arXiv subjects

Joseph D. Romano

Publications and source records attributed to Joseph D. Romano.

At least 91 records · Page 5Linked to original sources

arXiv2013

A Rømer time-delay determination of the gravitational-wave propagation speed

In 1676 Olaus Rømer presented the first observational evidence for a finite light velocity $\cem$. He formed his estimate by attributing the periodically varying discrepancy between the observed and expected occultation times of the Galilean satellite Io by its planetary host Jupiter to the time it takes light to cross Earth's orbital diameter. Given a stable celestial clock that can be observed in gravitational waves the same principle can be used to measure the propagation speed $\cgw$ of gravitational radiation. Space-based "LISA"-like detectors will, and terrestrial LIGO-like detectors may, observe such clocks and thus be capable of directly measuring the propagation velocity of gravitational waves. In the case of space-based detectors the clocks will be galactic close white dwarf binary systems; in the case of terrestrial detectors, the most likely candidate clock is the periodic gravitational radiation from a rapidly rotating non-axisymmetric neutron star. Here we evaluate the accuracy that may be expected of such a Rømer-type measurement of $\cgw$ by foreseeable future space-based and terrestrial detectors. For space-based, LISA-like detectors, periodic sources are plentiful: by the end of the first year of scientific operations a LISA-like detector will have measured $\cgw$ to better than a part in a thousand. Periodic sources may not be accessible in terrestrial detectors available to us in the foreseeable future; however, if such a source is detected then with a year of observations we could measure $\cgw$ to better than a part in a million.

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arXiv2012

Treatment of Calibration Uncertainty in Multi-Baseline Cross-Correlation Searches for Gravitational Waves

Uncertainty in the calibration of gravitational-wave (GW) detector data leads to systematic errors which must be accounted for in setting limits on the strength of GW signals. When cross-correlation measurements are made using data from a pair of instruments, as in searches for a stochastic GW background, the calibration uncertainties of the individual instruments can be combined into an uncertainty associated with the pair. With the advent of multi-baseline GW observation (e.g., networks consisting of multiple detectors such as the LIGO observatories and Virgo), a more sophisticated treatment is called for. We describe how the correlations between calibration factors associated with different pairs can be taken into account by marginalizing over the uncertainty associated with each instrument.

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arXiv2012

In an expanding universe, what doesn't expand?

The expansion of the universe is often viewed as a uniform stretching of space that would affect compact objects, atoms and stars, as well as the separation of galaxies. One usually hears that bound systems do not take part in the general expansion, but a much more subtle question is whether bound systems expand partially. In this paper, a very definitive answer is given for a very simple system: a classical "atom" bound by electrical attraction. With a mathemical description appropriate for undergraduate physics majors, we show that this bound system either completely follows the cosmological expansion, or -- after initial transients -- completely ignores it. This "all or nothing" behavior can be understood with techniques of junior-level mechanics. Lastly, the simple description is shown to be a justifiable approximation of the relativistically correct formulation of the problem.

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arXiv2009

Probing the anisotropies of a stochastic gravitational-wave background using a network of ground-based laser interferometers

We present a maximum-likelihood analysis for estimating the angular distribution of power in an anisotropic stochastic gravitational-wave background using ground-based laser interferometers. The standard isotropic and gravitational-wave radiometer searches (optimal for point sources) are recovered as special limiting cases. The angular distribution can be decomposed with respect to any set of basis functions on the sky, and the single-baseline, cross-correlation analysis is easily extended to a network of three or more detectors-that is, to multiple baselines. A spherical harmonic decomposition, which provides maximum-likelihood estimates of the multipole moments of the gravitational-wave sky, is described in detail. We also discuss: (i) the covariance matrix of the estimators and its relationship to the detector response of a network of interferometers, (ii) a singular-value decomposition method for regularizing the deconvolution of the detector response from the measured sky map, (iii) the expected increase in sensitivity obtained by including multiple baselines, and (iv) the numerical results of this method when applied to simulated data consisting of both point-like and di#use sources. Comparisions between this general method and the standard isotropic and radiometer searches are given throughout, to make contact with the existing literature on stochastic background searches.

