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The tilt-to-length coupling during the LISA Pathfinder mission has been numerically and analytically modeled for particular timespans. In this work, we investigate the long-term stability of the coupling coefficients of this noise. We show that they drifted slowly (by 1\,$\mu$m/rad and 6$\times10^{-6}$ in 100 days) and strongly correlated to temperature changes within the satellite (8\,$\mu$m/rad/K and 30$\times10^{-6}$/K). Based on analytical TTL coupling models, we attribute the temperature-driven coupling changes to rotations of the test masses and small distortions in the optical setup. Particularly, we show that LISA Pathfinder's optical baseplate was bent during the cooldown experiment, which started in late 2016 and lasted several months.

A precise characterization of the magnetic properties of LISA Pathfinder free falling test-masses is of special interest for future gravitational wave observatory in space. Magnetic forces have an important impact on the instrument sensitivity in the low frequency regime below the millihertz. In this paper we report on the magnetic injection experiments performed throughout LISA Pathfinder operations. We show how these experiments allowed a high precision estimate of the instrument magnetic parameters. The remanent magnetic moment was found to have a modulus of $(0.245\pm0.081)\,\rm{nAm}^2$, the x-component of the background magnetic field within the test masses position was measured to be $(414 \pm 74)$ nT and its gradient had a value of $(-7.4\pm 2.1)\,\mu$T/m. Finally, we also measured the test mass magnetic susceptibility to be $(-3.35\pm0.15)\times$10$^{-5}$ in the low frequency regime. All results are in agreement with on-ground estimates.

LISA Pathfinder was a mission designed to test key technologies required for gravitational wave detection in space. Magnetically driven forces play a key role in the instrument sensitivity in the low-frequency regime, which corresponds to the measurement band of interest for future space-borne gravitational wave observatories. Magnetic-induced forces couple to the test mass motion, introducing a contribution to the relative acceleration noise between the free falling test masses. In this Letter we present the first complete estimate of this term of the instrument performance model. Our results set the magnetic-induced acceleration noise during the February 2017 noise run of $\rm 0.25_{-0.08}^{+0.15}\,fm\,s^{-2}/\sqrt{Hz}$ at 1 mHz and $\rm 1.01_{-0.24}^{+0.73}\, fm\,s^{-2}/\sqrt{Hz}$ at 0.1 mHz. We also discuss how the non-stationarities of the interplanetary magnetic field can affect these values during extreme space weather conditions.

We present an in-depth analysis of the LISA Pathfinder differential acceleration performance over the entire course of its science operations, spanning approximately 500 days. We find that: 1) the evolution of the Brownian noise that dominates the acceleration amplitude spectral density (ASD), for frequencies $f\gtrsim 1\,\text{mHz}$, is consistent with the decaying pressure due to the outgassing of a single gaseous species. 2) between $f=36\,\mu\text{Hz}$ and $1\,\text{mHz}$, the acceleration ASD shows a $1/f$ tail in excess of the Brownian noise of almost constant amplitude, with $\simeq 20\%$ fluctuations over a period of a few days, with no particular time pattern over the course of the mission; 3) at the lowest considered frequency of $f=18\,\mu\text{Hz}$, the ASD significantly deviates from the $1/f$ behavior, because of temperature fluctuations that appear to modulate a quasi-static pressure gradient, sustained by the asymmetries of the outgassing pattern. We also present the results of a projection of the observed acceleration noise on the potential sources for which we had either a direct correlation measurement, or a quantitative estimate from dedicated experiments. These sources account for approximately $40\%$ of the noise power in the $1/f$ tail. Finally, we analyze the possible sources of the remaining unexplained fraction, and identify the possible measures that may be taken to keep those under control in LISA.

Electrostatic force actuation is a key component of the system of geodesic reference test masses (TM) for the LISA orbiting gravitational wave observatory and in particular for performance at low frequencies, below 1 mHz, where the observatory sensitivity is limited by stray force noise. The system needs to apply forces of order 10$^{-9}$ N while limiting fluctuations in the measurement band to levels approaching 10$^{-15}$ N/Hz$^{1/2}$. We present here the LISA actuation system design, based on audio-frequency voltage carrier signals, and results of its in-flight performance test with the LISA Pathfinder test mission. In LISA, TM force actuation is used to align the otherwise free-falling TM to the spacecraft-mounted optical metrology system, without any forcing along the critical gravitational wave-sensitive interferometry axes. In LISA Pathfinder, on the other hand, the actuation was used also to stabilize the TM along the critical $x$ axis joining the two TM, with the commanded actuation force entering directly into the mission's main differential acceleration science observable. The mission allowed demonstration of the full compatibility of the electrostatic actuation system with the LISA observatory requirements, including dedicated measurement campaigns to amplify, isolate, and quantify the two main force noise contributions from the actuation system, from actuator gain noise and from low frequency ``in band'' voltage fluctuations. These campaigns have shown actuation force noise to be a relevant, but not dominant, noise source in LISA Pathfinder and have allowed performance projections for the conditions expected in the LISA mission.

