This award will support research in the area of coherent network analysis --- detection and reconstruction of gravitational wave (GW) signals with multiple GW detectors (detector networks). Work will be done on development of the coherent network algorithms and their applications to burst searches which target detection of GW transients from the most violent events in the Universe. Coherent algorithms will enable not only a detection of gravitational waves, but also the astrophysical analyses of GW signals and measurements of source properties. Such measurements will lead to understanding of the underlying physics and the dynamics of GW sources, may reveal the origin of known cosmic events (such as short duration gamma-ray bursts), probe the equations of state of neutron stars and allow a thorough test of General Relativity. Work will be done on inclusion of source models into the coherent analysis in order to improve the confidence of detection, perform characterization of sources and confirm or rule out the models. This will be particularly important for the enhanced and advanced GW detectors which target the first detection and study of gravitational wave signals.
Interferometric gravitational wave detectors are among the most advanced instruments ever built to explore the Universe. Their complex design and sophisticated data analysis provide unique educational and research opportunities for students in all areas of physics. Graduate and undergraduate students will be involved with sophisticated methods for extraction of signals from noise, computational schemes for manipulation of large data sets, data processing on large computing clusters and modern astrophysical theories. The proposed research addresses problems of GW detection with the worldwide network of gravitational wave detectors. Participation in the joint data analysis conducted in collaboration with multinational teams will give students a rich research experience and exposure to diverse cultural approaches in conducting research and pursuing science to prepare them for a wide spectrum of career opportunities.
Coincident observations with multiple GW detectors are very important for the discovery and study of gravitational waves. On one hand, no single detector can alone make a reliable claim of a first detection. Numerous noise sources present in individual detectors can imitate a signature expected from the passage of a gravitational wave, thus making it extremely difficult to declare detection. On the other hand, the astrophysical interpretation of a GW event is heavily dependent on extraction of the signal waveforms. The response of a GW detector is such that no full reconstruction of a GW signal is possible with a single detector. In order to reconstruct a source position in the sky and the two polarization states of a gravitational wave signal, multiple observations of the same event must be made by geographically separated detectors. Analysis of data from such a network of detectors requires a coherent approach, which is different from the analysis of data from individual detectors. Development of such an approach, called Coherent Network Analysis (CNA), with focus on detection and reconstruction of GW signals, was the main objective of our research. The coordinate reconstruction is a necessary tool for the future GW astronomy. Prompt detection of GW signals and estimation of source coordinates enables coincident observations with other astronomical instruments, which can significantly increase the confidence of detection. For example, the source coordinates can be used to guide the optical instruments in order to search for a possible optical counterpart. It would greatly enhance the precision of source localization, potentially allowing the identification of a host galaxy and associated red shift. Such measurements may not only aid the first detection of gravitational waves but also they will give us fundamentally new information about the GW sources and their population distribution. Our research funded by NSF addressed the sky localization problem for short (less than few seconds in duration) generic GW signals often called "bursts". The first attached plot shows the reconstructed sky probability map for the event we discovered on September 16, 2010. This sky map was sent to the telescopes to search for a possible optical counterpart. The LIGO and Virgo collaborations studied this event in details and found it to be of a binary origin, where one of two component stars is a black hole. The PRD paper was written by the collaboration and prepared for the publication. However, this paper has never been published. On the collaboration meeting in March 2011 this event was announced to be a blind injection – a simulated event secretly injected into the LIGO and Virgo data streams to test our analysis algorithms and the detection procedure. At this moment we were given information, where in the sky the event was injected – shown with a white star, which is not far from the location found by our reconstruction algorithm. It has been actively used in the LIGO-Virgo burst searches during the last science run S6 in 2010. When the S6 run was complete, the LIGO detectors were decommissioned and LIGO started the construction (upgrade) of the advanced detectors with 10 times better sensitivity. One of the important questions for advanced detectors is how well they can localize GW sources. We did a detail study of this problem and demonstrated (as shown on the attached figure) that adding one more LIGO site in India can significantly improve the source sky localization. These results are published in Phys. Rev. D83 02001 (2011). The NSF supported the idea to move one of the LIGO detectors to a new site in India, which currently is being selected. In addition to the study of the coordinate reconstruction of GW sources, we also worked on the development of the time-frequency algorithms, which are actively used in the burst searches. We developed a novel time-frequency transformation capable to accurately localize signal energy on the time frequency plane and therefore efficiently capture the signal. This conceptually new time-frequency transformation is based on the Wilson-Daubechies approach. Combining it with the Meyers wavelet function we developed a new class of fast (by ~100 times faster than a conventional wavelet) wavelet transformations (called WDM), which combines advantages of both Meyer wavelet and the Fast Fourier Transform (FFT). This TF transform offers exceptional control over the spectral leakage. For example, the third attached figure shows the distribution of LIGO-Hanford spectral noise obtained with two transforms: WDM and FFT with Hann window. The WDM has lower leakage and what is even more important WDM is the orthonormal transform with existing inverse transform, which is not the case for windowed FFT. This unique transformation opens an opportunity for new data analysis algorithms in the communication and Digital Signal Processing. The paper describing the algorithm and acknowledging the NSF support has been published at J. Phys. Conf. Ser. 363 012032 (2012)