astro-ph.IM↗

arXiv2009

Detecting a Stochastic Gravitational-Wave Background: The Overlap Reduction Function

Detection of a gravitational-wave stochastic background via ground or space-based gravitational-wave detectors requires the cross-correlation of the response of two or more independent detectors. The cross-correlation involves a frequency-dependent factor -- the so-called overlap reduction function or Hellings-Downs curve -- that depends on the relative geometry of each detector pair: i.e., the detector separations and the relative orientation of their antenna patterns (beams). An incorrect formulation of this geometrical factor has appeared in the literature, leading to incorrect conclusions regarding the sensitivity of proposed detectors to a stochastic gravitational-wave background. To rectify these errors and as a reference for future work we provide here a complete, first-principles derivation of the overlap reduction function and assess the nature of the errors associated with the use of the incorrect expression that has appeared in the literature. We describe the behavior of the overlap reduction function in different limiting regimes, and show how the difference between the correct and incorrect expressions can be understood physically.

gr-qc↗

arXiv2002

Robust statistics for deterministic and stochastic gravitational waves in non-Gaussian noise. II: Bayesian analyses

In a previous paper (gr-qc/0105100) we derived a set of near-optimal signal detection techniques for gravitational wave detectors whose noise probability distributions contain non-Gaussian tails. The methods modify standard methods by truncating sample values which lie in those non-Gaussian tails. The methods were derived, in the frequentist framework, by minimizing false alarm probabilities at fixed false detection probability in weak signal limit. For stochastic signals, the resulting statistic consisted of a sum of an auto-correlation term and a cross-correlation term; it was necessary to discard by hand the auto-correlation term to obtain the correct, generalized cross-correlation statistic. In the present paper, we present an alternative Bayesian derivation of the same signal detection techniques. We compute the probability that a signal is present in the data, in the limit where the signal-to-noise ratio squared per frequency bin is small, where the integrated signal-to-noise ratio is large compared to one, and where the total probability in the non-Gaussian tail part of the noise distribution is small. We show that, for each model considered, the resulting probability is to a good approximation a monotonic function of the detection statistic derived in the previous paper. Moreover, for stochastic signals, the new Bayesian derivation automatically eliminates the problematic auto-correlation term.

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arXiv2001

Robust statistics for deterministic and stochastic gravitational waves in non-Gaussian noise I: Frequentist analyses

Gravitational wave detectors will need optimal signal-processing algorithms to extract weak signals from the detector noise. Most algorithms designed to date are based on the unrealistic assumption that the detector noise may be modeled as a stationary Gaussian process. However most experiments exhibit a non-Gaussian ``tail'' in the probability distribution. This ``excess'' of large signals can be a troublesome source of false alarms. This article derives an optimal (in the Neyman-Pearson sense, for weak signals) signal processing strategy when the detector noise is non-Gaussian and exhibits tail terms. This strategy is robust, meaning that it is close to optimal for Gaussian noise but far less sensitive than conventional methods to the excess large events that form the tail of the distribution. The method is analyzed for two different signal analysis problems: (i) a known waveform (e.g., a binary inspiral chirp) and (ii) a stochastic background, which requires a multi-detector signal processing algorithm. The methods should be easy to implement: they amount to truncation or clipping of sample values which lie in the outlier part of the probability distribution.

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arXiv2001

Progress on stochastic background search codes for LIGO

One of the types of signals for which the LIGO interferometric gravitational wave detectors will search is a stochastic background of gravitational radiation. We review the technique of searching for a background using the optimally-filtered cross-correlation statistic, and describe the state of plans to perform such cross-correlations between the two LIGO interferometers as well as between LIGO and other gravitational-wave detectors, in particular the preparation of software to perform such data analysis.

