Skip to main content

Thank you for visiting 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.

The effect of nuclear gas distribution on the mass determination of supermassive black holes


Supermassive black holes reside in the nuclei of most galaxies. During their active episodes, black holes are powered by accretion discs where gravitational energy is converted into radiation1. Accurately determining black hole masses is key to understand how the population evolves over time and how the black holes relate to their host galaxies2,3,4. Beyond the local universe, z 0.2, the mass is commonly estimated assuming a virialized motion of gas in the close vicinity of the active black holes, traced through broad emission lines5,6. However, this procedure has uncertainties associated with the unknown distribution of the gas clouds. Here, we show that the black hole masses derived from the properties of the accretion disk and virial mass estimates differ by a factor that is inversely proportional to the width of the broad emission lines. This leads to virial mass misestimations up to a factor of six. Our results suggest that a planar gas distribution that is inclined with respect to the line of sight may account for this effect. However, radiation pressure effects on the distribution of gas can also reproduce our results. Regardless of the physical origin, our findings contribute to mitigating the uncertainties in current black hole mass estimations and, in turn, will help us to better understand the evolution of distant supermassive black holes and their host galaxies.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Comparison of the accretion-disk- and single-epoch-based black hole mass determinations.
Fig. 2: Virial factor f as a function of FWHMobs for the Hα, Hβ, Mg ii and C iv broad emission lines.
Fig. 3: Virial factor–FWHMobs bi-dimensional distribution.


  1. 1.

    Shakura, N. I. & Sunyaev, R. A. Black holes in binary systems. Observational appearance. Astron. Astrophys. 24, 337–355 (1973).

    ADS  Google Scholar 

  2. 2.

    Ferrarese, L. & Merritt, D. A fundamental relation between supermassive black holes and their host galaxies. Astrophys. J. 539, L9–L12 (2000).

    ADS  Article  Google Scholar 

  3. 3.

    Xiao, T. et al. Exploring the low-mass end of the M BH -σ * relation with active galaxies. Astrophys. J. 739, 28 (2011).

    ADS  Article  Google Scholar 

  4. 4.

    Kormendy, J. & Ho, L. C. Coevolution (or not) of supermassive black holes and host galaxies. Annu. Rev. Astron. Astrophys. 51, 511–653 (2013).

    ADS  Article  Google Scholar 

  5. 5.

    Trakhtenbrot, B. & Netzer, H. Black hole growth to z = 2—I. Improved virial methods for measuring M BH and L/L Edd. Mon. Not. R. Astron. Soc. 427, 3081–3102 (2012).

    ADS  Article  Google Scholar 

  6. 6.

    Shen, Y. The mass of quasars. Bull. Astron. Soc. India 41, 61–115 (2013).

    ADS  Google Scholar 

  7. 7.

    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).

    ADS  Article  Google Scholar 

  8. 8.

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

    ADS  Article  Google Scholar 

  9. 9.

    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).

    ADS  Article  Google Scholar 

  10. 10.

    Graham, A. W. in Galactic Bulges (eds Laurikainen, E., Peletier, R. & Gadotti, D.) 263–313 (Springer, 2016).

  11. 11.

    Woo, J.-H., Yoon, Y., Park, S., Park, D. & Kim, S. C. The black hole mass–stellar velocity dispersion relation of narrow-LINE Seyfert 1 galaxies. Astrophys. J. 801, 38 (2015).

    ADS  Article  Google Scholar 

  12. 12.

    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).

    ADS  Article  Google Scholar 

  13. 13.

    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).

    ADS  Article  Google Scholar 

  14. 14.

    Denney, K. D. et al. Diverse kinematic signatures from reverberation mapping of the broad-line region in AGNs. Astrophys. J. 704, L80–L84 (2009).

    ADS  Article  Google Scholar 

  15. 15.

