We reanalyze the deep Chandra observations of the M87 jet , first examined by Wilson & Yang ( 2002 ) .
By employing an analysis chain that also includes image deconvolution , knots HST-1 and I are fully separated from adjacent emission .
We derive the spatially resolved X-ray spectrum of the jet using the most recent response functions , and find slight but significant variations in the spectral shape , with values of \alpha _ { x } ( S _ { \nu } \propto \nu ^ { - \alpha } ) ranging from \sim 1.2 - 1.4 ( in the nucleus , knots HST-1 , D and C ) to \sim 1.6 ( in knots F , A and B ) .
We make use of VLA radio observations , as well as HST imaging and polarimetry data ( Perlman et al .
1999 , 2001a ) , 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 the synchrotron-emitting knots , in which one holds constant both the filling factor , f _ { acc } , of the regions within which particles are accelerated and the energy spectrum of the injected particles , can not account for the flux or spectrum of the X-ray emission .
Instead , we propose that f _ { acc } is a function of both 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 energy of the emitted photon and E _ { e } is the energy of the emitting electron .
In this model , the index , p , of the relativistic electron energy spectrum at injection ( n ( E _ { e } ) \propto E _ { e } ^ { - p } ) is p = 2.2 at all energies and all locations along the jet , in excellent agreement with the predictions of models of cosmic ray acceleration by ultrarelativistic shocks ( p =2.23 ) .
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 .