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arXiv1999

Quasistationary binary inspiral. I. Einstein equations for the two Killing vector spacetime

The geometry of two infinitely long lines of mass moving in a fixed circular orbit is considered as a toy model for the inspiral of a binary system of compact objects due to gravitational radiation. The two Killing fields in the toy model are used, according to a formalism introduced by Geroch, to describe the geometry entirely in terms of a set of tensor fields on the two-manifold of Killing vector orbits. Geroch's derivation of the Einstein equations in this formalism is streamlined and generalized. The explicit Einstein equations for the toy model spacetime are derived in terms of the degrees of freedom which remain after a particular choice of gauge.

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arXiv1999

Detecting an association between Gamma Ray and Gravitational Wave Bursts

If $γ$-ray bursts (GRBs) are accompanied by gravitational wave bursts (GWBs) the correlated output of two gravitational wave detectors evaluated in the moments just prior to a GRB will differ from that evaluated at times not associated with a GRB. We can test for this difference independently of any model of the GWB signal waveform. If we invoke a model for the GRB source population and GWB radiation spectral density we can find a confidence interval or upper limit on the root-mean-square GWB signal amplitude in the detector waveband. To illustrate we adopt a simple, physically motivated model and estimate that initial LIGO detector observations coincident with 1000 GRBs could lead us to exclude, with 95% confidence, associated GWBs with $h_{RMS} \gtrsim 1.7 \times 10^{-22}$. This result does not require the detector noise be Gaussian or that any inter-detector correlated noise be measured or measurable; it does not require advanced or a priori knowledge of the source waveform; and the limits obtained on the wave-strength improve with the number of observed GRBs.

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arXiv1997

Detecting a stochastic background of gravitational radiation: Signal processing strategies and sensitivities

We analyze the signal processing required for the optimal detection of a stochastic background of gravitational radiation using laser interferometric detectors. Starting with basic assumptions about the statistical properties of a stochastic gravity-wave background, we derive expressions for the optimal filter function and signal-to-noise ratio for the cross-correlation of the outputs of two gravity-wave detectors. Sensitivity levels required for detection are then calculated. Issues related to: (i) calculating the signal-to-noise ratio for arbitrarily large stochastic backgrounds, (ii) performing the data analysis in the presence of nonstationary detector noise, (iii) combining data from multiple detector pairs to increase the sensitivity of a stochastic background search, (iv) correlating the outputs of 4 or more detectors, and (v) allowing for the possibility of correlated noise in the outputs of two detectors are discussed. We briefly describe a computer simulation which mimics the generation and detection of a simulated stochastic gravity-wave signal in the presence of simulated detector noise. Numerous graphs and tables of numerical data for the five major interferometers (LIGO-WA, LIGO-LA, VIRGO, GEO-600, and TAMA-300) are also given. The treatment given in this paper should be accessible to both theorists involved in data analysis and experimentalists involved in detector design and data acquisition.

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arXiv1996

Dirac Constraint Quantization of a Dilatonic Model of Gravitational Collapse

We present an anomaly-free Dirac constraint quantization of the string-inspired dilatonic gravity (the CGHS model) in an open 2-dimensional spacetime. We show that the quantum theory has the same degrees of freedom as the classical theory; namely, all the modes of the scalar field on an auxiliary flat background, supplemented by a single additional variable corresponding to the primordial component of the black hole mass. The functional Heisenberg equations of motion for these dynamical variables and their canonical conjugates are linear, and they have exactly the same form as the corresponding classical equations. A canonical transformation brings us back to the physical geometry and induces its quantization.

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arXiv1995

Internal Time Formalism for Spacetimes with Two Killing Vectors

The Hamiltonian structure of spacetimes with two commuting Killing vector fields is analyzed for the purpose of addressing the various problems of time that arise in canonical gravity. Two specific models are considered: (i) cylindrically symmetric spacetimes, and (ii) toroidally symmetric spacetimes, which respectively involve open and closed universe boundary conditions. For each model canonical variables which can be used to identify points of space and instants of time, {\it i.e.}, internally defined spacetime coordinates, are identified. To do this it is necessary to extend the usual ADM phase space by a finite number of degrees of freedom. Canonical transformations are exhibited that identify each of these models with harmonic maps in the parametrized field theory formalism. The identifications made between the gravitational models and harmonic map field theories are completely gauge invariant, that is, no coordinate conditions are needed. The degree to which the problems of time are resolved in these models is discussed.

