Viewing angle effects in quasar application to cosmology

Abstract

The symmetry axes of active galactic nuclei (AGN) are randomly distributed in space but highly inclined sources are heavily obscured and are not seen as quasars with broad emission lines. The obscuring torus geometry determines the average viewing angle, and if the torus geometry changes with the redshift, this average viewing angle will also change. Thus the ratio between the isotropic luminosity and observed luminosity may change systematically with redshift. Therefore, if we use quasars to measure the luminosity distance by evaluating the isotropic absolute luminosity and measuring the observed flux, we can have a redshift-dependent bias which can propagate to cosmological parameters. We propose a toy model for testing the effect of viewing angle uncertainty on measurement of the luminosity distance. The model is based on analytical description of the obscuring torus applied to one-parameter observational data. It illustrates the possible change of the torus covering factor between the two chosen redshift ranges. We have estimated the possible error on specific cosmological parameters (H 0 , Ω m ) for the flat ΛCDM cosmology if a method is calibrated at low redshift and applied to the higher redshift. The errors on cosmological parameters due to potential dependence of viewing angle on redshift are found to be potentially significant, and the effect will have to be accommodated in the future in all quasar-based cosmological methods. A careful systematic study of AGN mean viewing angle across redshift is necessary, with the use of appropriate samples and models which uniquely determine the inclination of each source.

Viewing angle observations and effects of evolution with redshift, black hole mass, and Eddington ratio in quasar based cosmology

“…He considered two population of sources: one in redshift bin 0.7 ≤ z ≤ 1.1 and other in redshift bin 2.0 ≤ z ≤ 2.4. His results show the clear increasing trend with redshift, which suggests the change in dusty torus structure at higher redshift, and we used these data in our previous study of potential bias in quasar-based cosmology (Prince et al 2021).…”

“…As we discussed in Prince et al (2021), any systematic trends of the viewing angle with redshift may lead to incorrect cosmological predictions for the quasar-based methods which use the emission from flat accretion disks (continuum time-delay approach, Collier et al 1999;Cackett et al 2007, emission line time-delay approach, Watson et al 2011;Haas et al 2011;Czerny et al 2013, or UV/X-ray relation Risaliti & Lusso (2015). According to our results, the viewing angle in all redshift bins is consistent with the mean value of 47.4 deg, measured from the symmetry axis.…”

“…In Prince et al (2021), we found relations between the possible systematic difference in the viewing angle of the low and the high redshift quasars, but the estimates were based on simple measurements of two quasar samples by Gu (2013).…”

“…Important parameters derived from the modeling are tabulated in the last three columns of Table 1. The optical depth is estimated along the line of sight (see Equation 1 in Prince et al 2021). As it can be seen in Table 1, there are few sources that have very low optical depth (≤ 2 × 10 −2 ) that can be considered as topview sources, and the sources with high optical depths can be considered as highly inclined.…”

“…In the standard scenario, authors use a single average viewing angle for all the sources, which span in a wider range of redshift, mass, and Eddington ratios. In our previous study (Prince et al 2021), we have discussed how the viewing angle of an individual quasar can affect the measurement of the Hubble constant or any other cosmological parameters. Our results show that the viewing angle effect is important when one is trying to constrain the cosmological parameters using quasars.…”