Modelling the 6.7 GHz Methanol Flaring in G358.93-0.03 Using the Maxwell-Bloch Framework

We model selected 6.7 GHz methanol flare profiles in G358.93-0.03 using the one-dimensional Maxwell-Bloch framework. The 2019 non-periodic flare, associated with an accretion burst, produced complex single-dish light curves characterized by sharp rises, multiple peaks, secondary structure, and extended decays. For six representative velocity channels, we model each light curve as a sum of scaled intensity responses from effective emitting systems driven by phenomenological pump pulses of fixed width but with component-dependent background rates, amplitudes, and arrival times. The inferred initial inverted column densities correspond to characteristic superradiance timescales $T_{R,0}\simeq 0.3$-$1.4\mathrm{d}$, which are shorter than the adopted dephasing and relaxation timescales, $T_2=6.9\mathrm{d}$ and $T_1=144.4\mathrm{d}$. The fitted components therefore lie in the fast-transient superradiance regime. Existent VLBI observations motivate the possibility that a single-dish velocity channel blends emission from multiple unresolved flaring regions, although these observations are not used as direct fitting constraints. Although the decomposition is not unique, it provides a physically motivated description of the complex flare morphology within a unified Maxwell-Bloch framework.