Gravitational waves

The theory of weak gravitational waves is discussed at length. The transverse traceless gauge is described, and the behaviour of plane wave solutions obtained. The impact of a wave on physical objects, and hence methods for their detection, are calculated. The laser interferometric gravitational wave detector is described. Sources such as binary stars are considered. The compact source approximation is employed, and the quadrupole formula relating the wave amplitude to the quadrupole of the source is obtained. Energy flux in gravitational waves is calculated by two methods, one more general, the other giving further physical insight. The total emitted power is obtained. These are lengthy calculations but they are presented in full. Finally they are applied in detail to a binary star with elliptical orbtis (the Hulse Taylor binary) and to a black hole merger detected by the LIGO interferometers.

Probing Gravitational Waves from Pulsars in Brans–Dicke Theory

This paper comprises the theoretical background for the data analysis of gravitational waves (GWs) from spinning neutron stars in Brans–Dicke (BD) theory. Einstein’s general theory of relativity (GR) predicts only two tensor polarization states, but a generic metric theory of gravity can also possess scalar and vector polarization states. The BD theory attempts to modify the GR by varying gravitational constant G, and it has three polarization states. The first two states are the same as in GR, and the third one is scalar polarization. We derive the response of a laser interferometric detector to the GW signal from a spinning neutron star in BD theory. We obtain a statistic based on the maximum likelihood principle to identify the signal in BD theory in the detector’s noise. This statistic generalizes the well known F-statistic used in the case of GR. We perform Monte Carlo simulations in Gaussian noise to test the detectability of the signal and the accuracy of estimation of its parameters.

Recent Observations of Gravitational Waves by LIGO and Virgo Detectors

In this paper we present the most recent observations of gravitational waves (GWs) by LIGO and Virgo detectors. We also discuss contributions of the recent Nobel prize winner, Sir Roger Penrose to understanding gravitational radiation and black holes (BHs). We make a short introduction to GW phenomenon in general relativity (GR) and we present main sources of detectable GW signals. We describe the laser interferometric detectors that made the first observations of GWs. We briefly discuss the first direct detection of GW signal that originated from a merger of two BHs and the first detection of GW signal form merger of two neutron stars (NSs). Finally we present in more detail the observations of GW signals made during the first half of the most recent observing run of the LIGO and Virgo projects. Finally we present prospects for future GW observations.

A bidirectional scanning method for scanning transmission X-ray microscopy

Scanning mode is a key factor for the comprehensive performance, including imaging efficiency, of scanning transmission X-ray microscopy (STXM). Herein is presented a bidirectional scanning method designed for STXM with an S-shaped moving track. In this method, artificially designed ramp waves are generated by a piezo-stage controller to control the two-dimensional scanning of the sample. The sample position information is measured using laser interferometric sensors and sent to a field-programmable gate array (FPGA) board which also acquires the X-ray signals simultaneously from the detector. Since the data recorded by the FPGA contain the real position of each scanned point, the influence of the backlash caused by the back-turning movement on the STXM image can be eliminated. By employing an adapted post-processing program, a re-meshed high-resolution STXM image can be obtained. This S-track bidirectional scanning method in fly-scan mode has been implemented on the STXM endstation at the Shanghai Synchrotron Radiation Facility (SSRF), and successfully resolved the ∼30 nm interval between the innermost strips of a Siemens star. This work removes the limitation on bidirectional scanning caused by motor backlash and vibration, and significantly improves the efficiency of STXM experiments.