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P Demoulin - One of the best experts on this subject based on the ideXlab platform.
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studying the transfer of magnetic Helicity in solar active regions with the connectivity based Helicity flux density method
The Astrophysical Journal, 2018Co-Authors: K Dalmasse, E Pariat, Gherardo Valori, Ju Jing, P DemoulinAbstract: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 regard 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 relating it to their flaring activity.
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studying the transfer of magnetic Helicity in solar active regions with the connectivity based Helicity flux density method
arXiv: Solar and Stellar Astrophysics, 2017Co-Authors: K Dalmasse, E Pariat, Gherardo Valori, Ju Jing, P DemoulinAbstract: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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successive injection of opposite magnetic Helicity in solar active region noaa 11928
Astronomy and Astrophysics, 2017Co-Authors: P Vemareddy, P DemoulinAbstract:Aims. Understanding the nature and evolution of the photospheric Helicity flux transfer is crucial to revealing the role of magnetic Helicity in coronal dynamics of solar active regions. Methods. We computed the boundary-driven Helicity flux with a 12-min cadence during the emergence of the AR 11928 using SDO/HMI photospheric vector magnetograms and the derived flow velocity field. Accounting for the footpoint connectivity defined by nonlinear, force-free magnetic extrapolations, we derived and analyzed the corrected distribution of Helicity flux maps. Results. The photospheric Helicity flux injection is found to change sign during the steady emergence of the AR. This reversal is confirmed with the evolution of the photospheric electric currents and with the coronal connectivity as observed in EUV wavelengths with SDO/AIA. During approximately the three first days of emergence, the AR coronal Helicity is positive while later on the field configuration is close to a potential field. As theoretically expected, the magnetic Helicity cancellation is associated with enhanced coronal activity. Conclusions. The study suggests a boundary driven transformation of the chirality in the global AR magnetic structure. This may be the result of the emergence of a flux rope with positive twist around its apex while it has negative twist in its legs. The origin of such mixed Helicity flux rope in the convective zone is challenging for models.
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successive injection of opposite magnetic Helicity in solar active region noaa 11928
arXiv: Solar and Stellar Astrophysics, 2016Co-Authors: P Vemareddy, P DemoulinAbstract:Understanding the nature and evolution of the photospheric Helicity flux transfer is a key to reveal the role of magnetic Helicity in coronal dynamics of solar active regions. Using SDO/HMI photospheric vector magnetograms and the derived flow velocity field, we computed boundary driven Helicity flux with a 12 minute cadence during the emergence of AR 11928. Accounting the foot point connectivity defined by non-linear force-free magnetic extrapolations, we derived and analyzed the corrected distribution of Helicity flux maps. The photospheric Helicity flux injection is found to changes sign during the steady emergence of the AR. This reversal is confirmed with the evolution of the photospheric electric currents and with the coronal connectivity as observed in EUV wavelengths with SDO/AIA. During about the three first days of emergence, the AR coronal Helicity is positive while later on the field configuration is close to a potential field. As theoretically expected, the magnetic Helicity cancelation is associated to enhanced coronal activity. The study suggests a boundary driven transformation of the chirality in the global AR magnetic structure. This may be the result of the emergence of a flux rope with positive twist around its apex while it has negative twist in its legs. The origin of such mixed Helicity flux rope in the convective zone is challenging for models.
