We performed spectroscopic observations of the small-separation lensed quasar SDSS J1001+5027, whose images have an angular separation $theta sim 2.^{!!primeprime}86$, and placed constraints on the physical properties of gas clouds in the vicinity of the quasar (i.e., in the outflowing wind launched from the accretion disk). The two cylinders of sight to the two lensed images go through the same region of the outflowing wind and they become fully separated with no overlap at a very large distance from the source ($sim 330$ pc). We discovered a clear difference in the profile of the CIV broad absorption line (BAL) detected in the two lensed images in two observing epochs. Because the kinematic components in the BAL profile do not vary in concert, the observed variations cannot be reproduced by a simple change of ionization state. If the variability is due to gas motion around the background source (i.e., the continuum source), the corresponding rotational velocity is $v_{rot}geq 18,000$ km/s, and their distance from the source is $rleq 0.06$ pc assuming Keplerian motion. Among three MgII and three CIV NAL systems that we detected in the spectra, only the MgII system at $z_{abs} = 0.8716$ shows a hint of variability in its MgI profile on a rest-frame time scale of $Delta t_{rest}$ $leq 191$ days and an obvious velocity shear between the sightlines whose physical separation is $sim 7$ kpc. We interpret this as the result of motion of a cosmologically intervening absorber, perhaps located in a foreground galaxy.
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