Co-variability Between the Broad Absorption Lines and Narrow Absorption Lines

Abstract

We investigate the relationship between the variability of broad absorption lines (BALs) or narrow absorption lines (NALs) and that of continuum using a dataset of two-epoch SDSS spectra containing 134 C\,{\footnotesize IV} NAL-BAL pairs. Our analysis reveals an anti-correlation between the fractional equivalent width (EW) variations in NALs (or BALs) and the fractional flux variations of the continuum, with Spearman rank correlation coefficients of $r$ = -0.47 ($p$ = 1E-08) and $r$ = -0.58 ($p$ = 1E-13), respectively. In addition, we find a positive correlation between the fractional EW variations in NALs and BALs ($r$ = 0.72, $p$ = 1E-22), and derive a regression equation $\Delta \mathrm{EW_{NAL}} / \langle\mathrm{EW_{NAL}}\rangle = 0.803\Delta \mathrm{EW_{BAL}} / \langle\mathrm{EW_{BAL}}\rangle + 0.008$, with an intrinsic scatter of 0.14. These results suggest that the variability in the ionizing continuum may play a significant role in the observed changes in C\,{\footnotesize IV} NALs and BALs, supporting the idea of photoionization-driven variability. The co-variability between C\,{\footnotesize IV} NALs and BALs may imply that they originate from outflows with similar physical conditions (e.g, high ionization state).