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On the helicity of open magnetic fields  

Anthony Yeates   Submitted: 2014-04-16 01:59

We reconsider the topological interpretation of magnetic helicity for magnetic fields in open domains, and relate this to the relative helicity. Specifically, our domains stretch between two parallel planes, and each of these ends may be magnetically open. It is demonstrated that, while the magnetic helicity is gauge-dependent, its value in any gauge may be physically interpreted as the average winding number among all pairs of field lines with respect to some orthonormal frame field. In fact, the choice of gauge is equivalent to the choice of reference field in the relative helicity, meaning that the magnetic helicity is no less physically meaningful. We prove that a particular gauge always measures the winding with respect to a fixed frame, and propose that this is normally the best choice. For periodic fields, this choice is equivalent to measuring relative helicity with respect to a potential reference field. But for aperiodic fields, we show that the potential field can be twisted. We prove by construction that there always exists a possible untwisted reference field.

Authors: Prior, C., Yeates, A. R.
Projects: None

Publication Status: Accepted for publication in ApJ
Last Modified: 2014-04-16 13:13
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The coronal energy input from magnetic braiding  

Anthony Yeates   Submitted: 2014-04-16 01:57

We estimate the energy input into the solar corona from photospheric footpoint motions, using observations of a plage region by the Hinode Solar Optical Telescope. Assuming a perfectly ideal coronal evolution, two alternative lower bounds for the Poynting flux are computed based on field line footpoint trajectories, without requiring horizontal magnetic field data. When applied to the observed velocities, a bound based solely on displacements between the two footpoints of each field line is tighter than a bound based on relative twist between field lines. Depending on the assumed length of coronal magnetic field lines, the higher bound is found to be reasonably tight compared with a Poynting flux estimate using an available vector magnetogram. It is also close to the energy input required to explain conductive and radiative losses in the active region corona. Based on similar analysis of a numerical convection simulation, we suggest that observations with higher spatial resolution are likely to bring the bound based on relative twist closer to the first bound, but not to increase the first bound substantially. Finally, we put an approximate upper bound on the magnetic energy by constructing a hypothetical ``unrelaxed'' magnetic field with the correct field line connectivity.

Authors: Yeates, A.R., Bianchi, F., Welsch, B. T., Bushby, P. J.
Projects: Hinode/SOT

Publication Status: Accepted for publication in A&A
Last Modified: 2014-04-16 13:13
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Coronal Magnetic Field Evolution from 1996 to 2012: Continuous Non-Potential Simulations  

Anthony Yeates   Submitted: 2013-04-03 02:20

Coupled flux transport and magneto-frictional simulations are extended to simulate the continuous magnetic field evolution in the global solar corona for over 15 years, from the start of Solar Cycle 23 in 1996. By simplifying the dynamics, our model follows the build-up and transport of electric currents and free magnetic energy in the corona, offering an insight into the magnetic structure and topology that extrapolation-based models can not. To enable these extended simulations, we have implemented a more efficient numerical grid, and have carefully calibrated the surface flux transport model to reproduce the observed large-scale photospheric radial magnetic field, using emerging active regions determined from observed line-of-sight magnetograms. This calibration is described in some detail. In agreement with previous authors, we find that the standard flux transport model is insufficient to simultaneously reproduce the observed polar fields and butterfly diagram during Cycle 23, and that additional effects must be added. For the best-fit model, we use automated techniques to detect the latitude-time profile of flux ropes and their ejections over the full solar cycle. Overall, flux ropes are more prevalent outside of active latitudes but those at active latitudes are more frequently ejected. Future possibilities for space-weather prediction with this approach are briefly assessed.

Authors: A. R. Yeates
Projects: Other,SoHO-LASCO

Publication Status: Solar Physics (in press)
Last Modified: 2013-04-03 12:09
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The Sun's Global Photospheric and Coronal Magnetic Fields: Observations and Models  

Anthony Yeates   Submitted: 2012-11-29 01:48

In this review, our present day understanding of the Sun's global photospheric and coronal magnetic fields is discussed from both observational and theoretical viewpoints. Firstly, the large-scale properties of photospheric magnetic fields are described, along with recent advances in photospheric magnetic flux transport models. Following this, the wide variety of theoretical models used to simulate global coronal magnetic fields are described. From this, the combined application of both magnetic flux transport simulations and coronal modeling techniques to describe the phenomena of coronal holes, the Sun's open magnetic flux and the hemispheric pattern of solar filaments is discussed. Finally, recent advances in non-eruptive global MHD models are described. While the review focuses mainly on solar magnetic fields, recent advances in measuring and modeling stellar magnetic fields are described where appropriate. In the final section key areas of future research are identified.

