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

Abstract

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., Hβ for RM and Paα for SA). Here we evaluate the size deviations measured by six pairs of hydrogen lines (e.g., Hβ, Hα, and Paα) 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 Paα(SA)/Hβ(RM) and Hα(SA)/Hβ(RM) pairs not only are closest to 1 but also have considerably smaller uncertainty. Considering the current technology of infrared interferometry, the Paα(SA)/Hβ(RM) pair is the ideal choice for low-redshift objects in the SARM project. In the future, the Hα(SA)/Hβ(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.