Dust cloud lifetimes of Scallop-shell stars
We investigate the survival of dust trapped in magnetically confined cool gas clouds (or {\it prominences}) around rapidly rotating M-dwarfs exhibiting the ``scallop-shell'' light-curve morphology. Using a two-dimensional magnetohydrodynamic simulation, we extend previous coronal prominence models to include a passive tracer field to allow for a single injection of collisionally charged dust grains. The tracer evolution reveals how recurrent centrifugal breakouts--the slingshot process--remove dust and gas from the prominence while chromospheric evaporation replenishes gas from below. For our simulated star, which has $R_{\ast} = 0.6 R_{\odot}$, $M_{\ast} = 0.3 M_{\odot}$, and $P_{\ast} = 0.32$ days, the resulting dust content decays exponentially with a minimum half-life of approximately 6 stellar rotations, representing a lower limit set by our assumption of fully coupled dust and gas dynamics. Synthetic velocity-phase diagnostics show a single, phase-locked feature that fades steadily, reproducing the behaviour of dips seen in TESS and K2 light curves. Comparison with observed river plots suggests a natural classification: (i) persistent, non-decaying features formed by quiescent prominences below co-rotation; (ii) gradually fading features produced by slingshot prominences near co-rotation; and (iii) abrupt disappearances linked to magnetic reconnection and flare-driven ejections. These results demonstrate that dust-bearing prominences--undergoing repeated slingshots--can persist for tens of rotations, linking the observed longevity of the scallop-shell photometric features with the dynamic cycle of prominence slingshot ejections.