Gravitational Microlensing of a Reverberating Quasar Broad Line Region -
  I. Method and Qualitative Results
  The kinematics and morphology of the broad emission line region (BELR) of
quasars are the subject of significant debate. The two leading methods for
constraining BELR properties are microlensing and reverberation mapping. Here
we combine these two methods with a study of the microlensing behaviour of the
BELR in Q2237+0305, as a change in continuum emission (a "flare") passes
through it. Beginning with some generic models of the BELR - sphere, bicones,
disk - we slice in velocity and time to produce brightness profiles of the BELR
over the duration of the flare. These are numerically microlensed to determine
whether microlensing of reverberation mapping provides new information about
the properties of BELRs. We describe our method and show images of the models
as they are flaring, and the unlensed and lensed spectra that are produced.
Qualitative results and a discussion of the spectra are given in this paper,
highlighting some effects that could be observed. Our conclusion is that the
influence of microlensing, while not strong, can produce significant observable
effects that will help in differentiating the properties of BELRs.
