We present the Suzaku broadband observations of two AGNs detected by the Swift BAT hard X-ray (>15 keV) survey that did not have previous X-ray data, SWIFT J0601.9-8636 and SWIFT J0138.6-4001. The Suzaku spectra reveal in both objects a heavily absorbed power-law component with a column density of N H ≃ 1023.5-1024 cm-2 that dominates above 10 keV and an intense reflection component with a solid angle ≳27π from a cold, optically thick medium. We find that these AGNs have an extremely small fraction of scattered light from the nucleus, ≲0.5% with respect to the intrinsic power-law component. This indicates that they are buried in a very geometrically thick torus with a small opening angle and/or have an unusually small amount of gas responsible for scattering. In the former case, the geometry of SWIFT J0601.9-8636 should be nearly face-on as inferred from the small absorption for the reflection component. The discovery of two such objects in this small sample implies that there must be a significant number of yet unrecognized, very Compton thick AGNs viewed at larger inclination angles in the local universe, which are difficult to detect even in the currently most sensitive optical or hard X-ray surveys.
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