  We present deep radio observations of four nearby dwarf spheroidal (dSph)
galaxies, designed to detect extended synchrotron emission resulting from
weakly interacting massive particle (WIMP) dark matter annihilations in their
halos. Models by Colafrancesco et al. (CPU07) predict the existence of
angularly large, smoothly distributed radio halos in such systems, that stem
from electron and positron annihilation products spiraling in a turbulent
magnetic field. We map a total of 40.5 deg^2 around the Draco, Ursa Major II,
Coma Berenices, and Willman 1 dSphs with the GBT at 1.4 GHz to detect this
annihilation signature, greatly reducing discrete-source confusion using the
NVSS catalog. We construct radial surface brightness profiles from each of the
subtracted maps, and jackknife the data to quantify the significance of the
features therein. At the 10 arcmin resolution of our observations, foregrounds
contribute a standard deviation of 1.8 - 5.7 mJy/beam to our high-latitude
maps, with the emission in the Draco and Coma dominated by foregrounds. On the
other hand, we find no significant emission in the Ursa Major II and Willman 1
fields, and explore the implications of non-detections in these fields for
particle dark matter using the fiducial models of CPU07. For a WIMP mass of 100
GeV annihilating into $b\bar{b}$ final states and B = 1 muG, upper limits on
the annihilation cross-section for Ursa Major II and Willman I are
log<ov,cm^3/s> < -25 for the prefereed set of charged particle propagation
parameters adopted by CPU07; this is comparable to that inferred at gamma-ray
energies from the two-year Fermi-LAT data. We discuss three avenues for
improving the constraints on <ov> presented here, and conclude that deep radio
observations of dSphs are highly complementary to indirect WIMP searches at
higher energies.
