RCW 86 is a young supernova remnant (SNR) showing a shell-type structure at several wavelengths and is thought to be an efficient cosmic-ray (CR) accelerator. Earlier textit{Fermi} Large Area Telescope results reported the detection of $gamma$-ray emission coincident with the position of RCW 86 but its origin (leptonic or hadronic) remained unclear due to the poor statistics. Thanks to 6.5 years of data acquired by the textit{Fermi}-LAT and the new event reconstruction Pass 8, we report the significant detection of spatially extended emission coming from RCW 86. The spectrum is described by a power-law function with a very hard photon index ($Gamma = 1.42 pm 0.1_{rm stat} pm 0.06_{rm syst}$) in the 0.1--500 GeV range and an energy flux above 100 MeV of ($2.91$ $pm$ $0.8_{rm stat}$ $pm$ $0.12_{rm syst}$) $times$ $10^{-11}$ erg cm$^{-2}$ s$^{-1}$. Gathering all the available multiwavelength (MWL) data, we perform a broadband modeling of the nonthermal emission of RCW 86 to constrain parameters of the nearby medium and bring new hints about the origin of the $gamma$-ray emission. For the whole SNR, the modeling favors a leptonic scenario in the framework of a two-zone model with an average magnetic field of 10.2 $pm$ 0.7 $mu$G and a limit on the maximum energy injected into protons of 2 $times$ 10$^{49}$ erg for a density of 1 cm$^{-3}$. In addition, parameter values are derived for the North-East (NE) and South-West (SW) regions of RCW 86, providing the first indication of a higher magnetic field in the SW region.
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