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The large-scale analysis task of deciphering gravitational wave signals in the LISA data stream will be difficult, requiring a large amount of computational resources and extensive development of computational methods. Its high dimensionality, multiple model types, and complicated noise profile require a global fit to all parameters and input models simultaneously. In this work, we detail our global fit algorithm, called "Erebor," designed to accomplish this challenging task. It is capable of analysing current state-of-the-art datasets and then growing into the future as more pieces of the pipeline are completed and added. We describe our pipeline strategy, the algorithmic setup, and the results from our analysis of the LDC2A Sangria dataset, which contains Massive Black Hole Binaries, compact Galactic Binaries, and a parameterized noise spectrum whose parameters are unknown to the user. We recover posterior distributions for all 15 (6) of the injected MBHBs in the LDC2A training (hidden) dataset. We catalog $\sim12000$ Galactic Binaries ($\sim8000$ as high confidence detections) for both the training and hidden datasets. All of the sources and their posterior distributions are provided in publicly available catalogs., Comment: 25 pages, 6 figures

In this work, we investigate the impact of tidal torques and mass transfer on the population of double white dwarfs (DWDs) that will be observed with LISA. Starting from a distribution of DWDs at formation predicted by numerical simulations, we use a semi-analytical model to evolve DWDs under different hypotheses for the efficiency of tidal coupling and the birth spins of white dwarfs. We then estimate the stochastic foreground and the population of resolvable binaries for LISA in each scenario. Our predicted DWD binary distribution can differ substantially from the distribution expected if only gravitational waves (GWs) are considered. If white dwarfs spin slowly, then we predict an excess of systems around a few mHz, due to binaries that outspiral after the onset of mass transfer. This excess of systems leads to differences in the confusion noise, which are most pronounced for strong tidal coupling. In that case, we find a significantly higher number of resolvable binaries than in the GW-only scenario. If instead white dwarfs spin rapidly and tidal coupling is weak, then we find no excess around a few mHz, and the confusion noise due to DWDs is very small. In that scenario, we also predict a subpopulation of outspiralling binaries below 0.1 mHz. Using the Fisher matrix approximation, we estimate the uncertainty on the GW-frequency derivative of resolvable systems. We estimate that, even for non-accreting systems, the mismodelling error due to neglect of effects other than GWs is larger than the statistical uncertainty, and thus this neglect would lead to biased estimates for mass and distance. Our results highlight the need for flexible tools in LISA data analysis. Because our semi-analytical model hinges upon a simplistic approach to determining the stability of mass accretion it will be important to deepen our comprehension of stability in mass-transferring DWD binaries., Comment: 11 pages, 7 figures, with appendix 12 and 9 respectively

The future space based gravitational wave detector LISA (Laser Interferometer Space Antenna) will observe millions of Galactic binaries constantly present in the data stream. A small fraction of this population (of the order of several thousand) will be individually resolved. One of the challenging tasks from the data analysis point of view will be to estimate the parameters of resolvable galactic binaries while disentangling them from each other and from other gravitational wave sources present in the data. This problem is quite often referred to as a global fit in the field of LISA data analysis. A Bayesian framework is often used to infer the parameters of the sources and their number. The efficiency of the sampling techniques strongly depends on the proposals, especially in the multi-dimensional parameter space. In this paper we demonstrate how we can use neural density estimators, and in particular Normalising flows, in order to build proposals which significantly improve the convergence of sampling. We also demonstrate how these methods could help in building priors based on physical models and provide an alternative way to represent the catalogue of identified gravitational wave sources.

