The X-ray Emissions from the M87 Jet: Diagnostics and Physical   Interpretation
  We reanalyze the deep Chandra observations of the M87 jet, first examined by Wilson & Yang (2002). By employing an analysis chain that includes image deconvolution, knots HST-1 and I are fully separated from adjacent emission. We find slight but significant variations in the spectral shape, with values of $\alpha_x$ ranging from $\sim 1.2-1.6$. We use VLA radio observations, as well as HST imaging and polarimetry data, to examine the jet's broad-band spectrum and inquire as to the nature of particle acceleration in the jet. As shown in previous papers, a simple continuous injection model for synchrotron-emitting knots, in which both the filling factor, $f_{acc}$, of regions within which particles are accelerated and the energy spectrum of the injected particles are constant, cannot account for the X-ray flux or spectrum. Instead, we propose that $f_{acc}$ is a function of position and energy and find that in the inner jet, $f_{acc} \propto E_\gamma^{-0.4 \pm 0.2} \propto E_e^{-0.2 \pm 0.1}$, and in knots A and B, $f_{acc} \propto E_\gamma^{-0.7 \pm 0.2} \propto E_e^{-0.35 \pm 0.1}$, where $E_\gamma$ is the emitted photon energy and and $E_e$ is the emitting electron energy. In this model, the index $p$ of the injected electron energy spectrum ($n(E_{e}) \propto E_{e}^{-p}$) is $p=2.2$ at all locations in the jet, as predicted by models of cosmic ray acceleration by ultrarelativistic shocks. There is a strong correlation between the peaks of X-ray emission and minima of optical percentage polarization, i.e., regions where the jet magnetic field is not ordered. We suggest that the X-ray peaks coincide with shock waves which accelerate the X-ray emitting electrons and cause changes in the direction of the magnetic field; the polarization is thus small because of beam averaging. 
Eric S. Perlman (JCA/UMBC and CAS/JHU) and Andrew S. Wilson (UMCP and   STScI)