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Evolution of angle of rotation φ for both the red and blue fieldlines as depicted in Figures 5a and 5b.
Source publication
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 o...
Contexts in source publication
Context 1
... Figure 7 a schematic has been included to help us visualise the meaning of the angle φ. Through the use of equation (9), the angle φ has been calculated for both the red and blue fieldline as displayed in Figure 8. As the two chosen fieldlines were initially Next, we consider the temporal rate of change of the angle of rotation, i.e. dφ/dt, as shown in Figure 9. ...
Context 2
... further investigate the magnetic helicity in the atmosphere we have calculated the time derivative of the magnetic helic- ity above the photosphere, both numerically using finite differ- encing and analytically. This helps us to understand the main Fig. 18: Evolution of the time derivative of the relative helicity H r when calculated above z = 0 in the solar atmosphere us- ing equation (13). The total time derivative (black solid line) is split into the dissipation term (purple solid line), the surface cor- rection term (yellow solid line), the shear term (red solid line) and emergence ...
Context 3
... first term on the right-hand side of equation (13) relates to the depletion of helicity by internal dissipation (dissipation term), the second corresponds to a surface correction to the re- sistive dissipation (surface correction term) , the third relates to the generation of helicity by horizontal motions of the boundary (shear term) and the last corresponds to the injection of helicity by direct emergence (emergence term). Let us consider the rate of change of atmospheric helicity in Figure 18. From the point the field emerges until t = 45, the helicity flux due to emergence (blue solid line) dominates the change in helicity. ...
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Citations
... One remarkable feature of the developed sunspots is their continued rotation. In the strong twist case, the two sunspots rotate in the same clockwise direction because the flux tube, endowed initially with right-handed torsion, releases its twist as it appears in the photosphere 36,44,45 . Observations show that many more flaring active regions show rotations of bipolar sunspots in the same directions than in the opposite directions 46 . ...
... This indicates that the local vortices streaming into the downflow plumes spin the magnetic pillars and drive the sunspot rotations in the photosphere. If the sunspot rotation is because of the release of magnetic twists, the two magnetic pillars (sunspots in the photosphere) should rotate in the same direction 44,45 . However, this is not the case. ...
Solar flares and coronal mass ejections, the primary space weather disturbances affecting the entire heliosphere and near-Earth environment, mainly emanate from sunspot regions harbouring high degrees of magnetic twist. However, it is not clear how magnetic helicity, the quantity for measuring the magnetic twist, is supplied to the upper solar atmosphere via the emergence of magnetic flux from the turbulent convection zone. Here, we report state-of-the-art numerical simulations of magnetic flux emergence from the deep convection zone. By controlling the twist of emerging flux, we find that with the support of convective upflow, the untwisted emerging flux can reach the solar surface without collapsing, in contrast to previous theoretical predictions, and eventually create sunspots. Because of the turbulent twisting of magnetic flux, the produced sunspots exhibit rotation and inject magnetic helicity into the upper atmosphere, amounting to a substantial fraction of injected helicity in the twisted cases that is sufficient to produce flare eruptions. This result indicates that the turbulent convection is responsible for supplying a non-negligible amount of magnetic helicity and potentially contributes to solar flares.
... The clockwise rotation at the photosphere reduced the positive magnetic helicity of the flux tube in the convection zone, and increased the positive helicity over the photosphere, transporting the positive helicity from the convection zone to the corona. This motion is consistent with the previous numerical experiments without convection (Fan 2009;Sturrock et al. 2015) and with convection (Toriumi & Hotta 2019). twist to the writhe. ...
... In the cases where the flux tubes were trapped by the downflow plume, the -type magnetic distribution with the strong nonpotential field was created in the photosphere due to the collision of positive and negative fluxes. The previous studies (Fan 2009;Sturrock et al. 2015;Toriumi & Hotta 2019) found the unipolar rotation of the sunspots transporting the magnetic helicity from the convection zone to the corona. We newly found the bipolar rotation of the -spots whose direction is opposite to the unipolar rotation. ...