    Denney, K. D. et al. Reverberation mapping measurements of black hole masses in six local Seyfert galaxies. Astrophys. J. 721, 715–737 (2010).

    ADS  Article  Google Scholar 

  16. 16.

    Gaskell, C. M. What broad emission lines tell us about how active galactic nuclei work. New Astron. Rev. 53, 140–148 (2009).

    ADS  Article  Google Scholar 

  17. 17.

    Wills, B. J. & Browne, I. W. A. Relativistic beaming and quasar emission lines. Astrophys. J. 302, 56–63 (1986).

    ADS  Article  Google Scholar 

  18. 18.

    Shen, Y. & Ho, L. C. The diversity of quasars unified by accretion and orientation. Nature 513, 210–213 (2014).

    ADS  Article  Google Scholar 

  19. 19.

    Runnoe, J. C., Brotherton, M. S., DiPompeo, M. A. & Shang, Z. The behaviour of quasar C IV emission-line properties with orientation. Mon. Not. R. Astron. Soc. 438, 3263–3274 (2014).

    ADS  Article  Google Scholar 

  20. 20.

    Collin, S., Kawaguchi, T., Peterson, B. M. & Vestergaard, M. Systematic effects in measurement of black hole masses by emission-line reverberation of active galactic nuclei: Eddington ratio and inclination. Astron. Astrophys. 456, 75–90 (2006).

    ADS  Article  Google Scholar 

  21. 21.

    Decarli, R., Dotti, M., Fontana, M. & Haardt, F. Are the black hole masses in narrow-line Seyfert 1 galaxies actually small? Mon. Not. R. Astron. Soc. 386, L15–L19 (2008).

    ADS  Article  Google Scholar 

  22. 22.

    Czerny, B., Du, P., Wang, J.-M. & Karas, V. A test of the formation mechanism of the broad line region in active galactic nuclei. Astrophys. J. 832, 15 (2016).

    ADS  Article  Google Scholar 

  23. 23.

    Capellupo, D. M., Netzer, H., Lira, P., Trakhtenbrot, B. & Meja-Restrepo, J. Active galactic nuclei at z 1.5—I. Spectral energy distribution and accretion discs. Mon. Not. R. Astron. Soc. 446, 3427–3446 (2015).

    ADS  Article  Google Scholar 

  24. 24.

    Capellupo, D. M., Netzer, H., Lira, P., Trakhtenbrot, B. & Meja-Restrepo, J. Active galactic nuclei at z 1.5—III. Accretion discs and black hole spin. Mon. Not. R. Astron. Soc. 460, 212–226 (2016).

    ADS  Article  Google Scholar 

  25. 25.

    Slone, O. & Netzer, H. The effects of disc winds on the spectrum and black hole growth rate of active galactic nuclei. Mon. Not. R. Astron. Soc. 426, 656–664 (2012).

    ADS  Article  Google Scholar 

  26. 26.

    Meja-Restrepo, J. E., Trakhtenbrot, B., Lira, P., Netzer, H. & Capellupo, D. M. Active galactic nuclei at z ~ 1.5—II. Black hole mass estimation by means of broad emission lines. Mon. Not. R. Astron. Soc. 460, 187–211 (2016).

    ADS  Article  Google Scholar 

  27. 27.

    Decarli, R., Labita, M., Treves, A. & Falomo, R. On the geometry of broad emission region in quasars. Mon. Not. R. Astron. Soc. 387, 1237–1247 (2008).

    ADS  Article  Google Scholar 

  28. 28.

    Nikołajuk, M., Czerny, B., Ziółkowski, J. & Gierliński, M. Consistency of the black hole mass determination in AGN from the reverberation and the X-ray excess variance method. Mon. Not. R. Astron. Soc. 370, 1534–1540 (2006).

    ADS  Article  Google Scholar 

  29. 29.

    Mortlock, D. J. et al. A luminous quasar at a redshift of z = 7.085. Nature 474, 616–619 (2011).