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photospheric injection of magnetic Helicity connectivity based flux density method
Solar Physics, 2014Co-Authors: K Dalmasse, E Pariat, P Demoulin, G AulanierAbstract:Magnetic Helicity quantifies the degree to which the magnetic field in a volume is globally sheared and/or twisted. This quantity is believed to play a key role in solar activity due to its conservation property. Helicity is continuously injected into the corona during the evolution of active regions (ARs). To better understand and quantify the role of magnetic Helicity in solar activity, the distribution of magnetic Helicity flux in ARs needs to be studied. The Helicity distribution can be computed from the temporal evolution of photospheric magnetograms of ARs such as the ones provided by SDO/HMI and Hinode/SOT. Most recent analyses of photospheric Helicity flux derived a proxy to the Helicity-flux density based on the relative rotation rate of photospheric magnetic footpoints. Although this proxy allows a good estimate of the photospheric Helicity flux, it is still not a true Helicity flux density because it does not take into account the connectivity of the magnetic field lines. For the first time, we implement a Helicity density that takes this connectivity into account. To use it for future observational studies, we tested the method and its precision on several types of models involving different patterns of Helicity injection. We also tested it on more complex configurations – from magnetohydrodynamics (MHD) simulations – containing quasi-separatrix layers. We demonstrate that this connectivity-based proxy is best-suited to map the true distribution of photospheric Helicity injection.
E Pariat - One of the best experts on this subject based on the ideXlab platform.
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threshold of non potential magnetic Helicity ratios at the onset of solar eruptions
The Astrophysical Journal, 2018Co-Authors: E Pariat, Gherardo Valori, F P Zuccarello, L LinanAbstract:The relative magnetic Helicity is a quantity that is often used to describe the level of entanglement of non-isolated magnetic fields, such as the magnetic field of solar active regions.The aim of this paper is to investigate how different kinds of photospheric boundary flows accumulate relative magnetic Helicity in the corona and if and how-well magnetic Helicity related quantities identify the onset of an eruption. We use a series of three-dimensional, parametric magnetohydrodynamic simulations of the formation and eruption of magnetic flux ropes. All the simulations are performed on the same grid, using the same parameters, but they are characterized by different driving photospheric flows, i.e., shearing, convergence, stretching, peripheral- and central- dispersion flows. For each of the simulations, the instant of the onset of the eruption is carefully identified by using a series of relaxation runs. We find that magnetic energy and total relative Helicity are mostly injected when shearing flows are applied at the boundary, while the magnetic energy and Helicity associated with the coronal electric currents increase regardless of the kind of photospheric flows. We also find that, at the onset of the eruptions, the ratio between the non-potential magnetic Helicity and the total relative magnetic Helicity has the same value for all the simulations, suggesting the existence of a threshold in this quantity. Such threshold is not observed for other quantities as, for example, those related to the magnetic energy.
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Computation of Relative Magnetic Helicity in Spherical Coordinates
Solar Physics, 2018Co-Authors: Kostas Moraitis, E Pariat, Antonia Savcheva, Gherardo ValoriAbstract:Magnetic Helicity is a quantity of great importance in solar studies because it is conserved in ideal magnetohydrodynamics. While many methods for computing magnetic Helicity in Cartesian finite volumes exist, in spherical coordinates, the natural coordinate system for solar applications, Helicity is only treated approximately. We present here a method for properly computing the relative magnetic Helicity in spherical geometry. The volumes considered are finite, of shell or wedge shape, and the three-dimensional magnetic field is considered to be fully known throughout the studied domain. Testing of the method with well-known, semi-analytic, force-free magnetic-field models reveals that it has excellent accuracy. Further application to a set of nonlinear force-free reconstructions of the magnetic field of solar active regions and comparison with an approximate method used in the past indicates that the proposed method can be significantly more accurate, thus making our method a promising tool in Helicity studies that employ spherical geometry. Additionally, we determine and discuss the applicability range of the approximate method.
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computation of relative magnetic Helicity in spherical coordinates
arXiv: Solar and Stellar Astrophysics, 2018Co-Authors: Kostas Moraitis, E Pariat, Antonia Savcheva, Gherardo ValoriAbstract:Magnetic Helicity is a quantity of great importance in solar studies because it is conserved in ideal magneto-hydrodynamics. While many methods to compute magnetic Helicity in Cartesian finite volumes exist, in spherical coordinates, the natural coordinate system for solar applications, Helicity is only treated approximately. We present here a method to properly compute relative magnetic Helicity in spherical geometry. The volumes considered are finite, of shell or wedge shape, and the three-dimensional magnetic field is considered fully known throughout the studied domain. Testing of the method with well-known, semi-analytic, force-free magnetic-field models reveals that it has excellent accuracy. Further application to a set of nonlinear force-free reconstructions of the magnetic field of solar active regions, and comparison with an approximate method used in the past, indicates that the proposed methodology can be significantly more accurate, thus making our method a promising tool in Helicity studies that employ the spherical geometry. Additionally, the range of applicability of the approximate method is determined and discussed.
