X-ray Spectral Analysis of the Jet Termination Shock in Pictor A on Sub-Arcsecond Scales with Chandra

Hotspots observed at the edges of extended radio lobes in high-power radio galaxies and quasars mark the position of mildly-relativistic termination shock, where the jet bulk kinetic energy is converted to the internal energy of the jet particles. These are the only astrophysical systems where mildly-relativistic shocks can be directly resolved at various wavelengths of the electromagnetic spectrum. The western hotspot in the radio galaxy Pictor\,A is an exceptionally good target in this respect, due to the combination of its angular size and high surface brightness. In our previous work, after a careful {\it Chandra} image deconvolution, we resolved this hotspot into a disk-like feature perpendicular to the jet axis, and identified this as the front of the jet termination shock. We argued for a synchrotron origin of the observed X-ray photons, which implied maximum electron energies of the order of 10--100\,TeV. Here we present a follow-up on that analysis, proposing in particular a novel method for constraining the shape of the X-ray continuum emission with sub-arcsec resolution. The method is based on a {\it Chandra} hardness map analysis, using separately de-convolved maps in the soft and hard X-ray bands. In this way, we have found there is a systematic, yet statistically significant gradient in the hardness ratio across the shock, such that the implied electron energy index ranges from $s\leq 2.2$ at the shock front to $s> 2.7$ in the near downstream. We discuss the implications of the obtained results for a general understanding of particle acceleration at mildly-relativistic shocks.