122439729
APPROXIMATE GRAVITATIONAL WAVES VIA DEFORMATIONS OF EMBEDDINGS
Many Einstein spaces can be embedded globally in pseudo-Euclidean spaces of dimension N > 4. The geometrical quantities characterizing the embedded manifold can be expressed by means of derivatives of the embedding functions zA (xµ), A, B, = 1, 2, …N, µ, ν, …= 0, 1, 2, 3. An infinitesimal deformation of embedding can be expanded into a series ${\tilde{z}}^A = z^A (x^{\mu}) + \varepsilon v^A \, (x^{\mu}) + \varepsilon^2 w^A \, (x^{\mu}) +.$, giving rise to a similar expansion of geometrical quantities of the embedded Einstein space, and the Einstein equations in vacuo, too. We show how gravitational wave solutions appear naturally in this context.
118457757
Towards a generic test of the strong field dynamics of general relativity using compact binary coalescence
Coalescences of binary neutron stars and/or black holes are amongst the most likely gravitational-wave signals to be observed in ground based interferometric detectors. Apart from the astrophysical importance of their detection, they will also provide us with our very first empirical access to the genuinely strong-field dynamics of General Relativity (GR). We present a new framework based on Bayesian model selection aimed at detecting deviations from GR, subject to the constraints of the Advanced Virgo and LIGO detectors. The method tests the consistency of coefficients appearing in the waveform with the predictions made by GR, without relying on any specific alternative theory of gravity. The framework is suitable for low signal-to-noise ratio events through the construction of multiple subtests, most of which involve only a limited number of coefficients. It also naturally allows for the combination of information from multiple sources to increase one's confidence in GR or a violation thereof. We expect it to be capable of finding a wide range of possible deviations from GR, including ones which in principle cannot be accommodated by the model waveforms, on condition that the induced change in phase at frequencies where the detectors are the most sensitive is comparable to the effect of a few percent change in one or more of the low-order post-Newtonian phase coefficients. In principle the framework can be used with any GR waveform approximant, with arbitrary parameterized deformations, to serve as model waveforms. In order to illustrate the workings of the method, we perform a range of numerical experiments in which simulated gravitational waves modeled in the restricted post-Newtonian, stationary phase approximation are added to Gaussian and stationary noise that follows the expected Advanced LIGO/Virgo noise curves.
118465419
Parameter estimation from gravitational waves generated by nonspinning binary black holes with laser interferometers: Beyond the Fisher information
In this paper we apply to gravitational waves from nonspinning binary systems a recently introduced frequentist methodology to calculate analytically the error for a maximum likelihood estimate of physical parameters. While existing literature focuses on using the Cramer Rao Lower bound and Monte Carlo simulations, we use a power expansion of the bias and covariance in inverse powers of the signal to noise ratio. The use of higher order derivatives of the likelihood function in the expansions makes the prediction also sensitive to the secondary lobes of the maximum likelihood estimate probability distribution. We discuss conditions for validity of the Cramer Rao Lower bound and predict new features in regions of the parameter space currently not explored. For example, we see how the bias can become the most important contributor to the parameters' errors for high mass systems (200M(circle dot) and above).
120094772
Gravitational waves as deformations of embedded Einstein spaces
We show how approximate radiative solutions of Einstein's equations can be constructed using small deformations of Einstein spacetimes embedded into a pseudo-Euclidean flat space of higher dimension. Infinitesimal deformations are seen then as vector fields in EN. All geometrical quantities can be then expressed in terms of embedding functions zA and their deformations . Then we require the deformations to keep Einstein equations satisfied up to a given order in e. The system obtained is then analyzed in particular cases of the Minkowski and Schwarzschild manifolds taken as a starting point, and solutions of deformations of Einstein's equations displaying radiative behavior are found up to the third order of expansion in small parameter e.
