Understanding Broad Mg II Variability in Quasars with Photoionization: Implications for Reverberation Mapping and Changing-Look Quasars

The broad Mg II line in quasars has distinct variability properties compared with broad Balmer lines: it is less variable, and usually does not display a "breathing" mode, the increase in the average cloud distance when luminosity increases. We demonstrate that these variability properties of Mg II can be reasonably well explained by simple Locally Optimally Emitting Cloud (LOC) photoionization models, confirming earlier photoionization results. In the fiducial LOC model, the Mg II-emitting gas is on average more distant from the ionizing source than the H$\alpha$/H$\beta$ gas, and responds with a lower amplitude to continuum variations. If the broad-line region (BLR) is truncated at a physical radius of $\sim 0.3$ pc (for a $10^{8.5}M_{\odot}$ BH accreting at Eddington ratio of 0.1), most of the Mg II flux will always be emitted near this outer boundary and hence will not display breathing. These results indicate that reverberation mapping results on broad Mg II, while generally more difficult to obtain due to the lower line responsivity, can still be used to infer the Mg II BLR size and hence black hole mass. But it is possible that Mg II does not have a well defined intrinsic BLR size-luminosity relation for individual quasars, even though a global one for the general population may still exist. The dramatic changes in broad H$\alpha$/H$\beta$ emission in the observationally-rare changing-look quasars are fully consistent with photoionization responses to extreme continuum variability, and the LOC model provides natural explanations for the persistence of broad Mg II in changing-look quasars defined on H$\alpha$/H$\beta$, and the rare population of broad Mg II emitters in the spectra of massive inactive galaxies.