Steady X-Ray Synchrotron Emission in the Northeastern Limb of SN 1006

We investigate time variations and detailed spatial structures of X-ray synchrotron emission in the northeastern limb of SN 1006, using two Chandra observations taken in 2000 and 2008. We extract spectra from a number of small ([approx]10'') regions. After taking account of proper motion and isolating the synchrotron from the thermal emission, we study time variations in the synchrotron emission in the small regions. We find that there are no regions showing strong flux variations. Our analysis shows an apparent flux decline in the overall synchrotron flux of [approx]4% at high energies, but we suspect that this is mostly a calibration effect, and that flux is actually constant to [approx]1%. This is much less than the variation found in other remnants where it was used to infer magnetic-field strengths up to 1 mG. We attribute the lack of variability to the smoothness of the synchrotron morphology, in contrast to the small-scale knots found to be variable in other remnants. The smoothness is to be expected for a Type Ia remnant encountering uniform material. Finally, we find a spatial correlation between the flux and the cutoff frequency in synchrotron emission. The simplest interpretation is that the cutoff frequency depends on the magnetic-field strength. This would require that the maximum energy of accelerated electrons is not limited by synchrotron losses, but by some other effect. Alternatively, the rate of particle injection and acceleration may vary due to some effect not yet accounted for, such as a dependence on shock obliquity.