Strong solar flares occur in $\delta $-spots characterized by the opposite-polarity magnetic fluxes in a single penumbra. Sunspot formation via flux emergence from the convection zone to the photosphere can be strongly affected by convective turbulent flows. It has not yet been shown how crucial convective flows are for the formation of $\delta$-spots. The aim of this study is to reveal the impact of convective flows in the convection zone on the formation and evolution of sunspot magnetic fields. We simulated the emergence and transport of magnetic flux tubes in the convection zone using radiative magnetohydrodynamics code R2D2. We carried out 93 simulations by allocating the twisted flux tubes to different positions in the convection zone. As a result, both $\delta$-type and $\beta$-type magnetic distributions were reproduced only by the differences in the convective flows surrounding the flux tubes. The $\delta $-spots were formed by the collision of positive and negative magnetic fluxes on the photosphere. The unipolar and bipolar rotations of the $\delta$-spots were driven by magnetic twist and writhe, transporting magnetic helicity from the convection zone to the corona. We detected a strong correlation between the distribution of the nonpotential magnetic field in the photosphere and the position of the downflow plume in the convection zone. The correlation could be detected $20$-$30$ h before the flux emergence. The results suggest that high free energy regions in the photosphere can be predicted even before the magnetic flux appears in the photosphere by detecting the downflow profile in the convection zone.
... In all but two cases, the rotation of sunspots is slowed down for several hours after an X-class flare, which would suggest that some of the energy in the rotating spots is being released in the flare as the overlying magnetic field is reconfigured. Estimations of the magnetic energy contributed by the sunspot rotations are of the same order of magnitude as the energies of subsequent flares, as noted by Li and Liu (2015), Liu et al. (2016), Sturrock et al. (2015), which could result in a decreased rotational velocity post-flare. Furthermore, the effect of the back-reaction from reconnection events on long-timescale rotations has not been established. ...
Sunspot rotations are closely linked with flaring activity. They are thought to contribute to the accumulation of helicity in magnetic flux tubes and to triggering magnetic reconnection in large solar flares. This link to solar flares has led to sunspot rotations being used as a parameter in solar flare prediction methods, but analysis for long-period observations of rotations in the literature is scarce. In this study, the rotation profiles of sunspots in a selection of six active regions are studied over time periods of 5 – 10 days to measure how sunspot rotation varies as active regions develop. The active regions are divided into two categories: high-flaring groups, which produced at least one X-class flare, and low-flaring regions that had little flaring activity. Comparison of the rotation profiles in these regions showed that young complex sunspot groups exhibit faster angular velocities and more frequent changes in rotation than older single-spot groups and, although the most rotating groups were also the most flare-productive, sudden changes in rotation were found to not definitively indicate an imminent eruption.
... That rotation is likely associated with an underlying large-scale twisted flux tube rising through the photosphere (e.g. Sturrock et al., 2015), and the helicity that enters the solar atmosphere on all scales from below has important implications for the structure and behavior of the field there. ...
The National Science Foundation’s Daniel K. Inouye Solar Telescope (DKIST) will revolutionize our ability to measure, understand, and model the basic physical processes that control the structure and dynamics of the Sun and its atmosphere. The first-light DKIST images, released publicly on 29 January 2020, only hint at the extraordinary capabilities that will accompany full commissioning of the five facility instruments. With this Critical Science Plan (CSP) we attempt to anticipate some of what those capabilities will enable, providing a snapshot of some of the scientific pursuits that the DKIST hopes to engage as start-of-operations nears. The work builds on the combined contributions of the DKIST Science Working Group (SWG) and CSP Community members, who generously shared their experiences, plans, knowledge, and dreams. Discussion is primarily focused on those issues to which DKIST will uniquely contribute.
... The emergence of a single sub-photospheric flux tube typically leads to the formation of a bipolar region, whose polarities separate over time. Photospheric motions commonly found in the vicinity of the region's PIL include: (i) shearing along the PIL, resulting from the Lorentz force developed at the photosphere due to the expansion of the emerging field (e.g., Fan, 2001;Manchester, 2001), (ii) rotation of the polarities driven by the propagation of a torsional Alfvén wave into the atmosphere (e.g., Longcope and Klapper, 1997;Fan, 2009b;Leake et al, 2013;Sturrock et al, 2015;Sturrock and Hood, 2016), and (iii) downflow of plasma towards the low-pressure region above the PIL as discussed above (e.g., Manchester et al, 2004). The combination of these motions induces converging flows towards the PIL (e.g., Archontis and Hood, 2010;Syntelis et al, 2017), which ultimately lead to the formation of an MFR. ...
A clear understanding of the nature of the pre-eruptive magnetic field configurations of Coronal Mass Ejections (CMEs) is required for understanding and eventually predicting solar eruptions. Only two, but seemingly disparate, magnetic configurations are considered viable; namely, sheared magnetic arcades (SMA) and magnetic flux ropes (MFR). They can form via three physical mechanisms (flux emergence, flux cancellation, helicity condensation). Whether the CME culprit is an SMA or an MFR, however, has been strongly debated for thirty years. We formed an International Space Science Institute (ISSI) team to address and resolve this issue and report the outcome here. We review the status of the field across modeling and observations, identify the open and closed issues, compile lists of SMA and MFR observables to be tested against observations and outline research activities to close the gaps in our current understanding. We propose that the combination of multi-viewpoint multi-thermal coronal observations and multi-height vector magnetic field measurements is the optimal approach for resolving the issue conclusively. We demonstrate the approach using MHD simulations and synthetic coronal images.
