arXiv subjects

Edward K. Porter

Publications and source records attributed to Edward K. Porter.

47 records · Page 3Linked to original sources

arXiv2006

MCMC Exploration of Supermassive Black Hole Binary Inspirals

The Laser Interferometer Space Antenna will be able to detect the inspiral and merger of Super Massive Black Hole Binaries (SMBHBs) anywhere in the Universe. Standard matched filtering techniques can be used to detect and characterize these systems. Markov Chain Monte Carlo (MCMC) methods are ideally suited to this and other LISA data analysis problems as they are able to efficiently handle models with large dimensions. Here we compare the posterior parameter distributions derived by an MCMC algorithm with the distributions predicted by the Fisher information matrix. We find excellent agreement for the extrinsic parameters, while the Fisher matrix slightly overestimates errors in the intrinsic parameters.

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arXiv2006

Catching Super Massive Black Hole Binaries Without a Net

The gravitational wave signals from coalescing Supermassive Black Hole Binaries are prime targets for the Laser Interferometer Space Antenna (LISA). With optimal data processing techniques, the LISA observatory should be able to detect black hole mergers anywhere in the Universe. The challenge is to find ways to dig the signals out of a combination of instrument noise and the large foreground from stellar mass binaries in our own galaxy. The standard procedure of matched filtering against a grid of templates can be computationally prohibitive, especially when the black holes are spinning or the mass ratio is large. Here we develop an alternative approach based on Metropolis-Hastings sampling and simulated annealing that is orders of magnitude cheaper than a grid search. We demonstrate our approach on simulated LISA data streams that contain the signals from binary systems of Schwarzschild Black Holes, embedded in instrument noise and a foreground containing 26 million galactic binaries. The search algorithm is able to accurately recover the 9 parameters that describe the black hole binary without first having to remove any of the bright foreground sources, even when the black hole system has low signal-to-noise.

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arXiv2005

A new and improved template for the detection of gravitational waves from compact binary systems using Chebyshev polynomials

We introduce a new template for the detection of gravitational waves from compact binary systems which is based on Chebyshev polynomials of the first kind. As well as having excellent convergence properties, these polynomials are also very closely related to the elusive minimax polynomial. In this study we have limited ourselves to the test-mass regime, where we model a test particle in a circular equatorial orbit around a Schwarzschild black hole. Our objective is to model the numerical gravitational wave flux function, starting with the post-Newtonian expansion from Black Hole Perturbation Theory. We introduce a new Chebyshev approximation to the flux function, which due to a process called Chebyshev economization gives a better model than either post-Newtonian or Pade based methods. A graphical examination of the new flux function shows that it gives an excellent fit to the numerical flux, but more importantly we find that at the last stable orbit the error is reduced, < 1.8%, at all orders of approximation. We also find that the templates constructed using the Chebyshev approximation give better fitting factors, in general > 0.99, and smaller errors, < 1/10%, in the estimation of the Chirp mass when compared to a fiducial exact waveform, constructed using the numerical flux and the exact expression for the orbital energy function, again at all orders of approximation. We also show that in the test-mass case, the new Chebyshev template is superior to both PN and Pade approximant templates, especially at lower orders of approximation.

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arXiv2005

Detecting gravitational waves from test-mass bodies orbiting a Kerr black hole with P-approximant templates

In this study we apply post-Newtonian (T-approximants) and resummed post-Newtonian (P-approximants) to the case of a test-particle in equatorial orbit around a Kerr black hole. We compare the two approximants by measuring their effectualness (i.e. larger overlaps with the exact signal), and faithfulness (i.e. smaller biases while measuring the parameters of the signal) with the exact (numerical) waveforms. We find that in the case of prograde orbits, T-approximant templates obtain an effectualness of ~0.99 for spins q < 0.75. For 0.75 < q < 0.95, the effectualness drops to about 0.82. The P-approximants achieve effectualness of > 0.99 for all spins up to q = 0.95. The bias in the estimation of parameters is much lower in the case of P-approximants than T-approximants. We find that P-approximants are both effectual and faithful and should be more effective than T-approximants as a detection template family when q > 0. For q < 0 both T- and P-approximants perform equally well so that either of them could be used as a detection template family. However, for parameter estimation, the P-approximant templates still outperforms the T-approximants.

