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Register a new userEstimates of current helicity and tilt of solar active regions and Joys law
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The tilt angle, current helicity and twist of solar magnetic fields can be observed in solar active regions. We carried out estimates of these parameters by two ways. Firstly, we consider the model of turbulent convective cells (super-granules) which have a loop floating structure towards the surface of the Sun. Their helical properties are attained during the rising process in the rotating stratified convective zone. The other estimate is obtained from a simple mean-field dynamo model that accounts magnetic helicity conservation. The both values are shown to be capable to give important contributions to the observable tilt, helicity and twist.
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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.
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 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.
We compare the coronal magnetic energy and helicity of two solar active regions (ARs), prolific in major eruptive (AR~11158) and confined (AR~12192) flaring, and analyze the potential of deduced proxies to forecast upcoming flares. Based on nonlinear force-free (NLFF) coronal magnetic field models with a high degree of solenoidality, and applying three different computational methods to investigate the coronal magnetic helicity, we are able to draw conclusions with a high level of confidence. Based on real observations of two solar ARs we checked trends regarding the potential eruptivity of the active-region corona, as suggested earlier in works that were based on numerical simulations, or solar observations. Our results support that the ratio of current-carrying to total helicity, $|H_mathrm{J}|/|H_mathrm{V}|$, shows a strong ability to indicate the eruptive potential of a solar AR. However, $|H_mathrm{J}|/|H_mathrm{V}|$ seems not to be indicative for the magnitude or type of an upcoming flare (confined or eruptive). Interpreted in context with earlier observational studies, our findings furthermore support that the total relative helicity normalized to the magnetic flux at the NLFF models lower boundary, $H_mathrm{V}/phi^2$, represents no indicator for the eruptivity.
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