The Effect of the LISA Response Function on Observations of Monochromatic Sources

TL;DR

This paper examines how the LISA transfer function's frequency-dependent effects influence detection and parameter estimation of monochromatic gravitational wave sources, showing that simple approximations are adequate for detection but less so for precise measurements.

Contribution

It provides a detailed analysis of the impact of the LISA transfer function on monochromatic source observations, highlighting the limitations of the long wavelength approximation.

Findings

Detection loss is negligible below 10mHz with simple filters.

Parameter estimation errors increase significantly above 3mHz.

The long wavelength approximation remains effective for detection but less accurate for parameter estimation.

Abstract

The Laser Interferometer Space Antenna (LISA) is expected to provide the largest observational sample of binary systems of faint sub-solar 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 about 10000 such systems, with a large fraction of them at frequencies above 3 mHz, where the wavelength of gravitational waves becomes comparable to or shorter than the LISA arm-length. 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 below 10mHz, therefore in a frequency range where one would actually expect the approximation to fail. For parameter estimation, we conclude that in the range 3mHz to 30mHz the errors associated with parameter measurements differ from about 5% up to a factor of 10 (depending on the actual source parameters and emission frequency) with respect to those computed using the long wavelength approximation.