Very High Energy Gamma-Ray Observations of a Strong Flaring Activity in M87 in 2008 February

M87 is the only known non blazar radio galaxy to emit very high energy (VHE) gamma-rays. During a monitoring program of M87, a rapid flare in VHE gamma-rays was detected by the MAGIC telescope in early 2008. The flux was found to be variable above 350 GeV on a timescale as short as 1 day at a significance level of $5.6\sigma$. The highest measured flux reached 15% of the Crab Nebula flux. We observed several substantial changes of the flux level during the 13 day observing period. The flux at lower energies (150 -- 350 GeV), instead, is compatible with being constant. The energy spectrum can be described by a power law with a photon index of $2.30 \pm 0.11_\mathrm{stat} \pm 0.20_\mathrm{syst}$. The observed day-scale flux variability at VHE prefers the M87 core as source of the emission and implies that either the emission region is very compact (just a few Schwarzschild radii) or the Doppler factor of the emitting blob is rather large in the case of a non expanding emission region.