We present a study of the tilt-to-length coupling noise during the LISA Pathfinder mission and how it depended on the system's alignment. Tilt-to-length coupling noise is the unwanted coupling of angular and lateral spacecraft or test mass motion into the primary interferometric displacement readout. It was one of the major noise sources in the LISA Pathfinder mission and is likewise expected to be a primary noise source in LISA. We demonstrate here that a recently derived and published analytical model describes the dependency of the LISA Pathfinder tilt-to-length coupling noise on the alignment of the two freely falling test masses. This was verified with the data taken before and after the realignments performed in March (engineering days) and June 2016, and during a two-day experiment in February 2017 (long cross-talk experiment). The latter was performed with the explicit goal of testing the tilt-to-length coupling noise dependency on the test mass alignment. Using the analytical model, we show that all realignments performed during the mission were only partially successful and explain the reasons why. In addition to the analytical model, we computed another physical tilt-to-length coupling model via a minimising routine making use of the long cross-talk experiment data. A similar approach could prove useful for the LISA mission.

A comprehensive summary of the measurements made to characterize test mass charging due to the space environment during the LISA Pathfinder mission is presented. Measurements of the residual charge of the test mass after release by the grabbing and positioning mechanism, show that the initial charge of the test masses was negative after all releases, leaving the test mass with a potential in the range $-12$ mV to $-512$ mV. Variations in the neutral test mass charging rate between $21.7$ e s$^{-1}$ and $30.7$ e s$^{-1}$ were observed over the course of the 17-month science operations produced by cosmic ray flux changes including a Forbush decrease associated with a small solar energetic particle event. A dependence of the cosmic ray charging rate on the test mass potential between $-30.2$ e s$^{-1}$ V$^{-1}$ and $-40.3$ e s$^{-1}$ V$^{-1}$ was observed and this is attributed to a contribution to charging from low-energy electrons emitted from the gold surfaces of the gravitational reference sensor. Data from the on-board particle detector show a reliable correlation with the charging rate and with other environmental monitors of the cosmic ray flux. This correlation is exploited to extrapolate test mass charging rates to a 20-year period giving useful insight into the expected range of charging rate that may be observed in the LISA mission., Comment: 17 pages, 10 figures

LISA Pathfinder (LPF) has been a space-based mission designed to test new technologies that will be required for a gravitational wave observatory in space. Magnetically driven forces play a key role in the instrument sensitivity in the low-frequency regime (mHz and below), the measurement band of interest for a space-based observatory. The magnetic field can couple to the magnetic susceptibility and remanent magnetic moment from the test masses and disturb them from their geodesic movement. LISA Pathfinder carried on-board a dedicated magnetic measurement subsystem with noise levels of 10 $ \rm nT \ Hz^{-1/2}$ from 1 Hz down to 1 mHz. In this paper we report on the magnetic measurements throughout LISA Pathfinder operations. We characterise the magnetic environment within the spacecraft, study the time evolution of the magnetic field and its stability down to 20 $\mu$Hz, where we measure values around 200 $ \rm nT \ Hz^{-1/2}$ and identify two different frequency regimes, one related to the interplanetary magnetic field and the other to the magnetic field originating inside the spacecraft. Finally, we characterise the non-stationary component of the fluctuations of the magnetic field below the mHz and relate them to the dynamics of the solar wind., Comment: 16 pages, 17 figures. MNRAS LaTeX style file version 3.0

We report on the results of the LISA Pathfinder (LPF) free-fall mode experiment, in which the control force needed to compensate the quasistatic differential force acting on two test masses is applied intermittently as a series of "impulse" forces lasting a few seconds and separated by roughly 350 s periods of true free fall. This represents an alternative to the normal LPF mode of operation in which this balancing force is applied continuously, with the advantage that the acceleration noise during free fall is measured in the absence of the actuation force, thus eliminating associated noise and force calibration errors. The differential acceleration noise measurement presented here with the free-fall mode agrees with noise measured with the continuous actuation scheme, representing an important and independent confirmation of the LPF result. An additional measurement with larger actuation forces also shows that the technique can be used to eliminate actuation noise when this is a dominant factor.

