During the eruptions, a commonly observed physical structure is magnetic flux rope (Burlaga et al 1988, Lepping et al 1990). It is a volumetric current channel with wrapped fieldlines around its central axis. Its preexistence, formation and role in eruptions are not well understood because it is believed that magnetic reconnection plays the main role and flux rope is treated as secondary.

Recent direct evidences of the flux rope come into existence as a conspicuous channel structure in the inner corona of the AR before and during a solar eruption (Zhang et al. 2012, Vemareddy et al 2012, and see Figure 1). This channel initially appears as a twisted and writhed sigmoidal structure in high temperature passbands. The channel evolves toward a semi-circular shape in the slow rise phase and then erupts upward rapidly in the impulsive acceleration phase, producing the front-cavity core components of the resulting CME (Zhang et al. 2012). The role of this hot channel in the eruption process is similar to that of flux rope in many numerical models (e.g., Aulanier et al. 2010; Fan & Gibson 2007) reproducing key features of eruptions. Filament channels are also regarded as flux ropes, which were recently recognized by Atmospheric Imaging Assembly onboard Solar Dynamics Observatory.

Under the line-tied assumption, the field lines anchors from the photosphere. These field lines build stress by continuous slow plasma motions, which include vertical and horizontal motions. These motions are believed to be prime factors of complexity of magnetic field and its energy buildup.

Magnetic helicity is an important topological property of solar active regions (ARs) and is a measure of twist and writhe of the field lines (Berger & Field 1984; Finn & Antonsen 1985). To derive the time rate of helicity injection by these plasma motions, time sequence of photospheric magnetic field are being used. In a study of three emerging ARs (Vemareddy 2015), we found that the coronal helicity flux is dominantly coming from the shear term that is related to horizontal flux motions, whereas energy flux is dominantly contributed by the emergence term. Moreover, the ARs with same sign of Helicity-flux over time are found to launch CMEs but NOT in the one with helicity flux changing sign over time. And the non-linear curve of coronal energy vs helcity is approximately fitted with linear force-free model.

During the evolution of ARs, the sunspots exhibit proper as well as rotational motions, believed to be associated with the storage of energy by increasing the magnetic non-potentiality and eventual release in the form of observed eruptive events. We studied the rotating sunspots in AR 11158 and their probable role in the observed activity. Figure 2(a) shows a huge coronal mass ejection pointed by arrow on February 14, 2011. The rectangular region in top-left panel is shown in panel (top-right) in continuum intensity observed by Heliosiesmic Magnetic Imager with the labeled sunspots. We have noticed intrinsic rotation of sunspots SN1 and SP1 by scrutinizing animations of these images. The sunspot SN1 is remapped to polar coordinate system to have the information about these rotational parameters like angular distance (θ) and angular velocity (dθ/dt) with respect to time. In bottom-right panel, we have plotted these parameters with respect to time, delineates that at maximum rotational speeds the CMEs occurred.

We further estimated various physical parameters representing non-potential nature as the AR evolves. The temporal profiles of twist parameters, namely, average shear angle, aav, abest, derived from HMI vector magnetograms, and the rate of helicity injection, obtained from the horizontal flux motions of HMI line-of-sight magnetograms, correspond well with the rotational profile of the sunspot in the CME-prone region, giving predominant evidence of rotational motion causing magnetic non-potentiality. Moreover, the mean value of free energy from the virial theorem calculated at the photospheric level shows a clear step-down decrease at the onset time of the flares revealing unambiguous evidence of energy release intermittently that is stored by flux emergence and/or motions in pre-flare phases. Additionally, distribution of helicity injection is homogeneous in the CME-prone region while in the flare-prone region it is not and often changes sign. This study provides a clear picture that both proper and rotational motions of the observed fluxes played significant roles in enhancing the magnetic non-potentiality of the AR by injecting helicity, twisting the magnetic fields and thereby increasing the free energy, leading to favourable conditions for the observed transient activity. [Ref: Vemareddy et al, 2012, Astrophys. J, 761, 60]

During the AR evolution, build-up of energy in the corona takes places through flux emergence and displacements for days (Schrijver 2009). Under these circumstances, the characteristic time of propagation of Alfven waves through the whole region is much less than the corresponding time of the global evolution of the AR, so that the dynamical effect is negligible. Moreover, the pressure and weight of plasma are also negligible in comparison with the magnetic pressure and tension, which therefore counterbalance each other to vanishing Lorentz force. Therefore, this slow change of AR evolution can be approximated by series of quasi-stationary, force-free equilibrium states in the low-plasma beta coronal environment.

