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.
