Constraining black hole–galaxy scaling relations and radiative efficiency from galaxy clustering

Abstract

The masses of supermassive black holes are observed to increase with either the total mass or the mean (random) velocity of the stars in their host galaxies. The origin of these correlations remains elusive due to observational systematics and biases that severely limit our knowledge of the local demography of supermassive black holes. Here, we show that the large-scale spatial distribution of local active galactic nuclei (AGN) can constrain the shape and normalization of the black hole–stellar mass relation, thus bypassing resolution-related observational biases. In turn, our results can set more stringent constraints on the AGN radiative efficiency, ε. For currently accepted values of the AGN obscured fractions and bolometric corrections, our estimated local supermassive black hole mass density favours mean ε values of ~10–20%, suggesting that the vast majority of supermassive black holes are spinning moderately to rapidly. With large-scale AGN surveys coming online, our methodology will enable even tighter constraints on the fundamental parameters that regulate the growth of supermassive black holes.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Fig. 1: Overview of local scaling relations between black hole mass and host (total) stellar mass.
Fig. 2: Predicted bias as a function of black hole mass, b(MBH).
Fig. 3: Comparing local and accreted mass functions.
Fig. 4: Comparing local and accreted integrated mass densities.

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. Source data for Fig. 3 are provided with the paper.

Code availability

The codes that support the findings of this study are available from the corresponding author upon reasonable request.

References

  1. 1.

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

  2. 2.

    Bardeen, J. M., Press, W. H. & Teukolsky, S. A. Rotating black holes: locally nonrotating frames, energy extraction, and scalar synchrotron radiation. Astrophys. J. 178, 347–370 (1972).

  3. 3.

    Soltan, A. Masses of quasars. Mon. Not. R. Astron. Soc. 200, 115–122 (1982).

  4. 4.

    Salucci, P., Szuszkiewicz, E., Monaco, P. & Danese, L. Mass function of dormant black holes and the evolution of active galactic nuclei. Mon. Not. R. Astron. Soc. 307, 637–644 (1999).

  5. 5.

    Marconi, A. et al. Local supermassive black holes, relics of active galactic nuclei and the X-ray background. Mon. Not. R. Astron. Soc. 351, 169–185 (2004).

  6. 6.

    Shankar, F., Weinberg, D. H. & Miralda-Escudé, J. Accretion-driven evolution of black holes: Eddington ratios, duty cycles and active galaxy fractions. Mon. Not. R. Astron. Soc. 428, 421–446 (2013).

  7. 7.

    Aversa, R., Lapi, A., de Zotti, G., Shankar, F. & Danese, L. Black hole and galaxy coevolution from continuity equation and abundance matching. Astrophys. J. 810, 74 (2015).

  8. 8.

    Shankar, F. et al. Selection bias in dynamically measured supermassive black hole samples: its consequences and the quest for the most fundamental relation. Mon. Not. R. Astron. Soc. 460, 3119–3142 (2016).

  9. 9.

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

  10. 10.

    Davis, B. L., Graham, A. W. & Cameron, E. Black hole mass scaling relations for spiral galaxies. II. M BHM *,tot and M BHM *,disk. Astrophys. J. 869, 113 (2018).

  11. 11.

    Busch, G. et al. A low-luminosity type-1 QSO sample. I. Overluminous host spheroidals or undermassive black holes. Astron. Astrophys. 561, A140 (2014).

  12. 12.

    Reines, A. E. & Volonteri, M. Relations between central black hole mass and total galaxy stellar mass in the local Universe. Astrophys. J. 813, 82 (2015).

  13. 13.

    Shankar, F. et al. Black hole scaling relations of active and quiescent galaxies: addressing selection effects and constraining virial factors. Mon. Not. R. Astron. Soc. 485, 1278–1292 (2019).

  14. 14.

    Bernardi, M., Sheth, R. K., Tundo, E. & Hyde, J. B. Selection bias in the M σ and M L correlations and its consequences. Astrophys. J. 660, 267–275 (2007).

  15. 15.

    Morabito, L. K. & Dai, X. A Bayesian Monte Carlo analysis of the Mσ relation. Astrophys. J. 757, 172 (2012).

  16. 16.

