In-depth analysis of LISA Pathfinder performance results: Time evolution, noise projection, physical models, and implications for LISA

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: (1) The evolution of the Brownian noise that dominates the acceleration amplitude spectral density (ASD), for frequencies ???1 mHz, is consistent with the decaying pressure due to the outgassing of a single gaseous species. (2) Between ??=36 ??Hz and 1 mHz, the acceleration ASD shows a 1/?? tail in excess of the Brownian noise of almost constant amplitude, with ?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 ??=18 ??Hz, the ASD significantly deviates from the 1/?? behavior, because of temperature fluctuations that appear to modulate a quasistatic 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/?? 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.