Increasing LIGO sensitivity by feedforward subtraction of auxiliary length control noise

LIGO, the Laser Interferometer Gravitational-wave Observatory, has been designed and constructed to measure gravitational wave strain via differential arm length. The LIGO 4 km Michelson arms with Fabry-Perot cavities have auxiliary length control servos for suppressing Michelson motion of the beam-splitter and arm cavity input mirrors, which degrades interferometer sensitivity. We demonstrate how a post facto pipeline improves a data sample from LIGO Science Run 6 with feedforward subtraction. Dividing data into 1024 s windows, we numerically fit filter functions representing the frequency-domain transfer functions from Michelson length channels into the gravitational-wave strain data channel for each window, then subtract the filtered Michelson channel noise (witness) from the strain channel (target). In this paper we describe the algorithm, assess achievable improvements in sensitivity to astrophysical sources, and consider relevance to future interferometry.