Authors: D. H. Mackay, A. R. Yeates
Projects: Mount Wilson Observatory,National Solar Observatory (Sac Peak)

Publication Status: Published: Living Rev. Solar Phys., 9 (2012) 6
Last Modified: 2012-12-01 23:52
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Chirality of High Latitude Filaments over Solar Cycle 23  

Anthony Yeates   Submitted: 2012-06-21 07:03

A non-potential quasi-static evolution model coupling the Sun's photospheric and coronal magnetic fields is applied to the problem of filament chirality at high latitudes. For the first time, we run a continuous 15 year simulation, using bipolar active regions determined from US National Solar Observatory, Kitt Peak magnetograms between 1996 and 2011. Using this simulation, we are able to address the outstanding question of whether magnetic helicity transport from active latitudes can overcome the effect of differential rotation at higher latitudes. Acting alone, differential rotation would produce high latitude filaments with opposite chirality to the majority type in each hemisphere. We find that differential rotation can indeed lead to opposite chirality at high latitudes, but only for around 5 years of the solar cycle following the polar field reversal. At other times, including the rising phase, transport of magnetic helicity from lower latitudes overcomes the effect of in situ differential rotation, producing the majority chirality even on the polar crowns at polar field reversal. These simulation predictions will allow for future testing of the non-potential coronal model. The results indicate the importance of long-term memory and helicity transport from active latitudes when modeling the structure and topology of the coronal magnetic field at higher latitudes.

Authors: A. R. Yeates, D. H. Mackay
Projects: Other

Publication Status: Accepted by ApJL
Last Modified: 2012-06-21 09:17
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Lagrangian coherent structures in photospheric flows and their implications for coronal magnetic structure  

Anthony Yeates   Submitted: 2012-06-21 07:01

Aims. We show how the build-up of magnetic gradients in the Sun's corona may be inferred directly from photospheric velocity data. This enables computation of magnetic connectivity measures such as the squashing factor without recourse to magnetic field extrapolation. Methods.Assuming an ideal evolution in the corona, and an initially uniform magnetic field, the subsequent field line mapping is computed by integrating trajectories of the (time-dependent) horizontal photospheric velocity field. The method is applied to a 12 hour high-resolution sequence of photospheric flows derived from Hinode/SOT magnetograms. Results. We find the generation of a network of quasi-separatrix layers in the magnetic field, which correspond to Lagrangian coherent structures in the photospheric velocity. The visual pattern of these structures arises primarily from the diverging part of the photospheric flow, hiding the effect of the rotational flow component: this is demonstrated by a simple analytical model of photospheric convection. We separate the diverging and rotational components from the observed flow and show qualitative agreement with purely diverging and rotational models respectively. Increasing the flow speeds in the model suggests that our observational results are likely to give a lower bound for the rate at which magnetic gradients are built up by real photospheric flows. Finally, we construct a hypothetical magnetic field with the inferred topology, that can be used for future investigations of reconnection and energy release.

Authors: A.R. Yeates, G. Hornig, and B.T. Welsch
Projects: Hinode/SOT

Publication Status: A&A 539, A1, 2012
Last Modified: 2012-06-21 09:17
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Solar Cycle Variation of Magnetic Flux Ropes in a Quasi-Static Coronal Evolution Model  

Anthony Yeates   Submitted: 2010-03-25 04:35

The structure of electric current and magnetic helicity in the solar corona is closely linked to solar activity over the 11-year cycle, yet is poorly understood. As an alternative to traditional current-free ''potential field'' extrapolations, we investigate a model for the global coronal magnetic field which is non-potential and time-dependent, following the build-up and transport of magnetic helicity due to flux emergence and large-scale photospheric motions. This helicity concentrates into twisted magnetic flux ropes, which may lose equilibrium and be ejected. Here, we consider how the magnetic structure predicted by this model-in particular the flux ropes-varies over the solar activity cycle, based on photospheric input data from six periods of cycle 23. The number of flux ropes doubles from minimum to maximum, following the total length of photospheric polarity inversion lines. However, the number of flux rope ejections increases by a factor of eight, following the emergence rate of active regions. This is broadly consistent with the observed cycle modulation of coronal mass ejections, although the actual rate of ejections in the simulation is about a fifth of the rate of observed events. The model predicts that, even at minimum, differential rotation will produce sheared, non-potential, magnetic structure at all latitudes.

