**8.4. Light Curve Modeling**

An alternative empirical way to find the gas distribution, is by fitting models to the observed emission line light curve. This is done by convolving the observed continuum light curve with several assumed transfer functions. The most likely geometry is the one resulting in the best fit to the observed line light curve. The result of this methods is not unique and several different geometries can give satisfactory fits. It can be very useful in eliminating some geometries, and reducing the parameter space. The main limitations are again the uncertain interpolation procedure and the non-linear response of the lines.

Having discussed the observations and several potential ways of analysis, we are now in a position to estimate the BLR size. In the time of writing there are only a hand-full of Seyfert 1 galaxies where the cross correlation size has been reliably measured. The range in luminosity is about 500 and the range in cross correlation size about 25. This incomplete data set, combined with a guess that the average BLR size is about double the cross-correlation size, suggest the following approximate relation for low luminosity AGNs:

(75) |

While the *L*^{1/2} dependence is only a guess at this
stage, it is in line with the
assumption that the average density and ionization parameter in
different BLRs
is not a strong function of the continuum luminosity. Further discussion
of this relation is given in chapter 10.