Optimal statistic for detecting gravitational wave signals from binary inspirals with LISA

TL;DR

This paper derives the optimal detection statistic for gravitational waves from binary inspirals in LISA data, accounting for the detector's orbital motion and sky position dependence, enabling more effective real-time searches.

Contribution

It introduces the optimal detection statistic for LISA's pseudo-detectors and demonstrates how to implement real-time searches using a template bank across sky positions.

Findings

Derived the optimal detection statistic for LISA data.

Analyzed how LISA's sensitivity varies with sky position and orbital phase.

Proposed a method for real-time inspiral signal detection using template banks.

Abstract

A binary compact object early in its inspiral phase will be picked up by its nearly monochromatic gravitational radiation by LISA. But even this innocuous appearing candidate poses interesting detection challenges. The data that will be scanned for such sources will be a set of three functions of LISA's twelve data streams obtained through time-delay interferometry, which is necessary to cancel the noise contributions from laser-frequency fluctuations and optical-bench motions to these data streams. We call these three functions pseudo-detectors. The sensitivity of any pseudo-detector to a given sky position is a function of LISA's orbital position. Moreover, at a given point in LISA's orbit, each pseudo-detector has a different sensitivity to the same sky position. In this work, we obtain the optimal statistic for detecting gravitational wave signals, such as from compact binaries early in their inspiral stage, in LISA data. We also present how the sensitivity of LISA, defined by this optimal statistic, varies as a function of sky position and LISA's orbital location. Finally, we show how a real-time search for inspiral signals can be implemented on the LISA data by constructing a bank of templates in the sky positions.