Residual test mass acceleration in LISA Pathfinder: in-depth statistical analysis and physical sources

LISA Pathfinder (LPF) has been a space mission led by ESA with NASA contributions, operating between March 2016 and July 2017. LPF demonstrated the feasibility of setting bodies in space along freely-falling geodetic trajectories, complying with the residual acceleration requirements of the future gravitational-wave observatory LISA. After operations, the LPF Collaboration pointed out that two phenomena, affecting the sub-mHz performance, were not completely understood and needed deeper analyses. This, despite performing better than requirements. Such phenomena are, namely, the low-frequency acceleration noise, and the sub-pN transient acceleration glitches. This thesis work focuses entirely on analyzing these observations, in view of the future mission LISA. Regarding the low-frequency sub-mHz noise, first, we make a preliminary analysis. We investigate its evolution in time, its properties, its stability, and its nature. We find that the low-frequency noise has had a remarkably stable behavior for nearly two years, but noise fluctuations are not compatible with an overall unique noise. We develop results on multivariate spectral estimation. Implementing results from complex-variable statistics, we show that cross-power spectral density matrices follow complex-Wishart probability distributions; we develop a Bayesian tool for the posterior inference of spectral parameters. We develop decorrelation tools to understand the measured noise's physical origin. In particular, we aim at finding, if any, correlations between the main acceleration measurement and synchronously measured time series. Then, we summarize the most recent understanding of the LPF acceleration performance. We expand previous analyses about the LPF outgassing environment, through the analysis of the white "Brownian" noise, and the long-term quasi-static acceleration drift observed on LPF, proposing a physical model. We extensively analyze the second phenomenon impacting low-frequency performances, the acceleration transient glitches. We show that LPF glitches spanned a wide range of amplitudes, transferring impulses between a few fN s, to some nN s, and showing durations ranging from a few seconds to hours. We show that LPF glitches fall into two rather distinct categories: fast transients in the interferometric motion readout and long-lasting sub-pN force transient events, acting on the test masses. We present an analysis of the physical and statistical properties of both, including a cross-investigation with other time series and other dynamical variables, and examine the possible sources of glitches, identifying the most likely ones.