    Cooray, A. & Sheth, R. Halo models of large scale structure. Phys. Rep. 372, 1–129 (2002).

  17. 17.

    Shankar, F. et al. Revisiting the bulge–halo conspiracy. I. Dependence on galaxy properties and halo mass. Astrophys. J. 840, 34 (2017).

  18. 18.

    Grylls, P. J., Shankar, F., Zanisi, L. & Bernardi, M. A statistical semi-empirical model: satellite galaxies in groups and clusters. Mon. Not. R. Astron. Soc. 483, 2506–2523 (2019).

  19. 19.

    Shankar, F., Weinberg, D. H. & Shen, Y. Constraints on black hole duty cycles and the black hole–halo relation from SDSS quasar clustering. Mon. Not. R. Astron. Soc. 406, 1959–1966 (2010).

  20. 20.

    Krumpe, M. et al. The spatial clustering of ROSAT All-Sky Survey active galactic nuclei. IV. More massive black holes reside in more massive dark matter halos. Astrophys. J. 815, 21 (2015).

  21. 21.

    Davé, R. et al. Simba: cosmological simulations with black hole growth and feedback. Mon. Not. R. Astron. Soc. 486, 2827–2849 (2019).

  22. 22.

    Savorgnan, G. A. D., Graham, A. W., Marconi, A. & Sani, E. Supermassive black holes and their host spheroids. II. The red and blue sequence in the M BHM *,sph diagram. Astrophys. J. 817, 21 (2016).

  23. 23.

    Sahu, N., Graham, A. W. & Davis, B. L. Black hole mass scaling relations for early-type galaxies. I. M BHM * ,sph and M BHM *,gal. Astrophys. J. 876, 155 (2019).

  24. 24.

    Baron, D. & Ménard, B. Black hole mass estimation for active galactic nuclei from a new angle. Mon. Not. R. Astron. Soc. 487, 3404–3418 (2019).

  25. 25.

    Shankar, F., Bernardi, M. & Sheth, R. K. Selection bias in dynamically measured supermassive black hole samples: dynamical masses and dependence on Sérsic index. Mon. Not. R. Astron. Soc. 466, 4029–4039 (2017).

  26. 26.

    Sarria, J. E. et al. The M BHM star relation of obscured AGNs at high redshift. Astron. Astrophys. 522, L3 (2010).

  27. 27.

    Falomo, R., Bettoni, D., Karhunen, K., Kotilainen, J. K. & Uslenghi, M. Low-redshift quasars in the Sloan Digital Sky Survey Stripe 82. The host galaxies. Mon. Not. R. Astron. Soc. 440, 476–493 (2014).

  28. 28.

    Tinker, J. et al. Toward a halo mass function for precision cosmology: the limits of universality. Astrophys. J. 688, 709–728 (2008).

  29. 29.

    Powell, M. C. et al. The Swift/BAT AGN spectroscopic survey. IX. The clustering environments of an unbiased sample of local AGNs. Astrophys. J. 858, 110 (2018).

  30. 30.

    Krumpe, M., Miyaji, T., Coil, A. L. & Aceves, H. Spatial clustering and halo occupation distribution modelling of local AGN via cross-correlation measurements with 2MASS galaxies. Mon. Not. R. Astron. Soc. 474, 1773–1786 (2018).

  31. 31.

    Sheth, R. K. & Tormen, G. Large-scale bias and the peak background split. Mon. Not. R. Astron. Soc. 308, 119–126 (1999).

  32. 32.

    Ueda, Y., Akiyama, M., Hasinger, G., Miyaji, T. & Watson, M. G. Toward the standard population synthesis model of the X-ray background: evolution of X-ray luminosity and absorption functions of active galactic nuclei including Compton-thick populations. Astrophys. J. 786, 104 (2014).

  33. 33.

    Yang, G. et al. Linking black hole growth with host galaxies: the accretion–stellar mass relation and its cosmic evolution. Mon. Not. R. Astron. Soc. 475, 1887–1911 (2018).

  34. 34.

    Harrison, F. A. et al. The NuSTAR extragalactic surveys: the number counts of active galactic nuclei and the resolved fraction of the cosmic X-ray background. Astrophys. J. 831, 185 (2016).

  35. 35.

