Effect of the LISA response function on observations of monochromatic sources

The Laser Interferometer Space Antenna (LISA) is expected to provide the largest observational sample of binary systems of faint subsolar mass compact objects, in particular, white-dwarfs, whose radiation is monochromatic over most of the LISA observational window. Current astrophysical estimates suggest that the instrument will be able to resolve similar to10(4) such systems, with a large fraction of them at frequencies greater than or similar to3 mHz, where the wavelength of gravitational waves becomes comparable to or shorter than the LISA armlength. This affects the structure of the so-called LISA transfer function which cannot be treated as constant in this frequency range: it introduces characteristic phase and amplitude modulations that depend on the source location in the sky and the emission frequency. Here we investigate the effect of the LISA transfer function on detection and parameter estimation for monochromatic sources. For signal detection we show that filters constructed by approximating the transfer function as a constant (long-wavelength approximation) introduce a negligible loss of signal-to-noise ratio-the fitting factor always exceeds 0.97-for fless than or equal to10 mHz, therefore in a frequency range where one would actually expect the approximation to fail. For parameter estimation, we conclude that in the range 3 mHzless than or similar tofless than or similar to30 mHz the errors associated with parameter measurements differ from similar or equal to5% up to a factor similar to10 (depending on the actual source parameters and emission frequency) with respect to those computed using the long-wavelength approximation.