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Register a new userMagnetic helicity and energy spectra of a solar active region
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Hongqi Zhang
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We compute for the first time magnetic helicity and energy spectra of the solar active region NOAA 11158 during 11-15 February 2011 at 20^o southern heliographic latitude using observational photospheric vector magnetograms. We adopt the isotropic representation of the Fourier-transformed two-point correlation tensor of the magnetic field. The sign of magnetic helicity turns out to be predominantly positive at all wavenumbers. This sign is consistent with what is theoretically expected for the southern hemisphere. The magnetic helicity normalized to its theoretical maximum value, here referred to as relative helicity, is around 4% and strongest at intermediate wavenumbers of k ~ 0.4 Mm^{-1}, corresponding to a scale of 2pi/k ~ 16 Mm. The same sign and a similar value are also found for the relative current helicity evaluated in real space based on the vertical components of magnetic field and current density. The modulus of the magnetic helicity spectrum shows a k^{-11/3} power law at large wavenumbers, which implies a k^{-5/3} spectrum for the modulus of the current helicity. A k^{-5/3} spectrum is also obtained for the magnetic energy. The energy spectra evaluated separately from the horizontal and vertical fields agree for wavenumbers below 3 Mm^{-1}, corresponding to scales above 2 Mm. This gives some justification to our assumption of isotropy and places limits resulting from possible instrumental artefacts at small scales.
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Context. In September 2017 the largest X-class flare of Solar Cycle 24 occurred from the most active region (AR) of this cycle, AR 12673. The AR attracted much interest because of its unique morphological and evolution characteristics. Among the parameters examined in the AR was magnetic helicity, but either only approximately, and/or intermittently. Aims. This work is interested in studying the evolution of the relative magnetic helicity and of the two components of its decomposition, the non-potential, and the volume-threading one, in the time interval around the highest activity of AR 12673. Special emphasis is given on the study of the ratio of the non-potential to total helicity, that was recently proposed as an indicator of ARs eruptivity. Methods. For these, we first approximate the coronal magnetic field of the AR with two different optimization-based extrapolation procedures, and choose the one that produces the most reliable helicity value at each instant. Moreover, in one of these methods, we weight the optimization by the uncertainty estimates derived from the Helioseismic and Magnetic Imager (HMI) instrument, for the first time. We then follow an accurate method to compute all quantities of interest. Results. The first observational determination of the evolution of the non-potential to total helicity ratio seems to confirm the quality it has in indicating eruptivity. This ratio increases before the major flares of AR 12673, and afterwards it relaxes to smaller values. Additionally, the evolution patterns of the various helicity, and energy budgets of AR 12673 are discussed and compared with other works.
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.
A hemispheric preference in the dominant sign of magnetic helicity has been observed in numerous features in the solar atmosphere: i.e., left-handed/right-handed helicity in the northern/southern hemisphere. The relative importance of different physical processes which may contribute to the observed hemispheric sign preference (HSP) of magnetic helicity is still under debate. Here, we estimate magnetic helicity flux ($dH/dt$) across the photospheric surface for 4,802 samples of 1,105 unique active regions (ARs) that appeared over an 8-year period from 2010 to 2017 during solar cycle 24, using photospheric vector magnetic field observations by the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO). The estimates of $dH/dt$ show that 63% and 65% of the investigated AR samples in the northern and southern hemispheres, respectively, follow the HSP. We also find a trend that the HSP of $dH/dt$ increases from ~50-60% up to ~70-80% as ARs (1) appear at the earlier inclining phase of the solar cycle or higher latitudes; (2) have larger values of $|dH/dt|$, the total unsigned magnetic flux, and the average plasma flow speed. These observational findings support the enhancement of the HSP mainly by the Coriolis force acting on a buoyantly rising and expanding flux tube through the turbulent convection zone. In addition, the differential rotation on the solar surface as well as the tachocline $alpha$-effect of flux-transport dynamo may reinforce the HSP for ARs at higher latitudes.
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.
Line-of-sight magnetograms for 217 active regions (ARs) of different flare rate observed at the solar disk center from January 1997 until December 2006 are utilized to study the turbulence regime and its relationship to the flare productivity. Data from {it SOHO}/MDI instrument recorded in the high resolution mode and data from the BBSO magnetograph were used. The turbulence regime was probed via magnetic energy spectra and magnetic dissipation spectra. We found steeper energy spectra for ARs of higher flare productivity. We also report that both the power index, $alpha$, of the energy spectrum, $E(k) sim k^{-alpha}$, and the total spectral energy $W=int E(k)dk$ are comparably correlated with the flare index, $A$, of an active region. The correlations are found to be stronger than that found between the flare index and total unsigned flux. The flare index for an AR can be estimated based on measurements of $alpha$ and $W$ as $A=10^b (alpha W)^c$, with $b=-7.92 pm 0.58$ and $c=1.85 pm 0.13$. We found that the regime of the fully-developed turbulence occurs in decaying ARs and in emerging ARs (at the very early stage of emergence). Well-developed ARs display under-developed turbulence with strong magnetic dissipation at all scales.
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