We analyze observations obtained with the Chandra X-ray Observatory of bright Compton thick active galactic nuclei (AGNs), those with column densities in excess of 1.5 x 10^{24} cm^{-2} along the lines of sight. We therefore view the powerful central engines only indirectly, even at X-ray energies. Using high spatial resolution and considering only galaxies that do not contain circumnuclear starbursts, we reveal the variety of emission AGNs alone may produce. Approximately 1% of the continuums intrinsic flux is detected in reflection in each case. The only hard X-ray feature is the prominent Fe K alpha fluorescence line, with equivalent width greater than 1 keV in all sources. The Fe line luminosity provides the best X-ray indicator of the unseen intrinsic AGN luminosity. In detail, the morphologies of the extended soft X-ray emission and optical line emission are similar, and line emission dominates the soft X-ray spectra. Thus, we attribute the soft X-ray emission to material that the central engines photoionize. Because the resulting spectra are complex and do not reveal the AGNs directly, crude analysis techniques such as hardness ratios would mis-classify these galaxies as hosts of intrinsically weak, unabsorbed AGNs and would fail to identify the luminous, absorbed nuclei that are present. We demonstrate that a three-band X-ray diagnostic can correctly classify Compton thick AGNs, even when significant soft X-ray line emission is present. The active nuclei produce most of the galaxies total observed emission over a broad spectral range, and much of their light emerges at far-infrared wavelengths. Stellar contamination of the infrared emission can be severe, however, making long-wavelength data alone unreliable indicators of the buried AGN luminosity.
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