The Laser Interferometer Space Antenna (LISA) is the first scientific endeavour to detect and study gravitational waves from space. LISA will survey the sky for Gravitational Waves in the 0.1 mHz to 1 Hz frequency band which will enable the study of a vast number of objects ranging from Galactic binaries and stellar mass black holes in the Milky Way, to distant massive black-hole mergers and the expansion of the Universe. This definition study report, or Red Book, presents a summary of the very large body of work that has been undertaken on the LISA mission over the LISA definition phase., Comment: 155 pages, with executive summary and table of contents

We explore the potential for detecting rotational instabilities in the post-merger phase of binary neutron star mergers using different network configurations of upgraded and next-generation gravitational wave detectors. Our study employs numerically generated post-merger waveforms, which reveal the re-excitation of the $l=m=2$ $f$-mode at a time of $O(10{\rm})$ms after merger. We evaluate the detectability of these signals by injecting them into colored Gaussian noise and performing a reconstruction as a sum of wavelets using Bayesian inference. Computing the overlap between the reconstructed and injected signal, restricted to the instability part of the post-merger phase, we find that one could infer the presence of rotational instabilities with a network of planned 3rd-generation detectors, depending on the total mass and distance to the source. For a recently suggested high-frequency detector design, we find that the instability part would be detectable even at 200 Mpc, significantly increasing the anticipated detection rate. For a network consisting of the existing HLV detectors, but upgraded to twice the A+ sensitivity, we confirm that the peak frequency of the whole post-merger gravitational-wave emission could be detectable with a network signal-to-noise ratio of 8 at a distance of 40Mpc., Comment: 18 pages, 15 captured figures, submitted to PRD

Neutron star-white dwarf (NS+WD) binaries offer a unique opportunity for studying NS-specific phenomena with gravitational waves. In this paper, we employ the binary population synthesis technique to study the Galactic population of NS+WDs with the future Laser Interferometer Space Antenna (LISA). We anticipate approximately $\mathcal{O}(10^2)$ detectable NS+WDs by LISA, encompassing both circular and eccentric binaries formed via different pathways. Despite the challenge of distinguishing NS+WDs from more prevalent double white dwarfs in the LISA data (especially at frequencies below 2 mHz), we show that their eccentricity and chirp mass distributions may provide avenues to explore the NS natal kicks and common envelope evolution. Additionally, we investigate the spatial distribution of detectable NS+WDs relative to the Galactic plane and discuss prospects for identifying electromagnetic counterparts at radio wavelengths. Our results emphasise LISA's capability to detect and characterise NS+WDs and to offer insights into the properties of the underlying population. Our conclusions carry significant implications for shaping LISA data analysis strategies and future data interpretation., Comment: Accepted for publication by MNRAS

Finding a stochastic gravitational-wave background (SGWB) of astrophysical or primordial origin is one of the quests of current and future gravitational-wave observatories. While detector networks such as LIGO-Virgo-Kagra or pulsar timing arrays can use cross-correlations to tell instrumental noise and SGWB apart, LISA is likely to be the only flying detector of its kind in 2035. This particularity poses a challenge for data analysis. To tackle it, we present a strategy based on Bayesian model selection. We use a flexible noise power spectral density~(PSD) model and the knowledge of noise and signal transfer functions to allow SGWBs detection when the noise PSD is unknown. With this technique, we then probe the parameter space accessible by LISA for power-law SGWB shapes., Comment: 5 pages, 1 figure, contribution to the 2023 Gravitation session of the 57th Rencontres de Moriond

In recent years, the field of Gravitational Wave Astronomy has flourished. With the advent of more sophisticated ground-based detectors and space-based observatories, it is anticipated that Gravitational Wave events will be detected at a much higher rate in the near future. One of the future data analysis challenges is performing robust statistical inference in the presence of detector noise transients or non-stationarities, as well as in the presence of stochastic Gravitational Wave signals of possible astrophysical and/or cosmological origin. The incomplete knowledge of the total noise of the observatory can introduce challenges in parameter estimation of detected sources. In this work, we propose a heavy-tailed, Hyperbolic likelihood, based on the Generalized Hyperbolic distribution. With the Hyperbolic likelihood we obtain a robust data analysis framework against data outliers, noise non-stationarities, and possible inaccurate modeling of the noise power spectral density. We apply this methodology to examples drawn from gravitational wave astronomy, and in particular to synthetic data sets from the planned LISA mission., Comment: 18 pages, 7 figures, matches published version

