Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

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

Nature Astronomy volume 4, pages 517–525 (2020)Cite this article

Subjects

Abstract

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 tools5,6,7. 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 \(551.{5}_{-78.7}^{+97.3} \) Mpc and \({H}_{0}=71.{5}_{-10.6}^{+11.9}\ {\rm{km}}\ {{\rm{s}}}^{-1}\ {{\rm{Mpc}}}^{-1} \). 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 H0 tension.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Joint fittings of RM and GRAVITY observations.
Fig. 2: Results of black hole mass and distances.

Similar content being viewed by others

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

Code availability

All the codes used in this paper are available from the corresponding author upon reasonable request.

References

  1. Peacock, J. A. Cosmological Physics (Cambridge Univ. Press, 1999).

  2. de Grijs, R. & Cartwright, S. An Introduction to Distance Measurement in Astronomy (Wiley Online Library, 2011).

  3. Freedman, W. L. & Madore, B. F. The Hubble constant. Annu. Rev. Astron. Astrophys. 48, 673–710 (2010).

    Article  ADS  Google Scholar 

  4. Weinberg, D. H. et al. Observational probes of cosmic acceleration. Phys. Rep. 530, 87–255 (2013).

    Article  ADS  MathSciNet  Google Scholar 

  5. Freedman, W. L. Cosmology at a crossroads. Nat. Astron. 1, 121 (2017).

    Article  ADS  Google Scholar 

  6. Planck Collaboration et al. Planck 2018 results. VI. Cosmological parameters. Preprint at https://arxiv.org/abs/1807.06209 (2018).

  7. Riess, A. G., Casertano, S., Yuan, W., Macri, L. M. & Scolnic, D. Large Magellanic Cloud cepheid standards provide a 1% foundation for the determination of the Hubble constant and stronger evidence for physics beyond ΛCDM. Astrophys. J. 876, 85 (2019).

    Article  ADS  Google Scholar 

  8. Gravity Collaboration et al. First light for gravity: phase referencing optical interferometry for the Very Large Telescope interferometer. Astron. Astrophys. 602, A94 (2017).

    Article  Google Scholar 

  9. Gravity Collaboration et al. Spatially resolved rotation of the broad-line region of a quasar at sub-parsec scale. Nature 563, 657–660 (2018).

    Article  ADS  Google Scholar 

  10. Blandford, R. D. & McKee, C. F. Reverberation mapping of the emission line regions of Seyfert galaxies and quasars. Astrophys. J. 255, 419–439 (1982).

    Article  ADS  Google Scholar 

  11. Peterson, B. M. Reverberation mapping of active galactic nuclei. Publ. Astron. Soc. Pac. 105, 247–268 (1993).

    Article  ADS  Google Scholar 

  12. Zhang, Z.-X. et al. Kinematics of the broad-line region of 3C 273 from a 10 yr reverberation mapping campaign. Astrophys. J. 876, 49 (2019).

    Article  ADS  Google Scholar 

  13. Riess, A. G. et al. Observational evidence from supernovae for an accelerating universe and a cosmological constant. Astron. J. 116, 1009–1038 (1998).

    Article  ADS  Google Scholar 

  14. Perlmutter, S. et al. Measurements of Ω and Λ from 42 high-redshift supernovae. Astrophys. J. 517, 565–586 (1999).

    Article  ADS  MATH  Google Scholar 

  15. Osterbrock, D. E. & Mathews, W. G. Emission-line regions of active galaxies and QSOs. Annu. Rev. Astron. Astrophys. 24, 171–203 (1986).

    Article  ADS  Google Scholar 

  16. Osterbrock, D. E. Astrophysics of Gaseous Nebulae and Active Galactic Nuclei (University Science Books, 1989).

  17. Ho, L. C. Nuclear activity in nearby galaxies. Annu. Rev. Astron. Astrophys. 46, 475–539 (2008).

    Article  ADS  Google Scholar 

  18. Bailey, J. A. Spectroastrometry: a new approach to astronomy on small spatial scales. Proc. SPIE 3355, 932–939 (1998).

