We investigate the diffusion of cosmic rays into molecular cloud complexes.
Using the cosmic-ray diffusion formalism of Protheroe, et al. (2008), we
examine how cosmic rays diffuse into clouds exhibiting different density
structures, including a smoothed step-function, as well as Gaussian and
inverse-r density distributions, which are well known to trace the structure
of star-forming regions. These density distributions were modelled as an
approximation to the Galactic centre cloud G0.216+0.016, a recently-discovered
massive dust clump that exhibits limited signs of massive star formation and
thus may be the best region in the Galaxy to observe synchrotron emission from
secondary electrons and positrons. Examination of the resulting synchrotron
emission, produced by the interaction of cosmic ray protons interacting with
ambient molecular matter producing secondary electrons and positrons reveals
that, due to projection effects, limb-brightened morphology results in all
cases. However, we find that the Gaussian and inverse-r density distributions
show much broader flux density distributions than step-function distributions.
Significantly, some of the compact (compared to the 2.2′′ resolution, 5.3 GHz
JVLA observations) sources show non-thermal emission, which may potentially be
explained by the density structure and the lack of diffusion of cosmic rays
into the cloud. We find that we can match the 5.3 and 20 GHz flux densities of
the non-thermal source JVLA~1 and 6 from Rodr\'{\i}guez & Zapata (2014) with a
local cosmic ray flux density, a diffusion coefficient suppression factor of
χ=0.1−0.01 for a coefficient of 3×1027 cm2 s−1, and a
magnetic field strength of 470 μG.Comment: 4 pages, 2 figures, accepted for publication in the Astrophysical
Journal Letter