Using HMI magnetic field measurements as bottom boundary conditions, we modelled the coronal magnetic field of AR 11166 around the time of X1.5 flare occurence. The magnetic structure reveals a null point topology with dome-like fan saperatrix surface and tail-like spine connecting remote ribbons (Vemareddy & Wiegelmann 2014). Fan-separatrix surface intersects the photosphere along the observed flare ribbons. It suggests that the reconnection triggers at the pre-existing null point, from where particles impinge along field lines to form chromospheric flare ribbons.

Electric currents in the astrophysical plasmas are generated by distortion of the magnetic field by external forces applied by field free plasma (Parker 1979). In the Sun, these currents enter the corona through embedded emerging magnetic fields from the convection zone to the corona through the photosphere. Despite their generation mechanisms, these currents are believed to play vital role in the magnetic solar eruptions. However, the Parker's theoretical prediction (Parker 1996) of neutralized net vertical current over a cross-section of flux tube at the photosphere is inconsistent to their role in eruptions. In many studied ARs (Ravindra et al 2012, Georgoulis et al 2012, Vemareddy et al 2015), however the observance of the non-neutralized net current is therefore needs proper explanation.

Breakdown of net current neutralisation has implications to CME activity from the AR. The hoop-force of CME flux rope is proportional to square of the net current in the flux rope channel (Zakharov & Shafranov 1989), which is the algebraic sum of net direct current (DC) and return current (RC). The equilibrium and stability properties of the flux rope then requires the neutralisation of net current for which hoop force vanishes. Numerical simulations showed that a major breakdown occurs during emerging phase of AR (Torok et al 2014), during which opposite polarity regions are compact with a sheared PIL. Observational studies also found that the sheared PIL is the major contributor to DC and proposed the degree of current-neutralisation as the proxy for assessing the ability of ARs to produce CMEs (Liu et al 2017).

Using HMI photospheric vector magnetic field, we can only measure vertical component of electric current from Ampere's Law. In Figure 6, we plot the ratio of |DC/RC| (blue) in both polarities of flaring-only AR 11166 and CME-rich AR 12371. The evolution of this ratio is well above unity due to highly non-neutralized current in AR12371, whereas it is near unity indicating nearly neutralized currents in AR 11166. The red curve is the |DC/RC| for twist current, which follows above that of net current (blue). This is due to the fact first found in Vemareddy (2017) that the twist current is opposite in sign dominantly to that of shear current, which comes from gradient of field strength. From a study of 20 ARs of different activity, we conclude that the non-neutralised currents arise from sheared polarity inversion lines, whose segmented nature links to the flare/CME activity in the AR. (Ref: Vemareddy 2019, MNRAS)

Magnetic clouds (MCs) are large scale, organised magnetic structures in interplanetary space which are observed in situ as interplanetary coronal mass ejection (ICMEs).They are generally preceded by the occurrence of major coronal mass ejections (CMEs) at the Sun. It is now believed and shown from a variety of independent studies that MCs are magnetic flux ropes (MFRs) of locally straight cylindrical geometry (Burlaga 1988, Shodhan et al 2000, Liu et al 2008, Gopalaswamy et al 2013a). In this picture (see Figure 11), the MC is thought to be part of a large-scale bent flux rope extending from the Sun into interplanetary space with its feet possibly still connected to the Sun (Burlaga et al 1990, Bothmer and Schwenn 1998, Ferrugia et al 1993b, Schwenn 1998, Webb et al 2000). From the point of Sun-Earth connection, a major interesting, important question is how the solar source regions are connected to the in situ MCs, which should lead to important clues on how to forecast the internal magnetic field of CMEs around Earth and other planets.