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studying the transfer of magnetic Helicity in solar active regions with the connectivity based Helicity flux density method
The Astrophysical Journal, 2018Co-Authors: K Dalmasse, E Pariat, Gherardo Valori, Ju Jing, P DemoulinAbstract: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 regard 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 relating it to their flaring activity.
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studying the transfer of magnetic Helicity in solar active regions with the connectivity based Helicity flux density method
arXiv: Solar and Stellar Astrophysics, 2017Co-Authors: K Dalmasse, E Pariat, Gherardo Valori, Ju Jing, P DemoulinAbstract: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.
Gherardo Valori - One of the best experts on this subject based on the ideXlab platform.
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threshold of non potential magnetic Helicity ratios at the onset of solar eruptions
The Astrophysical Journal, 2018Co-Authors: E Pariat, Gherardo Valori, F P Zuccarello, L LinanAbstract:The relative magnetic Helicity is a quantity that is often used to describe the level of entanglement of non-isolated magnetic fields, such as the magnetic field of solar active regions.The aim of this paper is to investigate how different kinds of photospheric boundary flows accumulate relative magnetic Helicity in the corona and if and how-well magnetic Helicity related quantities identify the onset of an eruption. We use a series of three-dimensional, parametric magnetohydrodynamic simulations of the formation and eruption of magnetic flux ropes. All the simulations are performed on the same grid, using the same parameters, but they are characterized by different driving photospheric flows, i.e., shearing, convergence, stretching, peripheral- and central- dispersion flows. For each of the simulations, the instant of the onset of the eruption is carefully identified by using a series of relaxation runs. We find that magnetic energy and total relative Helicity are mostly injected when shearing flows are applied at the boundary, while the magnetic energy and Helicity associated with the coronal electric currents increase regardless of the kind of photospheric flows. We also find that, at the onset of the eruptions, the ratio between the non-potential magnetic Helicity and the total relative magnetic Helicity has the same value for all the simulations, suggesting the existence of a threshold in this quantity. Such threshold is not observed for other quantities as, for example, those related to the magnetic energy.
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Computation of Relative Magnetic Helicity in Spherical Coordinates
Solar Physics, 2018Co-Authors: Kostas Moraitis, E Pariat, Antonia Savcheva, Gherardo ValoriAbstract:Magnetic Helicity is a quantity of great importance in solar studies because it is conserved in ideal magnetohydrodynamics. While many methods for computing magnetic Helicity in Cartesian finite volumes exist, in spherical coordinates, the natural coordinate system for solar applications, Helicity is only treated approximately. We present here a method for properly computing the relative magnetic Helicity in spherical geometry. The volumes considered are finite, of shell or wedge shape, and the three-dimensional magnetic field is considered to be fully known throughout the studied domain. Testing of the method with well-known, semi-analytic, force-free magnetic-field models reveals that it has excellent accuracy. Further application to a set of nonlinear force-free reconstructions of the magnetic field of solar active regions and comparison with an approximate method used in the past indicates that the proposed method can be significantly more accurate, thus making our method a promising tool in Helicity studies that employ spherical geometry. Additionally, we determine and discuss the applicability range of the approximate method.
