Sensitivity and parameter-estimation precision for alternate LISA configurations

TL;DR

This paper introduces a framework to evaluate LISA's sensitivity and parameter-estimation accuracy under various link failure scenarios, revealing how measurement reductions impact performance and confirming invariance properties of the analysis.

Contribution

It provides a simple, adaptable method to assess LISA's performance with missing links and demonstrates the invariance of SNR and Fisher matrix to TDI basis choices.

Findings

Five-link configuration has minor SNR loss at high frequencies.

Four-link configuration shows significant SNR reduction, especially at high frequencies.

Parameter-estimation precision decreases with fewer links, correlating with SNR reductions.

Abstract

We describe a simple framework to assess the LISA scientific performance (more specifically, its sensitivity and expected parameter-estimation precision for prescribed gravitational-wave signals) under the assumption of failure of one or two inter-spacecraft laser measurements (links) and of one to four intra-spacecraft laser measurements. We apply the framework to the simple case of measuring the LISA sensitivity to monochromatic circular binaries, and the LISA parameter-estimation precision for the gravitational-wave polarization angle of these systems. Compared to the six-link baseline configuration, the five-link case is characterized by a small loss in signal-to-noise ratio (SNR) in the high-frequency section of the LISA band; the four-link case shows a reduction by a factor of sqrt(2) at low frequencies, and by up to ~2 at high frequencies. The uncertainty in the estimate of polarization, as computed in the Fisher-matrix formalism, also worsens when moving from six to five, and then to four links: this can be explained by the reduced SNR available in those configurations (except for observations shorter than three months, where five and six links do better than four even with the same SNR). In addition, we prove (for generic signals) that the SNR and Fisher matrix are invariant with respect to the choice of a basis of TDI observables; rather, they depend only on which inter-spacecraft and intra-spacecraft measurements are available.