We present the first study of an Iwasawa-Taniguchi/X-ray Baldwin effect for Compton-thick active galactic nuclei (AGN). We report a statistically significant anti-correlation between the rest-frame equivalent width (EW) of the narrow core of the neutral Fe K$alpha$ fluorescence emission line, ubiquitously observed in the reflection spectra of obscured AGN, and the mid-infrared 12$,mu$m continuum luminosity (taken as a proxy for the bolometric AGN luminosity). Our sample consists of 72 Compton-thick AGN selected from pointed and deep-field observations covering a redshift range of $zsim0.0014-3.7$. We employ a Monte Carlo-based fitting method, which returns a Spearmans Rank correlation coefficient of $rho=-0.28pm0.12$, significant to 98.7% confidence. The best fit found is ${rm log}({rm EW}_{{rm Fe,K}alpha}),propto,-0.08pm0.04,{rm log}(L_{12,mu{rm m}})$, which is consistent with multiple studies of the X-ray Baldwin effect for unobscured and mildly obscured AGN. This is an unexpected result, as the Fe K$alpha$ line is conventionally thought to originate from the same region as the underlying reflection continuum, which together constitute the reflection spectrum. We discuss the implications this could have if confirmed on larger samples, including a systematic underestimation of the line of sight X-ray obscuring column density and hence the intrinsic luminosities and growth rates for the most luminous AGN.
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