Bimodality in Rotational Modulation of Planet-Hosting Stars

Stellar magnetic activity is governed by the interplay between rotation, convection, and the evolution of surface magnetic structures, yet the role of planetary systems in shaping these processes remains uncertain. Here, we analyze \textit{Kepler} photometry of more than 1,300 stars to investigate rotational modulation in stars with and without confirmed exoplanets. Using a time--frequency analysis, we measure the photometric proxy of rotational modulation dispersion, $S_{\rm phot}$, tracing the temporal coherence of surface magnetic features. Stars hosting confirmed exoplanets exhibit systematically enhanced $S_{\rm phot}$ values compared to stars without detected planets ($\Delta S_{\rm phot}=0.17 \pm 0.01$ rad d$^{-1}$; $p<10^{-25}$). More importantly, the $S_{\rm phot}$ distribution of planet hosts is bimodal, with peaks at $0.12$ and $0.44$ rad d$^{-1}$ (Hartigan's Dip Test $p<10^{-6}$; $\Delta \mathrm{BIC}=188.7$), a feature absent in the control sample. We interpret $S_{\rm phot}$ as a proxy for rotational modulation dispersion, reflecting spot evolution rather than true differential rotation. The two regimes correspond to stable magnetic coherence with long-lived active regions and rapidly evolving activity patterns. The presence of these distinct regimes exclusively among planet-hosting stars suggests that planetary systems may influence the temporal organization of stellar magnetic activity and indirectly affect stellar dynamos.