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 broad emission-line region (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 ηeff, delay and maximum of the cross-correlation function are correlated for characteristic continuum variability time-scales T char less than the maximum delay for that line τmax(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. Conversely, geometric dilution is minimized if T char ≥ τmax(line). 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 (for irregularly sampled data). 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 towards larger BLR radii, in line with photoionization calculations.