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Register a new userMagnetic helicity estimations in models and observations of the solar magnetic field. Part IV: Application to solar observations
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In this ISSI-supported series of studies on magnetic helicity in the Sun, we systematically implement different magnetic helicity calculation methods on high-quality solar magnetogram observations. We apply finite-volume, discrete flux tube (in particular, connectivity-based) and flux-integration methods to data from Hinodes Solar Optical Telescope. The target is NOAA active region 10930 during a ~1.5 day interval in December 2006 that included a major eruptive flare (SOL2006-12-13T02:14X3.4). Finite-volume and connectivity-based methods yield instantaneous budgets of the coronal magnetic helicity, while the flux-integration methods allow an estimate of the accumulated helicity injected through the photosphere. The objectives of our work are twofold: A cross-validation of methods, as well as an interpretation of the complex events leading to the eruption. To the first objective, we find (i) strong agreement among the finite-volume methods, (ii) a moderate agreement between the connectivity-based and finite-volume methods, (iii) an excellent agreement between the flux-integration methods, and (iv) an overall agreement between finite-volume and flux-integration based estimates regarding the predominant sign and magnitude of the helicity. To the second objective, we are confident that the photospheric helicity flux significantly contributed to the coronal helicity budget, and that a right-handed structure erupted from a predominantly left-handed corona during the X-class flare. Overall, we find that the use of different methods to estimate the (accumulated) coronal helicity may be necessary in order to draw a complete picture of an active-region corona, given the careful handling of identified data (preparation) issues, which otherwise would mislead the event analysis and interpretation.
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We study the writhe, twist and magnetic helicity of different magnetic flux ropes, based on models of the solar coronal magnetic field structure. These include an analytical force-free Titov--Demoulin equilibrium solution, non force-free magnetohydrodynamic simulations, and nonlinear force-free magnetic field models. The geometrical boundary of the magnetic flux rope is determined by the quasi-separatrix layer and the bottom surface, and the axis curve of the flux rope is determined by its overall orientation. The twist is computed by the Berger--Prior formula that is suitable for arbitrary geometry and both force-free and non-force-free models. The magnetic helicity is estimated by the twist multiplied by the square of the axial magnetic flux. We compare the obtained values with those derived by a finite volume helicity estimation method. We find that the magnetic helicity obtained with the twist method agrees with the helicity carried by the purely current-carrying part of the field within uncertainties for most test cases. It is also found that the current-carrying part of the model field is relatively significant at the very location of the magnetic flux rope. This qualitatively explains the agreement between the magnetic helicity computed by the twist method and the helicity contributed purely by the current-carrying magnetic field.
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 removal of magnetic flux from the quiet-sun photosphere is important for maintaining the statistical steady-state of the magnetic field there, for determining the magnetic flux budget of the Sun, and for estimating the rate of energy injected into the upper solar atmosphere. Magnetic feature death is a measurable proxy for the removal of detectable flux. We used the SWAMIS feature tracking code to understand how nearly 20000 detected magnetic features die in an hour-long sequence of Hinode/SOT/NFI magnetograms of a region of quiet Sun. Of the feature deaths that remove visible magnetic flux from the photosphere, the vast majority do so by a process that merely disperses the previously-detected flux so that it is too small and too weak to be detected. The behavior of the ensemble average of these dispersals is not consistent with a model of simple planar diffusion, suggesting that the dispersal is constrained by the evolving photospheric velocity field. We introduce the concept of the partial lifetime of magnetic features, and show that the partial lifetime due to Cancellation of magnetic flux, 22 h, is 3 times slower than previous measurements of the flux turnover time. This indicates that prior feature-based estimates of the flux replacement time may be too short, in contrast with the tendency for this quantity to decrease as resolution and instrumentation have improved. This suggests that dispersal of flux to smaller scales is more important for the replacement of magnetic fields in the quiet Sun than observed bipolar cancellation. We conclude that processes on spatial scales smaller than those visible to Hinode dominate the processes of flux emergence and cancellation, and therefore also the quantity of magnetic flux that threads the photosphere.
We propose a novel approach to reconstruct the surface magnetic helicity density on the Sun or sun-like stars. The magnetic vector potential is determined via decomposition of vector magnetic field measurements into toroidal and poloidal components. The method is verified using data from a non-axisymmetric dynamo model. We apply the method to vector field synoptic maps from Helioseismic and Magnetic Imager (HMI) onboard of Solar Dynamics Observatory (SDO) to study evolution of the magnetic helicity density during solar cycle 24. It is found that the mean helicity density of the non-axisymmetric magnetic field of the Sun evolves in a way which is similar to that reported for the current helicity density of the solar active regions. It has predominantly the negative sign in the northern hemisphere, and it is positive in the southern hemisphere. Also, the hemispheric helicity rule for the non-axisymmetric magnetic field showed the sign inversion at the end of cycle 24. Evolution of magnetic helicity density of large-scale axisymmetric magnetic field is different from that expected in dynamo theory. On one hand, the mean large- and small-scale components of magnetic helicity density display the hemispheric helicity rule of opposite sign at the beginning of cycle 24. However, later in the cycle, the two helicities exhibit the same sign in contrast with the theoretical expectations.
Potential field extrapolations are widely used as minimum-energy models for the Suns coronal magnetic field. As the reference to which other magnetic fields are compared, they have -- by any reasonable definition -- no global (signed) magnetic helicity. Here we investigate the internal topological structure that is not captured by the global helicity integral, by splitting it into individual field line helicities. These are computed using potential field extrapolations from magnetogram observations over Solar Cycle 24, as well as for a simple illustrative model of a single bipolar region in a dipolar background. We find that localised patches of field line helicity arise primarily from linking between strong active regions and their overlying field, so that the total unsigned helicity correlates with the product of photospheric and open fluxes. Within each active region, positive and negative helicity may be unbalanced, but the signed helicity is only around a tenth of the unsigned helicity. Interestingly, in Cycle 24, there is a notable peak in unsigned helicity caused by a single large active region. On average, the total unsigned helicity at the resolution considered is approximately twice the typical signed helicity of a single real active region, according to non-potential models in the literature.
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