Context: After the successful launch of the Spectrum-Roentgen-Gamma (SRG) mission in July 2019, eROSITA, the soft X-ray instrument aboard SRG, performed scanning observations of a large contiguous field, namely the eROSITA Final Equatorial Depth Survey (eFEDS), ahead of the planned four-year all-sky survey. eFEDS yielded a large sample of X-ray sources with very rich multi-band photometric and spectroscopic coverage. Aims: We present here the eFEDS Active Galactic Nuclei (AGN) catalog and the eROSITA X-ray spectral properties of the eFEDS sources. Methods: Using a Bayesian method, we perform a systematic X-ray spectral analysis for all eFEDS sources. The appropriate model is chosen based on the source classification and the spectral quality, and, in the case of AGN, including the possibility of intrinsic (rest-frame) absorption and/or soft excess emission. Hierarchical Bayesian modeling (HBM) is used to estimate the spectral parameter distribution of the sample. Results: X-ray spectral properties are presented for all eFEDS X-ray sources. There are 21952 candidate AGN, which comprise 79% of the eFEDS sample. Despite a large number of faint sources with low photon counts, our spectral fitting provides meaningful measurements of fluxes, luminosities, and spectral shapes for a majority of the sources. This AGN catalog is dominated by X-ray unobscured sources, with an obscured (logNH>21.5) fraction of 10% derived by HBM. The power-law slope of the catalog can be described by a Gaussian distribution of 1.94+-0.22. Above a photon counts threshold of 500, nine out of 50 AGN have soft excess detected. For the sources with blue UV to optical color (type-I AGN), the X-ray emission is well correlated with the UV emission with the usual anti-correlation between the X-ray to UV spectral slope {alpha}_{OX} and the UV luminosity.
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