We present 21 examples of C IV Broad Absorption Line (BAL) trough disappearance in 19 quasars selected from systematic multi-epoch observations of 582 bright BAL quasars (1.9 < z < 4.5) by the Sloan Digital Sky Survey-I/II (SDSS-I/II) and SDSS-III. The observations span 1.1-3.9 yr rest-frame timescales, longer than have been sampled in many previous BAL variability studies. On these timescales, ~2.3% of C IV BAL troughs disappear and ~3.3% of BAL quasars show a disappearing trough. These observed frequencies suggest that many C IV BAL absorbers spend on average at most a century along our line of sight to their quasar. Ten of the 19 BAL quasars showing C IV BAL disappearance have apparently transformed from BAL to non-BAL quasars; these are the first reported examples of such transformations. The BAL troughs that disappear tend to be those with small-to-moderate equivalent widths, relatively shallow depths, and high outflow velocities. Other non-disappearing C IV BALs in those nine objects having multiple troughs tend to weaken when one of them disappears, indicating a connection between the disappearing and non-disappearing troughs, even for velocity separations as large as 10000-15000 km/s. We discuss possible origins of this connection including disk-wind rotation and changes in shielding gas.
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