Data analysis of gravitational-wave signals from spinning neutron stars. III. Detection statistics and computational requirements

We develop the analytic and numerical tools for data analysis of the continuous gravitational-wave signals from spinning neutron stars for ground-based laser interferometric detectors. The statistical data analysis method that we investigate is maximum likelihood detection which for the case of Gaussian noise reduces to matched filtering. We study in detail the statistical properties of the optimum functional that needs to be calculated in order to detect the gravitational-wave signal and estimate its parameters. We find it particularly useful to divide the parameter space into elementary cells such that the values of the optimal functional are statistically independent in different cells. We derive formulas for false alarm and detection probabilities both for the optimal and the suboptimal filters. We assess the computational requirements needed to do the signal search. We compare a number of criteria to build sufficiently accurate templates for our data analysis scheme. We verify the validity of our concepts and formulas by means of the Monte Carlo simulations. We present algorithms by which one can estimate the parameters of the continuous signals accurately. We find, confirming earlier work of other authors, that given a 100 Gflops computational power an all-sky search for observation time of 7 days and directed search for observation time of 120 days are possible whereas an all-sky search for 120 days of observation time is computationally prohibitive.