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.

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.

The science operations of the LISA Pathfinder mission have demonstrated the feasibility of sub-femto-g free fall of macroscopic test masses necessary to build a gravitational wave observatory in space such as LISA. While the main focus of interest, i.e., the optical axis or the $x$-axis, has been extensively studied, it is also of great importance to evaluate the stability of the spacecraft with respect to all the other degrees of freedom (d.o.f.). The current paper is dedicated to such a study: the exhaustive and quantitative evaluation of the imperfections and dynamical effects that impact the stability with respect to its local geodesic. A model of the complete closed-loop system provides a comprehensive understanding of each component of the in-loop coordinates spectral density. As will be presented, this model gives very good agreement with LISA Pathfinder flight data. It allows one to identify the noise source at the origin and the physical phenomena underlying the couplings. From this, the stability performance of the spacecraft with respect to its geodesic is extracted as a function of frequency. Close to 1 mHz, the stability of the spacecraft on the $X_{\mathrm{SC}}$, $Y_{\mathrm{SC}}$ and $Z_{\mathrm{SC}}$ d.o.f. is shown to be of the order of $5.0\times {10}^{-15}\mathrm{m}{\mathrm{s}}^{-2}{\mathrm{Hz}}^{-1/2}$ for $X$, $6.0\times {10}^{-14}\mathrm{m}{\mathrm{s}}^{-2}{\mathrm{Hz}}^{-1/2}$ for $Y$, and $4.0\times {10}^{-14}\mathrm{m}{\mathrm{s}}^{-2}{\mathrm{Hz}}^{-1/2}$ for $Z$. For the angular d.o.f., the values are of the order of $3\times {10}^{-12}\mathrm{rad}{\mathrm{s}}^{-2}{\mathrm{Hz}}^{-1/2}$ for ${\mathrm{\Theta }}_{\mathrm{SC}}$, $5\times {10}^{-13}\mathrm{rad}{\mathrm{s}}^{-2}{\mathrm{Hz}}^{-1/2}$ for $H_{\mathrm{SC}}$, and $3\times {10}^{-13}\mathrm{rad}{\mathrm{s}}^{-2}{\mathrm{Hz}}^{-1/2}$ for ${\mathrm{\Phi }}_{\mathrm{SC}}$. Below 1 mHz, however, the stability performances are worsened significantly by the effect of the star tracker noise on the closed-loop system. It is worth noting that LISA is expected to be spared from such concerns, as differential wave-front sensing, an attitude sensor system of much higher precision, will be utilized for attitude control.

The Space Technology 7 Disturbance Reduction System (ST7-DRS) is a NASA technology demonstration payload that operated from January 2016 through July 2017 on the European Space Agency’s (ESA) LISA Pathfinder spacecraft. The joint goal of the NASA and ESA missions was to validate key technologies for a future space-based gravitational wave observatory targeting the source-rich millihertz band. The two primary components of ST7-DRS are a micropropulsion system based on colloidal micro-Newton thrusters (CMNTs) and a control system that simultaneously controls the attitude and position of the spacecraft and the two free-flying test masses (TMs). This paper presents our main experimental results and summarizes the overall performance of the CMNTs and control laws. We find the CMNT performance to be consistent with preflight predictions, with a measured system thrust noise on the order of $100\mathrm{nN}/\sqrt{\mathrm{Hz}}$ in the $1\mathrm{mHz}\le f\le 30\mathrm{mHz}$ band. The control system maintained the TM-spacecraft separation with an RMS error of less than 2 nm and a noise spectral density of less than $3\mathrm{nm}/\sqrt{\mathrm{Hz}}$ in the same band. Thruster calibration measurements yield thrust values consistent with the performance model and ground-based thrust-stand measurements, to within a few percent. We also report a differential acceleration noise between the two test masses with a spectral density of roughly $3\mathrm{fm}/{\mathrm{s}}^2/\sqrt{\mathrm{Hz}}$ in the $1\mathrm{mHz}\le f\le 30\mathrm{mHz}$ band, slightly less than twice as large as the best performance reported with the baseline LISA Pathfinder configuration and below the current requirements for the Laser Interferometer Space Antenna mission.