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arXiv2005

Detecting Galactic Binaries with LISA

One of the main sources of gravitational waves for the LISA space-borne interferometer are galactic binary systems. The waveforms for these sources are represented by eight parameters, of which four are extrinsic, and four are intrinsic to the system. Geometrically, these signals exist in an 8-d parameter space. By calculating the metric tensor on this space, we calculate the number of templates needed to search for such sources. We show in this study that below a particular monochromatic frequency, we can ignore one of the intrinsic parameters and search over a 7-d space. Beyond this frequency, we have a sudden change in dimensionality of the parameter space from 7 to 8 dimensions, which results in a change in the scaling of the growth of template number as a function of monochromatic frequency.

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arXiv2004

Improved gravitational waveforms from spinning black hole binaries

The standard post-Newtonian approximation to gravitational waveforms, called T-approximants, from non-spinning black hole binaries are known not to be sufficiently accurate close to the last stable orbit of the system. A new approximation, called P-approximants, is believed to improve the accuracy of the waveforms rendering them applicable up to the last stable orbit. In this study we apply P-approximants to the case of a test-particle in equatorial orbit around a Kerr black hole parameterized by a spin parameter q that takes values between -1 and 1. In order to assess the performance of the two approximants we measure their effectualness (i.e. larger overlaps with the exact signal), and faithfulness (i.e. smaller biases while measuring the parameters of the signal) with the exact (numerical) waveforms. We find that in the case of prograde orbits, that is orbits whose angular momentum is in the same sense as the spin angular momentum of the black hole, T-approximant templates obtain an effectualness of ~ 0.99 for spins q < 0.75. For 0.75 < q < 0.95, the effectualness drops to about 0.82. The P-approximants achieve effectualness of > 0.99 for all spins up to q = 0.95. The bias in the estimation of parameters is much lower in the case of P-approximants than T-approximants. We find that P-approximants are both effectual and faithful and should be more effective than T-approximants as a detection template family when q>0. For q<0 both T- and P-approximants perform equally well so that either of them could be used as a detection template family.

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arXiv2003

Detection of a close supernova gravitational wave burst in a network of interferometers, neutrino and optical detectors

Trying to detect the gravitational wave (GW) signal emitted by a type II supernova is a main challenge for the GW community. Indeed, the corresponding waveform is not accurately modeled as the supernova physics is very complex; in addition, all the existing numerical simulations agree on the weakness of the GW emission, thus restraining the number of sources potentially detectable. Consequently, triggering the GW signal with a confidence level high enough to conclude directly to a detection is very difficult, even with the use of a network of interferometric detectors. On the other hand, one can hope to take benefit from the neutrino and optical emissions associated to the supernova explosion, in order to discover and study GW radiation in an event already detected independently. This article aims at presenting some realistic scenarios for the search of the supernova GW bursts, based on the present knowledge of the emitted signals and on the results of network data analysis simulations. Both the direct search and the confirmation of the supernova event are considered. In addition, some physical studies following the discovery of a supernova GW emission are also mentioned: from the absolute neutrino mass to the supernova physics or the black hole signature, the potential spectrum of discoveries is wide.

