Astronomy & Astrophysics (A&A) is an international journal which publishes papers on all aspects of astronomy and astrophysics

A previously unobservable mirror asymmetry of the solar magnetic field – a key ingredient of the dynamo mechanism which is believed to drive the 11-year activity cycle – has recently been measured. This was achieved through systematic monitoring of solar active regions carried out for more than 20 years at observatories in Mees, Huairou and Mitaka. In this Letter we report on detailed analysis of vector magnetic field data, obtained at Huairou Solar Observing Station in China. Electric current helicity (the product of current and magnetic field components in the same direction) was estimated from the data and a latitude–time plot of solar helicity during the last two solar cycles has been produced. We find that like sunspots helicity patterns propagate equatorwards, but unlike sunspot polarity helicity in each solar hemisphere does not change sign from cycle to cycle, thus confirming the theory. There are, however, two significant time–latitudinal domains in each cycle when the sign briefly inverts. Our findings shed new light on stellar and planetary dynamos and are yet to be included in the theory.

Observations of proxies of the magnetic helicity in the Sun over the past two solar cycles revealed reversals of the helicity hemispheric sign rule (negative in the North and positive in the South hemispheres). We apply the mean-field solar dynamo model to study the reversals of the magnetic helicity sign for the dynamo operating in the bulk of the solar convection zone. The evolution of the magnetic helicity is governed by the conservation law. We found that the reversal of the sign of the small-scale magnetic helicity follows the dynamo wave propagating inside the convection zone. Therefore, the spatial patterns of the magnetic helicity reversals reflect the processes which contribute to generation and evolution of the large-scale magnetic fields. At the surface, the patterns of the helicity sign reversals are determined by the magnetic helicity boundary conditions at the top of the convection zone. We demonstrate the impact of fluctuations in the dynamo parameters and variability in dynamo cycle amplitude on the reversals of the magnetic helicity sign rule. The obtained results suggest that the magnetic helicity of the large-scale axisymmetric field can be treated as an additional observational tracer for the solar dynamo and it probably can be used for the solar activity forecast as well.

We adopt an isotropic representation of the Fourier-transformed two-point correlation tensor of the magnetic field to estimate the magnetic energy and helicity spectra as well as current helicity spectra of two individual active regions (NOAA 11158 and NOAA 11515) and the change of the spectral indices during their development as well as during the solar cycle. The departure of the spectral indices of magnetic energy and current helicity from 5/3 are analyzed, and it is found that it is lower than the spectral index of the magnetic energy spectrum. Furthermore, the fractional magnetic helicity tends to increase when the scale of the energy-carrying magnetic structures increases. The magnetic helicity of NOAA 11515 violates the expected hemispheric sign rule, which is interpreted as an effect of enhanced field strengths at scales larger than 30–60 Mm with opposite signs of helicity. This is consistent with the general cycle dependence, which shows that around the solar maximum the magnetic energy and helicity spectra are steeper, emphasizing the large-scale field.

We develop a formalism that treats the calculation of solar kinetic energy and cross helicity spectra in an equal manner to that of magnetic energy and helicity spectra. The magnetic helicity spectrum is shown to be equal to the vertical part of the current helicity spectrum divided by the square of the wavenumber. For the cross helicity, we apply the recently developed two-scale approach globally over an entire active region to account for the sign change between the two polarities. Using vector magnetograms and Dopplergrams of NOAA 11158 and 12266, we show that kinetic and magnetic energy spectra have similar slopes at intermediate wavenumbers, where the contribution from the granulation velocity has been removed. At wavenumbers around , the magnetic helicity is found to be close to its maximal value. The cross helicity spectra are found to be within about 10% of the maximum possible value. Using the two-scale method for NOAA 12266, the global cross helicity spectrum is found to be particularly steep, similarly to what has previously been found in theoretical models of spot generation. In the quiet Sun, by comparison, the cross helicity spectrum is found to be small.