A parallax distance to 3C 273 through spectroastrometry and reverberation mapping

Distance measurements for extragalactic objects are a fundamental problem in astronomy1,2 and cosmology3,4. In the era of precision cosmology, we urgently need better measurements of cosmological distances to observationally test the increasing H0 tension of the Hubble constant measured from different tools5-7. Using spectroastrometry8, GRAVITY at The Very Large Telescope Interferometer successfully revealed the structure, kinematics and angular sizes of the broad-line region (BLR) of 3C 273 with an unprecedentedly high spatial resolution9. Fortunately, reverberation mapping (RM)10 of active galactic nuclei (AGNs) reliably provides linear sizes of their BLRs11. Here, we report a joint analysis of spectroastrometry and RM observations to measure AGN distances. We apply this analysis to 3C 273 observed by both GRAVITY9 and an RM campaign12, and find an angular distance of 551:5thorn97:3 78:7 I Mpc and H0 1/4 71:5thorn11:9 10:6 km s1 Mpc1 I. The advantages of the analysis are its pure geometrical measurements and that it simultaneously yields the mass of the central black hole. Moreover, we can conveniently repeat measurements of selected AGNs to efficiently reduce the statistical and systematic errors. Future observations of a reasonably sized sample (30 AGNs) will provide the distances of the AGNs and hence a new way of measuring H0 with a high precision (.3%) to test the H-0 tension.