We investigate the nature of a sample of 92 Spitzer/MIPS 24 micron selected galaxies in the CDFS, showing power law-like emission in the Spitzer/IRAC 3.6-8 micron bands. The main goal is to determine whether the galaxies not detected in X-rays (47% of the sample) are part of the hypothetical population of obscured AGN not detected even in deep X-ray surveys. The majority of the IR power-law galaxies are ULIRGs at z>1, and those with LIRG-like IR luminosities are usually detected in X-rays. The optical to IR spectral energy distributions (SEDs) of the X-ray detected galaxies are almost equally divided between a BLAGN SED class (similar to an optically selected QSO) and a NLAGN SED (similar to the BLAGN SED but with an obscured UV/optical continuum). A small fraction of SEDs resemble warm ULIRG galaxies (e.g., Mrk231). Most galaxies not detected in X-rays have SEDs in the NLAGN+ULIRG class as they tend to be optically fainter, and possibly more obscured. Moreover, the IR power-law galaxies have SEDs significantly different from those of high-z (z_sp>1) IR (24 micron) selected and optically bright (VVDS I_AB<=24) star-forming galaxies whose SEDs show a very prominent stellar bump at 1.6 micron. The galaxies detected in X-rays have 2-8 keV rest-frame luminosities typical of AGN. The galaxies not detected in X-rays have global X-ray to mid-IR SED properties that make them good candidates to contain IR bright X-ray absorbed AGN. If all these sources are actually obscured AGN, we would observe a ratio of obscured to unobscured 24 micron detected AGN of 2:1, whereas models predict a ratio of up to 3:1. Additional studies using Spitzer to detect X-ray-quiet AGN are likely to find more such obscured sources.
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