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'''Reverberation mapping''' is an [[astrophysics|astrophysical technique]] for measuring the structure of the [[broad emission-line region]] (BLR)<ref>http://arxiv.org/abs/1305.4357</ref> around a [[supermassive black hole]] at the center of an [[active galaxy]] and estimating the hole's mass. It is considered a "primary" mass estimation technique, i.e., the mass is measured directly from the motion that its gravitational force induces in the nearby gas.<ref name=DEGN>{{cite book|last=Merritt|first=David| authorlink=David Merritt | title=Dynamics and Evolution of Galactic Nuclei|year=2013|publisher=Princeton University Press|location=Princeton, NJ|isbn=9781400846122|url=http://openlibrary.org/works/OL16802359W/Dynamics_and_Evolution_of_Galactic_Nuclei}}</ref>

The black hole mass is measured from the formula

:<math> 
GM_\bullet = f R_\mathrm{BLR} (\Delta V)^2 .
</math>

In this formula, Δ''V'' is the rms velocity of gas moving near the black hole in the broad emission-line region, measured from the [[Doppler effect|Doppler broadening]] of the gaseous emission lines; ''R''<sub>BLR</sub> is the radius of the broad-line region; ''G'' is the [[constant of gravitation]]; and ''f'' is a poorly-known "form factor" that depends on the shape of the BLR.

The biggest difficulty with applying this formula is the measurement of ''R''<sub>BLR</sub>. One standard technique<ref>B.M. Peterson & K. Horne  [http://arxiv.org/abs/astro-ph/0407538 Reverberation Mapping of Active Galactic Nuclei] (2004)</ref> is based on the fact that the emission-line fluxes vary strongly in response to changes in the continuum, i.e., the light from the [[accretion disk]] near the black hole ("reverberation"). Furthermore, the emission-line response is found to be delayed with respect to changes in the continuum. Assuming that the delay is due to light travel times, the size of the broad emission-line region can be measured.

Only a small handful of AGN (less than 40) have been accurately "mapped" in this way. An alternative approach is to use an empirical correlation between ''R''<sub>BLR</sub> and the continuum luminosity.<ref name=DEGN/>

Another uncertainty is the value of ''f''. In principle, the response of the BLR to variations in the continuum could be used to map out the three-dimensional structure of the BLR. In practice, the amount and quality of data required to carry out such a [[deconvolution]] is prohibitive. Until about 2004, ''f'' was estimated ab initio based on simple models for the structure of the BLR. More recently, the value of ''f'' has been determined so as to bring the [[M-sigma relation]] for active galaxies into the best possible agreement with the M-sigma relation for quiescent galaxies.<ref name=DEGN/> When ''f'' is determined in this way, reverberation mapping becomes a "secondary", rather than "primary," mass estimation technique.

== See also ==

* [[Supermassive black holes]]

== References and notes ==
<references/>

== External links ==
* [http://physics.uwyo.edu/~shikatt/reverberationmapping.pdf Reverberation Mapping] ppt-presentation (2005)

[[Category:Observational astronomy]]
[[Category:Active galaxies]]
[[Category:Supermassive black holes]]
[[Category:Signal processing]]
[[Category:Astronomical imaging]]