Time-domain analysis of a dynamically tuned signal recycled interferometer for the detection of chirp gravitational waves from coalescing compact binaries

In this article, we study a particular method of detection of chirp signals from coalescing compact binary stars---the so-called dynamical tuning, i.e., amplification of the signal via tracking of its instantaneous frequency by the tuning of a signal-recycled detector. The motion of the signal-recycling mirror, the position of which defines the tuning of the detector, causes nonstationarity of the detector. The dynamically tuned detector can be simulated in a quasistationary approximation if the mirror position, amplitude, and frequency of a chirp signal are changing slowly. A time-domain consideration developed for signal-recycled interferometers, in particular GEO 600, describes the signal and noise evolution in the more general case of a purely nonstationary detector. We prove that the shot noise from the dark port and optical losses remains white in this case. The analysis of the transient effects shows that during the perfect tracking of the chirp frequency only transients from fast amplitude changes arise because the transients from changes of the detector tuning and signal frequency completely cancel each other. The slow change of the amplitude in this case establishes a so-called virtually stationary detection, meaning the signal fields at the detector hold their stationary values at each instance of time, corresponding to the instantaneous parameters of the gravitational wave and of the detector. The signal-to-noise-ratio gain from the implementation of dynamical tuning, calculated in this paper, is $\ensuremath{\sim}17$ for a shot noise-limited GEO 600-like detector and $\ensuremath{\sim}7$ for a detector with both shot and displacement noise.