    Shankar, F., Cavaliere, A., Cirasuolo, M. & Maraschi, L. Optical–radio mapping: the kinetic efficiency of radio-loud AGNs. Astrophys. J. 676, 131–136 (2008).

  36. 36.

    Reynolds, C. S. Observing black holes spin. Nat. Astron. 3, 41–47 (2019).

  37. 37.

    Shankar, F. et al. The optical–UV emissivity of quasars: dependence on black hole mass and radio loudness. Astrophys. J. Lett. 818, L1 (2016).

  38. 38.

    Zhang, X. & Lu, Y. On constraining the growth history of massive black holes via their distribution on the spin–mass plane. Astrophys. J. 873, 101 (2019).

  39. 39.

    Elvis, M., Risaliti, G. & Zamorani, G. Most supermassive black holes must be rapidly rotating. Astrophys. J. Lett. 565, L75–L77 (2002).

  40. 40.

    Yu, Q. & Lu, Y. Toward precise constraints on the growth of massive black holes. Astrophys. J. 689, 732–754 (2008).

  41. 41.

    Merloni, A. et al. eROSITA science book: mapping the structure of the energetic universe. Preprint at https://arxiv.org/abs/1209.3114 (2012).

  42. 42.

    Bell, E. F., McIntosh, D. H., Katz, N. & Weinberg, M. D. The optical and near-infrared properties of galaxies. I. Luminosity and stellar mass functions. Astrophys. J. Suppl. 149, 289–312 (2003).

  43. 43.

    Bernardi, M. et al. The high-mass end of the stellar mass function: dependence on stellar population models and agreement between fits to the light profile. Mon. Not. R. Astron. Soc. 467, 2217–2233 (2017).

  44. 44.

    Sesana, A., Shankar, F., Bernardi, M. & Sheth, R. K. Selection bias in dynamically measured supermassive black hole samples: consequences for pulsar timing arrays. Mon. Not. R. Astron. Soc. 463, L6–L11 (2016).

  45. 45.

    Shankar, F. et al. Revisiting the bulge–halo conspiracy. II. Towards explaining its puzzling dependence on redshift. Mon. Not. R. Astron. Soc. 475, 2878–2890 (2018).

  46. 46.

    Jiang, F. & van den Bosch, F. C. Statistics of dark matter substructure. I. Model and universal fitting functions. Mon. Not. R. Astron. Soc. 458, 2848–2869 (2016).

  47. 47.

    Giocoli, C., Tormen, G. & van den Bosch, F. C. The population of dark matter subhaloes: mass functions and average mass-loss rates. Mon. Not. R. Astron. Soc. 386, 2135–2144 (2008).

  48. 48.

    Bernardi, M. et al. The massive end of the luminosity and stellar mass functions: dependence on the fit to the light profile. Mon. Not. R. Astron. Soc. 436, 697–704 (2013).

  49. 49.

    Bernardi, M. et al. The massive end of the luminosity and stellar mass functions and clustering from CMASS to SDSS: evidence for and against passive evolution. Mon. Not. R. Astron. Soc. 455, 4122–4135 (2016).

  50. 50.

    Tinker, J. L. et al. The correlation between halo mass and stellar mass for the most massive galaxies in the Universe. Astrophys. J. 839, 121 (2017).

  51. 51.

    Kravtsov, A. V., Vikhlinin, A. A. & Meshcheryakov, A. V. Stellar mass–halo mass relation and star formation efficiency in high-mass halos. Astron. Lett. 44, 8–34 (2018).

  52. 52.

    Behroozi, P., Wechsler, R., Hearin, A. & Conroy, C. UNIVERSEMACHINE: the correlation between galaxy growth and dark matter halo assembly from z = 0−10. Mon. Not. R. Astron. Soc. 488, 3143–3194 (2019).

  53. 53.

    Moster, B. P., Naab, T. & White, S. D. M. EMERGE—an empirical model for the formation of galaxies since z ~ 10. Mon. Not. R. Astron. Soc. 477, 1822–1852 (2018).

  54. 54.

    Huertas-Company, M., Aguerri, J. A. L., Bernardi, M., Mei, S. & Sánchez Almeida, J. Revisiting the Hubble sequence in the SDSS DR7 spectroscopic sample: a publicly available Bayesian automated classification. Astron. Astrophys. 525, A157 (2011).

