M. Rakhmanov

Constraint likelihood analysis for a network of gravitational wave detectors

We propose a coherent method for detection and reconstruction of gravitational wave signals with a network of interferometric detectors. The method is derived by using the likelihood ratio functional for unknown signal waveforms. In the likelihood analysis, the global maximum of the likelihood ratio over the space of waveforms is used as the detection statistic. We identify a problem with this approach. In the case of an aligned pair of detectors, the detection statistic depends on the cross correlation between the detectors as expected, but this dependence disappears even for infinitesimally small misalignments. We solve the problem by applying constraints on the likelihood functional and obtain a new class of statistics. The resulting method can be applied to data from a network consisting of any number of detectors with arbitrary detector orientations. The method allows us reconstruction of the source coordinates and the waveforms of two polarization components of a gravitational wave. We study the performance of the method with numerical simulations and find the reconstruction of the source coordinates to be more accurate than in the standard likelihood method.

Response of test masses to gravitational waves in the local Lorentz gauge

The response of laser interferometers to gravitational waves has been calculated in a number of different ways, particularly in the transverse-traceless and the local Lorentz gauges. At first sight, it would appear that these calculations lead to different results when the separation between the test masses becomes comparable to the wavelength of the gravitational wave. In this paper this discrepancy is resolved. We describe the response of free test masses to plane gravitational waves in the coordinate frame of a local observer and show that it acquires contributions from three different effects: the displacement of the test masses, the apparent change in the photon velocity, and the variation in the clock speed of the local observer, all of which are induced by the gravitational wave. Only when taken together do these three effects represent a quantity which is translationally invariant. This translationally-invariant quantity is identical to the response function calculated in the transverse-traceless gauge. We thus resolve the well-known discrepancy between the two coordinates systems, and show that the results found in the coordinate frame of a local observer are valid for large separation between the masses.

Dynamic resonance of light in Fabry-Perot cavities

The dynamics of light in Fabry–Perot cavities with varying length and input laser frequency are analyzed. At high frequencies, the response to length variations is very different from the response to laser frequency variations. Implications for kilometerscale Fabry–Perot cavities such as those utilized in gravitational-wave detectors are discussed.  2002 Elsevier Science B.V. All rights reserved.

Rank deficiency and Tikhonov regularization in the inverse problem for gravitational-wave bursts

Coherent techniques for searches of gravitational-wave bursts effectively combine data from several detectors, taking into account differences in their responses. The efforts are now focused on the maximum likelihood principle as the most natural way to combine data, which can also be used without prior knowledge of the signal. Recent studies however have shown that straightforward application of the maximum likelihood method to gravitational waves with unknown waveforms can lead to inconsistencies and unphysical results such as discontinuity in the residual functional, or divergence of the variance of the estimated waveforms for some locations in the sky. So far the solutions to these problems have been based on rather different physical arguments. Following these investigations, we now find that all these inconsistencies stem from the rank deficiency of the underlying network response matrix. In this paper we show that the detection of gravitational-wave bursts with a network of interferometers belongs to the category of ill-posed problems. We then apply the method of Tikhonov regularization to resolve the rank deficiency and introduce a minimal regulator which yields a well-conditioned solution to the inverse problem for all locations on the sky.

Adaptive beam shaping by controlled thermal lensing in optical elements.

We describe an adaptive optical system for use as a tunable focusing element. The system provides adaptive beam shaping via controlled thermal lensing in the optical elements. The system is agile, remotely controllable, touch free, and vacuum compatible; it offers a wide dynamic range, aberration-free focal length tuning, and can provide both positive and negative lensing effects. Focusing is obtained through dynamic heating of an optical element by an external pump beam. The system is especially suitable for use in interferometric gravitational wave interferometers employing high laser power, allowing for in situ control of the laser modal properties and compensation for thermal lensing of the primary laser. Using CO(2) laser heating of fused-silica substrates, we demonstrate a focal length variable from infinity to 4.0 m, with a slope of 0.082 diopter/W of absorbed heat. For on-axis operation, no higher-order modes are introduced by the adaptive optical element. Theoretical modeling of the induced optical path change and predicted thermal lens agrees well with measurement.

Adaptive control of laser modal properties

An adaptive optical system for precise control of a laser beams mode structure has been developed. The system uses a dynamic lens based on controlled optical path deformation in a dichroic optical element that is heated with an auxiliary laser. Our method is essentially aberration free, has high dynamic range, and can be implemented with high average power laser beams where other adaptive optics methods fail. A quantitative model agrees well with our experimental data and demonstrates the potential of our method as a mode-matching and beam-shaping element for future large-scale gravitational wave detectors.

Characterization of the LIGO 4 km Fabry–Perot cavities via their high-frequency dynamic responses to length and laser frequency variations

Recent measurements at the LIGO Hanford Observatory have confirmed the predicted high-frequency dynamic response of km scale Fabry–Perot cavities to length and laser frequency variations. The dynamic response functions have been exploited to determine a number of cavity parameters including the cavity length and the resonance width. A new technique based on a variation of these measurements has been utilized to measure the interferometer arm cavity lengths with a precision of 80 µm. We present an overview of these measurements and discuss how the dynamic field responses could be used to measure the cavity g factors which are related to the mirror radii of curvature.

Performance of the waveburst algorithm on LIGO data

In this paper we describe the performance of the WaveBurst algorithm which was designed for detection of gravitational wave bursts in interferometric data. The performance of the algorithm was evaluated on the test dataset collected during the second LIGO Scientific run. We have measured the false alarm rate of the algorithm as a function of the threshold and estimated its detection efficiency for simulated burst waveforms.

Searches for gravitational waves associated with pulsar glitches using a coherent network algorithm

Pulsar glitches are a potential source of gravitational waves for current and future interferometric gravitational wave detectors. Some pulsar glitch events were observed by radio and x-ray telescopes during the fifth LIGO science run. It is expected that glitches from these same pulsars should also be seen in the future. We carried out Monte Carlo simulations to estimate the sensitivity of possible gravitational wave signals associated with a pulsar glitch using a coherent network analysis method. We show the detection efficiency and evaluate the reconstruction accuracy of gravitational waveforms using a matched filter analysis on the estimated gravitational waveforms from the coherent analysis algorithm.

A cross-correlation method for burst searches with networks of misaligned gravitational-wave detectors

Coherent detection techniques are beginning to play more and more prominent roles in searches for gravitational-wave bursts with networks of interferometric detectors. Such techniques often involve cross-correlations of data streams from different detectors and therefore rely on similarity of their signals, which occurs only when the detectors are closely aligned. A simple extension of the cross-correlation test which can be applied even to completely misaligned interferometers is presented here. In this method, searches for bursts in one of the detectors are performed with noisy templates built out of the data streams from other detectors in the network. The efficiency of this algorithm is studied with numerical simulations. We show that by properly mixing the signals from misaligned detectors one can achieve a degree of their correlation which is close to that of a perfectly aligned pair of detectors. The redundancy in the signal mixing is used to improve the detection efficiency.