# Bayesian analysis of burst gravitational waves from galactic neutron stars

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## Abstract

This thesis summarises my work in relation to data analysis for gravitational wave detection. Most of the personal contribution relates to the assessment of the detectability of potential burst-type gravitational wave signals from the galactic population of neutron stars and to the parameter estimation of the models used to represent these signals. A small part of the work, confined to the last chapter, describes the experimental work carried at the beginning of the research period and aimed to measure the shot-noise level of the modulated laser-light in the gravitational wave detectors. Chapter 1 is introductory and presents generic information about gravitational wave radiation, a postulate of the theory of general relativity. The polarisation of the radiation and the approximate values of amplitudes and frequencies of the signals expected from astrophysical events are presented, together with most important gravitational radiation sources for ground-based detectors. Chapter 2 presents the study on the detectability of burst-type gravitational wave signals incoming from neutron stars located in our galaxy. Three differently shaped galactic neutron star populations are introduced and the detectability of ground-based detectors to signals of different polarisation degree coming from these source populations is investigated. Based on the time- and polarisation-averaged antenna pattern and antenna power values, approximated by Monte Carlo methods, detectability is measured in terms of a) the geographical location and orientation of hypothetical detectors, and b) the current detectors, either working individually or as a part of a network. Also, the sidereal times at which each detector is more sensitive to the sources of the neutron star populations defined are inferred. Chapter 3 introduces a mathematical model of the burst-type gravitational wave ringdown signal investigated in this work, which represents a short-lived gravitational polarised radiation generated by an oscillating neutron star: an exponentially damped sinusoid comprised of a sine and a cosine component, of the same frequency but different amplitude, as the two polarisation components of the signal. The model of the signal is given, in the time- and in the frequency-domain. Chapter 4 is devoted to present the Bayesian probability tools necessary to carry out ‘model comparison’ and ‘parameter estimation’ for the detectability study of our particular burst-type signal. Comparison of models allows choosing the one that better represents the data and subsequently focusing on in order to compute the most likely parameter values of that model. Also, in this section, the way in which the detector data can be simulated in the frequency domain, combining the signal and a noise realisation corresponding to the power spectrum of the noise that characterizes the detector, is explained. The likelihood function for a signal corresponding to one oscillation mode and seen by one detector is derived both in the time- and in the frequency-domain. The nested sampling technique is summarised, a useful tool to compute effectively the marginal likelihood of the hypotheses considered. Chapter 5 presents the results of the model selection and the parameter estimation exercise. The expression of the likelihood is generalised so that it can adopt more than one oscillation mode and been seen by various detectors of a network. Depending whether one, f-mode, or two oscillation modes, f and p, are suspect, two different scenarios of various hypotheses are considered. For each hypothesis the minimum strength of the signal to claim detection is studied and a parameter estimation exercise is carried out to characterise the signal and define the location of the source in the sky. Signals of known parameters and differing strengths were injected into the synthetic noise of three advanced detectors comprising a network. The values of the parameters were estimated using Bayesian inference for two different scenarios: when only the f-mode is suspect (scenario 1), or when both f- and p-modes are suspect (scenario 2). Posterior probabilities of the parameters in Scenario 1 are better defined and constrained than those for Scenario 2, due to the added uncertainty of including another oscillation mode. As expected, the uncertainty of the probability distributions of the parameter values decreases and the mode shifts toward the exact injected value as the signal strength increases. For both scenarios the frequency value can be accurately estimated, but not so well the damping time, especially for the p-mode oscillation, which is suspected to have longer time durations than f-modes, typically several seconds. The ability to estimate the polarisation degree of the signal is also quite limited and strong signals are required for the mode of the distribution to approximate the exact value. Similarly, determining the most probable location for the source is possible in both scenarios. The two-fold degeneracy of the sky position and related to the travel time of the signal to the detectors has been broken; relatively strong (high SNR) signals, especially for scenario 2, are needed for the source location to be constrained with accuracy. Chapter 6 presents the experimental work carried out, by which the measuring of the shot-noise level of differently modulated and demodulated laser light was intended. Due to the poor outcome of this experiment and the lack of useful results the emphasis has been placed on a detailed description of the modulation apparatus, opto-electronic set up and the control system put together. Chapter 7 looks to the future and briefly presents how to take this data analysis work forward.

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