Effect of Nonlinear Surface Inflows into Activity Belts on Solar Cycle Modulation

Abstract Converging flows are visible around bipolar magnetic regions (BMRs) on the solar surface, according to observations. Average flows are created by these inflows combined, and the strength of these flows depends on the amount of flux present during the solar cycle. In models of the solar cycle, this average flow can be depicted as perturbations to the meridional flow. In this article, we study the effects of introducing surface inflow to the surface flux transport models (SFT) as a possible nonlinear mechanism in the presence of latitude quenching for an inflow profile whose amplitude varies within a cycle depending on the magnetic activity. Using a grid based on one-dimensional SFT models, we methodically investigate the extent of the nonlinearity caused by inflows, latitude quenching (LQ), and their combinations. The results show that including surface inflows in the model in the presence of both LQ and tilt quenching (TQ) produced a polar field within a $\pm 1\sigma $ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>±</mml:mo> <mml:mn>1</mml:mn> <mml:mi>σ</mml:mi> </mml:math> of an average cycle polar field ( $\sigma $ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>σ</mml:mi> </mml:math> is the standard deviation) with a correlation coefficient of 0.85. We confirm that including inflows produces a lower net contribution to the dipole moment (10 – 25%). Furthermore, the relative importance of LQ vs. inflows is inversely correlated with the dynamo effectivity range ( $\lambda _{R}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>λ</mml:mi> <mml:mi>R</mml:mi> </mml:msub> </mml:math> ). With no decay term, introducing inflows into the model results in a less significant net contribution to the dipole moment. Including inflows in the SFT model shows a possible nonlinear relationship between the surface inflows and the solar dipole moment, suggesting a potential nonlinear mechanism contributing to the saturation of the global dynamo. For lower $\lambda _{R}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>λ</mml:mi> <mml:mi>R</mml:mi> </mml:msub> </mml:math> ( $\lessapprox 10^{\circ }$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>⪅</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mo>∘</mml:mo> </mml:msup> </mml:math> ), TQ always dominates LQ, and for higher $\lambda _{R}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>λ</mml:mi> <mml:mi>R</mml:mi> </mml:msub> </mml:math> , LQ dominates. However, including inflows makes the domination earlier in case of having a decay term in the model.