  We present a spatially resolved spectral analysis of full ASCA observations
of the remnant of the supernova of 1006 AD. This remnant shows both nonthermal
X-ray emission from bright limbs, generally interpreted as synchrotron emission
from the loss-steepened tail of the nonthermal electron population also
responsible for radio emission, and thermal emission from elsewhere in the
remnant. In earlier work, we showed that the spatially integrated spectrum was
well described by a theoretical synchrotron model in which shock acceleration
of electrons was limited by escape, in combination with thermal models
indicating high levels of iron from ejecta. Here we use new spatially resolved
subsets of the earlier theoretical nonthermal models for the analysis. We find
that emission from the bright limbs remains well described by those models, and
refine the values for the characteristic break frequency. We show that
differences between the northeast and southwest nonthermal limbs are small, too
small to account easily for the presence of the northeast limb, but not the
southwest, in TeV gamma-rays. Comparison of spectra of the nonthermal limbs and
other regions confirms that simple cylindrically symmetric nonthermal models
cannot describe the emission, and we put limits on nonthermal contributions to
emission from the center and the northwest and southeast limbs. We can rule out
solar-abundance models in all regions, finding evidence for elevated
abundances. However, more sophisticated models will be required to accurately
characterize these abundances.
