  We present an analysis of Planck satellite data on the Coma Cluster observed
via the Sunyaev-Zeldovich effect. Planck is able, for the first time, to detect
SZ emission up to r ~ 3 X R_500. We test previously proposed models for the
pressure distribution in clusters against the azimuthally averaged data. We
find that the Arnaud et al. universal pressure profile does not fit Coma, and
that their pressure profile for merging systems provides a good fit of the data
only at r<R_500: by r=2XR_500 it underestimates the observed y profile by a
factor of ~2. This may indicate that at these larger radii either i) the
cluster SZ emission is contaminated by unresolved SZ sources along the line of
sight or ii) the pressure profile of Coma is higher at r>R_500 than the mean
pressure profile predicted by the simulations. The Planck image shows
significant local steepening of the y profile in two regions about half a
degree to the west and to the south-east of the cluster centre. These features
are consistent with the presence of shock fronts at these radii, and indeed the
western feature was previously noticed in the ROSAT PSPC mosaic as well as in
the radio. Using Planck y profiles extracted from corresponding sectors we find
pressure jumps of 4.5+0.4-0.2 and 5.0+1.3-0.1 in the west and southeast,
respectively. Assuming Rankine-Hugoniot pressure jump conditions, we deduce
that the shock waves should propagate with Mach number M_w=2.03+0.09-0.04 and
M_se=2.05+0.25-0.02 in the West and Southeast, respectively. Finally, we find
that the y and radio-synchrotron signals are quasi-linearly correlated on Mpc
scales with small intrinsic scatter. This implies either that the energy
density of cosmic-ray electrons is relatively constant throughout the cluster,
or that the magnetic fields fall off much more slowly with radius than
previously thought.