We use the latest constraints on the population of stellar origin binary black holes (SOBBH) from LIGO/Virgo/KAGRA (LVK) observations, to estimate the stochastic gravitational wave background (SGWB) they generate in the frequency band of LISA. We account for the faint and distant binaries, which contribute the most to the SGWB, by extending the merger rate at high redshift assuming it tracks the star formation rate. We adopt different methods to compute the SGWB signal: an analytical evaluation, Monte Carlo sums over SOBBH population realisations, and a method that accounts for the role of the detector by simulating LISA data and iteratively removing resolvable signals until only the confusion noise is left, allowing for the extraction of both the expected SGWB and the number of resolvable SOBBHs. Since the latter are few for SNR thresholds larger than five, we confirm that the spectral shape of the SGWB in the LISA band follows the analytical prediction of a power law. We infer the probability distribution of the SGWB amplitude from the LVK GWTC-3 posterior of the binary population model; its interquartile range of $h^2\Omega_\mathrm{GW}(f=3\times10^{-3}\,\mathrm{Hz}) \in [5.65,\,11.5]\times10^{-13}$ is in agreement with most previous estimates. We perform a MC analysis to assess LISA's capability to detect and characterise this signal. Accounting for both the instrumental noise and the galactic binaries foreground, with four years of data, LISA will be able to detect the SOBBH SGWB with percent accuracy, narrowing down the uncertainty on the amplitude by one order of magnitude with respect to the range of possible amplitudes inferred from the population model. A measurement of this signal by LISA will help to break the degeneracy among some of the population parameters, and provide interesting constraints, in particular on the redshift evolution of the SOBBH merger rate., Comment: 39 pages, 15 figures. Prepared for submission to JCAP

In recent years, methods for Bayesian inference have been widely used in many different problems in physics where detection and characterization are necessary. Data analysis in gravitational-wave astronomy is a prime example of such a case. Bayesian inference has been very successful because this technique provides a representation of the parameters as a posterior probability distribution, with uncertainties informed by the precision of the experimental measurements. During the last couple of decades, many specific advances have been proposed and employed in order to solve a large variety of different problems. In this work, we present a Markov Chain Monte Carlo (MCMC) algorithm that integrates many of those concepts into a single MCMC package. For this purpose, we have built {\tt Eryn}, a user-friendly and multipurpose toolbox for Bayesian inference, which can be utilized for solving parameter estimation and model selection problems, ranging from simple inference questions, to those with large-scale model variation requiring trans-dimensional MCMC methods, like the LISA global fit problem. In this paper, we describe this sampler package and illustrate its capabilities on a variety of use cases., Comment: 21 pages, 7 figures

Detecting stochastic background radiation of cosmological origin is an exciting possibility for current and future gravitational-wave (GW) detectors. However, distinguishing it from other stochastic processes, such as instrumental noise and astrophysical backgrounds, is challenging. It is even more delicate for the space-based GW observatory LISA since it cannot correlate its observations with other detectors, unlike today's terrestrial network. Nonetheless, with multiple measurements across the constellation and high accuracy in the noise level, detection is still possible. In the context of GW background detection, previous studies have assumed that instrumental noise has a known, possibly parameterized, spectral shape. To make our analysis robust against imperfect knowledge of the instrumental noise, we challenge this crucial assumption and assume that the single-link interferometric noises have an arbitrary and unknown spectrum. We investigate possible ways of separating instrumental and GW contributions by using realistic LISA data simulations with time-varying arms and second-generation time-delay interferometry. By fitting a generic spline model to the interferometer noise and a power-law template to the signal, we can detect GW stochastic backgrounds up to energy density levels comparable with fixed-shape models. We also demonstrate that we can probe a region of the GW background parameter space that today's detectors cannot access., Comment: 15 pages, 10 figures. Added references and minor changes

Extreme mass ratio inspirals (EMRIs) are among the primary targets for the Laser Interferometer Space Antenna (LISA). The extreme mass ratios of these systems result in relatively weak GW signals, that can be individually resolved only for cosmologically nearby sources (up to $z\approx2$). The incoherent piling up of the signal emitted by unresolved EMRIs generate a confusion noise, that can be formally treated as a stochastic GW background (GWB). In this paper, we estimate the level of this background considering a collection of astrophysically motivated EMRI models, spanning the range of uncertainties affecting EMRI formation. To this end, we employed the innovative Augmented Analytic Kludge waveforms and used the full LISA response function. For each model, we compute the GWB SNR and the number of resolvable sources. Compared to simplified computations of the EMRI signals from the literature, we find that for a given model the GWB SNR is lower by a factor of $\approx 2$ whereas the number of resolvable sources drops by a factor 3-to-5. Nonetheless, the vast majority of the models result in potentially detectable GWB which can also significantly contribute to the overall LISA noise budget in the 1-10 mHz frequency range.

