Elements and Patterns in the Solar Magnetic Field

Using a developing delta-class solar active region (NOAA 12673) as a case study, we analyzed the distribution of solar vector magnetic fields and derived the corresponding magnetic energy and helicity densities from vector magnetograms to characterize the relationship between free magnetic energy and potential energy. Our findings indicate that the accumulation of magnetic free energy density and the dynamic evolution of the current helicity primarily occur near the magnetic neutral line associated with the magnetic flux emergence. The free magnetic energy density is found to originate from two sources: the nonpotential energy density ( B n 2 / 8 π ) and the interactive magnetic energy density ( B n · B p /4 π ), where B n represents the nonpotential component and B p the potential component of the magnetic field. Notably, the interactive term B n · B p also provides a significant contribution to the free energy in the solar atmosphere. Furthermore, we examined correlations between physical parameters, such as nonpotential magnetic energy and current helicity, and flare activity during the energy accumulation phase over the long-term evolution to avoid limitations in studies of solar eruptive activity caused by the lack of magnetic field observations in the upper solar atmosphere. It is found that the energy derived from the photospheric transverse magnetic field persists in accumulating even as the apparent magnetic field gradually weakens, until the onset of the X-class flares. Our analysis established reference thresholds for predicting M-class and X-class flares in newly emerging magnetically active regions. Understanding how magnetic energy accumulates to trigger solar flares and coronal mass ejections is crucial for advancing our knowledge of solar activity and space weather forecasting.

Axisymmetric magnetohydrodynamic (MHD) simulations are used to study the evolution of general magnetic field configurations where a magnetic field B threads different radii of a differentially rotating accretion disk. The differential rotation of the footpoints of B field loops at different radii on the disk surface causes a twisting of the coronal magnetic field, an increase in the coronal magnetic energy, and an opening of the loops in the region where the magnetic pressure is larger than the matter pressure (β ≲ 1). In the region where β ≳ 1, the loops may be only partially opened. Current layers form in the narrow regions that separate oppositely directed magnetic field lines. Reconnection occurs in these layers as a result of the small numerical magnetic diffusivity of the code. In contrast with the case of the solar coronal magnetic field, the combination of magnetic and centrifugal forces leads to significant matter outflow from the disk. The faster rotation of the inner part of the disk gives a stronger outflow from this part of the disk. The outflow accelerates with increasing distance from the disk up to velocities in excess of the escape speed. The outflows show some collimation within the computational region and have a large power output mainly in the form of a Poynting flux. Thus these outflows are pertinent to the origin of astrophysical jets. We present results of a survey of simulation runs for the behavior of magnetic loops and outflows for a wide range of field strengths B and mass outflow rates j. The model and processes observed are relevant to the coronae of accretion disks around stellar-mass objects, including pre-main-sequence stars, compact stars, and black holes, as well as the coronae of disks around massive black holes in active galactic nuclei. Opening of magnetic field loops may lead to transient and/or steady outflows, while reconnection events may be responsible for X-ray flares in such objects.

In this study we present the old and new observational data concerning the problem of extreme magnetic fields (  5 kG) in the Sun's atmosphere. We emphasize that the upper limit of the intensity of the magnetic field in the solar atmosphere is unknown to date. Severny (1957) heuristically suggested that the magnetic fields in the sunspots could reach 50 kG. As for the observational data, at least three arguments in favor of the magnetic fields of the order of 104 G can be specified: (1) the dependence of the measured magnetic field on the factor geff2 of magnetosensitive lines (Gopasyuk et al., 1973; Lozitsky, 1980), (2) local extremums in splitting of bisectors in the profiles I ± V for lines with different Lande factors (Lozitsky, 1980; 2015) and (3) the reliable splitting of emission peaks in Fe I lines with very low Lande factors, about 0.01, in the spectra of powerful solar flares (Lozitsky, 1993; 1998). Theoretically, superstrong fields should have gigantic magnetic pressure and can exist only with a specific topology of field lines, apparently of a force-free type (Soloviev and Lozitsky, 1986). To further develop this problem, we are analyzing new observational data obtained with the NIRIS spectropolarimeter of the largest GST solar telescope of the Big Bear Solar Observatory (BBSO). Our observations relate to the active region NOAA 12673, which was the most flare-productive in the 24th cycle. Stokes-metric measurements are made in the FeI 15648.5 Е line with a signal-to-noise ratio of about 10-4. In this active region, superstrong magnetic field of 5.57 kG was discovered recently by Wang et al. (2018). An additional study of about 70 different places in this active region suggested that there were two types of places that can be conventionally called typical and peculiar. In typical areas, the magnitude of the magnetic field in general is the greater, the less the intensity in the spectral continuum, and the maximum field here does not exceed 4 kG. All peculiar places correspond to positions with the highest intensity in the spectral continuum, and the magnetic field strength is here in the range of 3.0-5.7 kG. Notice, such strong magnetic fields were firstly discovered outside the sunspot umbra. The orientation of the magnetic field vector in peculiar places is close to the transversal, which is also atypical for typical regions and can reflect strong twisting of field lines.

