On the Scatter in the Radius - Luminosity Relationship for Active Galactic Nuclei

We investigate and quantify the observed scatter in the empirical relationship between the broad line region size R and the luminosity of the active galactic nucleus (AGN), in order to better understand its origin. This study is motivated by the indispensable role of this relationship in the mass estimation of cosmologically distant black holes, but may also be relevant to the recently proposed application of this relationship for measuring cosmic distances. We study six nearby reverberation-mapped AGN for which simultaneous UV and optical monitoring data exist. We also examine the long-term optical luminosity variations of Seyfert 1 galaxy NGC 5548 and employ Monte Carlo simulations to study the effects of the intrinsic variability of individual objects on the scatter in the global relationship for a sample of ~40 AGN. We find the scatter in this relationship has a correctable dependence on color. For individual AGN, the size of the Hbeta emitting region has a steeper dependence on the nuclear optical luminosity than on the UV luminosity, that can introduce a scatter of ~0.08 dex into the global relationship, due the non-linear relationship between the variations in the ionizing continuum and those in the optical continuum. Also, our analysis highlights the importance of understanding and minimizing the scatter in the relationship traced by the intrinsic variability of individual AGN, since it propagates directly into the global relationship. We find that using the UV luminosity as a substitute for the ionizing luminosity can reduce a sizable fraction of the current observed scatter of ~0.13 dex.