The Deviation of the Size of the Broad-line Region between Reverberation Mapping and Spectroastrometry

The combination of the linear size from reverberation mapping (RM) and the angular distance of the broad-line region (BLR) from spectroastrometry (SA) in active galactic nuclei can be used as a standard ruler to measure the Hubble constant H (0). Recently, Wang et al. successfully employed this approach and estimated H (0) from 3C 273. However, there may be a systematic deviation between the response-weighted radius (RM measurement) and luminosity-weighted radius (SA measurement), especially when different broad lines are adopted for size indicators (e.g., H beta for RM and Pa alpha for SA). Here we evaluate the size deviations measured by six pairs of hydrogen lines (e.g., H beta, H alpha, and Pa alpha) via the locally optimally emitting cloud (LOC) models of the BLR. We find that the radius ratios K (=R (SA)/R (RM)) of the same line deviated systematically from 1 (0.85-0.88) with dispersions between 0.063 and 0.083. Surprisingly, the K values from the Pa alpha(SA)/H beta(RM) and H alpha(SA)/H beta(RM) pairs not only are closest to 1 but also have considerably smaller uncertainty. Considering the current technology of infrared interferometry, the Pa alpha(SA)/H beta(RM) pair is the ideal choice for low-redshift objects in the SARM project. In the future, the H alpha(SA)/H beta(RM) pair could be used for high-redshift luminous quasars. These theoretical estimations of the SA/RM radius pave the way for future SARM measurements to further constrain the standard cosmological model.

Automated summary

The study evaluates the size deviations of six pairs of hydrogen lines in active galactic nuclei, finding significant deviations in the radius ratios of the same line. However, the ratios for the Pa alpha(SA)/H beta(RM) and H alpha(SA)/H beta(RM) pairs are closest to 1 with smaller uncertainties, making them ideal choices for the SARM project. These theoretical estimations pave the way for future measurements to further constrain the standard cosmological model.