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1. Magnetic helicity and eruptivity in active region 12673

   https://doi.org/10.1051/0004-6361/201935870  

   Moraitis, K.; Sun, X.; Pariat, É.; Linan, L. (August 2019, Astronomy & Astrophysics)

   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. This AR attracted much interest because of its unique morphological and evolution characteristics. Among the parameters that were examined in the AR was magnetic helicity, but either only approximately, or intermittently, or both. Aims . We here study 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. We especially focus on the ratio of the non-potential to total helicity, which has recently been proposed as an indicator of AR eruptivity. Methods . We first approximated the coronal magnetic field of the AR with two different optimization-based extrapolation procedures, and chose the method that produced the most reliable helicity value at each instant. Moreover, in one of these methods, we weighted the optimization by the uncertainty estimates derived from the Helioseismic and Magnetic Imager (HMI) instrument for the first time. We then followed 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 increased before the major flares of AR 12673 and afterwards relaxed to lower values. Additionally, we discuss the evolution patterns of the various helicity and energy budgets of AR 12673 and compare them with results from other works. 

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2. Deducing the reliability of relative helicities from nonlinear force-free coronal models

   https://doi.org/10.1051/0004-6361/202038921  

   Thalmann, J. K.; Sun, X.; Moraitis, K.; Gupta, M. (November 2020, Astronomy & Astrophysics)

   null (Ed.)

   Aims. We study the relative helicity of active region (AR) NOAA 12673 during a ten-hour time interval centered around a preceding X2.2 flare (SOL2017-09-06T08:57) and also including an eruptive X9.3 flare that occurred three hours later (SOL2017-09-06T11:53). In particular, we aim for a reliable estimate of the normalized self-helicity of the current-carrying magnetic field, the so-called helicity ratio, | H J |/| H 𝒱 |, a promising candidate to quantity the eruptive potential of solar ARs. Methods. Using Solar Dynamics Observatory Helioseismic and Magnetic Imager vector magnetic field data as an input, we employ nonlinear force-free (NLFF) coronal magnetic field models using an optimization approach. The corresponding relative helicity, and related quantities, are computed using a finite-volume method. From multiple time series of NLFF models based on different choices of free model parameters, we are able to assess the spread of | H J |/| H 𝒱 |, and to estimate its uncertainty. Results. In comparison to earlier works, which identified the non-solenoidal contribution to the total magnetic energy, E div / E , as selection criterion regarding the required solenoidal quality of magnetic field models for subsequent relative helicity analysis, we propose to use in addition the non-solenoidal contribution to the free magnetic energy, | E mix |/ E J , s . As a recipe for a reliable estimate of the relative magnetic helicity (and related quantities), we recommend to employ multiple NLFF models based on different combinations of free model parameters, to retain only those that exhibit smallest values of both E div / E and | E mix |/ E J , s at a certain time instant, to subsequently compute mean estimates, and to use the spread of the individually contributing values as an indication for the uncertainty. 

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3. Three-dimensional Hybrid Simulation Results of a Variable Magnetic Helicity Signature at Proton Kinetic Scales

   https://doi.org/10.3847/1538-4357/ac3bbc  

   Vasquez, Bernard J.; Markovskii, Sergei A.; Smith, Charles W. (January 2022, The Astrophysical Journal)

   Abstract Three-dimensional hybrid kinetic simulations are conducted with particle protons and warm fluid electrons. Alfvénic fluctuations initialized at large scales and with wavevectors that are highly oblique with respect to the background magnetic field evolve into a turbulent energy cascade that dissipates at proton kinetic scales. Accompanying the proton scales is a spectral magnetic helicity signature with a peak in magnitude. A series of simulation runs are made with different large-scale cross helicity and different initial fluctuation phases and wavevector configurations. From the simulations a so-called total magnetic helicity peak is evaluated by summing contributions at a wavenumber perpendicular to the background magnetic field. The total is then compared with the reduced magnetic helicity calculated along spacecraft-like trajectories through the simulation box. The reduced combines the helicity from different perpendicular wavenumbers and depends on the sampling direction. The total is then the better physical quantity to characterize the turbulence. On average the ratio of reduced to total is 0.45. The total magnetic helicity and the reduced magnetic helicity show intrinsic variability based on initial fluctuation conditions. This variability can contribute to the scatter found in the observed distribution of solar wind reduced magnetic helicity as a function of cross helicity. 

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4. A Magnetogram-matching Method for Energizing Magnetic Flux Ropes Toward Eruption

   https://doi.org/10.3847/1538-4357/ac874e  

   Titov, V. S.; Downs, C.; Török, T.; Linker, J. A. (September 2022, The Astrophysical Journal)

   Abstract We propose a new “helicity-pumping” method for energizing coronal equilibria that contain a magnetic flux rope (MFR) toward an eruption. We achieve this in a sequence of magnetohydrodynamics relaxations of small line-tied pulses of magnetic helicity, each of which is simulated by a suitable rescaling of the current-carrying part of the field. The whole procedure is “magnetogram-matching” because it involves no changes to the normal component of the field at the photospheric boundary. The method is illustrated by applying it to an observed force-free configuration whose MFR is modeled with our regularized Biot–Savart law method. We find that, in spite of the bipolar character of the external field, the MFR eruption is sustained by two reconnection processes. The first, which we refer to as breakthrough reconnection, is analogous to breakout reconnection in quadrupolar configurations. It occurs at a quasi-separator inside a current layer that wraps around the erupting MFR and is caused by the photospheric line-tying effect. The second process is the classical flare reconnection, which develops at the second quasi-separator inside a vertical current layer that is formed below the erupting MFR. Both reconnection processes work in tandem with the magnetic forces of the unstable MFR to propel it through the overlying ambient field, and their interplay may also be relevant for the thermal processes occurring in the plasma of solar flares. The considered example suggests that our method will be beneficial for both the modeling of observed eruptive events and theoretical studies of eruptions in idealized magnetic configurations. 

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5. Magnetic Helicity Associated with the Proton Temperature Anisotropy Instabilities in the Presence of an Imbalanced Solar Wind Turbulence

   https://doi.org/10.3847/1538-4357/acdb66  

   Markovskii, S. A.; Vasquez, Bernard J. (July 2023, The Astrophysical Journal)

   Abstract Some of the most common processes in the solar wind, such as turbulence and wave generation by instabilities, are associated with spectral magnetic helicity. Therefore, the helicity is a convenient tool to investigate these processes. We use three-dimensional nonlinear kinetic simulations with particle ions and fluid electrons to analyze the magnetic helicity produced by proton temperature anisotropy instabilities coexisting with an ambient turbulence. The symmetry of the unstable system is violated by alpha-particle streaming with respect to protons along the mean magnetic field. At the same time, the turbulent fluctuations are also imbalanced by a nonzero cross-helicity. We show that in the nonlinear phase of the instability the resulting helicity structure is different from the prediction of the linear theory. In particular, it contains sign reversals and multiple domains of nonzero helicity. The turbulence generates its own magnetic helicity signature, which extends over a wide range of angles around the direction perpendicular to the mean magnetic field, and can have a sign the same as or opposite to that of the instability. These findings are consistent with the observed helicity spectra in the solar wind. 

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