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±0.1  fm s^{-2}/sqrt[Hz], or (0.54±0.01)×10^{-15}  g/sqrt[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±0.3)  fm/sqrt[Hz], about 2 orders of magnitude better than requirements. At f≤0.5  mHz we observe a low-frequency tail that stays below 12  fm s^{-2}/sqrt[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  μHz. The Letter presents the measured differential acceleration noise figure, which is at (1.74±0.05)  fm s^{-2}/sqrt[Hz] above 2 mHz and (6±1)×10  fm s^{-2}/sqrt[Hz] at 20  μHz, 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.

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LISA Pathfinder (LPF) is a science and technology demonstrator planned by the European Space Agency in view of the LISA mission. As a scientific payload, the LISA Technology Package on board LPF will be the most precise geodesics explorer flown as of today, both in terms of displacement and acceleration sensitivity. The challenges embodied by LPF make it a unique mission, paving the way towards the space-borne detection of gravitational waves with LISA. This paper summarizes the basics of LPF, and the progress made in preparing its effective implementation in flight. We hereby give an overview of the experiment philosophy and assumptions to carry on the measurement. We report on the mission plan and hardware design advances and on the progress on detailing measurements and operations. Some light will be shed on the related data processing algorithms. In particular, we show how to single out the acceleration noise from the spacecraft motion perturbations, how to account for dynamical deformation parameters distorting the measurement reference and how to decouple the actuation noise via parabolic free flight.

We report on residual gas damping of the motion of a macroscopic test mass enclosed in a nearby housing in the molecular flow regime. The damping coefficient, and thus the associated thermal force noise, is found to increase significantly when the distance between test mass and surrounding walls is smaller than the test mass itself. The effect has been investigated with two torsion pendulums of different geometry and has been modelled in a numerical simulation whose predictions are in good agreement with the measurements. Relevant to a wide variety of small-force experiments, the residual-gas force noise power for the test masses in the LISA gravitational wave observatory is roughly a factor 15 larger than in an infinite gas volume, though still compatible with the target acceleration noise of 3 fm s −2 Hz −1/2 at the foreseen pressure below 10 −6 Pa. The fluctuation-dissipation theorem [1] states that any system with dissipation exhibits fluctuations analogous to Brownian motion that can be modelled with an external driving force with power spectral densitywhere k is Boltzmann's constant, T is the temperature of the system, and Z(ω) is the mechanical impedance of the system. Those equilibrium fluctuations are a fundamental limit of precision metrology experiments employing macroscopic test-masses nominally in perfect free-fall to define geodesic reference frames. An unavoidable source of dissipation comes from residual gas in the experimental volume, which yields a viscous, frequency independent, impedance Z(ω) = β. Theoretical calculations for small force experiments [2-4] and direct observations [5,6] show the gas damping coefficient β to be proportional to residual gas pressure P and to some effective surface area, which depends on the test mass geometry.A recent calculation [7] for a cubic test mass has found that the translational damping coefficient iswhere s is the side length of the test mass, and m is the mass of the gas molecules. For rotation, relevant for the experiments we will present shortly, the coefficient isThis calculation assumes that gas and test mass are in thermodynamic equilibrium, that gas molecule collisions with the test mass are completely inelastic, with prompt stochastic re-emission from the surface with a MaxwellBoltzmann velocity distribution and cosine law angular distribution. Importantly, this and other calculations assume that the test mass is surrounded by an infinite volume of collisionless gas, hence the superscript ∞, such that a molecule emitted from the test mass surface disappears into the surrounding volume, and that the momentum it imparts on the test mass is uncorrelated with any subsequent collisions. This assumption breaks down when the distance between the test mass and the surrounding enclosure is only a fraction of the test mass size, as in the geometry studied here, where the gap is roughly one tenth of the test mass size.Our experimental setup probes small forces relevant to the quality of free fall achievable for the test masses of the Laser Interferometer S...