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

To explore the combined effects of partial thermal stable stratification and magnetic back-reaction within Earth’s tangent cylinder, we study the onset of magnetoconvection in an infinite plane layer subject to horizontal magnetic field imposed perpendicular to the rotation axis. Three stratification models-fully unstable, weakly stable, and strongly stable-are considered to examine their influence on convective onset. A broad range of rotation rates and diffusivity ratios captures the effects of rotation and thermal-to-magnetic diffusivity contrast, while magnetic back-reaction is analyzed by varying the imposed magnetic field strength. To assess the impact of stratification on convection threshold and flow structure, we derive local scaling laws for critical onset parameters and compute penetration percentages to quantify convective intrusion into the stable layer. Results show that stable stratification promotes earlier onset and smaller-scale flows, with stronger effects in rotation-dominated regimes-hallmarks of penetrative convection. In weak magnetic fields, faster rotation enhances columnarity and intensifies stratification effects while delaying onset. Under strong magnetic fields, thicker rolls persist even at rapid rotation, with limited but noticeable penetration into the stable layer. Magnetic stabilization is more effective at low to moderate diffusivity ratios but weakens at high diffusivity ratio. Penetration decreases with stronger magnetic fields and rotation, especially under strong stratification, but varies non-monotonically with rotation in weak stratification and magnetic regimes. These findings highlight the complex interplay among stratification, rotation, and magnetic field strength in setting the onset and structure of rotating convection relevant to planetary interiors.