Planck intermediate results. XXXIV. The magnetic field structure in the
  Rosette Nebula
  Planck has mapped the polarized dust emission over the whole sky, making it
possible to trace the Galactic magnetic field structure that pervades the
interstellar medium (ISM). We combine polarization data from Planck with
rotation measure (RM) observations towards a massive star-forming region, the
Rosette Nebula in the Monoceros molecular cloud, to study its magnetic field
structure and the impact of an expanding HII region on the morphology of the
field. We derive an analytical solution for the magnetic field, assumed to
evolve from an initially uniform configuration following the expansion of
ionized gas and the formation of a shell of swept-up ISM. From the RM data we
estimate a mean value of the line-of-sight component of the magnetic field of
about 3microG (towards the observer) in the Rosette Nebula, for a uniform
electron density of about 12cm-3. The dust shell that surrounds the Rosette HII
region is clearly observed in the Planck intensity map at 353 GHz, with a
polarization signal significantly different from that of the local background
when considered as a whole. The Planck observations constrain the
plane-of-the-sky orientation of the magnetic field in the Rosette's parent
molecular cloud to be mostly aligned with the large-scale field along the
Galactic plane. The Planck data are compared with the analytical model, which
predicts the mean polarization properties of a spherical and uniform dust shell
for a given orientation of the field. This comparison leads to an upper limit
of about 45degr on the angle between the line of sight and the magnetic field
in the Rosette complex, for an assumed intrinsic dust polarization fraction of
4%. This field direction can reproduce the RM values detected in the ionized
region if the magnetic field strength in the Monoceros molecular cloud is in
the range 6.5--9microG.
