Large-Scale Properties of the Tilt of Sunspot Groups and Joy’s Law Near the Solar Equator

Kuzanyan, K. M.; Safiullin, Nikolai; Kleeorin, N.; Поршнев, С. В.

doi:10.1007/s10511-019-09579-2

Cited by 6 publications

(5 citation statements)

References 25 publications

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“…We refer to this phenomenon as high latitude saturation. A similar phenomenon has been found in numerical studies of sun-like stars for a range of rotation rates (Işık et al 2018b (Kleeorin et al 2020;Kuzanyan et al 2019). Physically we prefer a zero tilt angle at the equator.…”

Section: Recovering Joy's Lawsupporting

confidence: 83%

Sunspot tilt angles revisited: Dependence on the solar cycle strength

Jiao,

Jiang,

Wang

2021

Preprint

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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 anticorrelated 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 ∆s > 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 ∆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 (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.

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Section: Recovering Joy's Lawsupporting

confidence: 83%

Sunspot tilt angles revisited: Dependence on the solar cycle strength

Jiao,

Jiang,

Wang

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…We refer to this phenomenon as high latitude saturation. A similar phenomenon has been found in numerical studies of sunlike stars for a range of rotation rates (Işık et al 2018b (Kleeorin et al 2020;Kuzanyan et al 2019). Physically we prefer a zero tilt angle at the equator.…”

Section: Recovering Joy's Lawsupporting

confidence: 83%

Sunspot tilt angles revisited: Dependence on the solar cycle strength

Jiao

Jiang

Wang

2021

A&A

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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.

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“…For example, larger tilts will enhance the poleward transport of the magnetic flux of trailing polarity, and depending on the polarity orientation, could either strengthen or weaken the polar field (e.g., Baumann et al, 2004;Whitbread et al, 2017;Petrovay and Talafha, 2019). Several studies of the Hale polarity rule and the tilt angle of active regions were published in recent years (Illarionov et al, 2015;Li, 2018;Tlatova et al, 2018;Kuzanyan et al, 2019;Kleeorin et al, 2020;Poisson et al, 2020). Thus, for example, Poisson et al (2020) emphasized the importance of, so called, magnetic tongues in the determination of active region tilts using longitudinal magnetograms.…”

Section: East-west Orientation Of Active Regionsmentioning

confidence: 99%

“…The non-zero tilts at the equator could be explained by a displacement of the magnetic equator relative to the rotational equator. Recently, Kuzanyan et al (2019) and Kleeorin et al (2020) proposed an alternative explanation; that the active region tilt could be a joint action of the Coriolis force and magnetic tension (Ampére's force). At high latitudes, the tilt will be determined mostly by the Coriolis force action.…”

Section: East-west Orientation Of Active Regionsmentioning

confidence: 99%

Long-term studies of photospheric magnetic fields on the Sun

Pevtsov

Bertello

Nagovitsyn

et al. 2021

J. Space Weather Space Clim.

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We briefly review the history of observations of magnetic fields on the Sun, and describe early magnetograps for full disk measurements. Changes in instruments and detectors, the cohort of observers, the knowledge base etc may result in non-uniformity of the long-term synoptic datasets. Still, such data are critical for detecting and understanding the long-term trends in solar activity. We demonstrate the value of historical data using studies of active region tilt (Joy's law) and the evolution of polar field and its reversal. Using the longest dataset of sunspot field strength measurements from Mount Wilson Observatory (1917-present) supplemented by shorter datasets from Pulkovo (1956--1997) and Crimean (1956--present) observatories we demonstrate that the magnetic properties of sunspots did not change over the last hundred years. We also show that the relationship between the sunspot area and its magnetic flux can be used to extend the studies of magnetic field in sunspots to periods with no direct magnetic field measurements. Finally, we show how more recent full disk observations of the vector magnetic field can be used to study the long-term (solar cycle) variations in magnetic helicity on the Sun.

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Large-Scale Properties of the Tilt of Sunspot Groups and Joy’s Law Near the Solar Equator

Cited by 6 publications

References 25 publications

Sunspot tilt angles revisited: Dependence on the solar cycle strength

Sunspot tilt angles revisited: Dependence on the solar cycle strength

Sunspot tilt angles revisited: Dependence on the solar cycle strength

Long-term studies of photospheric magnetic fields on the Sun

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