  55. 55.

    Small, T. A. & Blandford, R. D. Quasar evolution and the growth of black holes. Mon. Not. R. Astron. Soc. 259, 725–737 (1992).

  56. 56.

    Yu, Q. & Tremaine, S. Observational constraints on growth of massive black holes. Mon. Not. R. Astron. Soc. 335, 965–976 (2002).

  57. 57.

    Shankar, F., Salucci, P., Granato, G. L., De Zotti, G. & Danese, L. Supermassive black hole demography: the match between the local and accreted mass functions. Mon. Not. R. Astron. Soc. 354, 1020–1030 (2004).

  58. 58.

    Cao, X. Cosmological evolution of massive black holes: effects of Eddington ratio distribution and quasar lifetime. Astrophys. J. 725, 388–393 (2010).

  59. 59.

    Yu, Q. & Lu, Y. Constraints on QSO models from a relation between the QSO luminosity function and the local black hole mass function. Astrophys. J. 602, 603–624 (2004).

  60. 60.

    Shankar, F., Weinberg, D. H. & Miralda-Escudé, J. Self-consistent models of the AGN and black hole populations: duty cycles, accretion rates, and the mean radiative efficiency. Astrophys. J. 690, 20–41 (2009).

  61. 61.

    Goulding, A. D., Alexander, D. M., Lehmer, B. D. & Mullaney, J. R. Towards a complete census of active galactic nuclei in nearby galaxies: the incidence of growing black holes. Mon. Not. R. Astron. Soc. 406, 597–611 (2010).

  62. 62.

    Shankar, F. Black hole demography: from scaling relations to models. Class. Quantum Grav. 30, 244001 (2013).

  63. 63.

    Ghisellini, G., Haardt, F., Della Ceca, R., Volonteri, M. & Sbarrato, T. The role of relativistic jets in the heaviest and most active supermassive black holes at high redshift. Mon. Not. R. Astron. Soc. 432, 2818–2823 (2013).

  64. 64.

    Zubovas, K. AGN must be very efficient at powering outflows. Mon. Not. R. Astron. Soc. 479, 3189–3196 (2018).

  65. 65.

    Starikova, S. et al. Constraining halo occupation properties of X-ray active galactic nuclei using clustering of Chandra sources in the Boötes survey region. Astrophys. J. 741, 15 (2011).

  66. 66.

    Shen, Y. et al. Cross-correlation of SDSS DR7 quasars and DR10 BOSS galaxies: the weak luminosity dependence of quasar clustering at z ~ 0.5. Astrophys. J. 778, 98 (2013).

  67. 67.

    Leauthaud, A. et al. The dark matter haloes of moderate luminosity X-ray AGN as determined from weak gravitational lensing and host stellar masses. Mon. Not. R. Astron. Soc. 446, 1874–1888 (2015).

  68. 68.

    Rodríguez-Torres, S. A. et al. Clustering of quasars in the first year of the SDSS-IV eBOSS survey: interpretation and halo occupation distribution. Mon. Not. R. Astron. Soc. 468, 728–740 (2017).

  69. 69.

    Man, Z.-y. et al. The dependence of AGN activity on environment in SDSS. Mon. Not. R. Astron. Soc. 488, 89–98 (2019).

  70. 70.

    Tinker, J. L., Weinberg, D. H., Zheng, Z. & Zehavi, I. On the mass-to-light ratio of large-scale structure. Astrophys. J. 631, 41–58 (2005).

  71. 71.

    White, S. D. M. & Frenk, C. S. Galaxy formation through hierarchical clustering. Astrophys. J. 379, 52–79 (1991).

  72. 72.

    Smith, R. E. et al. Stable clustering, the halo model and non-linear cosmological power spectra. Mon. Not. R. Astron. Soc. 341, 1311–1332 (2003).

  73. 73.

    Gould, A. Chi^2 and linear fits. Preprint at https://arxiv.org/abs/astro-ph/0310577 (2003).

  74. 74.

    van Uitert, E., Cacciato, M., Hoekstra, H. & Herbonnet, R. Evolution of the luminosity-to-halo mass relation of LRGs from a combined analysis of SDSS-DR10+RCS2. Astron. Astrophys. 579, A26 (2015).