Solar energetic events are caused by the release of magnetic energy accumulated in the solar atmosphere. To understand their initiating physical mechanisms, the dynamics of the coronal magnetic fields must be studied. Unfortunately, the dominant mechanisms are still unclear due to a lack of direct measurements. Numerical simulations based on magnetohydrodynamics (MHD) can reproduce the dynamical evolution of solar coronal magnetic field, providing a useful tool to explore flare initiation. Data-driven MHD simulations, in which the time-series observational data of the photospheric magnetic field is used as the simulation boundary condition, can explore different mechanisms. To investigate the accumulation of free magnetic energy through a solar eruption, we simulated the first of several large flares in NOAA active region 11283. We used a data-driven model that was governed by zero-beta MHD, focusing on the free magnetic energy accumulation prior to the M5.3 flare (2011 September 6 at 01:59 UT). We reproduced the flare-associated eruption following the formation of twisted magnetic fields, or a magnetic flux rope (MFR), formed by photospheric motions at its footpoints. We found that the eruption was first triggered by the growth of the torus instability. The erupting MFR caused magnetic reconnections with neighboring magnetic field lines located along the direction of the eruption. Using the simulation results and an axial-radial decay index centered on the MFR, we find a natural explanation for the inclination of the eruption and a possible approach to predict the direction of solar eruptive events.

view Abstract Citations (3) References (9) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Pfirsch-Schlueter Currents in Solar Plasmas Boozer, Allen H. Abstract Plasma pressure near the feet of flux tubes in the solar atmosphere can drive a large, bidirectional current along the entire length of the flux tubes. In the corona, where the plasma pressure is negligible, this current is parallel to the field lines. The pressure-driven parallel current, which is called the Pfirsch-Schlüter current, can cause loss of equilibrium and disruptive phenomena. Here the author calculates the parallel current associated with the equilibrium of a plasma in magnetic and gravitational fields. The only major restriction on the calculation is the assumption of the existence of an enthalpy function. Publication: The Astrophysical Journal Pub Date: February 1988 DOI: 10.1086/166059 Bibcode: 1988ApJ...325..891B Keywords: Plasma Currents; Plasma Pressure; Solar Atmosphere; Solar Magnetic Field; Solar Wind; Convection Currents; Coronal Loops; Magnetic Field Configurations; Magnetic Flux; Solar Physics; HYDROMAGNETICS; SUN: MAGNETIC FIELDS full text sources ADS |

It is established that long-term variations of both the large-scale and global magnetic fields in the solar atmosphere are nonmonotonic. The existence of periods of fast global changes on the Sun is found in each 11-year cycle of solar activity. These variations are accompanied by anomalous manifestations in both the heliosphere and the geomagnetic field. These periods are regularly repeated in each cycle of solar activity. They are characterized by elevated flaring activity that reflects fast variations of magnetic structures. The concept of universality of physical processes, which includes interactions of different-scale magnetic fields in the solar atmosphere and manifestations of these processes in the solar atmosphere, is developed. This concept is confirmed by the comprehensive analysis of helio-geophysical data. In accordance with the model of the solar-wind formation [1‐3], properties of the heliosphere such as the space-time distribution of the solar wind velocity, the particle flux, and the interplanetary magnetic field are determined by large-scale solar magnetic fields existing on and by their dynamics. The origin of the large-scale inhomogeneities in the solar wind are of particular interest. On the one hand, they are manifestations of the solar variability in interplanetary space. On the other hand, they are the principal cause for disturbances of the geomagnetic field. The basic sources of the inhomogeneities are coronal holes, solar flares, and coronal mass ejections. Studies of these ejections are important for both understanding the formation mechanisms of the unsteady solar wind and predicting the space weather conditions, because the strongest geophysical disturbances are associated with sporadic phenomena occurring on the Sun. In [1, 2], periods of fast global variations of the solar magnetic fields were discovered. These variations are characteristic of each 11-year cycle of solar activity and are accompanied by anomalous disturbances of the solar wind, interplanetary magnetic field, cosmic-ray intensity, and geomagnetic activity.

