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The Fornax Deep Survey with VST. I. The extended and diffuse stellar halo of NGC~1399 out to 192 kpc

[Abrigded] We have started a new deep, multi-imaging survey of the Fornax cluster, dubbed Fornax Deep Survey (FDS), at the VLT Survey Telescope. In this paper we present the deep photometry inside two square degrees around the bright galaxy NGC1399 in the core of the cluster. We found a very extended and diffuse envelope surrounding the luminous galaxy NGC1399: we map the surface brightness out to 33 arcmin (~ 192 kpc) from the galaxy center and down to about 31 mag/arcsec^2 in the g band. The deep photometry allows us to detect a faint stellar bridge in the intracluster region between NGC1399 and NGC1387. By analyzing the integrated colors of this feature, we argue that it could be due to the ongoing interaction between the two galaxies, where the outer envelope of NGC1387 on its east side is stripped away. By fitting the light profile, we found that it exists a physical break radius in the total light distribution at R=10 arcmin (~58 kpc) that sets the transition region between the bright central galaxy and the outer exponential stellar halo. We discuss the main implications of this work on the build-up of the stellar halo at the center of the Fornax cluster. By comparing with the numerical simulations of the stellar halo formation for the most massive BCGs, we find that the observed stellar halo mass fraction is consistent with a halo formed through the multiple accretion of progenitors with a stellar mass in the range 10^8 - 10^11 M_sun. This might suggest that the halo of NGC1399 has also gone through a major merging event. The absence of a significant number of luminous stellar streams and tidal tails out to 192 kpc suggests that the epoch of this strong interaction goes back to an early formation epoch. Therefore, differently from the Virgo cluster, the extended stellar halo around NGC1399 is characterised by a more diffuse and well-mixed component, including the ICL.