evolve slowly with time, the next step was to remove that stable periodic component from the signal and inspect
the residuals. Fig. 12 shows them for telescope 1, together with the temperature readings in one of the on-board
computers (VPU5) and the number of stars observed in the astrometric and spectroscopic focal planes. Two
effects are clearly visible. First, there is a ∼24 hours slow evolution component in addition to the six hours main
period. Second, there are peaks related to the number of stars observed.

[Figure: Figure 11. Spin restart in July 2014. The basic angle variations started very soon after spacecraft spin resumed, giving support to a service module driven thermoelastic hypothesis.]

[Figure: Figure 12. Telescope 1 BAM Fourier fit residuals against the temperature of VPU5 (one computer in the service module, reversed scale) and the number of stars observed in the astrometric, photometric and spectroscopic focal planes.]

The 24 hours period was later identified as an effect of the way the downlink is operated. Even though the phased array antenna is never switched-off, the signal coding scheme changed between ground station contacts (complex signal encoding only when downlink was active). This meant the transponders consumed more power during the contacts, which are typically scheduled according to a 24 hour logic. It was decided to force signal encoding without data transmission in the antenna outside contacts (except when spacecraft ranging is needed). This action reduced the impact of the 24 hours basic variation by more than half.
The correlation with the number of stars was puzzling at first glance, due to the negligible brightness of stellar sources. However, many service module components are affected by a bigger data rate, most notably the computers and the on-board data storage. A clear correlation thus exists between e.g. VPU5 and the peak basic angle variations, giving further support to the thermoelastic hypothesis. The rule of thumb is a contribution of 0-100 µas basic angle variation per degree of thermal change amplitude for each equipment in the service module.
The normal succession of events on-board (e.g. safe modes, antenna and on-board storage switch-off, star tracker changes, ...) provided lots of data (events) to infer the influence of many systems in the basic angle variations. However, it was deemed necessary to carry out a systematic sensitivity analysis. In this way, two days of nominal mission time were devoted to ad-hoc tests just before a payload decontamination took place in June 2015. Short heat pulses were locally introduced using survival heaters throughout the spacecraft, beginning with the service module and ending with the mirrors in the payload, the temperature changes were recorded through house-keeping and confronted to the basic angle variations measured by the BAM. See Fig 13. This very clean data set confirmed many suspicions (impact of computers and antenna), and revealed interesting unknown effects, such as the link to the atomic clock and one mirror (M4B) in the service and payload modules, respectively. The newly found sensitivities, even if large, play a minor role, due to the very high thermal stability of these components (the effect is the product of the senstivity times the variation).
Three additional and crude simplfying assumptions were added to the basic thermoelastic hypothesis to gain further insight on the origin of the perturbations. First, the variations are the result of Sun-side SVM temperature variations alone. Second, the house keeping temperatures provide a sufficient temporal and spatial sampling of the major changes (a sort of extreme macro-node analysis). Third, the BAM signal can be decomposed as the linear sum of several such temperatures via principal component analysis. No time delays were considered. Several temperature combinations were tested. Two of them are shown in Fig. 14. The results confirm the major features in the basic angle variations can be reproduced in terms of the thermoelastic hypothesis. However, the decomposition is not unique, which prevents the identification of a single origin for the variations. This means such a minimalistic analysis is too simple, and the Fourier content of the service module temperature variations is the same for many systems.
An alternative explanation for the larger than expected basic angle variations relied on the Gaia opto-elastic rigidity being much smaller than the model predictions. That is, if there is something loose within the payload. This hypothesis was tested analysing the BAM readings obtained during spacecraft station keeping manoeuvres, which are carried out routinely to maintain the orbit around the metastable L2 point. They use the chemical propulsion thrusters, which apply forces in the range ∼1-10 N. Fig. 15 shows an example of actuation, together with the associated transient impact on the basic angle. A careful analysis of several actuations reveals the results are basically compatible with the opto-mechanical model, and refutes a simple mechanical origin (e.g. based on inertial forces) for the basic angle variations.