Context. Solar eruptions and high flare activity often accompany the rapid rotation of sunspots. The study of sunspot rotation and the mechanisms driving this motion are therefore key to our understanding of how the solar atmosphere attains the conditions necessary for large energy release. Aims. We aim to demonstrate and investigate the rotation of sunspots in a 3D numerical experiment of the emergence of a magnetic flux tube as it rises through the solar interior and emerges into the atmosphere. Furthermore, we seek to show that the sub-photospheric twist stored in the interior is injected into the solar atmosphere by means of a definitive rotation of the sunspots. Methods. A numerical experiment is performed to solve the 3D resistive magnetohydrodynamic (MHD) equations using a Lagrangian-Remap code. We track the emergence of a toroidal flux tube as it rises through the solar interior and emerges into the atmosphere investigating various quantities related to both the magnetic field and plasma. Results. Through detailed analysis of the numerical experiment, we find clear evidence that the photospheric footprints or sunspots of the flux tube undergo a rotation. Significant vertical vortical motions are found to develop within the two polarity sources after the field emerges. These rotational motions are found to leave the interior portion of the field untwisted and twist up the atmospheric portion of the field. This is shown by our analysis of the relative magnetic helicity as a significant portion of the interior helicity is transported to the atmosphere. In addition, there is a substantial transport of magnetic energy to the atmosphere. Rotation angles are also calculated by tracing selected fieldlines; the fieldlines threading through the sunspot are found to rotate through angles of up to 353 degrees over the course of the experiment.

Long-term variability of solar magnetic fields

view Abstract Citations (115) References (8) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Hydromagnetic surface waves. Wentzel, D. G. Abstract Plane and filamentary structures aligned with a magnetic field abound on the sun and in both interplanetary and interstellar space. When the Alfven speed changes across such boundaries, hydromagnetic surface waves can travel along them, carry energy, and provide heating. This paper surveys the nature of such surface waves, with emphasis on the dispersion relations, the spatial extent of the waves, the degree of gas compression, and the possibility of coupling to ordinary hydromagnetic waves. Explicit results are provided for the cases where the gas pressure is either much smaller or much larger than the magnetic pressure on either side of the surface. The waves are shear waves wherever the gas pressure is much smaller than the magnetic pressure. All surface waves involve finite gas compression, but this compression is negligible when the product of wave vector times magnetic-field vector is much smaller than the product of wave number times magnetic-field strength. Publication: The Astrophysical Journal Pub Date: January 1979 DOI: 10.1086/156732 Bibcode: 1979ApJ...227..319W Keywords: Interplanetary Magnetic Fields; Interstellar Magnetic Fields; Magnetohydrodynamic Waves; Solar Magnetic Field; Surface Waves; Wave Propagation; Coupled Modes; Energy Transfer; Gas Pressure; Magnetic Field Configurations; S Waves; Solar Atmosphere; Wave Dispersion; Astrophysics; Interplanetary Magnetic Field full text sources ADS |

Active regions on the solar surface are generally thought to originate from a strong toroidal magnetic field generated by a deep seated solar dynamo mechanism operating at the base of the solar convection zone. Thus the magnetic fields need to traverse the entire convection zone before they reach the photosphere to form the observed solar active regions. Understanding this process of active region flux emergence is therefore a crucial component for the study of the solar cycle dynamo. This article reviews studies with regard to the formation and rise of active region scale magnetic flux tubes in the solar convection zone and their emergence into the solar atmosphere as active regions.

Context. Recently, there have been some reports of unusually strong photospheric magnetic fields (which can reach values of over 7 kG) inferred from Hinode SOT/SP sunspot observations within penumbral regions. These superstrong penumbral fields are even larger than the strongest umbral fields on record and appear to be associated with supersonic downflows. The finding of such fields has been controversial since they seem to show up only when spatially coupled inversions are performed. Aims. Here, we investigate and discuss the reliability of those findings by studying in detail observed spectra associated with particularly strong magnetic fields at the inner edge of the penumbra of active region 10930. Methods. We applied classical diagnostic methods and various inversions with different model atmospheres to the observed Stokes profiles in two selected pixels with superstrong magnetic fields, and compared the results with a magnetohydrodynamic simulation of a sunspot whose penumbra contains localized regions with strong fields (nearly 5 kG at τ = 1) associated with supersonic downflows. Results. The different inversions provide different results: while the SPINOR 2D inversions consider a height-dependent single-component model and return B > 7 kG and supersonic positive vLOS (corresponding to a counter-Evershed flow), height-dependent two-component inversions suggest the presence of an umbral component (almost at rest) with field strengths ∼4 − 4.2 kG and a penumbral component with vLOS ∼ 16 − 18 km s−1 and field strengths up to ∼5.8 kG. Likewise, height-independent two-component inversions find a solution for an umbral component and a strongly redshifted (vLOS ∼ 15 − 17 km s−1) penumbral component with B ∼ 4 kG. According to a Bayesian information criterion, the inversions providing a better balance between the quality of the fits and the number of free parameters considered by the models are the height-independent two-component inversions, but they lie only slightly above the SPINOR 2D inversions. Since it is expected that the physical parameters all display considerable gradients with height, as supported by magnetohydrodynamic (MHD) sunspot simulations, the SPINOR 2D inversions are the preferred ones. Conclusions. According to the MHD sunspot simulation analyzed here, the presence of counter-Evershed flows in the photospheric penumbra can lead to the necessary conditions for the observation of ∼5 kG fields at the inner penumbra. Although a definite conclusion about the potential existence of fields in excess of 7 kG cannot be given, their nature could be explained (based on the simulation results) as the consequence of the extreme dynamical effects introduced by highly supersonic counter-Evershed flows (vLOS > 10 km s−1 and up to ∼30 km s−1 according to SPINOR 2D). The latter are much faster and more compressive downflows than those found in the MHD simulations and therefore could lead to field intensification up to considerably stronger fields. Also, a lower gas density would lead to a deeper depression of the τ = 1 surface, making possible the observation of deeper-lying stronger fields. The superstrong magnetic fields are expected to be nearly force-free, meaning that they can attain much larger strengths than expected when considering only balance between magnetic pressure and the local gas pressure.

