[O iii] λ5007 and X-ray properties of a complete sample of hard X-RAY selected AGNs in the local universe

We study the correlation between the [O iii] λ5007 and X-ray luminosities of local active galactic nuclei (AGNs), using a complete, hard X-ray (>10 keV) selected sample in the Swift/BAT 9-month catalog. From our optical spectroscopic observations at the South African Astronomical Observatory and the literature, a catalog of [O iii] λ5007 line flux for all 103 AGNs at Galactic latitudes of $|b|>{15}^{\circ }$ is compiled. Significant correlations with intrinsic X-ray luminosity ($L_X$) are found for both observed ($L_{\left[OIII\right]}$) and extinction-corrected ($L_{\left[OIII\right]}^{cor}$) luminosities, separately for X-ray unabsorbed and absorbed AGNs. We obtain the regression form of $L_{\left[OIII\right]}$ $\propto L_{2-10keV}^{1.18\pm 0.07}$ and $L_{\left[OIII\right]}^{cor}$ $\propto L_{2-10keV}^{1.16\pm 0.09}$ from the whole sample. The absorbed AGNs with low (<0.5%) scattering fractions in soft X-rays show on average smaller $L_{\left[OIII\right]}/L_X$ and $L_{\left[OIII\right]}^{cor}/L_X$ ratios than the other absorbed AGNs, while those in edge-on host galaxies do not. These results suggest that a significant fraction of this population is buried in tori with small opening angles. By using these $L_{\left[OIII\right]}$ versus $L_X$ correlations, the X-ray luminosity function (LF) of local AGNs (including Compton-thick AGNs) in a standard population synthesis model gives much better agreement with the [O iii] λ5007 LF derived from the Sloan Digital Sky Survey than previously reported. This confirms that hard X-ray observations are a very powerful tool to find AGNs with high completeness.