Can meridional flow variations explain the observed rising/declining phase asymmetry in the solar cycle?

TL;DR

The paper investigates whether the observed rise–decay asymmetry of the 11-year solar cycle can be explained by time-dependent meridional circulation, disentangling deterministic, stochastic, and hybrid influences within a Babcock–Leighton flux-transport dynamo. Using axisymmetric, kinematic simulations with distinct meridional-flow prescriptions and BL poloidal-source fluctuations, the authors characterize cycle asymmetry via $T_{rise}/T_{decay}$ and correlations with cycle amplitude, rise time, rise rate, and decay rate. They find that stochastic fluctuations in both the meridional flow and BL source fail to produce consistent decay-dominated cycles, while deterministic variations motivated by Lorentz-force feedback and especially latitude-dependent flow modulation tied to the butterfly diagram can reproduce the observed asymmetry and its correlation patterns; hybrid models also succeed but depend on parameter choices. The results highlight meridional-flow variability as a key driver of cycle asymmetry and emphasize the need for improved observational constraints on internal solar flows to enhance predictive tools such as Solar Predict, while suggesting diffusion-dominated flux-transport dynamics in their setup shape the timing and strength of cycles.

Abstract

Accurate prediction of the 11-year solar cycle remains a major challenge in solar physics and is important for space weather forecasting. A persistent property of the cycle is its asymmetry: the rise phase is usually much shorter than the decay phase. This asymmetry is often linked to variations in the Sun's meridional circulation, but it is unclear whether these variations are mainly deterministic, produced by Lorentz-force feedback, or stochastic in nature. We investigate this question using kinematic flux-transport dynamo simulations that include three types of time-dependent meridional flow: deterministic variations, stochastic fluctuations, and hybrid combinations of both. We evaluate cycle asymmetry using the ratio of rise to decay times and correlations of cycle amplitude with rise time, rise rate, and decay rate. Our results show that the temporal evolution of the meridional flow strongly controls cycle asymmetry. When both the meridional circulation and the Babcock-Leighton mechanism vary stochastically, the model does not produce cycles in which the decay phase is consistently longer than the rise phase. In contrast, deterministic variations motivated by Lorentz-force feedback and linked to the latitude of maximum toroidal field reproduce the observed asymmetry. In these cases, the meridional flow weakens near cycle maximum, stays reduced for some time, and then recovers, producing a longer decay phase. Hybrid models that mix deterministic and stochastic variability also match the observed rise-decay asymmetry. Across all simulations, cycle amplitude correlates strongly with rise rate, while correlations with rise time and decay rate are weaker but remain significant. These results highlight the key role of meridional flow variability in shaping solar cycle asymmetry and show that incorporating such variability can improve forecasting tools such as Solar Predict.

Figures (10)

• Figure 1: Observational evidence of solar cycle asymmetry in terms of rise and decay times. Top panel: Scatter plots of the ratio $\frac{T_{\mathrm{rise}}}{T_{\mathrm{decay}}}$ versus cycle number, obtained from the sunspot number (SN) data. Bottom panel: Scatter plots of $\frac{T_{\mathrm{rise}}}{T_{\mathrm{decay}}}$ versus cycle periodicity, based on the sunspot number data. The corresponding cycle numbers are annotated in blue in each scatter plot.
• Figure 2: Observational evidence of solar cycle asymmetry. (a) Scatter plots of peak sunspot number versus rise time (in years). (b) Scatter plots of peak sunspot number versus rise rate (in units of sunspot number per year). (c) Scatter plots of peak sunspot number versus decay rate near the end of the previous cycle minimum (in the same units as the rise rate). (d) Scatter plots of peak sunspot area versus rise time (in years). The corresponding cycle numbers are annotated in blue in each scatter plot.
• Figure 3: Asymmetries generated from our model by introducing $50 \%$ fluctuations in the poloidal field generation mechanism. (a) Scatter plot of the rise-to-decay time ratio versus cycle number. (b) Scatter plot of cycle amplitude (in Gauss) versus rise time (in years). (c) Scatter plot of cycle amplitude versus rise rate (in units of Tesla/year). (d) Scatter plot of cycle amplitude versus decay rate near the preceding cycle minimum (in Tesla/year).
• Figure 4: (a) Temporal evolution of $B_\phi^2$ and meridional flow speed when the flow decreases at the cycle maximum. The black curve (left y-axis) shows the variation of $B_\phi^2$ (a proxy for sunspot number), while the blue curve (right y-axis) shows the meridional flow speed decreasing from a higher to a lower value at the cycle peak. (b) Same as (a), but with the meridional flow increasing from a lower to a higher value at the cycle maximum. (c) Variation of the rise-to-decay time ratio as a function of flow asymmetry between the declining and rising phases, expressed as $v_{\rm declining} - v_{\rm rising}$. Red dot corresponds to the mean value of rise-to-decay time ratio.
• Figure 5: Asymmetry generated from our model when a higher meridional flow speed (29ms$^{-1}$) is applied during the rising phase and a slower flow (23ms$^{-1}$) during the decaying phase. Additionally, $50 \%$ fluctuations are introduced in the poloidal field generation mechanism. The four panels in this figure correspond to the same quantities shown in Figure \ref{['fig:wald-pol']}.