Euclid preparation. XCII. Controlling angular systematics in the Euclid spectroscopic galaxy sample

We present the strategy used to identify and mitigate potential sources of angular systematics in the \textit{Euclid} spectroscopic galaxy survey, and we quantify their impact on galaxy clustering measurements and cosmological parameter estimation. We first surveyed the \textit{Euclid} processing pipeline to identify all evident, potential sources of systematics, and classified them into two broad classes: angular systematics, which modulate the galaxy number density across the sky, and catastrophic redshift errors, which lead to interlopers in the galaxy sample. We then used simulated spectroscopic surveys to test our ability to mitigate angular systematics by constructing a random catalogue that represents the `visibility mask' of the survey; this is a dense set of intrinsically unclustered objects, subject to the same selection effects as the data catalogue. The construction of this random catalogue relies on a detection model, which gives the probability of reliably measuring the galaxy redshift as a function of the signal-to-noise ratio (S/N) of its emission lines. We demonstrate that, in the ideal case of a perfect knowledge of the visibility mask, the galaxy power spectrum in the presence of systematics is recovered, to within sub-per cent accuracy, by convolving a theory power spectrum with a window function obtained from the random catalogue itself. In the case of only approximate knowledge of the visibility mask, we test the stability of power spectrum measurements and cosmological parameter posteriors by using perturbed versions of the random catalogue. We find that significant effects are limited to very large scales, and parameter estimation remains robust; the most impacting effects are connected to the calibration of the detection model.