A MC passage through the space-craft in in-situ is generally identified by a strong magnetic field strength, low plasma beta, and rotation of any magnetic field component (reversal of sign during passage). In the flux rope scenario, cylindrically symmetric force-free models fit the in-situ MC observations well (see Figure 12). Since the direction of axial component (southward/northward) in MC decides the occurence of geo-magnetic storms, it is crucial to determine the orientation of the flux rope and its axial field polarity.

In the above flux rope scenario, MC magnetic field observations are fitted (Figure 4) with Cylindrically symmetric constant linear force-free Lundquist model (solid red) and non-linear force-free Gold-Hoyle (dashed blue) models. A recent study (Vemareddy et al 2016) found that Gold-Hoyle models best fits the observations, in terms of chisquare, especially when MC expansion is accounded in the model.

Active regions (ARs) with sigmoidal structure, generally seen in soft X-rays and EUV, are prone to CME-eruptions and associated flares. Some ARs show rapid succession of CMEs and flares over a timescale of few hours. Because the timescale is too small compared to typical timescale for energy build-up in ARs, emergence of magnetic flux was suggested to be responsible for repeated CMEs of such short timescale. On the other hand, successive CMEs also occur from ARs in a timescale comparable to energy build-up by footpoint motions in the post emergence phase. The velocity field derived from tracked magnetograms indicates frequently persistent shear and converging motions of polarity regions about the polarity inversion line. These motions introduce huge amounts of magnetic energy and helicity in the AR magnetic system enabling flares and CMEs. While stored energy configuration is vital, the persistence of sigmoidal structure is the central feature for the successive CME occurrence from a source AR and had been the central subject for eruptive activity.

AR 12371 is in post-emerged phase producing successive fast CMEs in a span of its disk transit (18-25 June, 2015). EUV observations at the Sun register the initiation times of four eruptions as 15:05UT on 18 (CME1), 00:45UT on 21 (CME2), 16:15UT on 22 (CME3), and 07:30UT on 25 (CME4) of June 2015, respectively. Subsequently, the disk integrated GOES X-ray light curve (Figure 6a) delineates that the CMEs are associated with long duration M-class flares. The EUV double dimming, three-part CME structure, and fast propagation speeds in LASCO FOV (>1000kms^-1) altogether characterize the CMEs as homologous events.

The magnetic evolution in this AR is summarised in Figure 6. The region of sigmoid is seen with persistent shearing and converging motions of opposite magnetic polarities over 7-days of evolution. At the same time, the net flux decreases over time (24%) with the build-up of magnetic twist (till 22nd June). The helicity flux, derived from footpoint motions, is negative and co-spatial with the coronal sigmoid. This implies qualitatively that the pumped helicity flux is being utilised in the repeated build-up of sheared core along the polarity inversion line. Besides injection helicity flux, the energy flux injection by flux motions is above 5x10²⁷ ergs/s, which amounts to that required by a fast CME (~10³³ergs) over about 50hours. Importantly, the normalised helicity flux is moderately high (0.15turns) compared to non-eruptive super AR 12192 (0.02 turns). A high value of magnetic flux normalized helicity flux typically suggests presence of a coherent twisted field.

