Quasimonochromatic LISA Sources in the Frequency Domain*

Among the binary sources of interest for LISA some are quasimonochromatic, in the sense that the change in the gravitational wave frequency △f is on the order of or smaller than 1 yr^-1 during the observation time. For example, most Galactic double white dwarfs fall into this category. For these sources, we revisit the stationary phase approximation (SPA) commonly used in Fisher matrix calculations in the frequency domain and show how it is modified by the Doppler shift induced by LISA's motion and by the LISA pattern functions. We compare our results with previous work in the time domain and discuss the transition from the quasimonochromatic case to the conventional SPA which applies in the opposite limit, i.e. △f is on the order of or higher than 1 yr^-1.