The Laser Interferometer Space Antenna (LISA) mission, scheduled for launch in the mid-2030s, is a gravitational wave observatory in space designed to detect sources emitting in the millihertz band. LISA is an ESA flagship mission, currently entering the Phase B development phase. It is expected to help us improve our understanding about our Universe by measuring gravitational wave sources of different types, with some of the sources being at very high redshifts $z\sim 20$. On the 23rd of February 2022 we organized the 1$^\mathrm{st}$ {\it LISA in Greece Workshop}. This workshop aimed to inform the Greek scientific and tech industry community about the possibilities of participating in LISA science and LISA mission, with the support of the Hellenic Space Center (HSC). In this white paper, we summarize the outcome of the workshop, the most important aspect of it being the inclusion of $15$ Greek researchers to the LISA Consortium, raising our total number to $22$. At the same time, we present a road-map with the future steps and actions of the Greek Gravitational Wave community with respect to the future LISA mission., Comment: 11 pages, 2 figures

The Laser Interferometer Space Antenna (LISA) will detect and characterize $\sim10^4$ Galactic Binaries consisting predominantly of two White Dwarfs (WD). An interesting prospect within this population is a third object--another WD star, a Circumbinary Exoplanet (CBP), or a Brown Dwarf (BD)--in orbit about the inner WD pair. We present the first fully Bayesian detection and posterior analysis of sub-stellar objects with LISA, focusing on the characterization of CBPs. We used an optimistic astrophysically motivated catalogue of these CBP third-body sources, including their orbital eccentricity around the inner binary for the first time. We examined Bayesian Evidence computations for detectability, as well as the effects on the posterior distributions for both the inner binary parameters and the third-body parameters. We find that the posterior behavior bifurcates based on whether the third-body period is above or below half the observation time. Additionally, we find that undetectable third-body sources can bias the inner binary parameters whether or not the correct template is used. We used the information retrieved from the study of the CBP population to make an initial conservative prediction for the number of detectable BD systems in the original catalogue. We end with commentary on the predicted qualitative effects on LISA global fitting and Galactic Binary population analysis. The procedure used in this work is generic and can be directly applied to other astrophysical effects expected within the Galactic Binary population., Comment: 15 pages, 7 figures, 1 table

Future gravitational wave detectors, such as the Laser Interferometer Space Antenna (\textit{LISA}), will be able to resolve a significant number of the ultra compact stellar-mass binaries in our own Galaxy and its neighborhood. These will be mostly double white dwarf (DWD) binaries, and their underlying population characteristics can be directly correlated to the different properties of the Galaxy. In particular, with \textit{LISA} we will be able to resolve $\sim\mathcal{O}(10^4)$ binaries, while the rest will generate a confusion foreground signal. Analogously to how the total electromagnetic radiation emitted by a galaxy can be related to the underlying total stellar mass, in this work we propose a framework to infer the same quantity by investigating the spectral shape and amplitude of the confusion foreground signal. For a fixed DWD evolution model, and thus a fixed binary fraction, we retrieve percentage-level relative errors on the total stellar mass, which improves for increasing values of the mass. At the same time, we find that variations in the Milky Way shape, at a fixed mass and at scale heights smaller than 500~pc, are not distinguishable based on the shape of stochastic signal alone. We perform this analysis on simulations of the LISA data, estimating the resolvable sources based on signal-to-noise criteria. Finally, we utilize the catalogue of resolvable sources to probe the characteristics of the underlying population of DWD binaries. We show that the DWD frequency, coalescence time and chirp mass (up to $<0.7\,$M$_\odot$) distributions can be reconstructed from \textit{LISA} data with no bias., Comment: 15 pages, 9 figures

The Laser Interferometer Space Antenna (LISA) has two scientific objectives of cosmological focus: to probe the expansion rate of the universe, and to understand stochastic gravitational-wave backgrounds and their implications for early universe and particle physics, from the MeV to the Planck scale. However, the range of potential cosmological applications of gravitational wave observations extends well beyond these two objectives. This publication presents a summary of the state of the art in LISA cosmology, theory and methods, and identifies new opportunities to use gravitational wave observations by LISA to probe the universe.

