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