Gaussianity of LISA’s confusion backgrounds

Abstract

Data analysis for the proposed Laser Interferometer Space Antenna (LISA) will be complicated by the huge number of sources in the LISA band. In the frequency band ~10-^4 - 2×10^-3 Hz, 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 LISA data searches: searches for EMRI signals buried in GWDB confusion noise, and searches for massive black hole binary signals buried in (i) GWDB noise, (ii) EMRI noise, and (iii) a sum of EMRI noise and Gaussian noise. Assuming reasonable short-distance cutoffs in the populations of confusion sources (since the very closest and hence strongest sources will be individually resolvable), modifications to the appropriate detection threshold, due to the non-Gaussianity of the confusion noise, turn out to be quite small for realistic cases. The smallness of the correction is partly due to the fact that these three types of sources evolve on quite different time scales, so no single background source closely resembles any search template. We also briefly discuss other types of LISA searches where the non-Gaussianity of LISA's confusion backgrounds could perhaps have a much greater impact on search reliability and efficacy.