Effect of Extinction on Quasar Luminosity Distances Determined from UV and X-Ray Flux Measurements

In Khadka et al., a sample of X-ray-detected reverberation-mapped quasars was presented and applied for the comparison of cosmological constraints inferred using two well-established relations in active galactic nuclei—the X-ray/UV luminosity (L _X –L _UV) relation and the broad-line region radius–luminosity (R–L) relation. L _X –L _UV and R–L luminosity distances to the same quasars exhibit a distribution of their differences that is generally asymmetric and positively shifted for the six cosmological models we consider. We demonstrate that this behavior can be interpreted qualitatively as arising as a result of the dust extinction of UV/X-ray quasar emission. We show that the extinction always contributes to the nonzero difference between L _X –L _UV-based and R–L-based luminosity distances and we derive a linear relationship between the X-ray/UV color index E _X‑UV and the luminosity-distance difference, which also depends on the value of the L _X –L _UV relation slope. Taking into account the median and the peak values of the luminosity-distance difference distributions, the average X-ray/UV color index falls in the range of ${\overline{E}}_{X-\mathrm{UV}}=0.03\mbox{--}0.28$ mag for the current sample of 58 sources. This amount of extinction is typical for the majority of quasars and can be attributed to the circumnuclear and interstellar media of host galaxies. After applying the standard hard X-ray and far-UV extinction cuts, heavily extincted sources are removed but overall the shift toward positive values persists. The effect of extinction on luminosity distances is more pronounced for the L _X –L _UV relation since the extinction of UV and X-ray emissions both contribute.