Observations of the Crab Nebula with the Chandra X-Ray Observatory

The Crab Nebula and its pulsar has been the subject of a number of detailed observations with the Chandra X-ray Observatory. The superb angular resolution of Chandra s high-resolution telescope has made possible numerous remarkable results. Here we describe a number of specific studies of the Crab that I and my colleagues have undertaken. We discuss the geometry of the system, which indicates that the "inner X-ray ring", typically identified with the termination shock of the pulsar s particle wind, is most likely not in the equatorial plane of the pulsar. Other topics are the northern wisps and their evolution with time; the characterization of features in the jet to the southeast; pulse-phase spectroscopy and possible correlations with the features at other wavelengths, particularly the optical polarization; and a search for correlations of the X-ray flux with the recently-discovered gamma -ray flares.