A nonlinear detection algorithm for periodic signals in gravitational wave detectors

Abstract

We present an algorithm for the detection of periodic sources of gravitational waves with interferometric detectors that is based on a special symmetry of the problem: the contributions to the phase modulation of the signal from the earth rotation are exactly equal and opposite at any two instants of time separated by half a sidereal day; the corresponding is true for the contributions from the earth orbital motion for half a sidereal year, assuming a circular orbit. The addition of phases through multiplications of the shifted time series gives a demodulated signal; specific attention is given to the reduction of noise mixing resulting from these multiplications. We discuss the statistics of this algorithm for all-sky searches (which include a parameterization of the source spin-down), in particular its optimal sensitivity as a function of required computational power. Two specific examples of all-sky searches (broad-band and narrow-band) are explored numerically, and their performances are compared with the stack-slide technique (P. R. Brady, T. Creighton, Phys. Rev. D, 61, 082001).