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arXiv2003

Coincidence and coherent data analysis methods for gravitational wave bursts in a network of interferometric detectors

Network data analysis methods are the only way to properly separate real gravitational wave (GW) transient events from detector noise. They can be divided into two generic classes: the coincidence method and the coherent analysis. The former uses lists of selected events provided by each interferometer belonging to the network and tries to correlate them in time to identify a physical signal. Instead of this binary treatment of detector outputs (signal present or absent), the latter method involves first the merging of the interferometer data and looks for a common pattern, consistent with an assumed GW waveform and a given source location in the sky. The thresholds are only applied later, to validate or not the hypothesis made. As coherent algorithms use a more complete information than coincidence methods, they are expected to provide better detection performances, but at a higher computational cost. An efficient filter must yield a good compromise between a low false alarm rate (hence triggering on data at a manageable rate) and a high detection efficiency. Therefore, the comparison of the two approaches is achieved using so-called Receiving Operating Characteristics (ROC), giving the relationship between the false alarm rate and the detection efficiency for a given method. This paper investigates this question via Monte-Carlo simulations, using the network model developed in a previous article.

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arXiv2003

Comparison of filters for detecting gravitational wave bursts in interferometric detectors

Filters developed in order to detect short bursts of gravitational waves in interferometric detector outputs are compared according to three main points. Conventional Receiver Operating Characteristics (ROC) are first built for all the considered filters and for three typical burst signals. Optimized ROC are shown for a simple pulse signal in order to estimate the best detection efficiency of the filters in the ideal case, while realistic ones obtained with filters working with several ``templates'' show how detection efficiencies can be degraded in a practical implementation. Secondly, estimations of biases and statistical errors on the reconstruction of the time of arrival of pulse-like signals are then given for each filter. Such results are crucial for future coincidence studies between Gravitational Wave detectors but also with neutrino or optical detectors. As most of the filters require a pre-whitening of the detector noise, the sensitivity to a non perfect noise whitening procedure is finally analysed. For this purpose lines of various frequencies and amplitudes are added to a Gaussian white noise and the outputs of the filters are studied in order to monitor the excess of false alarms induced by the lines. The comparison of the performances of the different filters finally show that they are complementary rather than competitive.

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arXiv2003

An elliptical tiling method to generate a 2-dimensional set of templates for gravitational wave search

Searching for a signal depending on unknown parameters in a noisy background with matched filtering techniques always requires an analysis of the data with several templates in parallel in order to ensure a proper match between the filter and the real waveform. The key feature of such an implementation is the design of the filter bank which must be small to limit the computational cost while keeping the detection efficiency as high as possible. This paper presents a geometrical method which allows one to cover the corresponding physical parameter space by a set of ellipses, each of them being associated to a given template. After the description of the main characteristics of the algorithm, the method is applied in the field of gravitational wave (GW) data analysis, for the search of damped sine signals. Such waveforms are expected to be produced during the de-excitation phase of black holes -- the so-called 'ringdown' signals -- and are also encountered in some numerically computed supernova signals.

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arXiv2002

Computational Resources to Filter Gravitational Wave Data with P-approximant Templates

The prior knowledge of the gravitational waveform from compact binary systems makes matched filtering an attractive detection strategy. This detection method involves the filtering of the detector output with a set of theoretical waveforms or templates. One of the most important factors in this strategy is knowing how many templates are needed in order to reduce the loss of possible signals. In this study we calculate the number of templates and computational power needed for a one-step search for gravitational waves from inspiralling binary systems. We build on previous works by firstly expanding the post-Newtonian waveforms to 2.5-PN order and secondly, for the first time, calculating the number of templates needed when using P-approximant waveforms. The analysis is carried out for the four main first-generation interferometers, LIGO, GEO600, VIRGO and TAMA. As well as template number, we also calculate the computational cost of generating banks of templates for filtering GW data. We carry out the calculations for two initial conditions. In the first case we assume a minimum individual mass of $1 M_{\odot}$ and in the second, we assume a minimum individual mass of $5 M_{\odot}$. We find that, in general, we need more P-approximant templates to carry out a search than if we use standard PN templates. This increase varies according to the order of PN-approximation, but can be as high as a factor of 3 and is explained by the smaller span of the P-approximant templates as we go to higher masses. The promising outcome is that for 2-PN templates the increase is small and is outweighed by the known robustness of the 2-PN P-approximant templates.

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