Authors: Yeates, A.R., Constable, J.A., and Martens, P.C.H.
Projects: SoHO-LASCO

Publication Status: Solar Physics (in press)
Last Modified: 2010-03-25 08:29
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Comparison of a Global Magnetic Evolution Model with Observations of Coronal Mass Ejections  

Anthony Yeates   Submitted: 2009-12-18 03:31

The relative importance of different initiation mechanisms for coronal mass ejections (CMEs) on the Sun is uncertain. One possible mechanism is the loss of equilibrium of coronal magnetic flux ropes formed gradually by large-scale surface motions. In this paper, the locations of flux rope ejections in a recently-developed quasi-static global evolution model are compared with observed CME source locations over a 4.5-month period in 1999. Using EUV data, the low-coronal source locations are determined unambiguously for 98 out of 330 CMEs. Despite the incomplete observations, positive correlation (with coefficient up to 0.49) is found between the distributions of observed and simulated ejections, but only when binned into periods of one month or longer. This binning timescale corresponds to the time interval at which magnetogram data are assimilated into the coronal simulations, and the correlation arises primarily from the large-scale surface magnetic field distribution; only a weak dependence is found on the magnetic helicity imparted to the emerging active regions. The simulations are limited in two main ways: they produce fewer ejections, and they do not reproduce the strong clustering of observed CME sources into active regions. Due to this clustering, the horizontal gradient of radial photospheric magnetic field is better correlated with the observed CME source distribution (coefficient 0.67). Our results suggest that, while the gradual formation of magnetic flux ropes over weeks can account for many observed CMEs, especially at higher latitudes, there exists a second class of CMEs (at least half) for which dynamic active region flux emergence on shorter timescales must be the dominant factor.

Authors: Yeates, A.R., Attrill, G.D.R., Nandy, D., Mackay, D.H., Martens, P.C.H., and van Ballegooijen, A.A.
Projects: SoHO-EIT,SoHO-LASCO

Publication Status: ApJ (in press)
Last Modified: 2009-12-21 12:28
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Initiation of Coronal Mass Ejections in a Global Evolution Model  

Anthony Yeates   Submitted: 2009-04-29 07:11

Loss of equilibrium of magnetic flux ropes is a leading candidate for the origin of solar coronal mass ejections (CMEs). The aim of this paper is to explore to what extent this mechanism can account for the initiation of CMEs in the global context. A simplified MHD model for the global coronal magnetic field evolution in response to flux emergence and shearing by large-scale surface motions is described and motivated. Using automated algorithms for detecting flux ropes and ejections in the global magnetic model, the effects of key simulation parameters on the formation of flux ropes and the number of ejections are considered, over a 177-day period in 1999. These key parameters include the magnitude and sign of magnetic helicity emerging in active regions, and coronal diffusion. The number of flux ropes found in the simulation at any one time fluctuates between about 28 and 48, sustained by the emergence of new bipolar regions, but with no systematic dependence on the helicity of these regions. However, the emerging helicity does affect the rate of flux rope ejections, which doubles from 0.67 per day if the bipoles emerge untwisted to 1.28 per day in the run with greatest emerging twist. The number of ejections in the simulation is also increased by 20%-30% by choosing the majority sign of emerging bipole helicity in each hemisphere, or by halving the turbulent diffusivity in the corona. For reasonable parameter choices, the model produces approximately 50% of the observed CME rate. This indicates that the formation and loss of equilibrium of flux ropes may be a key element in explaining a significant fraction of observed CMEs.

Authors: A.R. Yeates and D.H. Mackay
Projects: None

Publication Status: Accepted for publication in ApJ
Last Modified: 2009-04-29 09:25
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Modelling the Global Solar Corona III: Origin of the Hemispheric Pattern of Filaments  

Anthony Yeates   Submitted: 2008-10-03 08:37

We consider the physical origin of the hemispheric pattern of filament chirality on the Sun. Our 3D simulations of the coronal field evolution over a period of 6 months, based on photospheric magnetic measurements, were previously shown to be highly successful at reproducing observed filament chiralities. In this paper we identify and describe the physical mechanisms responsible for this success. The key mechanisms are found to be (1) differential rotation of north-south polarity inversion lines, (2) the shape of bipolar active regions, and (3) evolution of skew over a period of many days. As on the real Sun, the hemispheric pattern in our simulations holds in a statistical sense. Exceptions arise naturally for filaments in certain locations relative to bipolar active regions, or from interactions between a number of active regions.

Authors: Yeates, A. R. and Mackay, D. H.
Projects: None

Publication Status: Solar Physics (in press)
Last Modified: 2008-10-03 09:29
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Abstracts by Author
On the helicity of open magnetic fields
The coronal energy input from magnetic braiding
Coronal Magnetic Field Evolution from 1996 to 2012: Continuous Non-Potential Simulations
The Sun's Global Photospheric and Coronal Magnetic Fields: Observations and Models
Chirality of High Latitude Filaments over Solar Cycle 23
Lagrangian coherent structures in photospheric flows and their implications for coronal magnetic structure
Solar Cycle Variation of Magnetic Flux Ropes in a Quasi-Static Coronal Evolution Model
Comparison of a Global Magnetic Evolution Model with Observations of Coronal Mass Ejections
Initiation of Coronal Mass Ejections in a Global Evolution Model
Modelling the Global Solar Corona III: Origin of the Hemispheric Pattern of Filaments

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