[Paper Review] Three Cycles of the Solar Toroidal Magnetic Field and This Peculiar Minimum

Leyan Lo, J. T. Hoeksema+1 more|arXiv (Cornell University)|Mar 21, 2010

Solar and Space Plasma Dynamics3 citations

TL;DR

This study analyzes 34 years of WSO and 13 years of SOHO/MDI magnetograms to track the solar toroidal magnetic field's inclination angle, revealing that Cycle 24 began in 2003–2004 at high northern latitudes. Despite an unusually weak polar field during the current minimum, the toroidal field evolution closely mirrors previous cycles, indicating no clear link between toroidal field behavior and the duration or strength of the ensuing minimum.

ABSTRACT

Thirty-four years of WSO (Wilcox Solar Observatory) and thirteen years of SOHO/MDI (Michelson Doppler Imager on the Solar and Heliospheric Observatory) magnetograms have been studied to measure the east-west inclination angle, indicating the toroidal component of the photospheric magnetic field. This analysis reveals that the large-scale toroidal component of the global magnetic field is antisymmetric around the equator and reverses direction in regions associated with flux from one solar cycle compared to the next. The toroidal field revealed the first early signs of cycle 24 at high latitudes, especially in the northern hemisphere, appearing as far back as 2003 in the WSO data and 2004 in MDI. As in previous cycles, the feature moves gradually equatorward. Cycles overlap and the pattern associated with each cycle lasts about 17 years. Even though the polar field at the current solar minimum is significantly lower than the three previous minima, the toroidal field pattern is similar.

Motivation & Objective

• To investigate whether the toroidal magnetic field exhibited anomalous behavior during the peculiar solar minimum of Solar Cycle 24.
• To determine if the early emergence of Cycle 24's toroidal field pattern correlates with the unusually weak polar fields observed at the minimum.
• To assess whether the toroidal field's inclination angle, derived from line-of-sight magnetograms, reliably reflects the underlying dynamo processes.
• To compare WSO and SOHO/MDI data to evaluate consistency and identify instrumental artifacts, particularly in MDI data.
• To examine the temporal evolution of the toroidal field's equatorward migration and its relation to the 22-year magnetic cycle.

Proposed method

• Measured the east-west inclination angle α of the photospheric magnetic field using line-of-sight magnetic field data (B_l) across the solar disk for each Carrington rotation.
• Applied a sinusoidal fit to B_l(θ) = A cos(θ + α) to derive the average inclination angle α, using a least-squares fitting formula derived from Shrauner & Scherrer (1994).
• Generated separate inclination maps for positive and negative magnetic polarity, then computed their difference to isolate the east-west component of the toroidal field.
• Averaged inclination difference maps over longitude to produce latitude-time plots (contour and line plots) for both hemispheres.
• Tracked the emergence and equatorward migration of toroidal field features across three solar cycles using WSO (1977–2009) and MDI (1997–2009) data.
• Addressed potential MDI data artifacts by comparing with WSO and identifying periodic noise from SOHO spacecraft rolls after 2003.

Experimental results

Research questions

• RQ1 Did the toroidal magnetic field show anomalous behavior during the unusually weak solar minimum of Cycle 24?
• RQ2 When did the first signs of Cycle 24's toroidal field emerge in the photospheric data?
• RQ3 How does the evolution of the toroidal field's inclination angle compare between Cycle 24 and the preceding two cycles?
• RQ4 To what extent do instrumental effects in MDI data distort the measurement of the toroidal field's inclination?
• RQ5 Is the observed toroidal field pattern consistent with solar dynamo models predicting a 22-year cycle and antisymmetric field reversal across the equator?

Key findings

• The toroidal magnetic field associated with Cycle 24 first emerged in the northern hemisphere at high latitudes in 2003, based on WSO data, and in 2004 in MDI data.
• The equatorward migration of the toroidal field pattern for Cycle 24 followed the same 17-year duration as in the previous two cycles, despite the extended minimum.
• The inclination difference maps revealed that the toroidal field is antisymmetric about the equator and reverses direction between consecutive solar cycles.
• The sign flip in the average inclination difference in 2007 marked the onset of Cycle 24, consistent with the reversal of weak field regions in both hemispheres.
• Although the polar field at the current minimum was significantly weaker than in the three prior minima, the toroidal field pattern leading into the minimum was indistinguishable from previous cycles.
• MDI data showed similar overall patterns to WSO but exhibited periodic noise after 2003 due to SOHO spacecraft rolls, suggesting calibration challenges for high-resolution toroidal field measurements.