Reverberation mapping

Reverberation mapping is an astrophysical technique for measuring the structure of the broad emission-line region (BLR)[1] 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.[2]

The black hole mass is measured from the formula

${\displaystyle GM_{\bullet }=fR_{\mathrm {BLR} }(\Delta V)^{2}.}$

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[3] 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.[2]

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.[2] When f is determined in this way, reverberation mapping becomes a "secondary", rather than "primary," mass estimation technique.