Title: The X-ray and Mid-Infrared luminosities in Luminous Type 1 Quasars,
Abstract: 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 Boötes, 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.