Size and kinematics of the C iv broad emission line region from microlensing-induced line profile distortions in two gravitationally lensed quasars

Microlensing of the broad emission line region (BLR) in gravitationally lensed quasars produces line profile distortions that can be used to probe the BLR size, geometry, and kinematics. Based on single-epoch spectroscopic data, we analyzed the C iv line profile distortions due to microlensing in two quasars, SDSS J133907.13$+$131039.6 (J1339) and SDSS J113803.73$+$031457.7 (J1138), complementing previous studies of microlensing in the quasars Q2237$+$0305 and J1004$+$4112. J1339 shows a strong, asymmetric line profile deformation, while J1138 shows a more modest, symmetric deformation, confirming the rich diversity of microlensing-induced spectral line deformations. To probe the C iv BLR, we compared the observed line profile deformations to simulated ones. The simulations are based on three simple BLR models, a Keplerian disk (KD), an equatorial wind (EW), and a polar wind (PW), of various sizes, inclinations, and emissivities. These models were convolved with microlensing magnification maps specific to the microlensed quasar images, which produced a large number of distorted line profiles. The models that best reproduce the observed line profile deformations were then identified using a Bayesian probabilistic approach. We find that the line profile deformations can be reproduced with the simple BLR models under consideration, with no need for more complex geometries or kinematics. The models with disk geometries (KD and EW) are preferred, while the PW model is definitely less likely. In J1339, the EW model is favored, while the KD model is preferred in Q2237$+$0305, suggesting that various kinematical models can dominate the C iv BLR. For J1339, we find the C iv BLR half-light radii to be $r_ $ light-days and $r_ $ light-days from spectra obtained in 2014 and 2017, respectively. They do agree within uncertainties. For J1138, the amplitude of microlensing is smaller and more dependent on the macro-magnification factor. From spectra obtained in 2005 (single epoch), we find $r_ $ light-days and $r_ $ light-days for two extreme values of the macro-magnification factor. Combining these new measurements with those previously obtained for the quasars Q2237$+$0305 and J1004$+$4112, we show that the BLR radii estimated from microlensing do follow the C iv radius--luminosity relation obtained from reverberation mapping, although the microlensing radii seem to be systematically smaller, which could indicate either a selection bias or a real offset.