  19. Petrov, R. G. et al. in European Southern Observatory Conference and Workshop Proc. Vol. 39 435–443 (1992).

  20. Rakshit, S., Petrov, R. G., Meilland, A. & Hönig, S. F. Differential interferometry of QSO broad-line regions—I. Improving the reverberation mapping model fits and black hole mass estimates. Mon. Not. R. Astron. Soc. 447, 2420–2436 (2015).

    Article  ADS  Google Scholar 

  21. Schmidt, M. 3C 273: a star-like object with large red-shift. Nature 197, 1040–1040 (1963).

    Article  ADS  Google Scholar 

  22. Courvoisier, T. J. L. The bright quasar 3C 273. Astron. Astrophys. Rev. 9, 1–32 (1998).

    Article  ADS  Google Scholar 

  23. Walter, R. et al. Simultaneous observations of Seyfert 1 galaxies with IUE, ROSAT and GINGA. Astron. Astrophys. 285, 119–131 (1994).

    ADS  Google Scholar 

  24. Pancoast, A., Brewer, B. J. & Treu, T. Geometric and dynamical models of reverberation mapping data. Astrophys. J. 730, 139–153 (2011).

    Article  ADS  Google Scholar 

  25. Li, Y.-R., Wang, J.-M., Ho, L. C., Du, P. & Bai, J.-M. A Bayesian approach to estimate the size and structure of the broad-line region in agns using reverberation mapping data. Astrophys. J. 779, 110 (2013).

    Article  ADS  Google Scholar 

  26. Pancoast, A., Brewer, B. J. & Treu, T. Modelling reverberation mapping data—I. Improved geometric and dynamical models and comparison with cross-correlation results. Mon. Not. R. Astron. Soc. 445, 3055–3072 (2014).

    Article  ADS  Google Scholar 

  27. Li, Y.-R. et al. Untangling optical emissions of the jet and accretion disk in the flat-spectrum radio quasar 3C 273 with reverberation mapping data. Preprint at https://arxiv.org/abs/1909.04511 (2019).

  28. Horne, K., Welsh, W. F. & Peterson, B. M. Echo mapping of broad Hβ emission in NGC 5548. Astrophys. J. Lett. 367, 5–8 (1991).

    Article  ADS  Google Scholar 

  29. Cai, R.-G., Ma, Y.-Z., Tang, B. & Tuo, Z. L. Constraining the anisotropic expansion of the Universe. Phys. Rev. D 87, 123522 (2013).

    Article  ADS  Google Scholar 

  30. Weinberg, S. Cosmology (Oxford Univ. Press, 2008).

  31. Beckers, J. M. Differential speckle interferometry. Opt. Acta 29, 361–362 (1982).

    Article  ADS  Google Scholar 

  32. Petrov, R. G. in Diffraction-Limited Imaging with Very Large Telescopes (eds Alloin, D. M. & Mariotti, J. M.) 249 (NATO Advanced Science Institutes Series C, Vol. 274, 1989).

  33. Rees, M. J. Black hole models for active galactic nuclei. Annu. Rev. Astron. Astrophys. 22, 471–506 (1984).

    Article  ADS  Google Scholar 

  34. Bahcall, J. N., Kozlovsky, B.-Z. & Salpeter, E. E. On the time dependence of emission-line strengths from a photoionized nebula. Astrophys. J. 171, 467–482 (1972).

    Article  ADS  Google Scholar 

  35. Peterson, B. M. Measuring the masses of supermassive black holes. Space Sci. Rev. 183, 253–275 (2014).

    Article  ADS  Google Scholar 

  36. Ferrarese, L. & Ford, H. Supermassive black holes in galactic nuclei: past, present and future research. Space Sci. Rev. 116, 523–624 (2005).

    Article  ADS  Google Scholar 

  37. Kaspi, S. Studying the outskirts of reverberation mapped AGNs. Proc. IAU 324, 219–222 (2017).

    ADS  Google Scholar 

  38. Peterson, B. M. et al. Optical continuum and emission-line variability of Seyfert 1 galaxies. Astrophys. J. 501, 82–93 (1998).

