P. Vemareddy
Indian Institute of Astrophysics, Bangalore-560034, India
Magnetic flux ropes (MFRs) are energized twisted magnetic fields often visible in the solar atmosphere. These structures are unstable to lose equilibrium resulting in their eruption as coronal mass ejections (CMEs). When a CME occurs, a large amount of magnetic field and plasma is expelled from the sun into the interplanetary medium, which interacts with the earth magnetosphere to cause potential space weather consequences. The conditions and evolution that lead to the formation and eruption of magnetic flux ropes in the solar atmosphere is one of the fundamental scientific interests.
Simulating the flux ropes realistically is a formidable task due to several observational and numerical difficulties. Aiming to capture the formation and eruption of flux ropes (FRs) in the source active regions (ARs), we simulate the coronal magnetic field evolution of the AR 11429 employing the data-driven magneto-friction (MF) model[1]. The AR was in decay phase, producing three successive CMEs in a time span of about two days during its disk passage[2,3]. The initial field is driven by electric fields that are derived from time-sequence photospheric vector magnetic field observations by invoking ad hoc assumptions[4]. We use high-cadence and high-resolution vector magnetic field observations of the photosphere obtained from Helioseismic and Magnetic Imager (HMI) onboard Solar Dynamics Observatory. From the time-derivatives of vector magnetic fields, the electric fields are obtained by solving the Faraday law of induction equation[5]. The input Poynting flux from the derived electric field is constrained by comparing the injection of magnetic energy and helicity from the photospheric observations.
Figure 1| Comparison of pre-eruptive simulated magnetic structure with the coronal plasma tracers in AIA images of the AR 11429. (a) top view of rendered magnetic structure at 45th hour of simulation R2. Background image is the Bz distribution at z=0. (b-c) AIA 304, 171 images at 2:00 UT on March 9. The morphology in these images depicts the structured corona of twisted flux rope that resembles the simulated magnetic field. Black arrow points to the eruptive filament manifested by the twisted field in the southwest region. (d-f) Perspective view of the rendered magnetic structure at 45, 65, and 92 hr, respectively. From the initial potential field, the structure evolves to sheared field forming a well-developed twisted flux rope forms in a timescale of two days, which then runs into slow explosive stage in the corona.
The simulations reproduce the magnetic structure that mimics the coronal extreme ultraviolet (EUV) imaging observations remarkably (Figure 1). The simulated magnetic structure evolves from a potential field to a twisted field over the course of two days, followed by rise motion in the later evolution, depicting the formation of an MFR and its slow eruption later. The initial potential field becomes sheared progressively forming inverse J-shaped field lines surrounding the low-lying twisted core field along the polarity inversion line (PIL). In a time scale of two days a well-developed twisted flux builds up along the PIL. Thereafter the twisted magnetic structure ascends in height with time, especially the field in the south-west region. This rise motion corroborates the observations of the eruption from the south-west region of the AR.
Figure 2| Comparison of proxy emission maps with the coronal EUV images. Top row: AIA 304 Å and 335 Å observations of the AR 11429. Middle row: proxy emission maps synthesized from the simulated magnetic field of R2 at the time instances of 30 hr and 50 hr. The white dashed line refers to the position of the vertical slice plane. Bottom row: proxy emission in the vertical slice plane captures the twisted flux rope and its upward motion in time. Axes units are in Mm.
For further comparison, we produce proxy emission maps of coronal loops similar to EUV images (Cheung & DeRosa 2012). These maps are derived with the values of square of the total current density (J2) averaged along a magnetic field line. From Figure 2, it can be noticed a striking morphological similarity of the modeled emission with the diffuse plasma emission of the sigmoid captured in the 335 Å image and a trace of the dark filament present in the 304 Å image. This filament is regarded as flux rope in the models, and it is expanding and rising in time as observed in the vertical cross-section planes. The proxy emission maps are useful for a qualitative visualization of coronal loops in a magnetic model such as MF, however, these should not be confused with the ones derived from the thermodynamic variables from MHD models.
Figure 3| Comparison of QSLs with flare ribbons. (a) Log(Q) map at z = 1.45 Mm computed from the magnetic structure of R2 at the 50 hr time instant. Contours of Bz at ±150 G are overdrawn (red/blue curves), and QSLs with large Q values are identified by intense white traces in the strong field region. (b)–(d) AIA 1600, 304, and 131 Å images overlaid with contours of ln(Q) = [5, 6] (in cyan/orange color). Note the intense flare ribbon emission underneath the erupting flux rope is co-spatial with the QSL section in the SW subregion.
Theoretical studies predict that the flare ribbons are the photospheric/chromospheric footprints of quasi-separatrix layers (QSLs) that enclose a twisted flux rope. From the simulated magnetic structure, we computed squashing factor (Q) as displayed in Figure 3(a). In order to compare QSLs locations with the flare ribbon emission, the AIA 1600 Å, 304 Å, and 131 Å observations during the impulsive phase of the flare are displayed in the panels of Figures 3(b)–(d), respectively. The QSLs are distributed co-spatially with the observed flare ribbons. The observed morphology of QSLs delineates an inverse S shape with co-spatial hooks in the extreme ends, therefore, the extent of the twist and orientation of the erupting flux rope are indicated to be consistent with the real scenario in this case.
Plasma motions at the photosphere drive the magnetic field and the coronal field evolves accordingly. So, the formation of these localized twisted structures is decided by the characteristic evolution of plasma motions at the surface. The data-driven simulations are more generic to invoke observed magnetic evolution at the surface and then model coronal field evolution consistent with multiwavelength observations of the corona. The procedures of this physical driving by observed data are developed in publicly available PENCIL code. These simulations serve as initial conditions for full MHD simulations that are used to study coronal thermal (heating) conditions and are helpful to understand the complex dynamics of plasma and magnetic fields at different spatial and time scales.
References:
[1] Vemareddy, P. 2024, ApJ, 975, 251
[2] Dhakal S. K., Zhang J., Vemareddy P. and Karna N. 2020, ApJ, 901, 40
[3] Vemareddy P. 2021, FrP, 9, 605
[4] Cheung M. C. M. and DeRosa M. L. 2012, ApJ, 757, 147
[5] Fisher G. H., Welsch B. T., Abbett W. P. and Bercik D. J. 2010, ApJ, 715, 242