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Register a new userStudying the transfer of magnetic helicity in solar active regions with the connectivity-based helicity flux density method
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In the solar corona, magnetic helicity slowly and continuously accumulates in response to plasma flows tangential to the photosphere and magnetic flux emergence through it. Analyzing this transfer of magnetic helicity is key for identifying its role in the dynamics of active regions (ARs). The connectivity-based helicity flux density method was recently developed for studying the 2D and 3D transfer of magnetic helicity in ARs. The method takes into account the 3D nature of magnetic helicity by explicitly using knowledge of the magnetic field connectivity, which allows it to faithfully track the photospheric flux of magnetic helicity. Because the magnetic field is not measured in the solar corona, modeled 3D solutions obtained from force-free magnetic field extrapolations must be used to derive the magnetic connectivity. Different extrapolation methods can lead to markedly different 3D magnetic field connectivities, thus questioning the reliability of the connectivity-based approach in observational applications. We address these concerns by applying this method to the isolated and internally complex AR 11158 with different magnetic field extrapolation models. We show that the connectivity-based calculations are robust to different extrapolation methods, in particular with regards to identifying regions of opposite magnetic helicity flux. We conclude that the connectivity-based approach can be reliably used in observational analyses and is a promising tool for studying the transfer of magnetic helicity in ARs and relate it to their flaring activity.
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We demonstrate that the current helicity observed in solar active regions traces the magnetic helicity of the large-scale dynamo generated field. We use an advanced 2D mean-field dynamo model with dynamo saturation based on the evolution of the magnetic helicity and algebraic quenching. For comparison, we also studied a more basic 2D mean-field dynamo model with simple algebraic alpha quenching only. Using these numerical models we obtained butterfly diagrams both for the small-scale current helicity and also for the large-scale magnetic helicity, and compared them with the butterfly diagram for the current helicity in active regions obtained from observations. This comparison shows that the current helicity of active regions, as estimated by $-{bf A cdot B}$ evaluated at the depth from which the active region arises, resembles the observational data much better than the small-scale current helicity calculated directly from the helicity evolution equation. Here ${bf B}$ and ${bf A}$ are respectively the dynamo generated mean magnetic field and its vector potential. A theoretical interpretation of these results is given.
The electric current helicity density $displaystyle chi=langleepsilon_{ijk}b_ifrac{partial b_k}{partial x_j}rangle$ contains six terms, where $b_i$ are components of the magnetic field. Due to the observational limitations, only four of the above six terms can be inferred from solar photospheric vector magnetograms. By comparing the results for simulation we distinguished the statistical difference of above six terms for isotropic and anisotropic cases. We estimated the relative degree of anisotropy for three typical active regions and found that it is of order 0.8 which means the assumption of local isotropy for the observable current helicity density terms is generally not satisfied for solar active regions. Upon studies of the statistical properties of the anisotropy of magnetic field of solar active regions with latitudes and with evolution in the solar cycle, we conclude that the consistency of that assumption of local homogeneity and isotropy requires further analysis in the light of our findings.
The current helicity in solar active regions derived from vector magnetograph observations for more than 20 years indicates the so-called hemispheric sign rule; the helicity is predominantly negative in the northern hemisphere and positive in the southern hemisphere. In this paper we revisit this property and compare the statistical distribution of current helicity with Gaussian distribution using the method of normal probability paper. The data sample comprises 6630 independent magnetograms obtained at Huairou Solar Observing Station, China, over 1988-2005 which correspond to 983 solar active regions. We found the following. (1) For the most of cases in time-hemisphere domains the distribution of helicity is close to Gaussian. (2) At some domains (some years and hemispheres) we can clearly observe significant departure of the distribution from a single Gaussian, in the form of two- or multi-component distribution. (3) For the most non-single-Gaussian parts of the dataset we see co-existence of two or more components, one of which (often predominant) has a mean value very close to zero, which does not contribute much to the hemispheric sign rule. The other component has relatively large value of helicity that often determines agreement or disagreement with the hemispheric sign rule in accord with the global structure of helicity reported by Zhang et al. (2010).
The alpha effect is believed to play a key role in the generation of the solar magnetic field. A fundamental test for its significance in the solar dynamo is to look for magnetic helicity of opposite signs in the two hemispheres, and at small and large scales. However, measuring magnetic helicity is compromised by the inability to fully infer the magnetic field vector from observations of solar spectra, caused by what is known as the pi ambiguity of spectropolarimetric observations. We decompose linear polarisation into parity-even and parity-odd E and B polarisations, which are not affected by the pi ambiguity. Furthermore, we study whether the correlations of spatial Fourier spectra of B and parity-even quantities such as E or temperature T are a robust proxy for magnetic helicity of solar magnetic fields. We analyse polarisation measurements of active regions observed by the Helioseismic and Magnetic Imager on board the Solar Dynamics observatory. Theory predicts the magnetic helicity of active regions to have, statistically, opposite signs in the two hemispheres. We then compute the parity-odd E B and T B correlations, and test for systematic preference of their sign based on the hemisphere of the active regions. We find that: (i) E B and T B correlations are a reliable proxy for magnetic helicity, when computed from linear polarisation measurements away from spectral line cores, and (ii) E polarisation reverses its sign close to the line core. Our analysis reveals Faraday rotation to not have a significant influence on the computed parity-odd correlations. The EB decomposition of linear polarisation appears to be a good proxy for magnetic helicity independent of the pi ambiguity. This allows us to routinely infer magnetic helicity directly from polarisation measurements.
The emergence of dipolar magnetic features on the solar surface is an idealization. Most of the magnetic flux emergence occurs in complex multipolar regions. Here, we show that the surface pattern of magnetic structures alone can reveal the sign of the underlying magnetic helicity in the nearly force-free coronal regions above. The sign of the magnetic helicity can be predicted to good accuracy by considering the three-dimensional position vectors of three spots on the sphere ordered by their relative strengths at the surface and compute from them the skew product. This product, which is a pseudoscalar, is shown to be a good proxy for the sign of the coronal magnetic helicity.
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