Interpreting broad emission-line variations I : Factors influencing the
  emission-line response
  We investigate the sensitivity of the measured broad emission-line
responsivity dlog f_line/dlog f_cont to continuum variations in the context of
straw-man BLR geometries of varying size with fixed BLR boundaries, and for
which the intrinsic emission-line responsivity is known a priori. We find for a
generic emission-line that the measured responsivity, delay and maximum of the
cross-correlation function are correlated for characteristic continuum
variability timescales T_char less than the maximum delay for that line
tau_max(line) for a particular choice of BLR geometry and observer orientation.
The above correlations are manifestations of geometric dilution arising from
reverberation effects within the spatially extended BLR. When present,
geometric dilution reduces the measured responsivity, delay and maximum of the
cross-correlation function. We also find that the measured responsivity and
delay show a strong dependence on light-curve duration, with shorter campaigns
resulting in smaller than expected values, and only a weak dependence on
sampling rate.
  The observed strong negative correlation between continuum level and line
responsivity found in previous studies cannot be explained by differences in
the sampling pattern, light-curve duration or in terms of purely geometrical
effects. To explain this and to satisfy the observed positive correlation
between continuum luminosity and BLR size in an individual source, the
responsivity-weighted radius must increase with increasing continuum
luminosity. For a BLR with fixed inner and outer boundaries this requires
radial surface emissivity distributions which deviate significantly from a
simple power-law, and in such a way that the intrinsic emission-line
responsivity increases toward larger BLR radii, in line with photoionisation
calculations.