    Article  ADS  Google Scholar 

  39. Kaspi, S. et al. Reverberation measurements for 17 quasars and the size–mass–luminosity relations in active galactic nuclei. Astrophys. J. 533, 631–649 (2000).

    Article  ADS  Google Scholar 

  40. Bentz, M. C. et al. The low-luminosity end of the radius-luminosity relationship for active galactic nuclei. Astrophys. J. 767, 149 (2013).

    Article  ADS  Google Scholar 

  41. Du, P. et al. Supermassive black holes with high accretion rates in active galactic nuclei. IX. 10 new observations of reverberation mapping and shortened Hβ lags. Astrophys. J. 856, 6 (2018).

    Article  ADS  Google Scholar 

  42. Du, P. & Wang, J.-M. The radius–luminosity relationship depends on optical spectra in active galactic nuclei. Astrophys. J. 886, 42 (2019).

    Article  ADS  Google Scholar 

  43. Abramowicz, M. A., Czerny, B., Lasota, J. P. & Szuszkiewicz, E. Slim accretion disks. Astrophys. J. 332, 646–658 (1988).

    Article  ADS  Google Scholar 

  44. Wang, J.-M. & Zhou, H.-Y. Self-similar solution of optically thick advection-dominated flows. Astrophys. J. 516, 420–424 (1999).

    Article  ADS  Google Scholar 

  45. Wang, J.-M. et al. Supermassive black holes with high accretion rates in active galactic nuclei. II. The most luminous standard candles in the universe. Astrophys. J. 793, 108 (2014).

    Article  ADS  Google Scholar 

  46. Wang, J.-M., Qiu, J., Du, P. & Ho, L. C. Self-shadowing effects of slim accretion disks in AGNs: the diverse appearance of the broad-line region. Astrophys. J. 797, 65 (2014).

    Article  ADS  Google Scholar 

  47. Grier, C. J. et al. The structure of the broad-line region in active galactic nuclei. I. Reconstructed velocity-delay maps. Astrophys. J. 764, 47 (2013).

    Article  ADS  Google Scholar 

  48. Lu, K.-X. et al. Reverberation mapping of the broad-line region in NGC 5548: evidence for radiation pressure? Astrophys. J. 827, 118 (2016).

    Article  ADS  Google Scholar 

  49. Du, P. et al. Supermassive black holes with high accretion rates in active galactic nuclei. VI. Velocity-resolved reverberation mapping of the Hβ line. Astrophys. J. 820, 27 (2016).

    Article  ADS  Google Scholar 

  50. Xiao, M. et al. A high-quality velocity-delay map of the broad-line region in NGC 5548. Astrophys. J. 865, L8 (2018).

    Article  ADS  Google Scholar 

  51. Peterson, B. M. et al. Central masses and broad-line region sizes of active galactic nuclei. II. A homogeneous analysis of a large reverberation-mapping database. Astrophys. J. 613, 682–699 (2004).

    Article  ADS  Google Scholar 

  52. Peterson, B. M. & Wandel, A. Evidence for supermassive black holes in active galactic nuclei from emission-line reverberation. Astrophys. J. 540, L13–L16 (2000).

    Article  ADS  Google Scholar 

  53. Kollatschny, W., Ulbrich, K., Zetzl, M., Kaspi, S. & Haas, M. Broad-line region structure and kinematics in the radio galaxy 3C 120. Astron. Astrophys. 566, A106 (2014).

    Article  ADS  Google Scholar 

  54. Li, Y.-R. et al. Supermassive black holes with high accretion rates in active galactic nuclei. VIII. Structure of the broad-line region and mass of the central black hole in mrk 142. Astrophys. J. 869, 137 (2018).

    Article  ADS  Google Scholar 

  55. Williams et al. The lick AGN monitoring project 2011: dynamical modeling of the broad-line region. Astrophys. J. 866, 75 (2018).

