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Measuring the Masses of Supermassive Black Holes

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Abstract

Supermassive black holes reside at the centers of most, if not all, massive galaxies: the difference between active and quiescent galaxies is due to differences in mass accretion rate and radiative efficiency rather than whether or not they have nuclear black holes. In this contribution, methods for measuring the masses of supermassive black holes are discussed, with emphasis on reverberation mapping which is most generally applicable to accreting supermassive black holes and, in particular, to distant quasars where time resolution can be used as a surrogate for angular resolution. Indirect methods based on scaling relationships from reverberation mapping studies are also discussed, along with their current limitations.

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Notes

  1. The phrase “not surprisingly” in this context is used because Sgr A* is 100 times closer than any other supermassive black hole so it is possible to observe the motions of individual stars around the black hole in its vicinity. But the very fact that individual stars at the Galactic Center can be observed, despite 30 mag of visual extinction, is surprising, one of the things the author least expected to see in his own scientific lifetime.

  2. The discrepancy between theory and observation was due to an oversimplified theory; it was implicitly assumed in photoionization equilibrium modeling that all BLR “clouds” are intrinsically identical. A successful photoionization model was one that correctly predicts the emission-line intensity ratios in the emitted spectrum of some “standard” cloud. A key intensity ratio is C iv  λ1549/C iii] λ1909. Moreover, the very presence of C iii] λ1909 set an upper limit to the density as this line is collisionally suppressed above 109.5 cm−3. The implicit assumption that C iv  λ1549 and C iii] λ1909 are produced cospatially was incorrect. The first high-sampling rate reverberation program (Clavel et al. 1991) showed that C iv  λ1549 and C iii] λ1909 arise at different distances from the central source, thus obviating the earlier arguments. The C iv-emitting zone is now believed to have a higher density, ∼1011 cm−3 (Ferland et al. 1992).

  3. Brewer et al. (2011) define the inclination angle to be the complement of the usual astronomical convention where i=0 is face-on. The value given here is corrected to the standard astronomical convention.

  4. Note that the errors quoted in Table 1 are statistical. Systematic errors have not been included.

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Acknowledgements

The author is grateful for support by the US National Science Foundation through grant AST-1008882 to The Ohio State University and for the kind hospitality of the International Space Science Institute in Bern, where this work was first presented. The author thanks Misty Bentz for providing Figs. 4 and 8, Kate Grier for Figs. 1, 5 and 6, and Jong-Hak Woo for Fig. 7. The author also thanks Misty Bentz, Kelly Denney, Stephan Frank, Kate Grier, Peter Jonker, Smita Mathur, Ian McHardy, Yue Shen, Marianne Vestergaard, and an anonymous referee for advice, criticism, and comments on the manuscript.

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    Bradley M. Peterson

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Peterson, B.M. Measuring the Masses of Supermassive Black Holes. Space Sci Rev 183, 253–275 (2014). https://doi.org/10.1007/s11214-013-9987-4

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