2.3.2 The Hard X-ray Power Law

Early X-ray observations ⁴² of mainly low-luminosity Seyfert 1 galaxies suggested that the spectra in hard X-rays (2-20 keV) in general conform to a power law with an index ~ 0.7. A lot of effort ^{43 - 46} has been devoted to ``explaining'' this power law in terms of the so-called standard pair model, in which monoenergetic relativistic electrons are continuously injected into a spherical, homogeneous region, filled with soft photons. The electrons would produce -rays through inverse Compton scattering, which leads to pair production from photon-photon interactions involving the -rays. The pairs would then constitute a secondary injection, producing new pairs and so forth, resulting in a pair cascade. The latter is called saturated ⁴⁵ if practically all the y-rays are reprocessed into hard X-rays, in which case the spectral index becomes ~ 1. This model failed because a relevant spectral index and the MeV break required by the observed -ray background could not be obtained. ^{47, 48}

Subsequent Ginga observations ⁴⁹ revealed that the emission in the 1-30 keV range has a multicomponent structure, including an incident power law with a spectral index ^int ~ 0.9 and an excess above 10 keV. Zdziarski et al. ⁵⁰ suggested that these features could be explained by the standard pair model, if hard X-rays from the pair plasma become Compton reflected in the inner disk. It is unclear whether the standard pair model can be saved in this way. One remaining concern is the connection to the environment, since the proposed physical scenarios seem oversimplified. In particular, both the coupling to a physically relevant accretion disk and various time-dependent effects warrant further investigation. Other uncertainties are the unspecified injection mechanism for the electrons and their accumulation within the source after cooling (the ``dead electron problem''). In addition, the recent HEXE observations may have ruled out the Zdziarski et al. model in the case of 3C 273 and Cen A. ⁵¹

The (electron) temperature is self-regulated in thermal pair models, due to the combined influence of heating, cooling and pair processes. Haardt and Maraschi ⁵² considered a coupled two-phase thermal model, in which the cool disk provides the soft photon input for Comptonization in the corona. The hard photons produced contribute to the heating of the cool phase, so that the total spectrum becomes a sum of the power law from the hot phase and the blackbody emission from the disk. Relevant spectra were only obtained when almost all of the energy was dissipated in the hot phase, which the authors argued was due to magnetic reconnection, even though no calculation of magnetic effects was included. Moreover, this model did not include relevant physics associated with pairs (e.g., their stability), as well as with the accretion disk (e.g., transonic flow, advective cooling, multi-temperature structure).

Maraschi and Molendi ^{53, 54} argued that Comptonization in an optically thin inner disk region should give rise to both the hard X-ray power law and the soft excess. However, the disk model used was of the usual Shakura-Sunyaev type, inappropriate when ~ 1. Furthermore, pair production was neglected even though T 10⁸ K. One may also note that Comptonization cannot reproduce the observed hard X-ray lag in Cyg X-1. ⁵⁵

A hard X-ray power law with a slope (0.5-1.0) is also found in stellar black hole candidates (SBHCs), indicating a production mechanism common to both AGN and SBHC. ⁵⁶ Obviously, this should then be insensitive to a change in central mass by a factor of ~ 10⁸. The slope should also be independent of , since an observed flux variation of about three orders of magnitude in GS2000 + 25 had not effect on this parameter. ⁵⁷