Our key conclusion is that the differentiation of pre-eruptive configurations in terms of SMAs and MFRs seems artificial. Both observations and modeling can be made consistent if the pre-eruptive configuration exists in a hybrid state that is continuously evolving from an SMA to an MFR. Thus, the ‘dominant’ nature of a given configuration will largely depend on its evolutionary stage (SMA-like early-on, MFR-like near the eruption).
... The emergence of a single sub-photospheric flux tube typically leads to the formation of a bipolar region, whose polarities separate over time. Photospheric motions commonly found in the vicinity of the region's PIL include: (i) shearing along the PIL, resulting from the Lorentz force developed at the photosphere due to the expansion of the emerging field (e.g., Fan 2001;Manchester 2001), (ii) rotation of the polarities driven by the propagation of a torsional Alfvén wave into the atmosphere (e.g., Longcope and Klapper 1997;Fan 2009b;Leake et al. 2013;Sturrock et al. 2015;Sturrock and Hood 2016), and (iii) downflow of plasma towards the low-pressure region above the PIL as discussed above (e.g., Manchester et al. 2004). The combination of these motions induces converging flows towards the PIL (e.g., Archontis and Hood 2010; Syntelis et al. 2017), which ultimately lead to the formation of an MFR. ...
A clear understanding of the nature of the pre-eruptive magnetic field configurations of Coronal Mass Ejections (CMEs) is required for understanding and eventually predicting solar eruptions. Only two, but seemingly disparate, magnetic configurations are considered viable; namely, sheared magnetic arcades (SMA) and magnetic flux ropes (MFR). They can form via three physical mechanisms (flux emergence, flux cancellation, helicity condensation) . Whether the CME culprit is an SMA or an MFR, however, has been strongly debated for thirty years. We formed an International Space Science Institute (ISSI) team to address and resolve this issue and report the outcome here. We review the status of the field across modeling and observations, identify the open and closed issues, compile lists of SMA and MFR observables to be tested against observations and outline research activities to close the gaps in our current understanding. We propose that the combination of multi-viewpoint multi-thermal coronal observations and multi-height vector magnetic field measurements is the optimal approach for resolving the issue conclusively. We demonstrate the approach using MHD simulations and synthetic coronal images. Our key conclusion is that the differentiation of pre-eruptive configurations in terms of SMAs and MFRs seems artificial. Both observations and modeling can be made consistent if the pre-eruptive configuration exists in a hybrid state that is continuously evolving from an SMA to an MFR. Thus, the 'dominant' nature of a given configuration will largely depend on its evolutionary stage (SMA-like early-on, MFR-like near the eruption).
... Observations of sunspots show that they rotate as they emerge (e.g., Evershed, 1909;Brown et al., 2003). That rotation is likely associated with an underlying large-scale twisted flux tube rising through the photosphere (e.g., Sturrock et al., 2015), and the helicity that enters solar atmosphere on all scales from below is important for the structure and behavior of the field there. ...
The Daniel K. Inouye Solar Telescope (DKIST) will revolutionize our ability to measure, understand and model the basic physical processes that control the structure and dynamics of the Sun and its atmosphere. The first-light DKIST images, released publicly on 29 January 2020, only hint at the extraordinary capabilities which will accompany full commissioning of the five facility instruments. With this Critical Science Plan (CSP) we attempt to anticipate some of what those capabilities will enable, providing a snapshot of some of the scientific pursuits that the Daniel K. Inouye Solar Telescope hopes to engage as start-of-operations nears. The work builds on the combined contributions of the DKIST Science Working Group (SWG) and CSP Community members46, who generously shared their experiences, plans, knowledge and dreams. Discussion is primarily focused on those issues to which DKIST will uniquely contribute.
... The first one is the depth where the initial flux tube is placed; both the simulations we used here have a flux tube placed near the solar surface, while with a flux tube placed much deeper in the interior, it can expand and stretch with more time to relax during its rising and should become more forcefree than initially(e.g., Toriumi & Yokoyama 2011;Syntelis et al. 2019). The second one is the twist degree of the initial flux tube; stronger twist can of course create increased torque during its emerging in the photosphere (Sturrock et al. 2015;Sturrock & Hood 2016). The third one might be attributed to geometry of the emerging tube and how it couples with twist and the size of the flux tube, which has been discussed in Syntelis et al. (2019). ...
