Broad absorption lines ( BALs ) in quasar spectra are prominent signatures of high-velocity outflows , which might be present in all quasars and could be a major contributor to feedback to galaxy evolution .
Studying the variability in these BALs allows us to further our understanding of the structure , evolution , and basic physical properties of the outflows .
This is the third paper in a series on a monitoring programme of 24 luminous BAL quasars at redshifts 1.2 < z < 2.9 .
We focus here on the time-scales of variability in C iv \lambda 1549 BALs in our full multi-epoch sample , which covers time-scales from 0.02 - 8.7 yr in the quasar rest-frame .
Our sample contains up to 13 epochs of data per quasar , with an average of 7 epochs per quasar .
We find that both the incidence and the amplitude of variability are greater across longer time-scales .
Part of our monitoring programme specifically targeted half of these BAL quasars at rest-frame time-scales \leq 2 months .
This revealed variability down to the shortest time-scales we probe ( 8 - 10 days ) .
Observed variations in only portions of BAL troughs or in lines that are optically thick suggest that at least some of these changes are caused by clouds ( or some type of outflow substructures ) moving across our lines of sight .
In this crossing cloud scenario , the variability times constrain both the crossing speeds and the absorber locations .
Specific results also depend on the emission and absorption geometries .
We consider a range of geometries and use Keplerian rotational speeds to derive a general relationship between the variability times , crossing speeds , and outflow locations .
Typical variability times of order \sim 1 year indicate crossing speeds of a few thousand km/s and radial distances near \sim 1 pc from the central black hole .
However , the most rapid BAL changes occurring in 8-10 days require crossing speeds of 17 000 - 84 000 km s ^ { -1 } and radial distances of only 0.001 - 0.02 pc .
These speeds are similar to or greater than the observed radial outflow speeds , and the inferred locations are within the nominal radius of the broad emission line region .