    Article  ADS  Google Scholar 

  56. Wang, J.-M. et al. Tidally disrupted dusty clumps as the origin of broad emission lines in active galactic nuclei. Nat. Astron. 1, 775–783 (2017).

    Article  ADS  Google Scholar 

  57. Czerny, B. & Hryniewicz, K. The origin of the broad line region in active galactic nuclei. Astron. Astrophys. 525, L8 (2011).

    Article  ADS  Google Scholar 

  58. Kelly, B. C., Bechtold, J. & Siemiginowska, A. Are the variations in quasar optical flux driven by thermal fluctuations? Astrophys. J. 698, 895–910 (2009).

    Article  ADS  Google Scholar 

  59. Zu, Y., Kochanek, C. S., Kozłowski, S. & Udalski, A. Is quasar optical variability a damped random walk? Astrophys. J. 765, 106 (2013).

    Article  ADS  Google Scholar 

  60. Welsh, W. F. On the reliability of cross-correlation function lag determinations in active galactic nuclei. Publ. Astron. Soc. Pac. 111, 1347–1366 (1999).

    Article  ADS  Google Scholar 

  61. Blandford, R. D. & Levinson, A. Pair cascades in extragalactic jets. I. γ-rays. Astrophys. J. 441, 79–95 (1995).

    Article  ADS  Google Scholar 

  62. Meyer, M., Scargle, J. D. & Blandford, R. D. Characterizing the γ-ray variability of the brightest flat spectrum radio quasars observed with the Fermi-LAT. Astrophys. J. 877, 39 (2019).

    Article  ADS  Google Scholar 

  63. Brewer, B. J. & Foreman-Mackey, D. DNest4: diffusive nested sampling in C++ and Python. J. Stat. Softw. 86, 1–33 (2018).

    Article  Google Scholar 

  64. Sandage, A. The existence of a major new constituent of the Universe: the quasi-stellar galaxies. Astrophys. J. 141, 1560–1579 (1965).

    Article  ADS  Google Scholar 

  65. Hoyle, F. Relation between the red-shifts of quasi-stellar objects and their radio and optical magnitudes. Nature 210, 1346–1347 (1966).

    Article  ADS  Google Scholar 

  66. Longair, M. S. & Scheuer, P. A. G. Red-shift magnitude relation for quasi-stellar objects. Nature 215, 919–922 (1967).

    Article  ADS  Google Scholar 

  67. Baldwin, J. A. Luminosity indicators in the spectra of quasi-stellar objects. Astrophys. J. 214, 679–684 (1977).

    Article  ADS  Google Scholar 

  68. Humphreys, E. M. L., Reid, M. J., Moran, J. M., Greenhill, L. J. & Argon, A. L. Toward a new geometric distance to the active galaxy NGC 4258. III. Final results and the Hubble constant. Astrophys. J. 775, 13 (2013).

    Article  ADS  Google Scholar 

  69. Hönig, S. F., Watson, D., Kishimoto, M. & Hjorth, J. A dust-parallax distance of 19 megaparsecs to the supermassive black hole in NGC 4151. Nature 515, 528–530 (2014).

    Article  ADS  Google Scholar 

  70. Kishimoto, M. et al. The innermost dusty structure in active galactic nuclei as probed by the Keck interferometer. Astron. Astrophys. 527, 121 (2011).

    Article  Google Scholar 

  71. Soldi, S. et al. The multiwavelength variability of 3C 273. Astron. Astrophys. 486, 411–425 (2008).

    Article  ADS  Google Scholar 

  72. Elvis, M. & Karovska, M. Quasar parallax: a method for determining direct geometrical distances to quasars. Astrophys. J. Lett. 581, 67–70 (2002).

    Article  ADS  Google Scholar 

  73. Quercellini, C., Cabella, P., Amendola, L., Quartin, M. & Balbi, A. Cosmic parallax as a probe of late time anisotropic expansion. Phys. Rev. D 80, 3527 (2009).