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computation of relative magnetic Helicity in spherical coordinates
arXiv: Solar and Stellar Astrophysics, 2018Co-Authors: Kostas Moraitis, E Pariat, Antonia Savcheva, Gherardo ValoriAbstract:Magnetic Helicity is a quantity of great importance in solar studies because it is conserved in ideal magneto-hydrodynamics. While many methods to compute magnetic Helicity in Cartesian finite volumes exist, in spherical coordinates, the natural coordinate system for solar applications, Helicity is only treated approximately. We present here a method to properly compute relative magnetic Helicity in spherical geometry. The volumes considered are finite, of shell or wedge shape, and the three-dimensional magnetic field is considered fully known throughout the studied domain. Testing of the method with well-known, semi-analytic, force-free magnetic-field models reveals that it has excellent accuracy. Further application to a set of nonlinear force-free reconstructions of the magnetic field of solar active regions, and comparison with an approximate method used in the past, indicates that the proposed methodology can be significantly more accurate, thus making our method a promising tool in Helicity studies that employ the spherical geometry. Additionally, the range of applicability of the approximate method is determined and discussed.
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studying the transfer of magnetic Helicity in solar active regions with the connectivity based Helicity flux density method
The Astrophysical Journal, 2018Co-Authors: K Dalmasse, E Pariat, Gherardo Valori, Ju Jing, P DemoulinAbstract: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 regard 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 relating it to their flaring activity.
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studying the transfer of magnetic Helicity in solar active regions with the connectivity based Helicity flux density method
arXiv: Solar and Stellar Astrophysics, 2017Co-Authors: K Dalmasse, E Pariat, Gherardo Valori, Ju Jing, P DemoulinAbstract: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.
D D Sokoloff - One of the best experts on this subject based on the ideXlab platform.
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evolution of magnetic Helicity and energy spectra of solar active regions
The Astrophysical Journal, 2016Co-Authors: Hongqi Zhang, Axel Brandenburg, D D SokoloffAbstract:We adopt an isotropic representation of the Fourier-transformed two-point correlation tensor of the magnetic field to estimate the magnetic energy and Helicity spectra as well as current Helicity spectra of two individual active regions (NOAA. 11158 and NOAA. 11515) and the change of the spectral indices during their development as well as during the solar cycle. The departure of the spectral indices of magnetic energy and current Helicity from 5/ 3 are analyzed, and it is found that it is lower than the spectral index of the magnetic energy spectrum. Furthermore, the fractional magnetic Helicity tends to increase when the scale of the energy-carrying magnetic structures increases. The magnetic Helicity of NOAA. 11515 violates the expected hemispheric sign rule, which is interpreted as an effect of enhanced field strengths at scales larger than 30-60Mm with opposite signs of Helicity. This is consistent with the general cycle dependence, which shows that around the solar maximum the magnetic energy and Helicity spectra are steeper, emphasizing the large-scale field.
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magnetic Helicity and energy spectra of a solar active region
The Astrophysical Journal, 2014Co-Authors: Hongqi Zhang, Axel Brandenburg, D D SokoloffAbstract:We compute for the first time the magnetic Helicity and energy spectra of the solar active region NOAA 11158 during 2011 February 11-15 at 20° 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 the 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 2π/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 artifacts at small scales.
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magnetic Helicity and energy spectra of a solar active region
arXiv: Solar and Stellar Astrophysics, 2013Co-Authors: Hongqi Zhang, Axel Brandenburg, D D SokoloffAbstract: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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the radial distribution of magnetic Helicity in the solar convective zone observations and dynamo theory
Monthly Notices of the Royal Astronomical Society, 2006Co-Authors: Hui Zhang, D D Sokoloff, I Rogachevskii, D Moss, V G Lamburt, K Kuzanyan, N KleeorinAbstract:We continue our attempt to connect observational data on current Helicity in solar active regions with solar dynamo models. In addition to our previous results about temporal and latitudinal distributions of current Helicity, we argue that some information concerning the radial profile of the current Helicity averaged over time, and latitude can be extracted from the available observations. The main feature of this distribution can be presented as follows. Both shallow and deep active regions demonstrate a clear dominance of one sign of current Helicity in a given hemisphere during the whole cycle. Broadly speaking, current Helicity has opposite polarities in the Northern and Southern hemispheres, although there are some active regions that violate this polarity rule. The relative number of active regions violating the polarity rule is significantly higher for deeper active regions. A separation of active regions into ‘shallow’, ‘middle’ and ‘deep’ is made by comparing their rotation rate and the helioseismic rotation law. We use a version of Parker’s dynamo model in two spatial dimensions, which employs a nonlinearity based on magnetic Helicity conservation arguments. The predictions of this model about the radial distribution of solar current Helicity appear to be in remarkable agreement with the available observational data; in particular the relative volume occupied by the current Helicity of ‘wrong’ sign grows significantly with the depth.
