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Context: The blazar Markarian 421 is one of the brightest TeV gamma-raysources of the northern sky. From December 2007 until June 2008 it wasintensively observed in the very high energy (VHE, E > 100 GeV) band by thesingle-dish Major Atmospheric Gamma-ray Imaging Cherenkov telescope (MAGIC-I).Aims: We aimed to measure the physical parameters of the emitting region of theblazar jet during active states. Methods: We performed a dense monitoring ofthe source in VHE with MAGIC-I, and also collected complementary data in softX-rays and optical-UV bands; then, we modeled the spectral energy distributions(SED) derived from simultaneous multi-wavelength data within the synchrotronself--compton (SSC) framework. Results: The source showed intense and prolongedgamma-ray activity during the whole period, with integral fluxes (E > 200 GeV)seldom below the level of the Crab Nebula, and up to 3.6 times this value.Eight datasets of simultaneous optical-UV (KVA, Swift/UVOT), soft X-ray(Swift/XRT) and MAGIC-I VHE data were obtained during different outburstphases. The data constrain the physical parameters of the jet, once thespectral energy distributions obtained are interpreted within the framework ofa single-zone SSC leptonic model. Conclusions: The main outcome of the study isthat within the homogeneous model high Doppler factors (40 <= delta <= 80) areneeded to reproduce the observed SED; but this model cannot explain theobserved short time-scale variability, while it can be argued thatinhomogeneous models could allow for less extreme Doppler factors, more intensemagnetic fields and shorter electron cooling times compatible with hour orsub-hour scale variability.

Mrk 421 active state in 2008: the MAGIC view, simultaneous multi-wavelength observations and SSC model constrained