  We present an extensive study of the BL Lac object Mrk 501 based on a data
set collected during the multi-instrument campaign spanning from 2009 March 15
to 2009 August 1 which includes, among other instruments, MAGIC, VERITAS,
Whipple 10-m, Fermi-LAT, RXTE, Swift, GASP-WEBT and VLBA. We find an increase
in the fractional variability with energy, while no significant interband
correlations of flux changes are found in the acquired data set. The higher
variability in the very high energy (>100 GeV, VHE) gamma-ray emission and the
lack of correlation with the X-ray emission indicate that the highest-energy
electrons that are responsible for the VHE gamma-rays do not make a dominant
contribution to the ~1 keV emission. Alternatively, there could be a very
variable component contributing to the VHE gamma-ray emission in addition to
that coming from the synchrotron self-Compton (SSC) scenarios. The space of SSC
model parameters is probed following a dedicated grid-scan strategy, allowing
for a wide range of models to be tested and offering a study of the degeneracy
of model-to-data agreement in the individual model parameters. We find that
there is some degeneracy in both the one-zone and the two-zone SSC scenarios
that were probed, with several combinations of model parameters yielding a
similar model-to-data agreement, and some parameters better constrained than
others. The SSC model grid-scan shows that the flaring activity around 2009 May
22 cannot be modeled adequately with a one-zone SSC scenario, while it can be
suitably described within a two-independent-zone SSC scenario. The observation
of an electric vector polarization angle rotation coincident with the gamma-ray
flare from 2009 May 1 resembles those reported previously for low frequency
peaked blazars, hence suggesting that there are many similarities in the
flaring mechanisms of blazars with different jet properties.