Axel Brandenburg - One of the best experts on this subject based on the ideXlab platform.
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solar kinetic energy and cross Helicity spectra
The Astrophysical Journal, 2018Co-Authors: Hongqi Zhang, Axel BrandenburgAbstract:We develop a formalism that treats the calculation of solar kinetic energy and cross Helicity spectra in an equal manner to that of magnetic energy and Helicity spectra. The magnetic Helicity spect ...
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solar kinetic energy and cross Helicity spectra
arXiv: Solar and Stellar Astrophysics, 2018Co-Authors: Hongqi Zhang, Axel BrandenburgAbstract:We develop a formalism that treats the calculation of solar kinetic energy and cross Helicity spectra in an equal manner to that of magnetic energy and Helicity spectra. The magnetic Helicity spectrum is shown to be equal to the vertical part of the current Helicity spectrum divided by the square of the wavenumber. For the cross Helicity, we apply the recently developed two-scale approach globally over an entire active region to account for the sign change between the two polarities. Using vector magnetograms and Dopplergrams of NOAA 11158 and 12266, we show that kinetic and magnetic energy spectra have similar slopes at intermediate wavenumbers, where the contribution from the granulation velocity has been removed. At wavenumbers around 0.3 Mm$^{-1}$, the magnetic Helicity is found to be close to its maximal value. The cross Helicity spectra are found to be within about 10% of the maximum possible value. Using the two-scale method for NOAA 12266, the global cross Helicity spectrum is found to be particularly steep, similarly to what has previously been found in theoretical models of spot generation. In the quiet Sun, by comparison, the cross Helicity spectrum is found to be small.
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evolution of magnetic Helicity and energy spectra of solar active regions
The Astrophysical Journal, 2016Co-Authors: Hongqi Zhang, Axel Brandenburg, D D SokoloffAbstract:We adopt an isotropic representation of the Fourier-transformed two-point correlation tensor of the magnetic field to estimate the magnetic energy and Helicity spectra as well as current Helicity spectra of two individual active regions (NOAA. 11158 and NOAA. 11515) and the change of the spectral indices during their development as well as during the solar cycle. The departure of the spectral indices of magnetic energy and current Helicity from 5/ 3 are analyzed, and it is found that it is lower than the spectral index of the magnetic energy spectrum. Furthermore, the fractional magnetic Helicity tends to increase when the scale of the energy-carrying magnetic structures increases. The magnetic Helicity of NOAA. 11515 violates the expected hemispheric sign rule, which is interpreted as an effect of enhanced field strengths at scales larger than 30-60Mm with opposite signs of Helicity. This is consistent with the general cycle dependence, which shows that around the solar maximum the magnetic energy and Helicity spectra are steeper, emphasizing the large-scale field.
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magnetic Helicity and energy spectra of a solar active region
The Astrophysical Journal, 2014Co-Authors: Hongqi Zhang, Axel Brandenburg, D D SokoloffAbstract:We compute for the first time the magnetic Helicity and energy spectra of the solar active region NOAA 11158 during 2011 February 11-15 at 20° 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 the 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 2π/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 artifacts at small scales.
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magnetic Helicity and energy spectra of a solar active region
arXiv: Solar and Stellar Astrophysics, 2013Co-Authors: Hongqi Zhang, Axel Brandenburg, D D SokoloffAbstract: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.