    Article  Google Scholar 

  74. Wang, J.-M., Du, P., Valls-Gabaud, D., Hu, C. & Netzer, H. Super-Eddington accreting massive black holes as long-lived cosmological standards. Phys. Rev. Lett 110, 081301 (2013).

    Article  ADS  Google Scholar 

  75. Du, P. et al. Supermassive black holes with high accretion rates in AGNs. I. First results from a new reverberation mapping campaign. Astrophys. J. 782, 45 (2014).

    Article  ADS  Google Scholar 

  76. Marziani, P. & Sulentic, J. W. Quasars and their emission lines as cosmological probes. Mon. Not. R. Astron. Soc. 442, 1211–1229 (2014).

    Article  ADS  Google Scholar 

  77. Cai, R.-G., Guo, Z.-K., Huang, Q.-G. & Yang, T. Super-Eddington accreting massive black holes explore high-z cosmology: Monte-Carlo simulations. Phys. Rev. D 97, 123502 (2018).

    Article  ADS  Google Scholar 

  78. Watson, D., Denney, K. D., Vestergaard, M. & Davis, T. M. A new cosmological distance measure using active galactic nuclei. Astrophys. J. 740, L49 (2011).

    Article  ADS  Google Scholar 

  79. Czerny, B. et al. Towards equation of state of dark energy from quasar monitoring: reverberation strategy. Astron. Astrophys. 556, A97 (2013).

    Article  Google Scholar 

  80. King, A. L. et al. Simulations of the OzDES AGN reverberation mapping project. Mon. Not. R. Astron. Soc. 453, 1701–1726 (2015).

    Article  ADS  Google Scholar 

  81. Martínez-Aldama, M. L. et al. Can reverberation-measured quasars be used for cosmology? Astrophys. J. 883, 170 (2019).

    Article  ADS  Google Scholar 

  82. Yoshii, Y., Kobayashi, Y., Minezaki, T., Koshida, S. & Peterson, B. A. A new method for measuring extragalactic distances. Astrophys. J. 784, L11 (2014).

    Article  ADS  Google Scholar 

  83. LaFranca, F., Bianchi, S., Ponti, G., Branchini, E. & Matt, G. A new cosmological distance measure using active galactic nucleus X-ray variability. Astrophys. J. 787, L12 (2014).

    Article  ADS  Google Scholar 

  84. Risaliti, G. & Lusso, E. Cosmological constraints from the hubble diagram of quasars at high redshifts. Nat. Astron. 3, 272–277 (2019).

    Article  ADS  Google Scholar 

  85. Czerny, B. et al. Astronomical distance determination in the space age secondary distance indicators. Space Sci. Rev. 214, 32–100 (2018).

    Article  ADS  Google Scholar 

  86. Marziani, P. et al. Quasars: from the physics of line formation to cosmology. Atoms 7, 18–30 (2019).

    Article  ADS  Google Scholar 

  87. Czerny, B. et al. Time delay measurement of Mg ii line in CTS C30.10 with SALT. Astrophys. J. 880, 46 (2019).

    Article  ADS  Google Scholar 

  88. Hoormann, J. K. et al. C iv black hole mass measurements with the Australian Dark Energy Survey (OzDES). Mon. Not. R. Astron. Soc. 487, 3650–3663 (2019).

    Article  ADS  Google Scholar 

  89. Negrete, C. A. et al. Highly accreting quasars: the SDSS low-redshift catalog. Astron. Astrophys. 620, A118 (2018).

    Article  Google Scholar 

  90. Martínez-Aldama, M. L. et al. Extreme quasars at high redshift. Astron. Astrophys. 618, A179 (2018).

    Article  Google Scholar 

  91. Du, P. et al. The fundamental plane of the broad-line region in active galactic nuclei. Astrophys. J. 818, L14 (2016).

    Article  ADS  Google Scholar 

  92. Onken, C. A. et al. Supermassive black holes in active galactic nuclei. II. Calibration of the black hole mass–velocity dispersion relationship for active galactic nuclei. Astrophys. J. 615, 645–651 (2004).

