AMICO galaxy clusters in KiDS-DR3: sample properties and selection function.

We present the first catalogue of galaxy cluster candidates derived from the third data release of the Kilo-Degree Survey. The sample of clusters has been produced using the Adaptive Matched Identifier of Clustered Objects (AMICO) algorithm. In this analysis, AMICO considers the luminosity, spatial distribution, and photo-z of galaxies, without performing any selection based on their colours. In this way, we minimize the dependence of the selection function on the detectability or even absence of the red sequence in the clusters. The catalogue comprises 7988 candidate galaxy clusters in the redshift range 0.1 < z < 0.8 down to signal-to-noise ratio > 3.5 with a purity approaching 95 per cent over the entire redshift range. In addition to the catalogue of galaxy clusters, we also provide a catalogue of galaxies with their probabilistic association to the detected clusters. We quantify the sample purity, completeness, and the uncertainties of the detections properties, such as richness, redshift, and position, by means of mock galaxy catalogues. The simulations are derived directly from the data to fully reproduce their statistical properties including photo-z uncertainties, unknown absorption across the survey, missing data, spatial correlation of galaxies, and galaxy clusters. Being based on real data, such mock catalogues do not have to rely on the assumptions on which numerical simulations and semi-analytic models are based on. This paper is the first of a series of papers in which we discuss the details and physical properties of the sample presented in this work.