LISA Pathfinder (LPF) was a technology pioneering mission designed to test key technologies required for gravitational wave detection in space. In the low frequency regime (milli-Hertz and below), where space-based gravitational wave observatories will operate, temperature fluctuations play a crucial role since they can couple into the interferometric measurement and the test masses' free-fall accuracy in many ways. A dedicated temperature measurement subsystem, with noise levels in 10$\,\mu$K$\,$Hz$^{-1/2}$ down to $1\,$mHz was part of the diagnostics unit on board LPF. In this paper we report on the temperature measurements throughout mission operations, characterize the thermal environment, estimate transfer functions between different locations and report temperature stability (and its time evolution) at frequencies as low as 10$\,\mu$Hz, where typically values around $1\,$K$\,$Hz$^{-1/2}$ were measured., Comment: 13 pages, 16 figures. MNRAS LaTeX style file version 3.0

The zodiacal dust complex, a population of dust and small particles that pervades the Solar System, provides important insight into the formation and dynamics of planets, comets, asteroids, and other bodies. Here we present a new set of data obtained using a novel technique: direct measurements of momentum transfer to a spacecraft from individual particle impacts. This technique is made possible by the extreme precision of the instruments flown on the LISA Pathfinder spacecraft, a technology demonstrator for a future space-based gravitational wave observatory that operated near the first Sun-Earth Lagrange point from early 2016 through Summer of 2017. Using a simple model of the impacts and knowledge of the control system, we show that it is possible to detect impacts and measure properties such as the transferred momentum (related to the particle's mass and velocity), direction of travel, and location of impact on the spacecraft. In this paper, we present the results of a systematic search for impacts during 4348 hours of Pathfinder data. We report a total of 54 candidates with momenta ranging from 0.2$\,\mu\textrm{Ns}$ to 230$\,\mu\textrm{Ns}$. We furthermore make a comparison of these candidates with models of micrometeoroid populations in the inner solar system including those resulting from Jupiter-family comets, Oort-cloud comets, Hailey-type comets, and Asteroids. We find that our measured population is consistent with a population dominated by Jupiter-family comets with some evidence for a smaller contribution from Hailey-type comets. This is in agreement with consensus models of the zodiacal dust complex in the momentum range sampled by LISA Pathfinder., Comment: 22 pages, 14 figures, accepted in ApJ

Non-recurrent short term variations of the galactic cosmic-ray (GCR) flux above 70 MeV n$^{-1}$ were observed between 2016 February 18 and 2017 July 3 aboard the European Space Agency LISA Pathfinder (LPF) mission orbiting around the Lagrange point L1 at 1.5$\times$10$^6$ km from Earth. The energy dependence of three Forbush decreases (FDs) is studied and reported here. A comparison of these observations with others carried out in space down to the energy of a few tens of MeV n$^{-1}$ shows that the same GCR flux parameterization applies to events of different intensity during the main phase. FD observations in L1 with LPF and geomagnetic storm occurrence is also presented. Finally, the characteristics of GCR flux non-recurrent variations (peaks and depressions) of duration $<$ 2 days and their association with interplanetary structures are investigated. It is found that, most likely, plasma compression regions between subsequent corotating high-speed streams cause peaks, while heliospheric current sheet crossing cause the majority of the depressions.

The Space Technology 7 Disturbance Reduction System (ST7-DRS) is a NASA technology demonstration payload that operated from January 2016 through July of 2017 on the European Space Agency's 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 the performance of the CMNTs and control laws. We find that the CMNT performance to be consistent with pre-flight predictions, with a measured system thrust noise on the order of $100\,\textrm{nN}/\sqrt{\textrm{Hz}}$ in the $1\,\textrm{mHz}\leq f \leq 30\,\textrm{mHz}$ 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 $3\,\textrm{nm}/\sqrt{\textrm{Hz}}$ 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 $3\,\textrm{fm}/\textrm{s}^2/\sqrt{\textrm{Hz}}$ in the $1\,\textrm{mHz}\leq f \leq 30\,\textrm{mHz}$ 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 (LISA) mission.

The LISA Pathfinder charge management device was responsible for neutralising the cosmic ray induced electric charge that inevitably accumulated on the free-falling test masses at the heart of the experiment. We present measurements made on ground and in-flight that quantify the performance of this contactless discharge system which was based on photo-emission under UV illumination. In addition, a two-part simulation is described that was developed alongside the hardware. Modelling of the absorbed UV light within the Pathfinder sensor was carried out with the GEANT4 software toolkit and a separate MATLAB charge transfer model calculated the net photocurrent between the test masses and surrounding housing in the presence of AC and DC electric fields. We confront the results of these models with observations and draw conclusions for the design of discharge systems for future experiments like LISA that will also employ free-falling test masses.

