Abstract: The Fornax galaxy cluster is the richest nearby (D ~ 20 Mpc) galaxy association in the southern sky. As such, it provides a wealth of oportunities to elucidate on the processes where environment holds a key role in transforming galaxies. Although it has been the focus of many studies, Fornax has never been explored with contiguous homogeneous wide-field imaging in 12 photometric narrow- and broad-bands like those provided by the Southern Photometric Local Universe Survey (S-PLUS). In this paper we present the S-PLUS Fornax Project (S+FP) that aims to comprehensively analyse the galaxy content of the Fornax cluster using S-PLUS. Our data set consists of 106 S-PLUS wide-field frames (FoV ~ 1.4 x 1.4 deg$^2$) observed in five SDSS-like ugriz broad-bands and seven narrow-bands covering specific spectroscopic features like [OII], CaII H+K, H$\delta$, G-band, Mg b triplet, H$\alpha$, and the CaII triplet. Based on S-PLUS specific automated photometry, aimed at correctly detecting Fornax galaxies and globular clusters in S-PLUS images, our dataset provides the community with catalogues containing homogeneous 12-band photometry for ~ 3 x 10$^6$ resolved and unresolved objects within a region extending over ~ 208 deg$^2$ (~ 5 Rvir in RA) around Fornax' central galaxy, NGC 1399. We further explore the EAGLE and IllustrisTNG cosmological simulations to identify 45 Fornax-like clusters and generate mock images on all 12 S-PLUS bands of these structures down to galaxies with M$\star \geq 10^8$ M$\odot$. The S+FP dataset we put forward in this first paper of a series will enable a variety of studies some of which are briefly presented.
Comment: 25 pages, 30 figures, accepted for publication in MNRAS
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