We introduce a novel method to derive rotation curves with light-day spatial resolution of the inner regions of lensed quasars. We aim to probe the kinematics of the inner part of the broad-line region by resolving the microlensing response—a proxy for the size of the emitting region—in the wings of the broad emission lines. Specifically, we assess the strength of the microlensing effects in the wings of the high-ionization lines Si iv and C iv across various velocity bins in five gravitationally lensed quasars: SDSS J1001+5027, SDSS J1004+4112, HE 1104−1805, SDSS J1206+4332, and SDSS J1339+1310. Using Bayesian methods to estimate the dimensions of the corresponding emission regions and adopting a Keplerian model as our baseline, we examine the consistency of the hypothesis of disklike rotation. Our results reveal a monotonic, smooth increase in microlensing magnification with velocity. The deduced velocity–size relationships inferred for the various quasars and emission lines closely conform to the Keplerian model of an inclined disk. This study provides the first direct evidence of Keplerian rotation in the innermost region of quasars across a range of radial distances spanning from ∼5 to 20 lt-days.

中文翻译：

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类星体内宽线区域开普勒自转的第一个直接证据


我们引入了一种新颖的方法来推导具有透镜类星体内部区域的光日空间分辨率的旋转曲线。我们的目标是通过解析宽发射线翼中的微透镜响应（发射区域大小的代表）来探测宽线区域内部的运动学。具体来说，我们评估了高电离线 Si 翼中微透镜效应的强度四号和静脉跨越五个引力透镜类星体的各种速度箱：SDSS J1001+5027、SDSS J1004+4112、HE 1104−1805、SDSS J1206+4332 和 SDSS J1339+1310。使用贝叶斯方法估计相应发射区域的尺寸并采用开普勒模型作为基线，我们检查了盘状旋转假设的一致性。我们的结果揭示了微透镜放大倍数随着速度的变化而单调、平滑地增加。针对各种类星体和发射线推断出的速度与尺寸关系与倾斜盘的开普勒模型非常一致。这项研究提供了类星体最内部区域开普勒自转的第一个直接证据，其径向距离范围从~5到20 lt-day。