The LISA Pathfinder (LPF) mission succeeded outstandingly in demonstrating key technological aspects of future space-borne gravitational-wave detectors, such as the Laser Interferometer Space Antenna (LISA). Specifically, LPF demonstrated with unprecedented sensitivity the measurement of the relative acceleration of two free-falling cubic test masses. Although most disruptive non-gravitational forces have been identified and their effects mitigated through a series of calibration processes, some faint transient signals of yet unexplained origin remain in the measurements. If they appear in the LISA data, these perturbations (also called glitches) could skew the characterization of gravitational-wave sources or even be confused with gravitational-wave bursts. For the first time, we provide a comprehensive census of LPF transient events. Our analysis is based on a phenomenological shapelet model allowing us to derive simple statistics about the physical features of the glitch population. We then implement a generator of synthetic glitches designed to be used for subsequent LISA studies, and perform a preliminary evaluation of the effect of the glitches on future LISA data analyses., Comment: 14 pages, 12 figures, to be submitted to PRD

Gravitational wave science is a dynamical, fast-expanding research field founded on results, tools and methodologies drawn from different research areas and communities. Early career scientists entering this field must learn and combine knowledge and techniques from a range of disciplines. The Workshop on Gravitational-Wave Astrophysics for Early Career Scientists (GWAECS), held virtually in May 2021, planted the seeds of an interdisciplinary, well-connected and all-inclusive community of early career scientists working on gravitational waves, able to exchange relevant information and ideas, build a healthy professional and international environment, share and learn valuable skills, and ensure that ongoing research efforts are perpetuated and expanded in order to attain the main scientific goals envisioned by the whole community. GWAECS was the first event unifying early career scientists belonging to different communities, historically associated with different large-scale gravitational wave experiments. It provided a broad perspective on the future of gravitational waves, offered training on soft and transferable skills and allowed ample time for informal discussions between early career scientists and well-known research experts. The essence of those activities is summarised and collected in the present document, which presents a recap of each session of the workshop and aims to provide all early career scientists with a long-lasting, useful reference which constitutes the legacy of all the ideas that circulated at GWAECS., Comment: 60 pages, 12 figures; Legacy document of the Workshop on Gravitational Wave Astrophysics for Early Career Scientists (GW{\AE}CS), Lorentz Center Workshop, online, 3-7 May 2021

Realistic models of the Galactic double white dwarf (DWD) population are crucial for testing and quantitatively defining the science objectives of the Laser Interferometer Space Antenna (LISA), a future European Space Agency's gravitational-wave observatory. In addition to numerous individually detectable DWDs, LISA will also detect an unresolved confusion foreground produced by the underlying Galactic population, which will affect the detectability of all LISA sources at frequencies below a few mHz. So far, the modelling of the DWD population for LISA has been based on binary population synthesis (BPS) techniques. The aim of this study is to construct an observationally driven population. To achieve this, we employ a model developed by Maoz, Hallakoun and Badenes (2018) for the statistical analysis of the local DWD population using two complementary large, multi-epoch, spectroscopic samples: the Sloan Digital Sky Survey (SDSS), and the Supernova Ia Progenitor surveY (SPY). We calculate the number of LISA-detectable DWDs and the Galactic confusion foreground, based on their assumptions and results. We find that the observationally driven estimates yield 1) 2 - 5 times more individually detectable DWDs than various BPS forecasts, and 2) a significantly different shape of the DWD confusion foreground. Both results have important implications for the LISA mission. A comparison between several variations to our underlying assumptions shows that our observationally driven model is robust, and that the uncertainty on the total number of LISA-detectable DWDs is in the order of 20 per cent., Comment: Published in Monthly Notices of the Royal Astronomical Society, Volume 511, Issue 4, pp.5936-5947