  75. 75.

    Tinker, J. L. et al. The large-scale bias of dark matter halos: numerical calibration and model tests. Astrophys. J. 724, 878–886 (2010).

  76. 76.

    Klypin, A., Yepes, G., Gottlöber, S., Prada, F. & Heß, S. MultiDark simulations: the story of dark matter halo concentrations and density profiles. Mon. Not. R. Astron. Soc. 457, 4340–4359 (2016).

  77. 77.

    Schulze, A. et al. The cosmic growth of the active black hole population at 1 < z < 2 in zCOSMOS, VVDS and SDSS. Mon. Not. R. Astron. Soc. 447, 2085–2111 (2015).

  78. 78.

    DiPompeo, M. A., Runnoe, J. C., Hickox, R. C., Myers, A. D. & Geach, J. E. The impact of the dusty torus on obscured quasar halo mass measurements. Mon. Not. R. Astron. Soc. 460, 175–186 (2016).

  79. 79.

    Jiang, N. et al. Differences in halo-scale environments between type 1 and type 2 AGNs at low redshift. Astrophys. J. 832, 111 (2016).

  80. 80.

    Lusso, E. et al. Bolometric luminosities and Eddington ratios of X-ray selected active galactic nuclei in the XMM-COSMOS survey. Mon. Not. R. Astron. Soc. 425, 623–640 (2012).

  81. 81.

    Hopkins, P. F., Richards, G. T. & Hernquist, L. An observational determination of the bolometric quasar luminosity function. Astrophys. J. 654, 731–753 (2007).

  82. 82.

    Zhang, X. & Lu, Y. On the mean radiative efficiency of accreting massive black holes in AGNs and QSOs. Sci. China Phys. Mech. Astron. 60, 109511 (2017).

  83. 83.

    Zhang, X., Lu, Y. & Yu, Q. The cosmic evolution of massive black holes and galaxy spheroids: global constraints at redshift z 1.2. Astrophys. J. 761, 5 (2012).

  84. 84.

    Vasudevan, R. V. & Fabian, A. C. Piecing together the X-ray background: bolometric corrections for active galactic nuclei. Mon. Not. R. Astron. Soc. 381, 1235–1251 (2007).

  85. 85.

    Shankar, F., Crocce, M., Miralda-Escudé, J., Fosalba, P. & Weinberg, D. H. On the radiative efficiencies, Eddington ratios, and duty cycles of luminous high-redshift quasars. Astrophys. J. 718, 231–250 (2010).

  86. 86.

    Vasudevan, R. V. et al. A selection effect boosting the contribution from rapidly spinning black holes to the cosmic X-ray background. Mon. Not. R. Astron. Soc. 458, 2012–2023 (2016).

  87. 87.

    Georgantopoulos, I. & Akylas, A. NuSTAR observations of heavily obscured Swift/BAT AGNs: constraints on the Compton-thick AGNs fraction. Astron. Astrophys. 621, A28 (2019).

  88. 88.

    Ananna, T. T. et al. The accretion history of AGNs. I. Supermassive black hole population synthesis model. Astrophys. J. 871, 240 (2019).

  89. 89.

    Kulier, A., Ostriker, J. P., Natarajan, P., Lackner, C. N. & Cen, R. Understanding black hole mass assembly via accretion and mergers at late times in cosmological simulations. Astrophys. J. 799, 178 (2015).

  90. 90.

    Ghez, A. M. et al. Measuring distance and properties of the Milky Way’s central supermassive black hole with stellar orbits. Astrophys. J. 689, 1044–1062 (2008).

  91. 91.

    Posti, L. & Helmi, A. Mass and shape of the Milky Way’s dark matter halo with globular clusters from Gaia and Hubble. Astron. Astrophys. 621, A56 (2019).