gr-qc↗

arXiv1995

Spherically Symmetric Scalar Field Collapse: An Example of the Spacetime Problem of Time

A canonical formalism for spherical symmetry, originally developed by Kuchař to describe vacuum Schwarzschild black holes, is extended to include a spherically symmetric, massless, scalar field source. By introducing the ADM mass as a canonical coordinate on phase space, one finds that the super-Hamiltonian and supermomentum constraints for the coupled system simplify considerably. Yet, despite this simplification, it is difficult to find a functional time formalism for the theory. First, the configuration variable that played the role of time for the vacuum theory is no longer a spacetime scalar once spherically symmetric matter is coupled to gravity. Second, although it is possible to perform a canonical transformation to a new set of variables in terms of which the super-Hamiltonian and supermomentum constraints can be solved, the new time variable also fails to be a spacetime scalar. As such, our solutions suffer from the so-called {\it spacetime problem of time}. A candidate for a time variable that {\it is} a spacetime scalar is presented. Problems with turning this variable into a canonical coordinate on phase space are discussed.

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arXiv1995

Gravitational Constraints which Generate a Lie Algebra

The coupling of gravity to dust helps to discover simple quadratic combinations of the gravitational super-Hamiltonian and supermomentum whose Poisson brackets strongly vanish. This leads to a new form of vacuum constraints which generate a true Lie algebra. We show that the coupling of gravity to a massless scalar field leads to yet another set of constraints with the same property, albeit not as simple as that based on the coupling to dust.

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arXiv1994

Embedding initial data for black hole collisions

We discuss isometric embedding diagrams for the visualization of initial data for the problem of the head-on collision of two black holes. The problem of constructing the embedding diagrams is explicitly presented for the best studied initial data, the Misner geometry. We present a partial solution of the embedding diagrams and discuss issues related to completing the solution.

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arXiv1993

On the Constraint Algebra of Degenerate Relativity

As shown by Ashtekar in the mid 80's, general relativity can be extended to incorporate degenerate metrics. This extension is not unique, however, as one can change the form of the hamiltonian constraints and obtain an {\it alternative} degenerate extension of general relativity that disagrees with Ashtekar's original theory when the triads vectors are degenerate. In this paper, the constraint algebra of a particular alternative theory is explicitly evaluated and compared with that of Ashtekar's original degenerate extension. A generic classification of the difference between the two theories is given in terms of the degeneracy and surface-forming properties of the triad vectors. (This classification is valid when the degeneracy and surface-forming properties of the triad vectors is the same everywhere in an open set about a point in space.) If the triad vectors are degenerate and surface-forming, then all the secondary constraints of the alternative degenerate extension are satisfied as a consequence of the primary constraints, and the constraints of this theory are weaker than those of Ashtekar's. If the degenerate triad vectors are not surface-forming, then the first secondary constraint of the alternative theory already implies equivalence with Ashtekar's degenerate extension. What happens when the degeneracy and surface-forming properties of the triad vectors change from point to point is an open question.

gr-qc↗

arXiv1993

Geometrodynamics vs. Connection Dynamics

The purpose of this review is to describe in some detail the mathematical relationship between geometrodynamics and connection dynamics in the context of the classical theories of 2+1 and 3+1 gravity. I analyze the standard Einstein-Hilbert theory (in any spacetime dimension), the Palatini and Chern-Simons theories in 2+1 dimensions, and the Palatini and self-dual theories in 3+1 dimensions. I also couple various matter fields to these theories and briefly describe a pure spin-connection formulation of 3+1 gravity. I derive the Euler-Lagrange equations of motion from an action principle and perform a Legendre transform to obtain a Hamiltonian formulation of each theory. Since constraints are present in all these theories, I construct constraint functions and analyze their Poisson bracket algebra. I demonstrate, whenever possible, equivalences between the theories.

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