Relation between the Variations in the Mg ii λ2798 Emission Line and 3000 Å Continuum

We investigate the relationship between the MgII $\lambda2798$ emission-line and the 3000 {\AA} continuum variations using a sample of 68 intermediate-redshift ($z\sim$ 0.65$-$1.50) broad-line quasars spanning a bolometric luminosity range of 44.49 erg s$^{-1} \leq \rm{log}$$L_{\rm{bol}} \leq 46.31$ erg s$^{-1}$ (Eddington ratio from $\sim$ 0.026 to 0.862). This sample is constructed from SDSS-DR7Q and BOSS-DR12Q, each with at least 2 spectroscopic epochs in SDSS-I/II/III surveys. Additionally, we adopt the following signal-to-noise ratio (S/N) selection criteria: a) for MgII and the 3000 {\AA} continuum, S/N $\geq$ 10; b) for narrow lines, S/N $\geq$ 5. All our quasar spectra are recalibrated based on the assumption of constant narrow emission-line fluxes. In an analysis of spectrum-to-spectrum variations, we find a fairly close correlation (Spearman $\rho = 0.593$) between the variations in broad MgII and in the continuum. This is consistent with the idea that MgII is varying in response to the continuum emission variations. Adopting the modified weighted least squares regression method, we statistically constrain the slopes (i.e., the responsivity $\alpha$ of the broad MgII) between the variations in both components for the sources in different luminosity bins after eliminating intrinsic biases introduced by the rescaling process itself. It is shown that the responsivity is quite small (average $\bar{\alpha} \approx$ 0.464) and anti-correlates with the quasar luminosity. Our results indicate that high signal-to-noise flux measurements are required to robustly detect the intrinsic variability and the time lag of MgII line.