In the years prior to launch, the Gaia Data Processing Consortium set up the Gaia Radiation Task Force, with the goal of developing the most effective model for the treatment of the effects of CTI on Gaia images. In the Task Force initial investigation, it soon became clear that to deal with the constraints posed by the very large volume of Gaia observations and the available computational resources, the only effective way to handle CTI without introducing a noise component of unknown characteristics in the data was through a ‘forward modelling’ approach, in which the model of a source signal is distorted using the adopted Article number, page 4
CTI algorithm, and the derived damaged stellar profile is then compared to the measured flux of the source. The first CTI modelling implementation proposed by the Radiation Task Force was completely empirical, and was intended to be simple and therefore computationally fast, to be built upon over time with more detailed and realistic models, closer to the true physical nature of the damage. The most sophisticated model that followed the initial approach was named ‘Charge Distortion Model 03’, CDM-03. In CDM-03, the proposed analytical model (Short et al. 2013) is based on the physical theory of charge traps known as Shockley-Read-Hall (SRH, Shockley & Read (1952)). Two aspects of this model are particularly important. Firstly, the process of capture of electrons by the traps is not assumed to be instantaneous, as in the case of more traditional CTI models, but instead follows a probabilistic mechanisms, that is a function of the number of electrons in the signal. Moreover, the concept of a ‘density driven’ regime to model the physical volume occupied by a signal charge cloud within a pixel was introduced in CDM-03. This was in contrast with the classical ‘volume driven’ CTI modelling, in which the occupied volume grows with the number of electrons in the signal. In the density driven regime the signal occupies all the available pixel volume, no matter its size. This choice was made to account for the results observed in Gaia irradiated devices before launch, that presented an unexpectedly large reduction in the measured CTI in the presence of a low, constant diffuse optical background. This was suggestive of the fact that the presence of a handful of electrons in each pixel of the detector had the effect of keeping the defects filled, mitigating the effects of CTI. The CTI model developed for this work, named CtiPixel, inherits the fundamental principles on which the initial Gaia Radiation Task Force approach and the CDM-03 model were based upon, and integrates them with tasks to closely reproduce the readout of charge signal in the serial register of Gaia CCDs. In particular, it implements a ‘forward modelling’ treatment of the CTI effects and a physical characterisation of radiation damage, including the stochastic nature of charge trapping and release. It also includes the modelling of the impact on CTI of the ‘scene’, intended as the set of components present in the image in addition to the source signal itself, such as the one from other nearby stars or from straylight. The additional components have an impact on dynamics of the traps statistics, as for example a diffuse background signal can fill traps and lower the measured effects of CTI (this is known as the ‘sacrificial charge’ effect). Finally, CtiPixel adopts a pixel based implementation, modelling the charge losses, the transfer of charge and the evolution of the trap statistics at the pixel level. The choice of a physical model over a set of empirically derived functions has a number of important advantages. For instance, linking the model parameters to the physical properties of the damage makes their interpretation straightforward, giving insights into the nature of the defects that are generated by space irradiation; moreover, the parameters derived from a physical model are independent of the CCD operating modes and settings, and can be directly applied to different data types and scenarios. The choice of a pixel level implementation comes at the cost of a high demand in computational resources and processing time, but avoids simplifications and approximations, providing a benchmark CDM version of the highest accuracy. CtiPixel has been employed to process the datasets acquired during the serial calibration activities that were described in Section 3. When the signal in the serial register line is processed the readout is simulated assuming an initial uniform A defect can capture an electron if its location is within the physical volume occupied by the signal (its confinement volume Vc).

[Figure: Fig. 2: Example charge trails from three epochs of Gaia in–orbit serial CTI calibration activities. The mean level of the charge injection in the image section CCD columns is shown before the start of the post-scan measurements illustrating the 2 orders–of– magnitude range in the commanded blocks. A small increase in serial CTI is observed from early to late epochs in the mission time line, particularly for the release signature at longer timescales. These data come from device AF5 on row 5 near the middle of the focal plane array.]