The science objectives of the LISA mission have been defined under the implicit assumption of a 4 yr continuous data stream. Based on the performance of LISA Pathfinder, it is now expected that LISA will have a duty cycle of $\approx 0.75$, which would reduce the effective span of usable data to 3 yr. This paper reports the results of a study by the LISA Science Group, which was charged with assessing the additional science return of increasing the mission lifetime. We explore various observational scenarios to assess the impact of mission duration on the main science objectives of the mission. We find that the science investigations most affected by mission duration concern the search for seed black holes at cosmic dawn, as well as the study of stellar-origin black holes and of their formation channels via multi-band and multi-messenger observations. We conclude that an extension to 6 yr of mission operations is recommended., Comment: 50 pages, 19 figures, 5 tables. Matches version published in GERG

Massive black hole binaries are expected to provide the strongest gravitational wave signals for the Laser Interferometer Space Antenna (LISA), a space mission targeting $\sim\,$mHz frequencies. As a result of the technological challenges inherent in the mission's design, implementation and long duration (4 yr nominal), the LISA data stream is expected to be affected by relatively long gaps where no data is collected (either because of hardware failures, or because of scheduled maintenance operations, such as re-pointing of the antennas toward the Earth). Depending on their mass, massive black hole binary signals may range from quasi-transient to very long lived, and it is unclear how data gaps will impact detection and parameter estimation of these sources. Here, we will explore this question by using state-of-the-art astrophysical models for the population of massive black hole binaries. We will investigate the potential detectability of MBHB signals by observing the effect of gaps on their signal-to-noise ratios. We will also assess the effect of the gaps on parameter estimation for these sources, using the Fisher Information Matrix formalism as well as full Bayesian analyses. Overall, we find that the effect of data gaps due to regular maintenance of the spacecraft is negligible, except for systems that coalesce within such a gap. The effect of unscheduled gaps, however, will probably be more significant than that of scheduled ones., Comment: 25 pages, 14 figures. Matches version published in Physical Review D

The Laser Interferometer Space Antenna (LISA) mission, scheduled for launch in the early 2030s, is a gravitational wave observatory in space designed to detect sources emitting in the milli-Hertz band. In contrast to the present ground based detectors, the LISA data are expected to be a signaldominated, with strong and weak gravitational wave signals overlapping in time and in frequency. Astrophysical population models predict a sufficient number of signals in the LISA band to blend together and form an irresolvable foreground noise. In this work, we present a generic method for characterizing the foreground signals originating from a given astrophysical population of coalescing compact binaries. Assuming idealized detector conditions and perfect data analysis technique capable of identifying and removing the bright sources, we apply an iterative procedure which allows us to predict the different levels of foreground noise.

We present a data analysis methodology for a model-independent reconstruction of the spectral shape of a stochastic gravitational wave background with LISA. We improve a previously proposed reconstruction algorithm that relied on a single Time-Delay-Interferometry (TDI) channel by including a complete set of TDI channels. As in the earlier work, we assume an idealized equilateral configuration. We test the improved algorithm with a number of case studies, including reconstruction in the presence of two different astrophysical foreground signals. We find that including additional channels helps in different ways: it reduces the uncertainties on the reconstruction; it makes the global likelihood maximization less prone to falling into local extrema; and it efficiently breaks degeneracies between the signal and the instrumental noise., Comment: 35 pages, 12 figures

The Laser Interferometer Space Antenna will be the first Gravitational Wave observatory in space. It is scheduled to fly in the early 2030's. LISA design predicts sensitivity levels that enable the detection a Stochastic Gravitational Wave Background signal. This stochastic type of signal is a superposition of signatures from sources that cannot be resolved individually and which are of various types, each one contributing with a different spectral shape. In this work we present a fast methodology to assess the detectability of a stationary, Gaussian, and isotropic stochastic signal in a set of frequency bins, combining information from the available data channels. We derive an analytic expression of the Bayes Factor between the instrumental noise-only and the signal plus instrumental noise models, that allows us to compute the detectability bounds of a given signal, as a function of frequency and prior knowledge on the instrumental noise spectrum., Comment: 15 pages, 3 figures

