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The BL Lac Markarian 501 exhibited two flaring activities in the very-high-energy (VHE) band in May 2009. The lack of correlation between X-rays and TeV gamma-rays without increasing in other bands suggested that more than one emission zone could be involved. Moreover, fast variability in the flaring state was observed, indicating that the emission zones responsible must have small sizes. We use a lepto-hadronic model with two-zone emission to explain the spectral energy distribution during quiescent and these flaring states. In the proposed scenario, the photopion processes explain the VHE flaring activities successfully, and variability constraints place the activity in a zone located near the jet's base or named inner blob, while synchrotron self-Compton emission describing the X-ray signature during that flaring state occurs in the zone situated far the central engine or named outer blob. [ABSTRACT FROM AUTHOR]

The emission of the so-called extreme BL Lacs poses challenges to the particle acceleration models. The hardness of their spectrum, ≲ 2, in the high-energy band demands unusual parameters using the standard one-zone synchrotron self-Compton (SSC) model with a deficient magnetized plasma. Some authors use either two-zone or hadronic/lepto-hadronic models to relax these atypical values. In this work, we present a lepto-hadronic two-zone model to explain the multi-wavelength observations of the six best-known extreme BL Lacs. The very-high-energy gamma-ray observations are described by the photo-hadronic processes in a blob close to the AGN core and by SSC and external inverse Compton-processes in an outer blob. The photo-hadronic interactions occur when accelerated protons in the inner blob interact with annihilation line photons from a sub-relativistic pair plasma. The X-ray observations are described by synchrotron radiation from the outer blob. The parameter values found from the description of the spectral energy distribution for each object with our phenomenological model are similar to each other, and lie in the typical range reported in BL Lacs. [ABSTRACT FROM AUTHOR]