    Article  ADS  Google Scholar 

  93. Welsh, W. F. & Horne, K. Echo images of broad-line regions in active galactic nuclei. Astrophys. J. 379, 586–591 (1991).

    Article  ADS  Google Scholar 

  94. Landt, H. et al. The near-infrared broad emission line region of active galactic nuclei. I. The observations. Astrophys. J. Suppl. 174, 282–312 (2008).

    Article  ADS  Google Scholar 

  95. Landt, H. et al. A near-infrared relationship for estimating black hole masses in active galactic nuclei. Mon. Not. R. Astron. Soc. 432, 113–126 (2013).

    Article  ADS  Google Scholar 

  96. Marconi, A. et al. The effect of radiation pressure on virial black hole mass estimates and the case of narrow-line Seyfert 1 galaxies. Astrophys. J. 678, 693–700 (2008).

    Article  ADS  Google Scholar 

  97. Netzer, H. & Marziani, P. The effect of radiation pressure on emission-line profiles and black hole mass determination in active galactic nuclei. Astrophys. J. 724, 318–328 (2010).

    Article  ADS  Google Scholar 

  98. Peterson, B. et al. Steps toward determination of the size and structure of the broad-line region in active galactic nuclei. XV. Long-term optical monitoring of NGC 5548. Astrophys. J. 510, 659–668 (1999).

    Article  ADS  Google Scholar 

  99. Pei, L. et al. Space telescope and optical reverberation mapping project. V. Optical spectroscopic campaign and emission-line analysis for NGC 5548. Astrophys. J. 837, 131 (2017).

    Article  ADS  Google Scholar 

  100. Stern, J., Hennawi, J. F. & Pott, J.-U. Spatially resolving the kinematics of the ≲100 μ as quasar broad-line region using spectroastrometry. Astrophys. J. 804, 57 (2015).

    Article  ADS  Google Scholar 

  101. Songsheng, Y.-Y., Wang, J.-M., Li, Y.-R. & Du, P. The VLT interferometric measurements of active galactic nuclei: effects of angular momentum distributions of clouds in the broad-line region. Astrophys. J. 883, 184 (2019).

    Article  ADS  Google Scholar 

  102. Smith, J. E., Robinson, A., Young, S., Axon, D. J. & Corbett, E. A. Equatorial scattering and the structure of the broad-line region in Seyfert nuclei: evidence for a rotating disc. Mon. Not. R. Astron. Soc. 359, 846–864 (2005).

    Article  ADS  Google Scholar 

  103. Songsheng, Y.-Y. & Wang, J.-M. Measuring black hole mass of type I active galactic nuclei by spectropolarimetry. Mon. Not. R. Astron. Soc. 473, L1–L5 (2018).

    Article  ADS  Google Scholar 

  104. Wang, J.-M., Songsheng, Y.-Y., Li, Y.-R. & Yu, Z. Kinematic signatures of reverberation mapping of close binaries of supermassive black holes in active galactic nuclei. Astrophys. J. 862, 171 (2018).

    Article  ADS  Google Scholar 

  105. Kovacevic, A., Wang, J.-M. & Popovic, L. Kinematic signatures of reverberation mapping of close binaries of supermassive black holes in active galactic nuclei. III. The case of elliptical orbits. Preprint at https://arxiv.org/abs/191008709 (2019).

  106. Songsheng, Y.-Y., Wang, J.-M., Li, Y.-R. & Du, P. Differential interferometric signatures of close binaries of supermassive black holes in active galactic nuclei. Astrophys. J. 881, 140 (2019).

    Article  ADS  Google Scholar 

  107. Burke-Spolaor, S. et al. The astrophysics of nanohertz gravitational waves. Astron. Astrophys. Rev. 27, 5–82 (2019).

    Article  ADS  Google Scholar 

  108. Boroson, T. A. & Green, R. F. The emission-line properties of low-redshift quasi-stellar objects. Astrophys. J. Suppl. 80, 109–135 (1992).

