Magnetic Structure in Successively Erupting Active Regions: Comparison of Flare-Ribbons With Quasi-Separatrix Layers

This paper studies the magnetic topology of successively erupting active regions (ARs) 11,429 and 12,371. Employing vector magnetic field observations from Helioseismic and Magnetic Imager, the pre-eruptive magnetic structure is reconstructed by a model of non-linear force-free field (NLFFF). For all the five CMEs from these ARs, the pre-eruptive magnetic structure identifies an inverse-S sigmoid consistent with the coronal plasma tracers in EUV observations. In all the eruption cases, the quasi-separatrix layers (QSLs) of large Q values are continuously enclosing core field bipolar regions in which inverse-S shaped flare ribbons are observed. These QSLs essentially represent the large connectivity gradients between the domains of twisted core flux within the inner bipolar region and the surrounding potential like arcade. It is consistent with the observed field structure largely with the sheared arcade. The QSL maps in the chromosphere are compared with the flare-ribbons observed at the peak time of the flares. The flare ribbons are largely inverse-S shape morphology with their continuity of visibility is missing in the observations. For the CMEs in the AR 12371, the QSLs outline the flare ribbons as a combination of two inverse J-shape sections with their straight parts being separated. These QSLs are typical with the weakly twisted flux rope. Similarly, for the CMEs in the AR 11429, the QSLs are co-spatial with the flare ribbons both in the middle of the PIL and in the hook sections. In the frame work of standard model of eruptions, the observed flare ribbons are the characteristic of the pre-eruptive magnetic structure being sigmoid which is reproduced by the NLFFF model with a weakly twisted flux rope at the core.

Preprocessing of magnetograms for magnetohydrostatic extrapolations

<p>Magnetohydrostatic (MHS) extrapolations are developed to model 3D magnetic fields and plasma structures in the solar low atmosphere by using measured vector magnetic fields on the photosphere. However, the photospheric magnetogram may be inconsistent with the MHS assumption. By applying Gauss‘ theorem to an isolated active region, we obtain a set of surface integrals of the magnetogram as criteria for a MHS system. The integrals are a subset of Aly’s criteria for a force-free field (FFF). Based on the new criteria, we preprocess the magnetogram to make it more consistent with the MHS assumption and, at the same time, close to the original data. As a byproduct, we also find the boundary integral that is used to compute the energy of a FFF usually underestimates the magnetic energy of an active region.</p>

Solar force-free magnetic fields

The structure and dynamics of the solar corona is dominated by the magnetic field. In most areas in the corona magnetic forces are so dominant that all non-magnetic forces such as plasma pressure gradients and gravity can be neglected in the lowest order. This model assumption is called the force-free field assumption, as the Lorentz force vanishes. This can be obtained by either vanishing electric currents (leading to potential fields) or the currents are co-aligned with the magnetic field lines. First we discuss a mathematically simpler approach that the magnetic field and currents are proportional with one global constant, the so-called linear force-free field approximation. In the generic case, however, the relationship between magnetic fields and electric currents is nonlinear and analytic solutions have been only found for special cases, like 1D or 2D configurations. For constructing realistic nonlinear force-free coronal magnetic field models in 3D, sophisticated numerical computations are required and boundary conditions must be obtained from measurements of the magnetic field vector in the solar photosphere. This approach is currently a large area of research, as accurate measurements of the photospheric field are available from ground-based observatories such as the Synoptic Optical Long-term Investigations of the Sun and the Daniel K. Inouye Solar Telescope (DKIST) and space-born, e.g., from Hinode and the Solar Dynamics Observatory. If we can obtain accurate force-free coronal magnetic field models we can calculate the free magnetic energy in the corona, a quantity which is important for the prediction of flares and coronal mass ejections. Knowledge of the 3D structure of magnetic field lines also help us to interpret other coronal observations, e.g., EUV images of the radiating coronal plasma.

