55961759
How serious can the stealth bias be in gravitational wave parameter estimation
The upcoming direct detection of gravitational waves will open a window to probing the strong-field regime of general relativity. As a consequence, waveforms that include the presence of deviations from general relativity have been developed (e.g., in the parametrized post-Einsteinian approach). TIGER, a data analysis pipeline which builds Bayesian evidence to support or question the validity of general relativity, has been written and tested. In particular, it was shown that the LIGO and Virgo detectors can probe deviations from general relativity in a regime than cannot be tested by Solar System tests or pulsar timing measurements. However, evidence from several detections is required before a deviation from general relativity can be confidently claimed. An interesting consequence is that, should general relativity not be the correct theory of gravity in its strong field regime, using standard general relativity templates for the matched filter analysis of interferometer data will introduce biases in the gravitational wave measured parameters with potentially serious consequences on the astrophysical inferences, such as the coalescence rate or the mass distribution. In this work we consider three heuristic possible deviations from general relativity and show that the biases introduced in the estimated parameters of gravitational waves emitted during the inspiral phase of spinless compact binary coalescence systems assuming the validity of general relativity manifest in various ways. The mass parameters are usually the most affected, with biases that can be as large as 30 standard deviations for the symmetric mass ratio, and nearly one percent for the chirp mass, which is usually estimated with subpercent accuracy. Other parameters do not show a significant bias. We conclude that statements about the nature of the observed sources, e.g., if both objects are neutron stars, depend critically on the explicit assumption that general relativity is the right theory of gravity in the strong field regime.
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.
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).
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
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.
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.
122158055
The LISA Pathfinder drift mode: implementation solutions for a robust algorithm
The drag-free experiment on-board LISA Pathfinder, the LISA Technology Package (LTP), has for its main science mission the proof of a low disturbance noise level. It is measured differentially between two test-masses whose relative motion is perturbed by their respective capacitive actuator noise. In order to suppress this noise source the drift mode actuation scheme uses very short impulses to produce kicks. This way the test-masses motion between two kicks is a free parabolic flight and can be used for a spectral estimation of the remaining noise sources, allowing us to distinguish between external noise sources and actuation noise. This mode will be helpful in the case of a high actuation noise or to investigate some unexpected external noise source, but the foremost reason being that this experiment is closer to the ultimate LISA experiment in terms of actuation noise. It must be implemented on-board taking into account the constraints of a space-borne experiment in terms of robustness, usability and existing software and hardware architecture.
118459662
Bayesian parameter estimation in the second LISA Pathfinder mock data challenge
A main scientific output of the LISA Pathfinder mission is to provide a noise model that can be extended to the future gravitational wave observatory, LISA. The success of the mission depends thus upon a deep understanding of the instrument, especially the ability to correctly determine the parameters of the underlying noise model. In this work we estimate the parameters of a simplified model of the LISA Technology Package instrument. We describe the LISA Technology Package by means of a closed-loop model that is used to generate the data, both injected signals and noise. Then, parameters are estimated using a Bayesian framework, and it is shown that this method reaches the optimal attainable error, the Cramer-Rao bound. We also address an important issue for the mission: how to efficiently combine the results of different experiments to obtain a unique set of parameters describing the instrument.
55218371
Brownian force noise from molecular collisions and the sensitivity of advanced gravitational wave observatories
We present an analysis of Brownian force noise from residual gas damping of reference test masses as a fundamental sensitivity limit in small force experiments. The resulting acceleration noise increases significantly when the distance of the test mass to the surrounding experimental apparatus is smaller than the dimension of the test mass itself. For the Advanced LIGO interferometric gravitational wave observatory, where the relevant test mass is a suspended 340 mm diameter cylindrical end mirror, the force noise power is increased by roughly a factor 40 by the presence of a similarly shaped reaction mass at a nominal separation of 5 mm. The force noise, of order 20 fN\rthz\ for $2 \times 10^{-6}$ Pa of residual H$_2$ gas, rivals quantum optical fluctuations as the dominant noise source between 10 and 30 Hz. We present here a numerical and analytical analysis for the gas damping force noise for Advanced LIGO, backed up by experimental evidence from several recent measurements. Finally, we discuss the impact of residual gas damping on the gravitational wave sensitivity and possible mitigation strategies.
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.
122404463
Calibration data diagnostic and data validation
This is a brief introductory overview to papers devoted to key steps in preparing data from Gravitational Wave detectors in view of a confident signal extraction.