We discuss the problem of the formation of a large-scale magnetic field in the accretion disks around black holes, taking into account the non-uniform vertical structure of the disk. The high electrical conductivity of the outer layers of the disk prevents the outward diffusion of the magnetic field. This implies a stationary state with a strong magnetic field in the inner parts of the accretion disk close to the black hole, and zero radial velocity at the surface of the disk. Structure of advective accretion disks is investigated, and conditions for formation of optically thin regions in central parts of the accretion disk are found. The problem of jet collimation by magneto-torsion oscillations is considered.

According to the standard model, an active galactic nucleus (AGN) consists of an inner accretion disk with a jet around a central massive black hole, and a number of outer broad line regions (BLRs) and narrow line regions (NLRs). The geometrical relationship between the BLRs and the accretion disk is not well understood. Assuming the motion of the BLRs is virialized and its configuration is disk-like, we derived its inclination to the line of sight for a sample of AGNs from their bulge stellar velocity dispersion, their size of the BLRs and their H$\beta$ linewidth. Compared with the inclination of the accretion disk obtained from the X-ray Fe K$\alpha$ emission lines, we found that there is no positive correlation between the two. Our results showed that BLRs are not coplanar with the accretion disk and that we should be cautious of using the BLRs inclination as the disk inclination. The non-coplanar geometry of the outer BLRs and the inner accretion disk provides clues to the origin of BLRs and the properties of the accretion disk. Our preferable interpretation is that BLRs arise out of the outer part of a warped accretion disk.

We present numerical solutions for stationary and axisymmetric equilibriums of compact stars associated with extremely strong magnetic fields. The interior of the compact stars is assumed to satisfy ideal magnetohydrodynamic (MHD) conditions, while in the region of negligible mass density the force-free conditions or electromagnetic vacuum are assumed. Solving all components of Einstein's equations, Maxwell's equations, ideal MHD equations, and force-free conditions, equilibriums of rotating compact stars associated with mixed poloidal and toroidal magnetic fields are obtained. It is found that in the extreme cases the strong mixed magnetic fields concentrating in a toroidal region near the equatorial surface expel the matter and form a force-free toroidal magnetotunnel. We also introduce a new differential rotation law for computing solutions associated with force-free magnetosphere, and present other extreme models without the magnetotunnel.

During the collapse of a massive star greater than 35- 40 M ⊙ , stellar core is considered to promptly collapse to a black hole. and stellar material may fall onto the hole greater than several solar masses with extremely high accretion rates (> 1 M ⊙ s -1 ). If the star has a sufficiently high angular momentum before the collapse, an accretion disk is likely to form around the black hole. Jets are suggested to be launched from the inner region of the accretion disk near the hole through magnetic and/or neutrino processes. Gamma-Ray Bursts (GRBs) are expected to be driven by the jets. This scenario of GRBs is called the collapsar model. Recently, magnetohydrodynamic (MHD) simulations were performed of the collapse of rapidly rotating, magnetized 25 M ⊙ and 40 M ⊙ stars in light of the collapsar model of GRBs (see papers listed at the end of the paper). For assumed angular velocity distributions and the uniform magnetic fields, the collapsars are shown to eject jets driven through the magnetic pressure. The simulations are however performed up to 4 s, which are shorter than durations of long GRBs ∼ 10 s. In the present work. we have performed long-tern (∼ 10 s), two-dimensional, MHD simulations of the collapse of a rapidly totaling, magnetized 40 M ⊙ star.