Magnetic flux generated and intensified by the solar dynamo emerges into the solar atmosphere, forming active regions (ARs) including sunspots. Existing theories of flux emergence suggest that the magnetic flux can rise buoyantly through the convection zone but is trapped at the photosphere, while its further rising into the atmosphere resorts to the Parker buoyancy instability. To trigger such an instability, the Lorentz force in the photosphere needs to be as large as the gas pressure gradient to hold up an extra amount of mass against gravity. This naturally results in a strongly non-force-free photosphere, which is indeed shown in typical idealized numerical simulations of flux tube buoyancy from below the photosphere into the corona. Here we conduct a statistical study of the extents of normalized Lorentz forces and torques in the emerging photospheric magnetic field with a substantially large sample of Solar Dynamics Observatory/Helioseismic and Magnetic Imager vector magnetograms. We found that the photospheric field has a rather small Lorentz force and torque on average, and thus is very close to a force-free state, which is not consistent with theories as well as idealized simulations of flux emergence. Furthermore, the small extents of forces and torques seem not to be influenced by the emerging AR’s size, the emergence rate, or the nonpotentiality of the field. This result puts an important constraint on future development of theories and simulations of flux emergence.
... The first one is the depth where the initial flux tube is placed; both the simulations we used here have a flux tube placed near the solar surface, while with a flux tube placed much deeper in the interior, it can expand and stretch with more time to relax during its rising and should become more force-free than initially (e.g., Toriumi & Yokoyama 2011;Syntelis et al. 2019). The second one is the twist degree of the initial flux tube; stronger twist can of course create increased torque during its emerging in the photosphere (Sturrock et al. 2015;Sturrock & Hood 2016). The third one might be attributed to geometry of the emerging tube and how it couples with twist and the size of the flux tube, which has been discussed in Syntelis et al. (2019). ...
Magnetic flux generated and intensified by the solar dynamo emerges into the solar atmosphere, forming active regions (ARs) including sunspots. Existing theories of flux emergence suggest that the magnetic flux can rise buoyantly through the convection zone but is trapped at the photosphere, while its further rising into the atmosphere resorts to the Parker buoyancy instability. To trigger such an instability, the Lorentz force in the photosphere needs to be as large as the gas pressure gradient to hold up an extra amount of mass against gravity. This naturally results in a strongly non-force-free photosphere, which is indeed shown in typical idealized numerical simulations of flux tube buoyancy from below the photosphere into the corona. Here we conduct a statistical study of the extents of normalized Lorentz forces and torques in the emerging photospheric magnetic field with a substantially large sample of SDO/HMI vector magnetograms. We found that the photospheric field has a rather small Lorentz force and torque on average, and thus is very close to a force-free state, which is not consistent with theories as well as idealized simulations of flux emergence. Furthermore, the small extents of forces and torques seem not to be influenced by the emerging AR's size, the emergence rate, or the non-potentiality of the field. This result puts an important constraint on future development of theories and simulations of flux emergence.
... Here we follow the computation method by Valori et al. (2012) for a Cartesian domain V=[x 1 , x 2 ]×[y 1 , y 2 ]×[z 1 , z 2 ], and the notations below are based on Sturrock et al. (2015). Because H R is gauge invariant, we are free to choose the gauge = A z 0 ·ˆsuch that it satisfies (165,165,330) for all the other cases. ...
For a better understanding of the magnetic field in the solar corona and dynamic activities such as flares and coronal mass ejections, it is crucial to measure the time-evolving coronal field and accurately estimate the magnetic energy. Recently, a new modeling technique called the data-driven coronal field model, in which the time evolution of magnetic field is driven by a sequence of photospheric magnetic and velocity field maps, has been developed and revealed the dynamics of flare-productive active regions. Here we report on the first qualitative and quantitative assessment of different data-driven models using a magnetic flux emergence simulation as a ground-truth (GT) data set. We compare the GT field with those reconstructed from the GT photospheric field by four data-driven algorithms. It is found that, at minimum, the flux rope structure is reproduced in all coronal field models. Quantitatively, however, the results show a certain degree of model dependence. In most cases, the magnetic energies and relative magnetic helicity are comparable to or at most twice of the GT values. The reproduced flux ropes have a sigmoidal shape (consistent with GT) of various sizes, a vertically standing magnetic torus, or a packed structure. The observed discrepancies can be attributed to the highly non-force-free input photospheric field, from which the coronal field is reconstructed, and to the modeling constraints such as the treatment of background atmosphere, the bottom boundary setting, and the spatial resolution.
