Quasar broad absorption line variability measurements using
  reconstructions of un-absorbed spectra
  We present a two-epoch Sloan Digital Sky Survey and Gemini/GMOS+William
Herschel Telescope/ISIS variability study of 50 broad absorption line quasars
of redshift range 1.9 < z < 4.2, containing 38 Si IV and 59 C IV BALs and
spanning rest-frame time intervals of approximately 10 months to 3.7 years. We
find that 35/50 quasars exhibit one or more variable BALs, with 58% of Si IV
and 46% of C IV BALs showing variability across the entire sample. On average,
Si IV BALs show larger fractional change in BAL pseudo equivalent width than C
IV BALs, as referenced to an unabsorbed continuum+emission-line spectrum
constructed using non-negative matrix factorisation. No correlation is found
between BAL variability and quasar luminosity, suggesting that ionizing
continuum changes do not play a significant role in BAL variability (assuming
the gas is in photoionization equilibrium with the ionizing continuum). A
subset of 14 quasars have one variable BAL from each of Si IV and C IV with
significant overlap in velocity space and for which variations are in the same
sense (strengthening or weakening) and which appear to be correlated (98%
confidence). We find examples of both appearing and disappearing BALs in
weaker/shallower lines with disappearance rates of 2.3% for C IV and 5.3% for
Si IV, suggesting average lifetimes of 142 and 43 years respectively. We
identify 5 objects in which the BAL is coincident with the broad emission-line,
but appears to cover only the continuum source. Assuming a clumpy inhomogeneous
absorber model and a typical size for the continuum source, we infer a maximum
cloud radius of 10^13 to 10^14 cm, assuming Eddington limited accretion.
