A sharp rise in the detection rate of broad absorption line variations
  in a quasar SDSS J141955.26+522741.1
  We present an analysis of the variability of broad absorption lines (BALs) in
a quasar SDSS J141955.26+522741.1 at $z=2.145$ with 72 observations from the
Sloan Digital Sky Survey Data Release 16 (SDSS DR16). The strong correlation
between the equivalent widths of BAL and the continuum luminosity, reveals that
the variation of BAL trough is dominated by the photoionization. The
photoionization model predicts that when the time interval $\Delta T$ between
two observations is longer than the recombination timescale $t_{\rm rec}$, the
BAL variations can be detected. This can be characterized as a "sharp rise" in
the detection rate of BAL variation at $\Delta T=t_{\rm rec}$. For the first
time, we detect such a "sharp rise" signature in the detection rate of BAL
variations. As a result, we propose that the $t_{\rm rec}$ can be obtained from
the "sharp rise" of the detection rate of BAL variation. It is worth mentioning
that the BAL variations are detected at the time-intervals less than the
$t_{\rm rec}$ for half an order of magnitude in two individual troughs. This
result indicates that there may be multiple components with different $t_{\rm
rec}$ but the same velocity in an individual trough.
