Non-axisymmetric Transport of Magnetic Flux Tubes: A Mechanism for Joy's Law and Poloidal Field Generation via Meridional Flows

Abstract

We present a new scenario for the solar $αω$-dynamo based on the interaction of asymmetric magnetic flux tubes with the near-surface meridional flow. Standard thin flux tube simulations indicate that the radial gradient of differential rotation ($\partialΩ/\partial r > 0$) breaks the spatial symmetry of emerging $Ω$-loops. The leading (western) leg becomes nearly vertical, while the trailing (eastern) leg is heavily stretched and flattens along the longitude. Upon emergence at the photosphere, the horizontal meridional flow toward the poles acts more efficiently on the trailing leg because the efficiency of the hydrodynamic entrainment by the plasma (the ``sail effect'') is directly proportional to the total spatial length of the magnetic flux tube arc elements. This creates a differential torque that drives the trailing sunspot poleward while the leading sunspot remains anchored due to its compact spatial geometry. Our model yields a tilt angle evolution rate of $\approx 0.3^\circ\,\mathrm{day}^{-1}$ at a latitude of $20^\circ$ for a bipolar separation of $15^\circ$, reproducing Joy's law without invoking the classical Coriolis-driven twist during the rise phase.