Force-free models of the AR are computed from the observed photospheric magnetic field. The computed magnetic structures reproduce the EUV sigmoid mostly with sheared arcades. Especially, the core-field is a combination of double inverse J-shaped and inverse S-shaped field lines with dips touching the photosphere. Such field-lines are formed by flux cancellation reconnection of opposite-J field-lines at bald-patch locations (where field-lines are tangent to the photosphere and curved upward (Figure 7). This study demonstrates the formation of a weakly twisted flux-rope from large scale sheared arcade field-lines. Further, our study infers a steep decrease of the background coronal field meeting the torus instability criteria at low height (~40Mm) in contrast to non-eruptive ARs. When the magnetic field becomes torus unstable, the weakly twisted flux rope is upward destabilised. This induces further reconnection below the flux rope and leads to a CME as the overlying magnetic field is weak. A new, but similar, stressed magnetic configuration is next reformed by photospheric motions leading to the repetition of the above scenario. This induces a series of homologous CMEs/flares. Finally, the modelled structure captured the major features sigmoid-to-arcade-to-sigmoid transformation, that is being cyclic under continuous photospheric flux motions. (also appeared as RHESSI sceince nugget)

Magnetic helicity is believed to play a fundamental role in generating large-scale activity on the Sun. Magnetic helicity describes the magnetic field complexity, including twist, writhe, knot, and linkages of magnetic field. When coronal magnetic field is being pumped with helicity and energy, the magnetic complexity and non-potentiality increases. Using simultaneous magnetic field and coronal observations, several studies focused on the magnetic non-potential parameters to understand their roles in CMEs and flares. From those studies, it is now believed that the magnetic flux rope is built up by line-tied photospheric flux motions, such as magnetic flux emergence or horizontal flows. These processes inject magnetic helicity into the higher solar atmosphere, increasing the twist and kink of a flux rope (self-helicity) and the linkage between different flux ropes (mutual helicity). Magnetic helicity is conserved in an ideal MHD process and changes very slowly in a resistive process[1]. Thus, a flux rope with continuous injection of magnetic helicity inevitably erupts to remove the accumulated helicity, manifested as a CME.

The above scenario of helicity role in the AR eruptivity is well portrayed in a recent study. Using the uninterrupted observations of space-borne Solar Dynamics Observatory, we studied the most violent AR 12673 that produced strongest flares in Solar Cycle 24. The AR emerged with two bipolar regions on September 2, 2017 in a pre-existing positive-polarity sunspot. The velocity field derived from tracked vector-magnetograms indicates persistent shear and converging motions of flux regions about the polarity inversion line (PIL). In Figure 8, the time evolution of the X-ray flux, net-electric current, helicity, energy flux injection are shown. A major helicity injection occurs during rapid flux emergence, consistent with the very fast flux emergence phase. While this helicity flux builds up the sigmoid by September 4, the helicity injection by the continued shear and converging motions in the later evolution contributes to the sigmoid sustenance and its core field twist, as a manifestation of the flux rope that erupts after exceeding critical value of twist. Moreover, the total length of the sheared PIL segments correlates with the non-neutralized currents and maintains a higher value in both polarity regions as a signature of eruptive capability of the AR, according to flux rope models. This result also implies that the non-neutralized currents arise in the vicinity of the sheared PIL. In Figure 9, an example of force-free extrapolation to the AR 12673 is displayed. The modeled magnetic structure well resembles the coronal observation of AIA 94Å, capturing major features like twisted core flux as flux rope, and hook-shaped sections connecting in the middle of the PIL. The emission in 304Å is also reproduced in vertical integration of volume electric current. The study of quasi-separatrix-layers reveals that the sheared arcade, enclosing the flux rope, is stressed to a critically stable state and its coronal height becomes doubled from September 4-6.

In order to have more insight on the helicity flux input, we compare normalized helicity flux injection (dH/dt/Φ²) from different ARs (Figure 10). This value is a measure of non-potentiality per unit flux per unit time and indicates how fast the AR accumulates energy and helicity in the corona. As is clear from the plot, this parameter evolves at a higher rate by a factor of 3 in AR 12673 compared to other ARs. The AR 12192 is a flare-prolific region without CMEs in contrast to the rest of the ARs[4], and has small injection value per flux tube. Interestingly, this value in the AR 12673 is quite stronger by a factor of 2 than the strong CME-prolific ARs 12371 and AR11429. This suggests that the normalized helicity flux is a key parameter to distinguish eruptive and non-eruptive ARs and also predicts the severe space-weather events. (also appeared as HMI sceince nugget)