Download references

Acknowledgements

F.S. thanks D. Weinberg, D. Baron, P. Behroozi, G. Calderone, B. Davis, F. Fiore, P. Gandhi, S. Hoenig, C. Knigge, C. Li, J. Miralda-Escudé, B. Moster, M. Powell, R. Vasudevan, C. Villforth and G. Yang for discussions and input, and acknowledges partial support from a Leverhulme Trust Research Fellowship and the European Union’s Horizon 2020 programme under the AHEAD project (grant agreement no. 654215). V.A. acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement no. 749348. M.B. acknowledges partial support from NSF grant AST-1816330. A.L. is supported by PRIN MIUR 2017 prot. 20173ML3WW_002 ‘Opening the ALMA window on the cosmic evolution of gas, stars and supermassive black holes’. M.K. acknowledges support from DLR grant 50OR1904. L.Z. and P.J.G. acknowledge funding from the Science and Technology Facilities Council (STFC).

Author information

F.S. performed the full set up of the AGN mocks, analysis of the results and writing up of the manuscript. V.A. independently checked all of the results on AGN clustering and contributed to text revisions and to the referee reports. M.B. was one of the core authors in the Shankar et al.8 paper on the intrinsic black hole scaling relations and contributed to revision of the manuscript. C.M. devised accurate determinations of the correlation functions in the MultiDark simulation. A.L. calculated the accreted black hole mass functions following the models presented in Aversa et al.7. N.M. contributed to the AGN accretion models. P.J.G. and L.Z. contributed to the galaxy mocks, independently tested some of the key results and provided comments. J.M. performed preliminary large-scale bias estimates of AGN at different luminosities in low-redshift galaxies. M.K. made available a number of datasets on galaxy and AGN clustering inclusive of full covariance matrices. R.D.B. performed independent calculations of some of the AGN mocks. F.R. contributed to the characterization of the scaling relations in optically selected type I and type II AGN and to revision of the paper. F.L.F. provided key insights into the use of different AGN bolometric corrections. R.K.S. was one of the core authors in the Shankar et al.8 paper on the intrinsic black hole scaling relations and provided support on the theoretical side and revision of the paper.

Correspondence to Francesco Shankar.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature Astronomy thanks Ryan Hickox 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.

Extended data

Extended Data Fig. 1 Predicted local black hole mass functions of elliptical galaxies.

Same format as Figure 2 but only for elliptical, bulge-dominated galaxies. Panels a and b show the comparison between, respectively, the observed and intrinsic Mbh-Mstar and Mbh-σ relations of early-type galaxies, as labelled.

Extended Data Fig. 2 Comparing host halo auto-correlation functions.

Comparison between the linear matter correlation function multiplied by the square of the halo bias from Tinker et al. (2005, dotted line) and Tinker et al. (2010, solid line), and the autocorrelation function in the MultiDark simulation of all central and satellite haloes with virial mass at infall in the range 13.3<log Mvir/Msun<13.7. For this comparison we adopt the same cosmological parameters as in the MultiDark simulation.

Extended Data Fig. 3 Direct comparison with the cross-correlation function of active galaxies.

Comparison between the DR4 (panels a and b) and DR7 (panels c and d) projected AGN-galaxy cross-correlation function derived by Krumpe et al. (2015, filled squares with their 1σ uncertainties), with the linear matter projected correlation function multiplied by the product of the galaxy and black hole large-scale biases with Qbh=1 (panels a and c) and Qbh=2 (panels b and d). The solid red and long-dashed black lines refer to the large-scale bias derived, respectively, from the observed and intrinsic Mbh-Mstar relations. It is clear that the models derived from the intrinsic Mbh-Mstar relation (solid red lines) provide a better match to the data (see text for details).

Extended Data Fig. 4 Predicted bias as a function of black hole mass.

Similar format to Figure 2 but now showing the function b(Mbh) expected from the observed/biased (dashed) and intrinsic (solid) Mbh-σ scaling relations.

Extended Data Fig. 5 Table 1.

Black hole mass function retrieved from the intrinsic Mbh-Mstar relation.

Source data

Source Data for Fig. 3

Data on the local black hole mass functions. Columns are: logMbh [Msun], log(Phi_intrinsic) [Mpc-3 dex-1], 1sigma uncertainty in log(Phi_intrinsic), log(Phi_biased) [Mpc-3 dex-1], 1sigma uncertainty in log(Phi_biased)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Shankar, F., Allevato, V., Bernardi, M. et al. Constraining black hole–galaxy scaling relations and radiative efficiency from galaxy clustering. Nat Astron (2019). https://doi.org/10.1038/s41550-019-0949-y

Download citation