Nonlinear detection algorithm for periodic signals in gravitational wave detectors

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 Earth’s 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 Earth’s 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 parametrization of the source spin-down), in particular its optimal sensitivity as a function of required computational power. Two specific examples of all-sky searches (broadband and narrowband) are explored numerically, and their performances are compared with the stack-slide technique [P. R. Brady and T. Creighton, Phys. Rev. D 61, 082001 (2000)].