Reverberation mapping
Reverberation mapping is an astrophysical technique for measuring the structure of the broad emission-line region (BLR) around a supermassive black hole at the center of an active galaxy, and thus 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.
The black hole mass is measured from the formula
In this formula, ΔV is the RMS velocity of gas moving near the black hole in the broad emission-line region, measured from the Doppler broadening of the gaseous emission lines; RBLR 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 RBLR. One standard technique 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 RBLR and the continuum luminosity.
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. When f is determined in this way, reverberation mapping becomes a "secondary", rather than "primary," mass estimation technique.
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