Since the 2017 Nobel Prize in Physics was awarded for the observation of gravitational waves, it is fair to say that the epoch of gravitational wave astronomy (GWs) has begun. However, a number of interesting sources of GWs can only be observed from space. To demonstrate the feasibility of the Laser Interferometer Space Antenna (LISA), a future gravitational wave observatory in space, the LISA Pathfinder satellite was launched on December, 3rd 2015. Measurements of the spurious forces accelerating an otherwise free-falling test mass, and detailed investigations of the individual subsystems needed to achieve the free-fall, have been conducted throughout the mission. This overview article starts with the purpose and aim of the mission, explains satellite hardware and mission operations and ends with a summary of selected important results and an outlook towards LISA. From the LISA Pathfinder experience, we can conclude that the proposed LISA mission is feasible., Comment: Preprint of an article submitted for consideration in Lepton-Photon 2017 conference proceedings \copyright 2019 copyright World Scientific Publishing Company

The science operations of the LISA Pathfinder mission has demonstrated the feasibility of sub-femto-g free-fall of macroscopic test masses necessary to build a LISA-like gravitational wave observatory in space. While the main focus of interest, i.e. the optical axis or the $x$-axis, has been extensively studied, it is also of interest to evaluate the stability of the spacecraft with respect to all the other degrees of freedom. The current paper is dedicated to such a study, with a focus set on an 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 part of the in-loop coordinates spectra. As will be presented, this model gives very good agreements with LISA Pathfinder flight data. It allows one to identify the physical noise source at the origin and the physical phenomena underlying the couplings. From this, the performances of the stability of the spacecraft, with respect to its geodesic, are extracted as a function of frequency. Close to $1 mHz$, the stability of the spacecraft on the $X_{SC}$, $Y_{SC}$ and $Z_{SC}$ degrees of freedom is shown to be of the order of $5.0\ 10^{-15} m\ s^{-2}/\sqrt{Hz}$ for X and $4.0 \ 10^{-14} m\ s^{-2}/\sqrt{Hz}$ for Y and Z. For the angular degrees of freedom, the values are of the order $3\ 10^{-12} rad\ s^{-2}/\sqrt{Hz}$ for $\Theta_{SC}$ and $3\ 10^{-13} rad\ s^{-2}/\sqrt{Hz}$ for $H_{SC}$ and $\Phi_{SC}$., Comment: 16 pages, 10 figures

During the On-Station Thermal Test campaign of the LISA Pathfinder the data and diagnostics subsystem was tested in nearly space conditions for the first time after integration in the satellite. The results showed the compliance of the temperature measurement system, obtaining temperature noise around $10^{-4}\,{\rm K}\, {\rm Hz}^{-1/2}$ in the frequency band of $1-30\;{\rm mHz}$. In addition, controlled injection of heat signals to the suspension struts anchoring the LISA Technology Package (LTP) Core Assembly to the satellite structure allowed to experimentally estimate for the first time the phase noise contribution through thermo-elastic distortion of the LTP interferometer, the satellite's main instrument. Such contribution was found to be at $10^{-12}\,{\rm m}\, {\rm Hz}^{-1/2}$, a factor of 30 below the measured noise at the lower end of the measurement bandwidth ($1\,{\rm mHz}$)., Comment: Submitted to CQG

LISA Pathfinder (LPF), ESA's precursor mission to a gravitational wave observatory, will measure the degree to which two test-masses can be put into free-fall, aiming to demonstrate a residual relative acceleration with a power spectral density (PSD) below 30 fm/s$^2$/Hz$^{1/2}$ around 1 mHz. In LPF data analysis, the measured relative acceleration data series must be fit to other various measured time series data. This fitting is required in different experiments, from system identification of the test mass and satellite dynamics to the subtraction of noise contributions from measured known disturbances. In all cases, the background noise, described by the PSD of the fit residuals, is expected to be coloured, requiring that we perform such fits in the frequency domain. This PSD is unknown {\it a priori}, and a high accuracy estimate of this residual acceleration noise is an essential output of our analysis. In this paper we present a fitting method based on Bayesian parameter estimation with an unknown frequency-dependent background noise. The method uses noise marginalisation in connection with averaged Welch's periodograms to achieve unbiased parameter estimation, together with a consistent, non-parametric estimate of the residual PSD. Additionally, we find that the method is equivalent to some implementations of iteratively re-weighted least-squares fitting. We have tested the method both on simulated data of known PSD, and to analyze differential acceleration from several experiments with the LISA Pathfinder end-to-end mission simulator., Comment: To appear Phys. Rev. D90 August 2014

