Sunspot tilt angles revisited: Dependence on the solar cycle strength

Abstract

Context. The tilt angle of sunspot groups is crucial in the Babcock-Leighton (BL) type dynamo for the generation of the poloidal magnetic field. Some studies have shown that the tilt coefficient, which excludes the latitudinal dependence of the tilt angles, 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. Aims. 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. Methods. We first analyzed the tilt angles from Debrecen Photoheliographic Database (DPD). Based on the methods applied in previous studies, we took two criteria (with or without angular separation constraint Δs > 2.​​°5) to select the data, along with the linear and square-root functions to describe Joy’s law, and three methods (normalization, binned fitting, and unbinned fitting) 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. Results. 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 Δs > 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 (r = −0.85 at 99% confidence level). Furthermore, we find that tilts tend to be more saturated at high latitudes for stronger cycles. The tilts tend to show a linear dependence on the latitudes for weak cycles and a square-root dependence for strong cycles. Conclusions. This study disentangles the cycle dependence of sunspot group tilt angles from the previous results that were shown to be controversial, spurring confusion in the field.

The Nonuniformity of Poleward Flux Transport on the Solar Surface: A Statistical Method Applied to Solar Cycles 21–24

“…| | with λ being the latitude. The scatter of tilt angle follows a Gaussian profile, the width of which is determined by the AR-area-tilt-scatter relationship given by Jiao et al (2021). We conduct 25 simulation runs for 10 yr each.…”

The nonuniformity of poleward flux transport on the solar surface: a statistical method applied to solar cycles 21-24

“…The tilt angles of ARs are determined by a typical form of the Joy's law, which is 1.3 × |λ| with λ being the latitude. The scatter of tilt angle follows a Gaussian profile, the width of which is determined by the AR area -tilt scatter relationship given by Jiao et al (2021). We conduct 25 simulation runs for 10 years each.…”

A Babcock–Leighton-type Solar Dynamo Operating in the Bulk of the Convection Zone

“…In this mechanism, the sunspot group tilt angles play a key role in the construction of the poloidal source term. Dasi-Espuig et al (2010), Olemskoy (2011), andJiao et al (2021) reveal that the observed sunspot group tilt angles vary systematically from cycle to cycle. The weak cycle 24 might result from abnormal tilt angles of sunspot groups in cycle 23 (Jiang et al 2015).…”