  Emission-line regions in active galactic nuclei and other photoionized
nebulae should become larger in size when the ionizing luminosity increases.
This 'breathing' effect is observed for the Hbeta emission in NGC 5548 by using
Hbeta and optical continuum lightcurves from the 13-year 1989-2001 AGN Watch
monitoring campaign. To model the breathing, we use two methods to fit the
observed lightcurves in detail: (i) parameterized models and, (ii) the MEMECHO
reverberation mapping code. Our models assume that optical continuum variations
track the ionizing radiation, and that the Hbeta variations respond with time
delays due to light travel time. By fitting the data using a delay map that is
allowed to change with continuum flux, we find that the strength of the Hbeta
response decreases and the time delay increases with ionizing luminosity. The
parameterized breathing models allow the time delay and the Hbeta flux to
depend on the continuum flux so that, the time delay is proportional to the
continuum flux to the power beta, and the Hbeta flux is proportional to the
continuum flux to the power alpha. Our fits give 0.1 < beta < 0.46 and 0.57 <
alpha < 0.66. alpha is consistent with previous work by Gilbert and Peterson
(2003) and Goad, Korista and Knigge (2004). Although we find beta to be flatter
than previously determined by Peterson et al. (2002) using cross-correlation
methods, it is closer to the predicted values from recent theoretical work by
Korista and Goad (2004).