LISA Pathfinder (LPF) was a European Space Agency mission with the aim to test key technologies for future space-borne gravitational-wave observatories like LISA. The main scientific goal of LPF was to demonstrate measurements of differential acceleration between free-falling test masses at the sub-femto-g level, and to understand the residual acceleration in terms of a physical model of stray forces, and displacement readout noise. A key step toward reaching the LPF goals was the correct calibration of the dynamics of LPF, which was a three-body system composed by two test-masses enclosed in a single spacecraft, and subject to control laws for system stability. In this work, we report on the calibration procedures adopted to calculate the residual differential stray force per unit mass acting on the two test-masses in their nominal positions. The physical parameters of the adopted dynamical model are presented, together with their role on LPF performance. The analysis and results of these experiments show that the dynamics of the system was accurately modeled and the dynamical parameters were stationary throughout the mission. Finally, the impact and importance of calibrating system dynamics for future space-based gravitational wave observatories is discussed.

Galactic cosmic-ray (GCR) energy spectra observed in the inner heliosphere are modulated by the solar activity, the solar polarity and structures of solar and interplanetary origin. A high counting rate particle detector (PD) aboard LISA Pathfinder (LPF), meant for subsystems diagnostics, was devoted to the measurement of galactic cosmic-ray and solar energetic particle integral fluxes above 70 MeV n$^{-1}$ up to 6500 counts s$^{-1}$. PD data were gathered with a sampling time of 15 s. Characteristics and energy-dependence of GCR flux recurrent depressions and of a Forbush decrease dated August 2, 2016 are reported here. The capability of interplanetary missions, carrying PDs for instrument performance purposes, in monitoring the passage of interplanetary coronal mass ejections (ICMEs) is also discussed.

Test mass charging caused by cosmic rays will be a significant source of acceleration noise for space-based gravitational wave detectors like LISA. Operating between December 2015 and July 2017, the technology demonstration mission LISA Pathfinder included a bespoke monitor to help characterise the relationship between test mass charging and the local radiation environment. The radiation monitor made in situ measurements of the cosmic ray flux while also providing information about its energy spectrum. We describe the monitor and present measurements which show a gradual 40% increase in count rate coinciding with the declining phase of the solar cycle. Modulations of up to 10% were also observed with periods of 13 and 26 days that are associated with co-rotating interaction regions and heliospheric current sheet crossings. These variations in the flux above the monitor detection threshold (approximately 70 MeV) are shown to be coherent with measurements made by the IREM monitor on-board the Earth orbiting INTEGRAL spacecraft. Finally we use the measured deposited energy spectra, in combination with a GEANT4 model, to estimate the galactic cosmic ray differential energy spectrum over the course of the mission.

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 fm/s^2/sqrt(Hz) across the 0.1-100 mHz frequency band that is crucial to an observatory such as 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 build up 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., Comment: 9 Pages, 3 figures

Future space borne gravitational wave detectors will require a precise definition of calibration signals to ensure the achievement of their design sensitivity. The careful design of the test signals plays a key role in the correct understanding and characterisation of these instruments. In that sense, methods achieving optimal experiment designs must be considered as complementary to the parameter estimation methods being used to determine the parameters describing the system. The relevance of experiment design is particularly significant for the LISA Pathfinder mission, which will spend most of its operation time performing experiments to characterise key technologies for future space borne gravitational wave observatories. Here we propose a framework to derive the optimal signals ---in terms of minimum parameter uncertainty--- to be injected to these instruments during its calibration phase. We compare our results with an alternative numerical algorithm which achieves an optimal input signal by iteratively improving an initial guess. We show agreement of both approaches when applied to the LISA Pathfinder case., Comment: 12 pages, 6 figures

The LISA Pathfinder mission will demonstrate the technology of drag-free test masses for use as inertial references in future space-based gravitational wave detectors. To accomplish this, the Pathfinder spacecraft will perform drag-free flight about a test mass while measuring the acceleration of this primary test mass relative to a second reference test mass. Because the reference test mass is contained within the same spacecraft, it is necessary to apply forces on it to maintain its position and attitude relative to the spacecraft. These forces are a potential source of acceleration noise in the LISA Pathfinder system that are not present in the full LISA configuration. While LISA Pathfinder has been designed to meet it's primary mission requirements in the presence of this noise, recent estimates suggest that the on-orbit performance may be limited by this `suspension noise'. The drift-mode or free-flight experiments provide an opportunity to mitigate this noise source and further characterize the underlying disturbances that are of interest to the designers of LISA-like instruments. This article provides a high-level overview of these experiments and the methods under development to analyze the resulting data., Comment: 13 pages, 5 figures. Accepted to Journal Of Physics, Conference Series. Presented at 10th International LISA Symposium, May 2014, Gainesville, FL, USA

