Effect of the LISA response function on observations of monochromatic sources

Abstract

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 $\ensuremath{\sim}{10}^{4}$ such systems, with a large fraction of them at frequencies $\ensuremath{\gtrsim}3\text{ }\text{ }\mathrm{m}\mathrm{H}\mathrm{z}$, 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 $f\ensuremath{\le}10\text{ }\text{ }\mathrm{m}\mathrm{H}\mathrm{z}$, therefore in a frequency range where one would actually expect the approximation to fail. For parameter estimation, we conclude that in the range $3\text{ }\text{ }\mathrm{m}\mathrm{H}\mathrm{z}\ensuremath{\lesssim}f\ensuremath{\lesssim}30\text{ }\text{ }\mathrm{m}\mathrm{H}\mathrm{z}$ the errors associated with parameter measurements differ from $\ensuremath{\simeq}5%$ up to a factor $\ensuremath{\sim}10$ (depending on the actual source parameters and emission frequency) with respect to those computed using the long-wavelength approximation.