Source confusion from neutron star binaries in ground-based gravitational wave detectors is minimal

Upgrades beyond the current second generation of ground-based gravitational wave detectors will allow them to observe tens of thousands neutron star and black hole binaries. Given the typical minute-to-hour duration of neutron star signals in the detector frequency band, a number of them will overlap in the time-frequency plane, resulting in a nonzero cross-correlation. We examine "source confusion" arising from overlapping signals whose time-frequency tracks cross. Adopting the median observed merger rate of $100{\mathrm{Gpc}}^{-3}{\mathrm{yr}}^{-1}$, each neutron star binary signal overlaps with an average of 42(4)[0.5] other signals when observed from 2(5)[10] Hz. The vast majority of overlaps occur at low frequencies where the inspiral evolution is slow: 91% of time-frequency overlaps occur in band below 5 Hz. The combined effect of overlapping signals does not satisfy the central limit theorem and source confusion cannot be treated as stationary, Gaussian noise: on average 0.91(0.17)[0.05] signals are present in a single adaptive time-frequency bin centered at 2(5)[10] Hz. We quantify source confusion under a realistic neutron star binary population and find that parameter uncertainty typically increases by less than 1% unless there are overlapping signals whose detector-frame chirp mass difference is $\lesssim 0.01M_{\odot }$ and the overlap frequency is $\gtrsim 40\mathrm{Hz}$. Out of $1\times {10}^6$ simulated signals, 0.14% fall within this region of detector-frame chirp mass differences, but their overlap frequencies are typically lower than 40 Hz. Source confusion for ground-based detectors, where events overlap instantaneously, is significantly milder than the equivalent Laser Interferometer Space Antenna problem, where many classes of events overlap for the lifetime of the mission.