  Adopting a spherically symmetric steady-state ballistic inflow as the
kinematic model for the gas distribution responsible for producing the
H{\alpha} emission line and a central black hole (BH) mass of 1.7 x10^6 M_sun,
determined from prior reverberation mapping, leads to the following dimensions
for the size of the broad line region (BLR) in NGC 4051; an inner radius ~3
lt-days and a lower limit to the outer radius ~ 475 lt-days. Thus, the
previously determined reverberation size for the BLR marks just the inner
radius of a much larger volume of ionized gas. The number of ionizing photons
required to sustain the H{\alpha} emission line luminosity exceeds the number
observed to be available from the central AGN by a factor of 3 - 4. Such a
large ionizing deficit can be reconciled if the BLR is ionized by a 10^5 K
accretion disk that is hidden from direct view by the high opacity of
intervening H gas. A new definition is introduced for the ionization parameter
that acknowledges the fact that H opacity significantly attenuates the flux of
ionizing photons in the large, partially ionized, nebula surrounding the AGN.
Collectively, these results have important implications for BH masses estimated
using reverberation radii and the structure of the BLR inferred from
velocity-delay maps.
