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

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Distance measurements for extragalactic objects are a fundamental problem in astronomy and cosmology. In the era of precision cosmology, we urgently need better measurements of cosmological distances to observationally test the increasing $H_{0}$ tension of the Hubble constant measured from different tools. Using spectroastrometry, 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 resolution. Fortunately, reverberation mapping (RM) of active galactic nuclei (AGNs) reliably provides linear sizes of their BLRs. 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 GRAVITY and an RM campaign,and find an angular distance of $551.5_{-78.7}^{+97.3}\, {\rm Mpc}$ and $H_{0}=71.5_{-10.6}^{+11.9}\,{\rm km\,s^{-1}\,Mpc^{-1}}$. Advantages of the analysis are 1) its pure geometrical measurements and 2) it simultaneously yields mass of the central black hole in the BLR. Moreover, we can conveniently repeat measurements of selected AGNs to efficiently reduce the statistical and systematic errors. Future observations of a reasonably sized sample ($\sim 30$ AGNs) will provide distances of the AGNs and hence a new way of measuring $H_{0}$ with a high precision $\left(\lesssim 3\%\right)$ to test the $H_{0}$ tension.