Concluding Remarks

Our Chandra study of Pictor A has shown that the X-ray emissions from the jet and the western hot spot are non-thermal. The spectra of both are well described by an absorbed power law with (flux density) spectral index $\alpha$ $\simeq$ 1.0. The X-ray spectrum of the hot spot is not a smooth extension of the radio to optical synchrotron spectrum, which turns down or cuts off near $\sim$ 10$^{14}$ Hz. Inverse Compton scattering of the synchrotron radio photons by the relativistic electrons responsible for the radio emission (i.e. a synchrotron self-Compton model) may be ruled out for the hot spot's X-ray emission, as the predicted spectrum differs from that observed. Inverse Compton scattering is also an unlikely explanation for the X-ray emission of the jet, for it requires a magnetic field a factor of 30 below equipartition. Further, it is hard to understand why the jet is brighter than the lobe (the opposite of the situation in the radio) in an inverse Compton scenario.

We considered the possible existence of a population of relativistic electrons in the hot spot that radiates synchrotron emission at frequencies below that at which its spectrum has been measured (i.e. $<$ 327 MHz). By choosing an appropriate index for the energy spectrum of these electrons, we constructed a successful synchrotron self-Compton model for the X-rays at the price of reducing the magnetic field to $\sim$ 1% of equipartition (see Fig. 9 and Model 3 in Tab. 4). More generally, relativistic electrons could exist in regions with weak or absent magnetic fields. Since the properties of such electron populations are unconstrained by radio observations, one can always create inverse Compton models that match the X-ray spectra. It is, however, difficult to understand why the X-rays from both the jet and the hot spot should correlate so well with synchrotron radio emission, which must arises in a relatively strong magnetic field. In general, we consider inverse Compton models for the X-ray emission as implausible.

The X-ray spectrum of the hot spot may be reproduced in a composite synchrotron plus synchrotron self-Compton model. In this picture, the spectral index of the synchrotron radiation is supposed to increase by 0.5 above the break near 10$^{14}$ Hz, as would be expected in a continuous injection model. Addition of this synchrotron emission to the synchrotron self-Compton emission expected for a magnetic field a factor of 9 below equipartition reproduces the observed spectrum (see Fig. 8 and Model 2, Tab. 4). The model is contrived, requiring similar fluxes from the two components in the Chandra band, but cannot be ruled out.

We feel that synchrotron radiation is the most likely X-ray emission process of both jet and hot spot. Strong, non-relativistic shocks are believed to accelerate relativistic particles yielding an energy spectrum n(E) $\propto$ E$^{\rm -p}$ with p = 2 at injection. Since the half lives of X-ray emitting electrons to synchrotron losses are very short ($\sim$ years), the spectrum steepens and a synchrotron spectral index of $\alpha$ = 1.0 is expected, in excellent accord with observations (Models 4a, b, Tab. 4). The separate population of radio-optical synchrotron emitting electrons remains unexplained; the radio spectral index - $\alpha_{r}$ = 0.740 $\pm$ 0.015 - is close to the average for non-thermal radio sources. Various processes, including acceleration in weak shocks, synchrotron losses and effects of tangled fields (see summary in Longair 1994, Ch. 21), have been invoked to account for the difference between the typical index seen in radio sources and the value $\alpha$ = 0.5 expected in the canonical model. Hot spots are, of course, associated with two shocks - an internal, mildly relativistic shock in the jet and a non-relativistic bow shock in the intergalactic medium. Both may reasonably be expected to accelerate cosmic rays and the resulting fluxes and energy spectra may differ.

As well as being directly accelerated in shocks, high $\gamma$ relativistic electrons may result from a `proton induced cascade' initiated by photopion production (e.g. Sikora et al. 1987; Biermann & Strittmatter 1987; Mannheim & Biermann 1989; Mannheim, Krülls & Biermann 1991). In this process, relativistic proton - photon collisions create $\pi^{0}$, $\pi^{+}$ and $\pi^{-}$. The last two decay into relativistic electrons, positrons, neutrinos and antineutrinos (e.g. Biermann & Strittmatter 1987). The process thus provides a supply of synchrotron X- and $\gamma$-ray emitting electrons and positrons from high energy protons accelerated by shocks. Mannheim, Krülls & Biermann (1991) considered this process for production of synchrotron X-ray emission in radio galaxy hot spots. Their calculations suggest that the proton induced cascade produces X-ray emission about an order of magnitude weaker and with a harder spectrum than is observed for the western hot spot of Pictor A. As they note, the predicted luminosity can be increased by increasing the number of relativistic protons or the number of photons (the latter might occur, for example, if the hot spot is illuminated by a beam of radiation from the galaxy nucleus). This process seems promising and further calculations of the expected X-ray luminosity and spectrum of a proton induced cascade would be worthwhile.

This research was supported by NASA through grant NAG 81027. We are extremely grateful to Rick Perley for providing the radio images published by PRM in numerical form. We also wish to thank the staff of the Chandra Science Center, especially Dan Harris and Shanil Svirani, for their help.

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