Extinction biases quasar luminosity distances determined from quasar UV and X-ray flux measurements

A sample of X-ray detected reverberation-mapped quasars provides a unique opportunity to compare cosmological constraints inferred using two well-established relations - the X-ray/UV luminosity ($L_{X}-L_{UV}$) relation and the broad-line region radius-UV monochromatic 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 positively skewed for the six cosmological models we consider. This behaviour can be interpreted qualitatively to arise as a result of the dust extinction of UV/X-ray quasar emission. We show that the extinction always contributes to the non-zero difference between $L_{X}-L_{UV}$-based and $R-L$-based luminosity distances and we derive a linear relationship between the X-ray/UV colour index $E_{X-UV}$ and the median/mean value of the luminosity-distance difference, which also depends on the value of the $L_{X}-L_{UV}$ relation slope. Taking into account the prevailing positive values of the luminosity-distance difference median, we estimate an average X-ray/UV colour index of $\overline{E}_{X-UV}=0.089 \pm 0.019$ mag, while the value based on the positive mean values of the difference is $\overline{E}_{X-UV}=0.050\pm 0.013$ mag. We demonstrate that this amount of extinction is typical for the majority of quasars since it originates in the circumnuclear and interstellar media of host galaxies. It can only be slightly alleviated by the standard hard X-ray and far-UV extinction cuts used by Lusso et al. (2020). Consequently, the $L_{X}-L_{UV}$ relation QSO data compilation of Lusso et al. (2020) cannot be used for cosmological purposes.
Comment: 12 pages, 7 figures, 3 tables; submitted to the MNRAS Main Journal, comments welcome