The Fornax Deep Survey (FDS) with the VST: IV. A size and magnitude limited catalog of dwarf galaxies in the area of the Fornax cluster

The Fornax Deep Survey (FDS), an imaging survey in the u', g', r', and i'-bands, has a supreme resolution and image depth compared to the previous spatially complete Fornax Cluster Catalog (FCC). Our new data allows us to study the galaxies down to r'-band magnitude m$_{r'}\approx$21 mag (M$_{r'}\approx$-10.5 mag). These data provide an important legacy dataset to study the Fornax cluster. We aim to present the Fornax Deep Survey (FDS) dwarf galaxy catalog, focusing on explaining the data reduction and calibrations, assessing the quality of the data, and describing the methods used for defining the cluster memberships for the catalog objects. As a first step we used the SExtractor fine-tuned for dwarf galaxy detection, to find galaxies from the FDS data, covering a 26 deg$^2$ area of the main cluster, and the area around the Fornax A substructure. We made 2D-decompositions of the identified galaxies using GALFIT. We used color-magnitude, luminosity-radius and luminosity-concentration relations to separate the cluster galaxies from the background galaxies. We then divided the cluster galaxies into early- and late-type galaxies according to their morphology and gave first order morphological classifications. Our final catalog includes 14,095 galaxies. We classify 590 galaxies as being likely Fornax cluster galaxies, of which 564 are dwarfs (M$_{r'}$ > -18.5 mag) consisting our Fornax dwarf catalog. Of the cluster dwarfs we classify 470 as early-types, and 94 as late-type galaxies. Our final catalog reaches its 50% completeness limit at magnitude M$_{r'}$ = -10.5 mag and surface brightness $\bar{\mu}_{e,r'}$ = 26 mag arcsec-2, which is approximately three magnitudes deeper than the FCC. Based on previous works and comparison with a spectroscopically confirmed subsample, we estimate that our final Fornax dwarf galaxy catalog has < 10% contamination from the background objects.