Constraining the geometry and kinematics of the quasar broad emission
  line region using gravitational microlensing. I. Models and simulations
  Recent studies have shown that line profile distortions are commonly observed
in gravitationally lensed quasar spectra. We investigate the effect of
gravitational microlensing on quasar broad emission line profiles and their
underlying continuum, combining the emission from simple representative BLR
models with generic microlensing magnification maps. Specifically, we
considered Keplerian disk, polar, and equatorial wind BLR models of various
sizes. The effect of microlensing has been quantified with four observables:
$\mu^{BLR}$, the total magnification of the broad emission line; $\mu^{cont}$,
the magnification of the underlying continuum; as well as red/blue, RBI and
wings/core, WCI, indices that characterize the line profile distortions. The
simulations showed that distortions of line profiles, such as those recently
observed in lensed quasars, can indeed be reproduced and attributed to the
differential effect of microlensing on spatially separated regions of the BLR.
While the magnification of the emission line $\mu^{BLR}$ sets an upper limit on
the BLR size and, similarly, the magnification of the continuum $\mu^{cont}$
sets an upper limit on the size of the continuum source, the line profile
distortions mainly depend on the BLR geometry and kinematics. We thus built
(WCI,RBI) diagrams that can serve as diagnostic diagrams to discriminate
between the various BLR models on the basis of quantitative measurements. It
appears that a strong microlensing effect puts important constraints on the
size of the BLR and on its distance to the high-magnification caustic. In that
case, BLR models with different geometries and kinematics are more prone to
produce distinctive line profile distortions for a limited number of caustic
configurations, which facilitates their discrimination.
