Interpreting broad emission-line variations II: Tensions between
  luminosity, characteristic size and responsivity
  We investigate the variability behaviour of the broad Hb emission-line to
driving continuum variations in the best-studied AGN NGC 5548. For a particular
choice of BLR geometry, Hb surface emissivity based on photoionization models,
and using a scaled version of the 13 yr optical continuum light curve as a
proxy for the driving ionizing continuum, we explore several key factors that
determine the broad emission line luminosity L, characteristic size R(RW), and
variability amplitude (i.e., responsivity) eta, as well as the interplay
between them.
  For fixed boundary models which extend as far as the hot-dust the predicted
delays for Hb are on average too long. However, the predicted variability
amplitude of Hb provides a remarkably good match to observations except during
low continuum states. We suggest that the continuum flux variations which drive
the redistribution in Hb surface emissivity F(r) do not on their own lead to
large enough changes in R(RW) or eta(eff). We thus investigate dust-bounded
BLRs for which the location of the effective outer boundary is modulated by the
continuum level and the dust-sublimation and dust-condensation timescales. We
find that in order to match the observed variability amplitude of broad Hb in
NGC 5548 a rather static outer boundary is preferred.
  Intriguingly, we show that the most effective way of reducing the Hb delay,
while preserving its responsivity and equivalent width, is to invoke a smaller
value in the incident ionizing photon flux Phi(H) for a given ionizing
source--cloud radial distance r, than is normally inferred from the observed UV
continuum flux and typical models of the continuum SED.