    ADS  Article  Google Scholar 

  30. 30.

    Wu, X.-B. et al. An ultraluminous quasar with a twelve-billion-solar-mass black hole at redshift 6.30. Nature 518, 512–515 (2015).

    ADS  Article  Google Scholar 

  31. 31.

    Kaspi, S. et al. The relationship between luminosity and broad-line region size in active galactic nuclei. Astrophys. J. 629, 61–71 (2005).

    ADS  Article  Google Scholar 

  32. 32.

    Bentz, M. C., Peterson, B. M., Netzer, H., Pogge, R. W. & Vestergaard, M. The radius–luminosity relationship for active galactic nuclei: the effect of host-galaxy starlight on luminosity measurements. II. The full sample of reverberation-mapped AGNs. Astrophys. J. 697, 160–181 (2009).

    ADS  Article  Google Scholar 

  33. 33.

    Baron, D., Stern, J., Poznanski, D. & Netzer, H. Evidence that most type 1 AGN are reddened by dust in the host ISM. Astrophys. J. 832, 8 (2016).

    ADS  Article  Google Scholar 

  34. 34.

    Dunn, O. J. & Clark, V. Correlation coefficients measured on the same individuals. J. Am. Stat. Assoc. 64, 366–377 (1969).

    Article  Google Scholar 

  35. 35.

    Greene, J. E. & Ho, L. C. Estimating black hole masses in active galaxies using the Hα emission line. Astrophys. J. 630, 122–129 (2005).

    ADS  Article  Google Scholar 

  36. 36.

    Glen, A. G., Leemis, L. M. & Drew, J. H. Computing the distribution of the product of two continuous random variables. Comput. Stat. Data Anal. 44, 451–464 (2004).

    MathSciNet  Article  MATH  Google Scholar 

  37. 37.

    Lopez, S. & Jenkins, J. S. The effects of viewing angle on the mass distribution of exoplanets. Astrophys. J. 756, 177 (2012).

    ADS  Article  Google Scholar 

  38. 38.

    Foreman-Mackey, D., Hogg, D. W., Lang, D. & Goodman, J. emcee: the MCMC hammer. Publ. Astron. Soc. Pac. 125, 306–312 (2013).

    ADS  Article  Google Scholar 

  39. 39.

    Ng, P. & Maechler, M. A fast and efficient implementation of qualitatively constrained quantile smoothing splines. Stat. Model. 7, 315–328 (2007).

    MathSciNet  Article  Google Scholar 

  40. 40.

    Afanasiev, V. L. & Popović, L. Č. Polarization in lines—a new method for measuring black hole masses in active galaxies. Astrophys. J. 800, L35 (2015).

    ADS  Article  Google Scholar 

Download references


Support for the work of J.E.M.-R was provided by ‘CONICYT-PCHA/doctorado Nacional para extranjeros/2013-63130316’. P.L. acknowledges support from Fondecyt Project #1161184. H.N. acknowledges support from the Israel Science Foundation grant 234/13. B.T. is a Zwicky postdoctoral fellow.

Author information




J.E.M.-R. and P.L. co-developed the idea and wrote the paper. J.E.M.-R., P.L. and D.M.C. wrote the codes needed for the different measurements and fittings procedures, J.E.M.-R. obtained the measurements and performed the analysis. H.N., D.M.C. and B.T. contributed to the accretion disc calculations, error estimates of the black hole mass, interpretation of the results and improvements to the paper.

Corresponding author

Correspondence to J. E. Mejía-Restrepo.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Additional information

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

Electronic supplementary material

Supplementary Information

Supplementary Table 1, Supplementary Figures 1–8 and Supplementary References

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Mejía-Restrepo, J.E., Lira, P., Netzer, H. et al. The effect of nuclear gas distribution on the mass determination of supermassive black holes. Nat Astron 2, 63–68 (2018).

Download citation

Further reading


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