometers), and 200 to 3000 solar masses out to about z=1 (advanced interferometers). The required number of templates is of order 6000 or less. Searches based on merger waves could increase the number of detected massive BBHs by a factor of order 10 or more over those found from inspiral and ringdown waves, without detailed knowledge of the waveform shapes, using a "noise monitoring" search algorithm. A full set of merger templates from numerical relativity could further increase the number of detected BBHs by an additional factor of up to 4.Comment: 40 pages, Revtex, psfig.tex, seven figures, submitted to Phys Rev

Equilibrium and stability of supermassive stars in binary systems

We investigate the equilibrium and stability of supermassive stars of mass M \agt 10^5M_{\odot} in binary systems. We find that corotating binaries are secularly unstable for close, circular orbits with r \alt 4R(M/10^6M_{\odot})^{1/6} where $r$ is the orbital separation and $R$ the stellar radius. We also show that corotation cannot be achieved for distant orbits with r \agt 12 R (M/10^6M_{\odot})^{-11/24}, since the timescale for viscous angular momentum transfer associated with tidal torques is longer than the evolution timescale due to emission of thermal radiation. These facts suggest that the allowed mass range and orbital separation for corotating supermassive binary stars is severely restricted. In particular, for supermassive binary stars of large mass M \agt 6\times 10^6M_{\odot}, corotation cannot be achieved, as viscosity is not adequate to mediate the transfer between orbital and spin angular momentum. One possible outcome for binary supermassive stars is the onset of quasi-radial, relativistic instability which drives each star to collapse prior to merger: We discuss alternative outcomes of collapse and possible spin states of the resulting black holes. We estimate the frequency and amplitude of gravitational waves emitted during several inspiral and collapse scenarios.Comment: 20 pages, to be published in PR

Gravitational waves from inspiralling compact binaries: Angular momentum flux, evolution of the orbital elements and the wave form to the second post-Newtonian order

The post-post-Newtonian (2PN) accurate mass quadrupole moment, for compact binaries of arbitrary mass ratio, moving in general orbits is obtained by the multi-polar post Minkowskian approach of Blanchet, Damour, and Iyer (BDI). Using this, for binaries in general orbits, the 2PN contributions to the gravitational waveform, and the associated far-zone energy and angular momentum fluxes are computed. For quasi-elliptic orbits, the energy and angular momentum fluxes are averaged over an orbital period, and employed to determine the 2PN corrections to the rate of decay of the orbital elements.Comment: 49 pages, No figures, accepted for publication in Phy. Rev. D (15

Second post-Newtonian gravitational wave polarizations for compact binaries in elliptical orbits

The second post-Newtonian (2PN) contribution to the `plus' and `cross' gravitational wave polarizations associated with gravitational radiation from non-spinning, compact binaries moving in elliptic orbits is computed. The computation starts from our earlier results on 2PN generation, crucially employs the 2PN accurate generalized quasi-Keplerian parametrization of elliptic orbits by Damour, Sch\"afer and Wex and provides 2PN accurate expressions modulo the tail terms for gravitational wave polarizations incorporating effects of eccentricity and periastron precession.Comment: 40 pages, 10 figures, To appear in Phys. Rev.

A Clustering Approach for Autism based Autistic Trait Classification

Machine learning (ML) techniques can be utilized by physicians, clinicians, as well as other users, to discover Autism Spectrum Disorder (ASD) symptoms based on historical cases and controls to enhance autism screening efficiency and accuracy. The aim of this study is to improve the performance of detecting ASD traits by reducing data dimensionality and eliminating redundancy in the autism dataset. To achieve this, a new semi-supervised ML framework approach called Clustering-based Autistic Trait Classification (CATC) is proposed that uses a clustering technique and validation of the classifiers is done by classification techniques. The proposed method identifies potential autism cases based on their similarity traits as opposed to a scoring function used by many ASD screening tools. Empirical results on different datasets involving children, adolescents, and adults were verified and compared to other common machine learning classification techniques. The results showed that CATC offers classifiers with higher predictive accuracy, sensitivity, and specificity rates than those of other intelligent classification approaches such as Artificial Neural Network (ANN), Random Forest, and Random Trees, and Rule Induction. These classifiers are useful as they are exploited by diagnosticians and other stakeholders involved in ASD screening

Taking a hike: Exploring leisure walkers embodied experiences

This paper uses walk along interviewing to investigate embodied experiences of walking on the South Downs Way, a long distance trail in southern England. Using a qualitative methodology - encompassing 93 walk-along interviews and auto-ethnographic reflections of two walker/researchers - it explores how walkers conceptualise their own walking experiences and captures this information while they are walking. It contributes to and extends the emerging body of literature which explores people’s experience, specifically aiming to develop a deeper understanding of leisure walking experiences in the dynamic space of the walk. It examines a range of bodily sensations and emotional states associated with the leisure walking experience in the context of temporal and environmental aspects, identifying those feelings that are innate and those which are mediated by external conditions. Current experiences intertwine with memories of other places and times in a process where connections are made between mind, body, the immediate physical environment, self and others, and disconnections from everyday life and the wider environment. These connections and disconnections create a sense of perspective, achievement and well-being

Shape recognition through multi-level fusion of features and classifiers

Shape recognition is a fundamental problem and a special type of image classification, where each shape is considered as a class. Current approaches to shape recognition mainly focus on designing low-level shape descriptors, and classify them using some machine learning approaches. In order to achieve effective learning of shape features, it is essential to ensure that a comprehensive set of high quality features can be extracted from the original shape data. Thus we have been motivated to develop methods of fusion of features and classifiers for advancing the classification performance. In this paper, we propose a multi-level framework for fusion of features and classifiers in the setting of gran-ular computing. The proposed framework involves creation of diversity among classifiers, through adopting feature selection and fusion to create diverse feature sets and to train diverse classifiers using different learn-Xinming Wang algorithms. The experimental results show that the proposed multi-level framework can effectively create diversity among classifiers leading to considerable advances in the classification performance

Elusive Copy Number Variation in the Mouse Genome

Array comparative genomic hybridization (aCGH) to detect copy number variants (CNVs) in mammalian genomes has led to a growing awareness of the potential importance of this category of sequence variation as a cause of phenotypic variation. Yet there are large discrepancies between studies, so that the extent of the genome affected by CNVs is unknown. We combined molecular and aCGH analyses of CNVs in inbred mouse strains to investigate this question.Using a 2.1 million probe array we identified 1,477 deletions and 499 gains in 7 inbred mouse strains. Molecular characterization indicated that approximately one third of the CNVs detected by the array were false positives and we estimate the false negative rate to be more than 50%. We show that low concordance between studies is largely due to the molecular nature of CNVs, many of which consist of a series of smaller deletions and gains interspersed by regions where the DNA copy number is normal.Our results indicate that CNVs detected by arrays may be the coincidental co-localization of smaller CNVs, whose presence is more likely to perturb an aCGH hybridization profile than the effect of an isolated, small, copy number alteration. Our findings help explain the hitherto unexplored discrepancies between array-based studies of copy number variation in the mouse genome