Simulating the Coronal Evolution of Bipolar Active Regions to Investigate the Formation of Flux Ropes

The coronal magnetic field evolution of 20 bipolar active regions (ARs) is simulated from their emergence to decay using the time-dependent nonlinear force-free field method of Mackay, Green, and van Ballegooijen (Astrophys. J. 729, 97, 2011). A time sequence of cleaned photospheric line-of-sight magnetograms, which covers the entire evolution of each AR, is used to drive the simulation. A comparison of the simulated coronal magnetic field with the 171 and 193 Å observations obtained by the Solar Dynamics Observatory (SDO)/Atmospheric Imaging Assembly (AIA), is made for each AR by manual inspection. The results show that it is possible to reproduce the evolution of the main coronal features such as small- and large-scale coronal loops, filaments and sheared structures for 80% of the ARs. Varying the boundary and initial conditions, along with the addition of physical effects such as Ohmic diffusion, hyperdiffusion and a horizontal magnetic field injection at the photosphere, improves the match between the observations and simulated coronal evolution by 20%. The simulations were able to reproduce the build-up to eruption for 50% of the observed eruptions associated with the ARs. The mean unsigned time difference between the eruptions occurring in the observations compared to the time of eruption onset in the simulations was found to be ≈5 hrs. The simulations were particularly successful in capturing the build-up to eruption for all four eruptions that originated from the internal polarity inversion line of the ARs. The technique was less successful in reproducing the onset of eruptions that originated from the periphery of ARs and large-scale coronal structures. For these cases global, rather than local, nonlinear force-free field models must be used. While the technique has shown some success, eruptions that occur in quick succession are difficult to reproduce by this method and future iterations of the model need to address this.

Particle Acceleration Driven by Null Electromagnetic Fields Near a Kerr Black Hole

Short timescale variability is often associated with a black hole system. The consequence of an electromagnetic outflow suddenly generated near a Kerr black hole is considered assuming that it is described by a solution of a force-free field with a null electric current. We compute charged particle acceleration induced by the burst field. We show that the particle is instantaneously accelerated to the relativistic regime by the field with a very large amplitude, which is characterized by a dimensionless number κ. Our numerical calculation demonstrates how the trajectory of the particle changes with κ. We also show that the maximum energy increases with κ2/3. The typical maximum energy attained by a proton for an event near a super massive black hole is Emax∼100 TeV, which is enough observed high-energy flares.

Preprocessing of vector magnetograms for magnetohydrostatic extrapolations

Context. Understanding the 3D magnetic field as well as the plasma in the chromosphere and transition region is important. One way is to extrapolate the magnetic field and plasma from the routinely measured vector magnetogram on the photosphere based on the assumption of the magnetohydrostatic (MHS) state. However, photospheric data may be inconsistent with the MHS assumption. Therefore, we must study the restriction on the photospheric magnetic field, which is required by the MHS system. Moreover, the data should be transformed accordingly before MHS extrapolations can be applied. Aims. We aim to obtain a set of surface integrals as criteria for the MHS system and use this set of integrals to preprocess a vector magnetogram. Methods. By applying Gauss’ theorem and assuming an isolated active region on the Sun, we related the magnetic energy and forces in the volume to the surface integral on the photosphere. The same method was applied to obtain restrictions on the photospheric magnetic field as necessary criteria for a MHS system. We used an optimization method to preprocess the data to minimize the deviation from the criteria as well as the measured value. Results. By applying the virial theorem to the active region, we find the boundary integral that is used to compute the energy of a force-free field usually underestimates the magnetic energy of a large active region. We also find that the MHS assumption only requires the x-, y-component of net Lorentz force and the z-component of net torque to be zero. These zero components are part of Aly’s criteria for a force-free field. However, other components of net force and torque can be non-zero values. According to new criteria, we preprocess the magnetogram to make it more consistent with the MHS system and, at the same time close, to the original data.