Quantifying the impact of variable BLR diffuse continuum contributions on measured continuum inter-band delays

We investigate the contribution of reprocessed continuum emission (1000A - 10,000A) originating in broad line region (BLR) gas, the diffuse continuum (DC), to the wavelength-dependent continuum delays measured in AGN disk reverberation mapping experiments. Assuming a spherical BLR geometry, we adopt a Local Optimally-emitting Cloud (LOC) model for the BLR that approximately reproduces the broad emission-line strengths of the strongest UV lines (Ly-alpha and C IV) in NGC 5548. Within this LOC framework, we explore how assumptions about the gas hydrogen density and column density distributions influence flux and delay spectra of the DC. We find that: (i) models which match well measured emission line luminosities and time delays also produce a significant DC component, (ii) increased nH and/or NH, particularly at smaller BLR radii, result in larger DC luminosities and reduced DC delays, (iii) in a given continuum band the relative importance of the DC component to the measured inter-band delays is proportional (though not 1:1) to its fractional contribution to the total light in that band, (iv) the measured DC delays and DC variability amplitude depends also on the variability amplitude and characteristic variability timescale of the driving continuum, (v) the DC radial surface emissivity distributions F(r) approximate power-laws in radius with indices close to -2 (approximately 1:1 response to variations in the driving continuum flux), thus their physics is relatively simple and less sensitive to the unknown geometry and uncertainties in radiative transfer. Finally, we provide a simple recipe for estimating the DC contribution in disk reverberation mapping experiments.