13092497
Application of asymptotic expansions for maximum likelihood estimators errors to gravitational waves from binary mergers: The single interferometer case
In this paper we apply to gravitational waves (GW) from the inspiral phase of binary systems a recently derived frequentist methodology to calculate analytically the error for a maximum likelihood estimate of physical parameters. We use expansions of the covariance and the bias of a maximum likelihood estimate in terms of inverse powers of the signal-to-noise ration (SNR)s where the square root of the first order in the covariance expansion is the Cramer Rao lower bound (CRLB). We evaluate the expansions, for the first time, for GW signals in noises of GW interferometers. The examples are limited to a single, optimally oriented, interferometer. We also compare the error estimates using the first two orders of the expansions with existing numerical Monte Carlo simulations. The first two orders of the covariance allow us to get error predictions closer to what is observed in numerical simulations than the CRLB. The methodology also predicts a necessary SNR to approximate the error with the CRLB and provides new insight on the relationship between waveform properties, SNR, dimension of the parameter space and estimation errors. For example the timing match filtering can achieve the CRLB only if the SNR is larger than the Kurtosis ofmore » the gravitational wave spectrum and the necessary SNR is much larger if other physical parameters are also unknown.« less
59497924
Towards a generic test of the strong field dynamics of general relativity using compact binary coalescence: Further investigations
In this paper we elaborate on earlier work by the same authors in which a novel Bayesian inference framework for testing the strong-field dynamics of General Relativity using coalescing compact binaries was proposed. Unlike methods that were used previously, our technique addresses the question whether one or more 'testing coefficients' (e.g. in the phase) parameterizing deviations from GR are non-zero, rather than all of them differing from zero at the same time. The framework is well-adapted to a scenario where most sources have low signal-to-noise ratio, and information from multiple sources as seen in multiple detectors can readily be combined. In our previous work, we conjectured that this framework can detect generic deviations from GR that can in principle not be accomodated by our model waveforms, on condition that the change in phase near frequencies where the detectors are the most sensitive is comparable to that induced by simple shifts in the lower-order phase coefficients of more than a few percent (~ 5 radians at 150 Hz). To further support this claim, we perform additional numerical experiments in Gaussian and stationary noise according to the expected Advanced LIGO/Virgo noise curves, and coherently injecting signals into the network whose phasing differs structurally from the predictions of GR, but with the magnitude of the deviation still being small. We find that even then, a violation of GR can be established with good confidence.
56213633
LISA Pathfinder: the experiment and the route to LISA
LISA Pathfinder (LPF) is a science and technology demonstrator planned by the European Space Agency in view of the LISA mission. As a scientific payload, the LISA Technology Package on board LPF will be the most precise geodesics explorer flown as of today, both in terms of displacement and acceleration sensitivity. The challenges embodied by LPF make it a unique mission, paving the way towards the space-borne detection of gravitational waves with LISA. This paper summarizes the basics of LPF, and the progress made in preparing its effective implementation in flight. We hereby give an overview of the experiment philosophy and assumptions to carry on the measurement. We report on the mission plan and hardware design advances and on the progress on detailing measurements and operations. Some light will be shed on the related data processing algorithms. In particular, we show how to single out the acceleration noise from the spacecraft motion perturbations, how to account for dynamical deformation parameters distorting the measurement reference and how to decouple the actuation noise via parabolic free flight.
122302793
Superfluid /sup 4/He analog of the rf superconducting quantum interference device and the detection of inertial and gravitational fields
Superfluid /sup 4/He filling a thin torus, interrupted by N weak links in series, is found to give an angular momentum contribution which depends parametrically on the steady absolute rotation of the torus. This in principle enables one to determine off-diagonal components of the local metric. Recent claims for a surprisingly high sensitivity of a similar system to gravitational waves and Lense-Thirring fields are unfortunately ill founded.
122580743
LISA Pathfinder data analysis
As the launch of LISA Pathfinder (LPF) draws near, more and more effort is being put in to the preparation of the data analysis activities that will be carried out during the mission operations. The operations phase of the mission will be composed of a series of experiments that will be carried out on the satellite. These experiments will be directed and analysed by the data analysis team, which is part of the operations team. The operations phase will last about 90 days, during which time the data analysis team aims to fully characterize the LPF, and in particular, its core instrument the LISA Technology Package. By analysing the various couplings present in the system, the different noise sources that will disturb the system, and through the identification of the key physical parameters of the system, a detailed noise budget of the instrument will be constructed that will allow the performance of the different subsystems to be assessed and projected towards LISA. This paper describes the various aspects of the full data analysis chain that are needed to successfully characterize the LPF and build up the noise budget during mission operations.
53667063
Upper limits to surface-force disturbances on LISA proof masses and the possibility of observing galactic binaries
We have measured surface-force noise on a hollow replica of a LISA proof mass surrounded by its capacitive motion sensor. Forces are detected through the torque exerted on the proof mass by means of a torsion pendulum in the 0.1-30 mHz range. The sensor and electronics have the same design as for the flight hardware, including 4 mm gaps around the proof mass. The measured upper limit for forces would allow detection of a number of galactic binaries signals with signal-to-noise ratio up to {approx_equal}40 for 1 yr integration. We also discuss how LISA Pathfinder will substantially improve this limit, approaching the LISA performance.
119241810
Space-borne gravitational wave detectors as time-delayed differential dynamometers
The basic constituent of many space-borne gravitational missions, in particular for interferometric gravitational waves detectors, is the so-called link made out of a satellite sending an electromagnetic beam to a second satellite. We illustrate how, by measuring the time derivative of the frequency of the received beam, the link behaves as a differential, time-delayed dynamometer in which the effect of gravity is exactly equivalent to an effective differential force applied to the two satellites. We also show that this differential force gives an integrated measurement of curvature along the beam. Finally, we discuss how this approach can be implemented to benefit the data analysis of gravitational wave detectors.