Gaussianity of LISA's confusion backgrounds

TL;DR

This paper investigates whether the confusion noise in LISA's data, caused by unresolved sources like white dwarf binaries and EMRIs, can be accurately modeled as Gaussian, especially in the extreme tails relevant for detection thresholds.

Contribution

It applies the Edgeworth expansion and large deviations theory to assess the Gaussianity of LISA's confusion noise in the context of matched-filter detection statistics.

Findings

Gaussian approximation may not hold in the tails of the distribution

Edgeworth expansion provides a more accurate model for tail probabilities

Implications for setting detection thresholds in LISA data analysis

Abstract

Data analysis for the proposed Laser Interferometer Space Antenna (LISA) will be complicated by the huge number of sources in the LISA band. Throughout much of the band, galactic white dwarf binaries (GWDBs) are sufficiently dense in frequency space that it will be impossible to resolve most of them, and "confusion noise" from the unresolved Galactic binaries will dominate over instrumental noise in determining LISA's sensitivity to other sources in that band. Confusion noise from unresolved extreme-mass-ratio inspirals (EMRIs) could also contribute significantly to LISA's total noise curve. To date, estimates of the effect of LISA's confusion noise on matched-filter searches and their detection thresholds have generally approximated the noise as Gaussian, based on the Central Limit Theorem. However in matched-filter searches, the appropriate detection threshold for a given class of signals may be located rather far out on the tail of the signal-to-noise probability distribution, where a priori it is unclear whether the Gaussian approximation is reliable. Using the Edgeworth expansion and the theory of large deviations, we investigate the probability distribution of the usual matched-filter detection statistic, far out on the tail of the distribution. We apply these tools to four somewhat idealized versions of specific LISA searches.