We have searched the region surrounding the Crab Nebula for the existence of a shock wave with the imaging instruments of the Einstein Observatory .
The search is complicated by the scattering of nebula and pulsar X-rays from the imperfectly polished surfaces of the telescope mirror , as well as from interstellar grains along the line of sight .
Both of these effects lead to the appearance of X-ray emission , in the form of an X-ray halo , beyond the boundaries of the nebula filaments .

We show that the size , shape , and intensity of the halo around the Crab Nebula , above the contribution of mirror scattering , is consistent with what is expected from the scattering from interstellar grains .
The upper limit on the X-ray emission from a shock wave is about 1 % of the total 0.5–4 keV luminosity of the Crab or about 2 \times 10 ^ { 35 } ~ { } erg~ { } s ^ { -1 } ( assuming a distance of 2.2 kpc ) .
This figure applies to a shell whose angular radius is 9 arcminutes .
The upper limit is smaller ( larger ) for a shell of larger ( smaller ) size .
This upper limit is an order of magnitude or more below the flux of Cas A , Tycho , and Kepler SNRs , which are 2 to 3 times younger , but it is still above that of SN 1006 .