Timing system of LIGO discoveries

LIGO's mission critical timing system has enabled gravitational wave and multi-messenger astrophysical discoveries as well as the rich science extracted. Achieving optimal detector sensitivity, detecting transient gravitational waves, and especially localizing gravitational wave sources, the underpinning of multi-messenger astrophysics, all require proper gravitational wave data time-stamping. Measurements of the relative arrival times of gravitational waves between different detectors allow for coherent gravitational wave detections, localization of gravitational wave sources, and the creation of skymaps. The carefully designed timing system achieves these goals by mitigating phase noise to avoid signal up-conversion and maximize gravitational wave detector sensitivity. The timing system also redundantly performs self-calibration and self-diagnostics in order to ensure reliable, extendable, and traceable time stamping. In this paper, we describe and quantify the performance of these core systems during the latest O3 scientific run of LIGO, Virgo, and KAGRA. We present results of the diagnostic checks done to verify the time-stamping for individual gravitational wave events observed during O3 as well as the timing system performance for all of O3 in LIGO Livingston and LIGO Hanford. We find that, after 3 observing runs, the LIGO timing system continues to reliably meet mission requirements of timing precision below 1 $\mu$s with a significant safety margin.