Synergistic Radiative Transfer Modeling of Mg <sc>II</sc> and Lyα Emission in Multiphase, Clumpy Galactic Environments: Application to Low-redshift Lyman Continuum Leakers

We conducted systematic radiative transfer (RT) modeling of the Mg ii doublet line profiles for 33 low-redshift Lyman continuum (LyC) leakers, and Ly alpha modeling for six of these galaxies, using a multiphase, clumpy circumgalactic medium (CGM) model. Our RT models successfully reproduced the Mg ii emission line profiles for all galaxies, revealing a necessary condition for strong LyC leakage: high maximum clump outflow velocity ( vMgII,max greater than or similar to 390kms-1 ) and low total Mg ii column density (NMgII, tot less than or similar to 1014.3 cm-2). These two parameters have the strongest influence on the emergent Mg ii profile. For the six galaxies with archival HST data, our Ly alpha modeling shows that their spectral properties do not consistently match conventional LyC leakage criteria. A direct comparison of the best-fit Mg ii and Ly alpha model parameters reveals no clear correlations in clump outflow velocities, column densities, or volume filling factors, suggesting that H i and Mg ii may not be kinematically or spatially coherent. The inferred LyC escape fraction from Ly alpha modeling is primarily governed by the number of optically thick H i clumps per sightline (fcl). Intriguingly, two galaxies with low observed LyC leakage exhibited the highest RT-inferred LyC escape fractions, due to having the lowest fcl values, driven by strong Ly alpha blue peaks. Future spatially resolved observations will be crucial for resolving this puzzle. Our results support a "picket fence" CGM geometry over a "density-bounded" scenario, where high Mg ii outflow velocities and low Mg ii column densities trace low-density H i channels that facilitate LyC escape.