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.