The X-ray and Mid-Infrared luminosities in Luminous Type 1 Quasars

Several recent studies have reported different intrinsic correlations between the AGN mid-IR luminosity ($L_{MIR}$) and the rest-frame 2-10 keV luminosity ($L_{X}$) for luminous quasars. To understand the origin of the difference in the observed $L_{X}-L_{MIR}$ relations, we study a sample of 3,247 spectroscopically confirmed type 1 AGNs collected from Bo\"{o}tes, XMM-COSMOS, XMM-XXL-North, and the SDSS quasars in the Swift/XRT footprint spanning over four orders of magnitude in luminosity. We carefully examine how different observational constraints impact the observed $L_{X}-L_{MIR}$ relations, including the inclusion of X-ray non-detected objects, possible X-ray absorption in type 1 AGNs, X-ray flux limits, and star formation contamination. We find that the primary factor driving the different $L_{X}-L_{MIR}$ relations reported in the literature is the X-ray flux limits for different studies. When taking these effects into account, we find that the X-ray luminosity and mid-IR luminosity (measured at rest-frame $6\mu m$, or $L_{6\mu m}$) of our sample of type 1 AGNs follow a bilinear relation in the log-log plane: $\log L_X =(0.84\pm0.03)\times\log L_{6\mu m}/10^{45}{\rm erg\;s^{-1}} + (44.60\pm0.01)$ for $L_{6\mu m} < 10^{44.79}{\rm erg\;s^{-1}}$, and $\log L_X = (0.40\pm0.03)\times\log L_{6\mu m}/10^{45}{\rm erg\;s^{-1}} +(44.51\pm0.01)$ for $L_{6\mu m} \geq 10^{44.79}{\rm erg\;s^{-1}}$. This suggests that the luminous type 1 quasars have a shallower $L_{X}-L_{MIR}$ correlation than the approximately linear relations found in local Seyfert galaxies. This result is consistent with previous studies reporting a luminosity-dependent $L_{X}-L_{MIR}$ relation, and implies that assuming a linear $L_{X}-L_{MIR}$ relation to infer the neutral gas column density for X-ray absorption might overestimate the column densities in luminous quasars.