We report the first results of the LISA Pathfinder in-flight experiment. The results demonstrate that two free-falling reference test masses, such as those needed for a space-based gravitational wave observatory like LISA, can be put in free fall with a relative acceleration noise with a square root of the power spectral density of $5.2\pm 0.1\mathrm{fm}{\mathrm{s}}^{-2}/\sqrt{\mathrm{Hz}}$, or $(0.54\pm 0.01)\times {10}^{-15}$g$/\sqrt{\mathrm{Hz}}$, with g the standard gravity, for frequencies between 0.7 and 20 mHz. This value is lower than the LISA Pathfinder requirement by more than a factor 5 and within a factor 1.25 of the requirement for the LISA mission, and is compatible with Brownian noise from viscous damping due to the residual gas surrounding the test masses. Above 60 mHz the acceleration noise is dominated by interferometer displacement readout noise at a level of $(34.8\pm 0.3)\mathrm{fm}/\sqrt{\mathrm{Hz}}$, about 2 orders of magnitude better than requirements. At $f\le 0.5\mathrm{mHz}$ we observe a low-frequency tail that stays below $12\mathrm{fm}{\mathrm{s}}^{-2}/\sqrt{\mathrm{Hz}}$ down to 0.1 mHz. This performance would allow for a space-based gravitational wave observatory with a sensitivity close to what was originally foreseen for LISA.

In the months since the publication of the first results, the noise performance of LISA Pathfinder has improved because of reduced Brownian noise due to the continued decrease in pressure around the test masses, from a better correction of noninertial effects, and from a better calibration of the electrostatic force actuation. In addition, the availability of numerous long noise measurement runs, during which no perturbation is purposely applied to the test masses, has allowed the measurement of noise with good statistics down to $20\mu \mathrm{Hz}$. The Letter presents the measured differential acceleration noise figure, which is at $(1.74\pm 0.05)\mathrm{fm}{\mathrm{s}}^{-2}/\sqrt{\mathrm{Hz}}$ above 2 mHz and $(6\pm 1)\times 10\mathrm{fm}{\mathrm{s}}^{-2}/\sqrt{\mathrm{Hz}}$ at $20\mu \mathrm{Hz}$, and discusses the physical sources for the measured noise. This performance provides an experimental benchmark demonstrating the ability to realize the low-frequency science potential of the LISA mission, recently selected by the European Space Agency.

The Laser Interferometer Space Antenna Pathfinder (LPF) main observable, labeled Δg, is the differential force per unit mass acting on the two test masses under free fall conditions after the contribution of all non-gravitational forces has been compensated. At low frequencies, the differential force is compensated by an applied electrostatic actuation force, which then must be subtracted from the measured acceleration to obtain Δg. Any inaccuracy in the actuation force contaminates the residual acceleration. This study investigates the accuracy of the electrostatic actuation system and its impact on the LPF main observable. It is shown that the inaccuracy is mainly caused by the rounding errors in the waveform processing and also by the random error caused by the analog to digital converter random noise in the control loop. Both errors are one order of magnitude smaller than the resolution of the commanded voltages. We developed a simulator based on the LPF design to compute the close-to-reality actuation voltages and, consequently, the resulting actuation forces. The simulator is applied during post-processing the LPF data.

We report on electrostatic measurements made on board the European Space Agency mission LISA Pathfinder. Detailed measurements of the charge-induced electrostatic forces exerted on free-falling test masses (TMs) inside the capacitive gravitational reference sensor are the first made in a relevant environment for a space-based gravitational wave detector. Employing a combination of charge control and electric-field compensation, we show that the level of charge-induced acceleration noise on a single TM can be maintained at a level close to $1.0\mathrm{fm}{\mathrm{s}}^{-2}{\mathrm{Hz}}^{-1/2}$ across the 0.1–100 mHz frequency band that is crucial to an observatory such as the Laser Interferometer Space Antenna (LISA). Using dedicated measurements that detect these effects in the differential acceleration between the two test masses, we resolve the stochastic nature of the TM charge buildup due to interplanetary cosmic rays and the TM charge-to-force coupling through stray electric fields in the sensor. All our measurements are in good agreement with predictions based on a relatively simple electrostatic model of the LISA Pathfinder instrument.