Measuring fN force variations in the presence of constant nN forces: a torsion pendulum ground test of the LISA Pathfinder free-fall mode

LISA Pathfinder is a differential accelerometer with the main goal being to demonstrate the near perfect free-fall of reference test masses, as is needed for an orbiting gravitational wave observatory, with a target sensitivity of 30 fm s⁻² ${Hz}^{-1/2}$ at 1 mHz. Any lasting background differential acceleration between the two test masses must be actively compensated, and noise associated with the applied actuation force can be a dominant source of noise. To remove this actuation, and the associated force noise, a 'free-fall' actuation control scheme has been designed; actuation is limited to brief impulses, with both test masses in free-fall in the time between the impulses, allowing measurement of the remaining acceleration noise sources. In this work, we present an on-ground torsion pendulum testing campaign of this technique and associated data analysis algorithms at a level nearing the sub-femto-g/$\sqrt{Hz}$ performance required for LISA Pathfinder. (paper)