  The pair of large radio lobes in the Virgo cluster, each about 23 kpc in
radius, have curiously sharp outer edges where the radio-synchrotron continuum
flux declines abruptly. However, just adjacent to this sharp transition, the
radio flux increases. This radio limb-brightening is observed over at least
half of the perimeter of both lobes. We describe slowly propagating steady
state diffusion fronts that explain these counterintuitive features. Because of
the natural buoyancy of radio lobes, the magnetic field is largely tangent to
the lobe boundary, an alignment that polarizes the radio emission and
dramatically reduces the diffusion coefficient of relativistic electrons. As
cosmic ray electrons diffuse slowly into the cluster gas, the local magnetic
field and gas density are reduced as gas flows back toward the radio lobe.
Radio emission peaks can occur because the synchrotron emissivity increases
with magnetic field and then decreases with the density of non-thermal
electrons. A detailed comparison of steady diffusion fronts with quantitative
radio observations may reveal information about the spatial variation of
magnetic fields and the diffusion coefficient of relativistic electrons. On
larger scales, some reduction of the gas density inside the Virgo lobes due to
cosmic ray pressure must occur and may be measurable. Such X-ray observations
could reveal important information about the presence of otherwise unobservable
non-thermal components such as relativistic electrons of low energy or proton
cosmic rays.
