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<p>Active regions (ARs) are the photospheric manifestation of magnetic flux ropes (FRs) emerging from the solar interior. A key parameter in their evolution is the tilt angle, defined as the inclination of the AR polarity axis relative to the solar equator. Despite its central role in flux-transport dynamo models, tilt measurements are affected by systematic biases—most notably magnetic tongues—particularly during the emergence phase. In this work we analyze tilt estimates for 108 bipolar active regions from Solar Cycle 23 using two methodologies: (1) the conventional magnetic barycenter method and (2) a Bayesian FR model that fits observed magnetograms with a synthetic model of an emerging twisted toroidal flux tube. We find notable differences between the two estimates, ranging from about <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math> <msup> <mn>30</mn> <mo>∘</mo> </msup> </math></EquationSource> <EquationSource Format="TEX">$30^{\circ }$</EquationSource> </InlineEquation> at early stages of emergence to <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math> <mo>∼</mo> <msup> <mn>10</mn> <mo>∘</mo> </msup> </math></EquationSource> <EquationSource Format="TEX">$\sim 10^{\circ }$</EquationSource> </InlineEquation> near the end. Our analysis shows that Joy’s law is already present at the earliest stages of AR emergence, although the tilt dispersion is significantly larger at these times. Tilt rotations are strongest during the early emergence phase, with no preferred sense of rotation, and decrease as ARs approach their maximum magnetic flux, suggesting an important role of near-surface convective motions. We also find that the quantitative characterization of Joy’s law depends on both the magnetic flux of ARs and the method used to estimate their tilt. The Bayesian framework adopted here provides a robust basis for future analyses by allowing known sources of scatter to be explicitly modeled within a consistent statistical formalism.</p>

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Tilt Angle of Bipolar Active Regions from Solar Cycle 23

  • 期刊论文

  • 发表日期：

    2026年6月2日

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  • Mariano Poisson,
  • Marcelo López Fuentes,
  • Cristina H. Mandrini,
  • Pascal Démoulin

摘要

Active regions (ARs) are the photospheric manifestation of magnetic flux ropes (FRs) emerging from the solar interior. A key parameter in their evolution is the tilt angle, defined as the inclination of the AR polarity axis relative to the solar equator. Despite its central role in flux-transport dynamo models, tilt measurements are affected by systematic biases—most notably magnetic tongues—particularly during the emergence phase. In this work we analyze tilt estimates for 108 bipolar active regions from Solar Cycle 23 using two methodologies: (1) the conventional magnetic barycenter method and (2) a Bayesian FR model that fits observed magnetograms with a synthetic model of an emerging twisted toroidal flux tube. We find notable differences between the two estimates, ranging from about 30 ∘ $30^{\circ }$ at early stages of emergence to ∼ 10 ∘ $\sim 10^{\circ }$ near the end. Our analysis shows that Joy’s law is already present at the earliest stages of AR emergence, although the tilt dispersion is significantly larger at these times. Tilt rotations are strongest during the early emergence phase, with no preferred sense of rotation, and decrease as ARs approach their maximum magnetic flux, suggesting an important role of near-surface convective motions. We also find that the quantitative characterization of Joy’s law depends on both the magnetic flux of ARs and the method used to estimate their tilt. The Bayesian framework adopted here provides a robust basis for future analyses by allowing known sources of scatter to be explicitly modeled within a consistent statistical formalism.