Theoretical Analysis And Digital Signal Processing For Ringdown Waveform Based On The Data Of LIGO

According to General Relativity, an unstable black hole, which occurs due to the coalescence of a black hole binary following their inspiral and subsequent merger and a compact stellar, will return to a stable configuration by the emission of gravitational radiation in a superposition of quasi-normal modes. In this paper, we focus on the late time of the waveform, which we refer to as Ringdown waveform. It has typical frequency and the amplitude exponential decaying with time. At present, LIGO (Laser Interferometer Gravitational Wave Observatory) locate on 3 different places, which are two in Hanford named H1 and H2 and, another one in Livingston named L1. In each of them, the data analysis process is well-known the method of matched filtering, which means base on the known waveform, we perform the correlation between data and the waveform, and pass the data with higher Signal-Noise-Ratio (SNR) than threshold. In order to reduce background noise, we apply the coincidence Analysis and timeslides analysis on two or three detectors after matched filtering in each detector. As one aim of LIGO data analysis, the Ringdown detection follows such pipline. Here we concern the intermediate mass black holes with 100 and 500 M⊙to a distance of up to 300 Mpc, because LIGO is sensitive to the dominant mode of perturbed black holes with such masses and region.1 The main works:As the source of this paper, the perturbed intermedate black holes will be occurred by two different mechanisms:①the compact stellar with spin (mass is near 20-500 M⊙) gravity collapse.②inspiral binary with smaller mass merge to black holes. At present, it is short for the research of the first mechanism; however, there is no accurate analytic whole waveform for the second one. In order to solve these issues, in this paper we calculate and analyze the whole waveform for the first one, get the approximate analytic result through curve fitting, which we make correlation analysis to current Ringdown waveform. The results show it is reasonable to make new template for LIGO data process since such ideal overlap between them. For the second one, there are two kinds of waveform (i.e., EOBNR, phenomenological waveform), which are the injection simulation for S5 LIGO data analysis. We find phenomenological waveform is much smoother and with higher accurate rate. Then it is hopeful to find accurate analytic result. 2 Innovations of this paper①At present, it is short for the research of compact stellar with spin gravity collapse. This paper calculates the analytic whole waveform in the collapse to fix this shortage.②The current Ringdown waveform is connected directly to a step function, which is inaccurate. Then as a part work of this paper, we match the collapse waveform to Ringdown smoothly. As a result, the template of LIGO data analysis is much more accurate.③It is a significant research of curve fitting and current Ringdown correlation. We find the energy of gravitational radiation is in different phase due to mass and spin difference. This conclusion is valuable.④So far, the S5 LIGO data is in the longest observation time and the largest detection region. With such data, we get the optimal coincidence test window size and compare EOBNR with phenomenological waveform, as a result, phenomenological waveform is much smoother and with higher accurate rate.3 Main conclusions①In the collapse, there is no gravitational radiation on the spin direction. With the same mass, the faster spin results bigger eccentricity and shorter collapse period; with the same spin, the bigger mass results bigger initial eccentricity and foci distance. In addition, the bigger initial density results weaker gravitational radiation.②For the compact stars with faster spin and bigger mass, most of the energy is in Ringdown phase; for the stars with slower spin and smaller mass, most of the energy is in collapse phase.③According to phenomenological and EOBNR waveform comparison, the optimal size of coincidence test is 0.4. However, the events of background increase with the size, and then we need to plot ROC (detection possibility and false alarm plot) curve to choose reasonable value.④The found injections of EOBNR are always in further area than phenomenological ones, because when the EOBNR waveform is made, its amplitude is lower than the phenomenological at the same injection time. Therefore, for the same matched template, EOBNR is the signal from further source.Most of our work is done in the Center for Gravitational Wave Astronomy (CGWA) of University of Texas at Brownsville (UTB) in U.S.A. and international LIGO science cooperation with the support of Unite States national science fund.