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, disc 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.