The Responsivity of Mg <scp>ii</scp> , C <scp>iv</scp> , H <i>α</i> , and H <i>β</i> Emission Lines in SDSS Quasars

Abstract This study systematically investigates the responsivity ( α ) of broad emission-line (BEL) variations (Mg ii λ 2798, C iv λ 1549, H α λ 6563 and H β λ 4861) to continuum variations in 24,847 quasars using matched spectroscopic data from Sloan Digital Sky Survey Data Releases 7 and 16. For these four types of BELs, we find a correlation between the variations in emission lines and in the continuum, and we measure average α values of 0.45 (Mg ii ), 0.35 (C iv ), 0.78 (H α ), and 0.60 (H β ). Our results also show that the α of Mg ii , H α , and H β exhibit a negative correlation with continuum luminosity, while C iv shows no statistically significant continuum luminosity dependence. Our results align with photoionization models and prior studies. These findings may provide new observational constraints on the structure and dynamics of the broad-line region across different ionization states.