Role of partial stable stratification on the onset of rotating magnetoconvection with a uniform vertical field

This study examines the onset of rotating magnetoconvection under an axially imposed magnetic field in the presence of partial thermal stable stratification. Three stratification models-fully unstable, weakly stable, and strongly stable-are analyzed across Ekman numbers $E = 10^{-3}, 10^{-4}$, and $10^{-5}$ (rotation rates) and Roberts numbers $q = 0.01, 1$ and $10$ (diffusivity ratios). Magnetic back-reaction is explored by varying the Elsasser number ($Λ$) from 0 to 10. Symmetry-breaking effects of stable layer are assessed via an asymmetry index. Additionally, local scaling laws are derived for onset parameters and convective penetration is quantified numerically. Results show that stable stratification promotes earlier onset and smaller-scale flows, with stronger effects in weak field regimes-hallmarks of penetrative convection. In weak magnetic fields, symmetry breaking is pronounced but weakens for strong field regime. Convective roll thickening peaks at $Λ= 1$, while columnarity persists in both weak and strong field regimes due to rotational constraints and elongation effects along imposed field direction, respectively. Magnetic stabilization is most effective at low to moderate values of $q$ but weakens in high $q$ regimes. Penetration depth is inversely related to the magnetic field strength and rotation rates, particularly under strong stratification, but varies non-monotonically with rotation in weakly stratified cases. In the non-magnetic limit, the critical Ekman number $E_c$, exhibiting maximum penetration effects, is obtained as $E_c = 10^{-4}$ for weak stable stratification and $E_c = 10^{-3}$ for strong stable stratification. Obtained results can provide insights into the complex interplay of various geophysical effects on planetary interiors.