INTEGRAL probes the morphology of the Crab nebula in hard X-rays/soft $\sf \gamma$-rays

Aims. We use the IBIS/ISGRI telescope on-board INTEGRAL to measure the position of the centroid of the 20–200 keV emission from the Crab region.Methods. We find that the astrometry of the IBIS telescope is affected by the temperature of the IBIS mask during the observation. After correcting for this effect, we show that the systematic errors in the astrometry of the telescope are of the order of 0.5 arcsec. In the case of the Crab nebula and several other bright sources, the very large number of photons renders the level of statistical uncertainty in the centroid smaller or comparable to this value.Results. We find that the centroid of the Crab nebula in hard X-rays (20–40 keV) is shifted by 8.0 arcsec with respect to the Crab pulsar in the direction of the X-ray centroid of the nebula. A similar shift is also found at higher energies (40–100 and 100–200 keV). We observe a trend of decreasing shift with energy, which can be explained by an increase in the pulsed fraction. To differentiate between the contribution of the pulsar and the nebula, we divide our data into an on-pulse and off-pulse sample. Surprisingly, the nebular emission (i.e., off-pulse) is located a significant distance away from the X-ray centroid of the nebula.Conclusions. In all 3 energy bands (20–40, 40–100 and 100–200 keV), we find that the centroid of the nebula is offset significantly from the predicted position. We interpret this shift in terms of a cut-off in the electron spectrum in the outer regions of the nebula, which is probably the origin of the observed spectral break around 100 keV. From a simple spherically-symmetric model for the nebula, we estimate that the electrons in the external regions of the torus ( pc from the pulsar) reach a maximal energy slightly below 1014 eV.