Deep phase modulation interferometry was proposed as a method to enhance homodyne interferometers to work over many fringes. In this scheme, a sinusoidal phase modulation is applied in one arm while the demodulation takes place as a post-processing step. In this contribution we report on the development to implement this scheme in a fiber coupled interferometer controlled by means of a FPGA, which includes a LEON3 soft-core processor. The latter acts as a CPU and executes a custom made application to communicate with a host PC. In contrast to usual FPGA-based designs, this implementation allows a real-time fine tuning of the parameters involved in the setup, from the control to the post-processing parameters., Comment: Proceedings of the X LISA Symposium, Gainesville, May 18-23, 2014

LISA Pathfinder is a mission planned by the European Space Agency to test the key technologies that will allow the detection of gravitational waves in space. The instrument on-board, the LISA Technology package, will undergo an exhaustive campaign of calibrations and noise characterisation campaigns in order to fully describe the noise model. Data analysis plays an important role in the mission and for that reason the data analysis team has been developing a toolbox which contains all the functionalities required during operations. In this contribution we give an overview of recent activities, focusing on the improvements in the modelling of the instrument and in the data analysis campaigns performed both with real and simulated data., Comment: Plenary talk presented at the 9th International LISA Symposium, 21-25 May 2012, Paris

The last century has seen enormous progress in our understanding of the Universe. We know the life cycles of stars, the structure of galaxies, the remnants of the big bang, and have a general understanding of how the Universe evolved. We have come remarkably far using electromagnetic radiation as our tool for observing the Universe. However, gravity is the engine behind many of the processes in the Universe, and much of its action is dark. Opening a gravitational window on the Universe will let us go further than any alternative. Gravity has its own messenger: Gravitational waves, ripples in the fabric of spacetime. They travel essentially undisturbed and let us peer deep into the formation of the first seed black holes, exploring redshifts as large as z ~ 20, prior to the epoch of cosmic re-ionisation. Exquisite and unprecedented measurements of black hole masses and spins will make it possible to trace the history of black holes across all stages of galaxy evolution, and at the same time constrain any deviation from the Kerr metric of General Relativity. eLISA will be the first ever mission to study the entire Universe with gravitational waves. eLISA is an all-sky monitor and will offer a wide view of a dynamic cosmos using gravitational waves as new and unique messengers to unveil The Gravitational Universe. It provides the closest ever view of the early processes at TeV energies, has guaranteed sources in the form of verification binaries in the Milky Way, and can probe the entire Universe, from its smallest scales around singularities and black holes, all the way to cosmological dimensions., Comment: 20 pages; submitted to the European Space Agency on May 24th, 2013 for the L2/L3 selection of ESA's Cosmic Vision program

Temperature fluctuations are expected to be one of the limiting factors for gravitational wave detectors in the very low frequency range. Here we report the characterisation of this noise source in the LISA Pathfinder optical bench and propose a method to remove its contribution from the data. Our results show that temperature fluctuations are indeed limiting our measurement below one millihertz, and that their subtraction leads to a factor 5.6 (15 dB) reduction in the noise level at the lower end of the LISA measurement band 10^{-4} Hz, which increases to 20.2 (26 dB) at even lower frequencies, i.e., 1.5x10^{-5} Hz. The method presented here can be applied to the subtraction of other noise sources in gravitational wave detectors in the general situation where multiple sensors are used to characterise the noise source., Comment: 8 pages, 6 figures

This paper presents a quantitative assessment of the performance of the upcoming LISA Pathfinder geodesic explorer mission. The findings are based on the results of extensive ground testing and simulation campaigns using flight hardware and flight control and operations algorithms. The results show that, for the central experiment of measuring the stray differential acceleration between the LISA test masses, LISA Pathfinder will be able to verify the overall acceleration noise to within a factor two of the LISA requirement at 1 mHz and within a factor 6 at 0.1 mHz. We also discuss the key elements of the physical model of disturbances, coming from LISA Pathfinder and ground measurement, that will guarantee the LISA performance., Comment: Proceedings of the 8th LISA Symposium. To appear Class. Quantum Grav. 28 (2011)