The STOC (Science and Technology Operations Centre) simulator of the LPF (LISA PathFinder) mission is intended to provide a validation tool for the mission operations tele-commanding chain, as well as for a deeper understanding of the underlying physical processes happening in the LTP (LISA Technology Package). Amongst the different physical effects that will appear onboard, temperature fluctuations in the Electrode Housing (EH) could generate disturbances on the interferometer (IFO) readouts, therefore they must be known and controlled. In this article we report on the latest progress in the analysis at IEEC of the LTP response to thermal signals injected by means of heaters. More specifically, we determine the transfer functions relating heat input signals to forces on the Test Masses (TMs) in the LTP frequency band, from 1 mHz to 30 mHz. A complete thermal model of the entire LPF spacecraft plus payload, elaborated and maintained at European Space Technology Center (ESTEC), was used to obtain temperature distributions in response to heat inputs at prescribed spots (heaters), which are later processed to calculate the associated dynamical effects on the Test Masses., Comment: Submitted to JPCS for the Proceedings of the 8th LISA Symposium (2011)

The thermal experiments to be carried out onboard LISA Pathfinder (LPF) will provide essential information of the dependences of the instrument with respect to temperature variations. These thermal experiments must be modelled and simulated both to be validated for mission operations purposes and also to develop a data analysis tool able to characterise the temperature noise contribution to the instrument performance. Here we will present the models developed and the simulated signals for some of the experiments together with the corresponding interferometer readouts, the latter being computed by combining the thermal models with the global LTP (LISA Technology Package) simulator of the LTP Data Analysis team., Comment: Submitted to ASP Conference Series for the Proceedings of the 9th International LISA Symposium, 21-25 May 2012, Paris

The main goal of the LISA Pathfinder (LPF) mission is to fully characterize the acceleration noise models and to test key technologies for future space-based gravitational-wave observatories similar to the eLISA concept. The data analysis team has developed complex three-dimensional models of the LISA Technology Package (LTP) experiment on-board LPF. These models are used for simulations, but more importantly, they will be used for parameter estimation purposes during flight operations. One of the tasks of the data analysis team is to identify the physical effects that contribute significantly to the properties of the instrument noise. A way of approaching this problem is to recover the essential parameters of a LTP model fitting the data. Thus, we want to define the simplest model that efficiently explains the observations. To do so, adopting a Bayesian framework, one has to estimate the so-called Bayes Factor between two competing models. In our analysis, we use three main different methods to estimate it: The Reversible Jump Markov Chain Monte Carlo method, the Schwarz criterion, and the Laplace approximation. They are applied to simulated LPF experiments where the most probable LTP model that explains the observations is recovered. The same type of analysis presented in this paper is expected to be followed during flight operations. Moreover, the correlation of the output of the aforementioned methods with the design of the experiment is explored.

The OSE (Offline Simulations Environment) simulator of the LPF (LISA Pathfinder) mission is intended to simulate the different experiments to be carried out in flight. Amongst these, the thermal diagnostics experiments are intended to relate thermal disturbances and interferometer readouts, thereby allowing the subtraction of thermally induced interferences from the interferometer channels. In this paper we report on the modelling of these simulated experiments, including the parametrisation of different thermal effects (radiation pressure effect, radiometer effect) that will appear in the Inertial Sensor environment of the LTP (LISA Technology Package). We report as well how these experiments are going to be implemented in the LTPDA toolbox, which is a dedicated tool for LPF data analysis that will allow full traceability and reproducibility of the analysis thanks to complete recording of the processes., Comment: 10 pages