The variability of the Crab nebula in radio: no radio counterpart to gamma-ray flares

We present new Jansky Very Large Array (VLA) radio images of the Crab nebula at 5.5 GHz, taken at two epochs separated by 6 d about 2 months after a gamma-ray flare in 2012 July. We find no significant change in the Crab's radio emission localized to a region of <2 light-months in radius, either over the 6-d interval between our present observations or between the present observations and ones from 2001. Any radio counterpart to the flare has a radio luminosity of less than or similar to 2 x 10(-4) times that of the nebula. Comparing our images to one from 2001, we do however find changes in radio brightness, up to 10 per cent in amplitude, which occur on decade time-scales throughout the nebula. The morphology of the changes is complex suggesting both filamentary and knotty structures. The variability is stronger, and the time-scales likely somewhat shorter, nearer the centre of the nebula. We further find that even with the excellent u - nu coverage and signal to noise of the VLA, deconvolution errors are much larger than the noise, being up to 1.2 per cent of peak brightness of the nebula in this particular case.