Expected integral flux from the Perseus cluster core within 0.15° and the associated 95%-c.l. MAGIC upper limits for the semi-analytical model (Left) and the extended model (Right). For the semi-analytical model, we show the spectrum predicted by Pinzke & Pfrommer (2010) (A_γ = 1, see text) and the one constrained by our upper limits for both cases with (solid lines) and without (dashed lines) EBL absorption. Arrows in light grey show our previous flux upper limits (MAGIC Collaboration 2012a). For both the semi-analytical and extended models, the EBL-absorbed spectra obtained by assuming that the Perseus radio mini-halo has a hadronic origin and fixing a central magnetic field value B₀ = 5,10, and 20 μG are shown in colours. We used as reference the radio surface brightness radial profile of the Perseus mini-halo at 1.4 GHz from Pedlar et al. (1990). Fluxes are integrated up to 10 TeV.