Sunspot tilt angles revisited: Dependence on the solar cycle strength

Abstract

The tilt angle of sunspot groups is crucial in the BL type dynamo. Some studies have shown that the tilt coefficient is anti-correlated with the cycle strength. If the anti-correlation exists, it will be shown to act as an effective nonlinearity of the BL-type dynamo to modulate the solar cycle. However, some studies have shown that the anti-correlation has no statistical significance. We aim to investigate the causes behind the controversial results of tilt angle studies and to establish whether the tilt coefficient is indeed anti-correlated with the cycle strength. We first analyzed the tilt angles from DPD. Based on the methods applied in previous studies, we took two criteria to select the data, along with the linear and square-root functions to describe Joy's law, and three methods to derive the tilt coefficients for cycles 21-24. This allowed us to evaluate different methods based on comparisons of the differences among the tilt coefficients and the tilt coefficient uncertainties. Then we utilized Monte Carlo experiments to verify the results. Finally, we extended these methods to analyze the separate hemispheric DPD data and the tilt angle data from Kodaikanal and Mount Wilson. The tilt angles exhibit an extremely wide scatter due to both the intrinsic mechanism for its generation and measurement errors, for instance, the unipolar regions included in data sets. Different methods to deal with the uncertainties are mainly responsible for the controversial character of the previous results. The linear fit to the tilt-latitude relation of sunspot groups with $\Delta s>2.5$ of a cycle carried out without binning the data can minimize the effect of the tilt scatter on the uncertainty of the tilt coefficient. Based on this method the tilt angle coefficient is anti-correlated with the cycle strength with strong statistical significance.

14 pages, 7 figures, 8 Tables, Accepted for publication in A&A

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Cited by in corpus (18)

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• Long-term modulation of solar cycles
• Physical Models for Solar Cycle Predictions
• Role of observable nonlinearities in solar cycle modulation
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• Modeling effects of starspots on stellar magnetic cycles
• A Potential New Mechanism for the Butterfly Diagram of the Solar Cycle: Latitude-dependent Radial Flux Transport
• The nonuniformity of poleward flux transport on the solar surface: a statistical method applied to solar cycles 21-24
• Average solar active region: I. Intensities, velocities, and the photospheric magnetic field
• Role of sunspot latitude versus tilt in determining the polar field and amplitude of the next cycle: Cause of the weak Solar Cycle 20
• Dependence of North--South Difference in the Slope of Joy's Law on Amplitude of Solar Cycle
• Extreme Fluctuations in the Sun's Activity over the Modern Maximum: Understanding the Enigmatic Solar Cycles 19-20
• Observation-Based Iterative Map for Solar Cycles. I. Nature of Solar Cycle Variability
• Relationship Between the Tilt Angle of Sunspot Group and the Properties of the Next Solar Cycle
• Effect of Nonlinear Surface Inflows into Activity Belts on Solar Cycle Modulation
• Solar Cycle Prediction: Challenges, Progress, and Future Perspectives
• Constraining the outer boundary condition for the Babcock-Leighton dynamo models
• Comparison Between Cycle-to-Cycle Variations in the Coefficient of Joy's Law and Covariance of Rotation Residuals and Meridional Motions of Sunspot Groups