We report detailed studies of the X-ray emission from the kiloparsec-scale jet in the nearest active galaxy, Centaurus A. By analyzing the highest quality X-ray data obtained with the Chandra ACIS-S, 41 compact sources (mostly bright jet knots) were found within the jet on angular scales less than 4'', 13 of which were newly identified. We construct the luminosity function for the detected jet knots and argue that the remaining emission is most likely to be truly diffuse, rather than resulting from the sum of many unresolved fainter knots. We subtracted the contributions of the bright knots from the total X-ray jet flux, and show that the remaining extended emission has a relatively flat-topped intensity profile in the transverse jet direction, with the intensity peaking at the jet boundaries between 50'' and 170''. We note that limb-brightened morphologies have been observed previously at radio frequencies in a few FR I and FR II jet sources, but never so clearly at higher photon energies. Our result therefore supports a stratified jet model, consisting of a relativistic outflow including a boundary layer with a velocity shear. In addition, we found that the X-ray spectrum of the diffuse component is almost uniform across and along the jet, with an X-ray energy spectral index of αX ≈ 1, similar to those observed in the compact knots. We discuss this spectral behavior within a framework of shock and stochastic particle acceleration processes, connected with the turbulent, supersonic, and nonsteady nature of the relativistic outflow. We note some evidence for a possible spectral hardening at the outer sheath of the jet, and manifesting itself in observed X-ray spectra of αX 0.5 in the most extreme cases. Due to the limited photon statistics of the present data, further deep observations of Centaurus A are required to determine the reality of this finding; however, we note that the existence of the hard X-ray features at outer jet boundaries would provide an important challenge to theories for the evolution of ultrarelativistic particles within extragalactic jets.
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