    Article  ADS  Google Scholar 

  109. Volonteri, M. & Rees, M. J. Rapid growth of high-redshift black holes. Astrophys. J. 633, 624–629 (2005).

    Article  ADS  Google Scholar 

  110. Wang, J.-M., Chen, Y.-M. & Zhang, F. Feedback limits rapid growth of seed black holes at high redshift. Astrophys. J. 637, L85–L88 (2006).

    Article  ADS  Google Scholar 

  111. Milosavljević, M., Bromm, V., Couch, S. M. & Oh, S. P. Accretion onto “seed" black holes in the first galaxies. Astrophys. J. 698, 766–780 (2009).

    Article  ADS  Google Scholar 

  112. Regan, J. A. et al. Super-Eddington accretion and feedback from the first massive seed black holes. Mon. Not. R. Astron. Soc. 486, 3892–3906 (2019).

    Article  ADS  Google Scholar 

  113. Nguyen, K. et al. Emission signatures from sub-parsec binary supermassive black holes. II. Effect of accretion disk wind on broad emission lines. Astrophys. J. 870, 16 (2019).

    Article  ADS  Google Scholar 

  114. Du, P. et al. Monitoring AGNs with Hβ asymmetry. I. First results: velocity-resolved reverberation mapping. Astrophys. J. 869, 142 (2018).

    Article  ADS  Google Scholar 

  115. Unwin, S. C. et al. Taking the measure of the universe: precision astrometry with SIM PlanetQuest. Publ. Astron. Soc. Pac. 120, 38–88 (2008).

    Article  ADS  Google Scholar 

  116. Ding, F. & Croft, R. A. C. Future dark energy constraints from measurements of quasar parallax: Gaia, SIM and beyond. Mon. Not. R. Astron. Soc. 397, 1739–1747 (2009).

    Article  ADS  Google Scholar 

  117. Widmann, F. et al. Improving GRAVITY towards observations of faint targets. Proc. SPIE 10701, 6 (2018).

    Google Scholar 

Download references

Acknowledgements

We acknowledge the support by National Key R&D Program of China through grant 2016YFA0400701, by NSFC through grants NSFC-11991050, -11873048, -11833008 and -11573026, and by grant no. QYZDJ-SSW-SLH007 from the Key Research Program of Frontier Sciences, CAS, by the Strategic Priority Research Program of the Chinese Academy of Sciences grant no. XDB23010400. E. Sturm is thanked for useful information of GRAVITY and the future GRAVITY\({}^{+} \) capabilities. J.-M.W. is grateful to M. Brotherton for careful reading the manuscript and useful discussions, to B.-W. Jiang, D.-W. Bao, W.-J. Guo and S.-S. Li who helped with the target selections.

Author information

Authors and Affiliations

  1. Key Laboratory for Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, China

    Jian-Min Wang, Yu-Yang Songsheng, Yan-Rong Li & Pu Du

  2. School of Astronomy and Space Science, University of Chinese Academy of Sciences, Beijing, China

    Jian-Min Wang

  3. National Astronomical Observatories of China, Chinese Academy of Sciences, Beijing, China

    Jian-Min Wang

  4. School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, China

    Yu-Yang Songsheng

  5. Department of Astronomy, Xiamen University, Xiamen, China

    Zhi-Xiang Zhang

Authors
  1. Jian-Min Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yu-Yang Songsheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yan-Rong Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Pu Du
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Zhi-Xiang Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

J.-M.W. conceived this project and wrote the paper. Y.-Y.S., Y.-R.L. and J.-M.W. made all calculations. Z.-X.Z. and P.D. made observations and performed the data reduction. J.-M.W., Z.-X.Z. and P.D. selected targets of the future SARM projects. All the authors discussed the contents of the paper.

Corresponding author

Correspondence to Jian-Min Wang.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature Astronomy thanks Suvendu Rakshit, Guido Risaliti and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, JM., Songsheng, YY., Li, YR. et al. A parallax distance to 3C 273 through spectroastrometry and reverberation mapping. Nat Astron 4, 517–525 (2020). https://doi.org/10.1038/s41550-019-0979-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41550-019-0979-5

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing