# 2.4.4 Basic angle variation determination

Author(s): Alcione Mora

The Gaia measurement principle is that differences in the transit time between stars observed by each telescope can be translated into angular measurements (see Gaia Collaboration et al. 2016 for details). All these measurements are affected if the basic angle (the angle between the two telescopes, $\Gamma=106\mbox{.\!\!^{\circ}}5$; Section 1.1.3) varies with time. Either the angle needs to be ultra-stable, or its variations be known to the mission accuracy level ($\approx$$\mu$as).

Gaia is largely self-calibrating (i.e., all calibration parameters are estimated from the science observations; see Gaia Collaboration et al. 2016 for details). Low-frequency variations of the basic angle ($f<1/2P_{\rm rot}$, with $P_{\rm rot}=6$ h) can be fully eliminated by self-calibration. High-frequency random variations are also not a concern because they are averaged during all transits. However, intermediate-frequency variations are difficult to eliminate by self-calibration, especially if they are synchronised with the spacecraft spin phase, such that the residuals can introduce systematic errors (biases) in the astrometric results (Michalik and Lindegren 2016; Butkevich et al. 2017). As a result, intermediate-frequency changes of the basic angle need to be monitored by metrology.

The BAM device (Section 1.1.3) is continuously measuring differential changes in the basic angle. It basically generates one fixed, artificial star per telescope by introducing two collimated laser beams into each primary mirror (see Figure 2.9). The BAM is composed of two optical benches in charge of producing the interference pattern for each telescope. A number of optical fibres, polarisers, beam splitters, and mirrors are used to generate all four beams from one common light source. See Gaia Collaboration et al. (2016) and Gielesen et al. (2012) for further details. Each Gaia telescope then generates an image on the same, dedicated BAM CCD, which is an interference pattern due to the coherent input light source. The relative along-scan displacement between the two fringe patterns is a direct measurement of the basic-angle variations.

A detailed description of the BAM data model, the data collection, fitting, and daily processing is outlined in Section 7 of Fabricius et al. (2016).