arXiv subjects

D. H. Mackay

Publications and source records attributed to D. H. Mackay.

33 records · Page 2Linked to original sources

arXiv2012

The Sun's Global Photospheric and Coronal Magnetic Fields: Observations and Models

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.

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arXiv2012

Solar Magnetic Carpet II: Coronal Interactions of Small-Scale Magnetic Fields

This paper is the second in a series of studies working towards constructing a realistic, evolving, non-potential coronal model for the solar magnetic carpet. In the present study, the interaction of two magnetic elements is considered. Our objectives are to study magnetic energy build up, storage and dissipation as a result of emergence, cancellation, and flyby of these magnetic elements. In the future these interactions will be the basic building blocks of more complicated simulations involving hundreds of elements. Each interaction is simulated in the presence of an overlying uniform magnetic field, which lies at various orientations with respect to the evolving magnetic elements. For these three small-scale interactions, the free energy stored in the field at the end of the simulation ranges from $0.2-2.1\times 10^{26}$ ergs, while the total energy dissipated ranges from $1.3-6.3\times 10^{26}$ ergs. For all cases, a stronger overlying field results in higher energy storage and dissipation. For the cancellation and emergence simulations, motion perpendicular to the overlying field results in the highest values. For the flyby simulations, motion parallel to the overlying field gives the highest values. In all cases, the free energy built up is sufficient to explain small-scale phenomena such as X-ray bright points or nanoflares. In addition, if scaled for the correct number of magnetic elements for the volume considered, the energy continually dissipated provides a significant fraction of the quiet Sun coronal heating budget.

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arXiv2012

Chirality of High Latitude Filaments over Solar Cycle 23

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.

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arXiv2012

Using Kepler transit observations to measure stellar spot belt migration rates

Planetary transits provide a unique opportunity to investigate the surface distributions of star spots. Our aim is to determine if, with continuous observation (such as the data that will be provided by the Kepler mission), we can in addition measure the rate of drift of the spot belts. We begin by simulating magnetic cycles suitable for the Sun and more active stars, incorporating both flux emergence and surface transport. This provides the radial magnetic field distribution on the stellar surface as a function of time. We then model the transit of a planet whose orbital axis is misaligned with the stellar rotation axis. Such a planet could occult spots at a range of latitudes. This allows us to complete the forward modelling of the shape of the transit lightcurve. We then attempt the inverse problem of recovering spot locations from the transit alone. From this we determine if transit lightcurves can be used to measure spot belt locations as a function of time. We find that for low-activity stars such as the Sun, the 3.5 year Kepler window is insufficient to determine this drift rate. For more active stars, it may be difficult to distinguish subtle differences in the nature of flux emergence, such as the degree of overlap of the "butterfly wings". The rate and direction of drift of the spot belts can however be determined for these stars. This would provide a critical test of dynamo theory.

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arXiv2010

A Non-potential Model for the Sun's Open Magnetic Flux

Measurements of the interplanetary magnetic field (IMF) over several solar cycles do not agree with computed values of open magnetic flux from potential field extrapolations. The discrepancy becomes greater around solar maximum in each cycle, when the IMF can be twice as strong as predicted by the potential field model. Here we demonstrate that this discrepancy may be resolved by allowing for electric currents in the low corona (below 2.5 solar radii). We present a quasi-static numerical model of the large-scale coronal magnetic evolution, which systematically produces these currents through flux emergence and shearing by surface motions. The open flux is increased by 75%-85% at solar maximum, but only 25% at solar minimum, bringing it in line with estimates from IMF measurements. The additional open flux in the non-potential model arises through inflation of the magnetic field by electric currents, with super-imposed fluctuations due to coronal mass ejections. The latter are modelled by the self-consistent ejection of twisted magnetic flux ropes.

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arXiv2010

Physics of Solar Prominences: II - Magnetic Structure and Dynamics

Observations and models of solar prominences are reviewed. We focus on non-eruptive prominences, and describe recent progress in four areas of prominence research: (1) magnetic structure deduced from observations and models, (2) the dynamics of prominence plasmas (formation and flows), (3) Magneto-hydrodynamic (MHD) waves in prominences and (4) the formation and large-scale patterns of the filament channels in which prominences are located. Finally, several outstanding issues in prominence research are discussed, along with observations and models required to resolve them.

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arXiv2009

Comparison of a Global Magnetic Evolution Model with Observations of Coronal Mass Ejections

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.

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arXiv2009

Initiation of Coronal Mass Ejections in a Global Evolution Model

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.

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arXiv2008

Modelling the Global Solar Corona III: Origin of the Hemispheric Pattern of Filaments

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.

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arXiv2008

Evolution and Distribution of Current Helicity in Full-Sun Simulations

Current helicity quantifies the location of twisted and sheared non-potential structures in a magnetic field. We simulate the evolution of magnetic fields in the solar atmosphere in response to flux emergence and shearing by photospheric motions. In our global-scale simulation over many solar rotations the latitudinal distribution of current helicity develops a clear statistical pattern, matching the observed hemispheric sign at active latitudes. In agreement with observations there is significant scatter and intermixing of both signs of helicity, where we find local values of current helicity density that are much higher than those predicted by linear force-free extrapolations. Forthcoming full-disk vector magnetograms from Solar Dynamics Observatory will provide an ideal opportunity to test our theoretical results on the evolution and distribution of current helicity, both globally and in single active regions.

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arXiv2007

Modelling the Global Solar Corona II: Coronal Evolution and Filament Chirality Comparison

The hemispheric pattern of solar filaments is considered using newly-developed simulations of the real photospheric and 3D coronal magnetic fields over a 6-month period, on a global scale. The magnetic field direction in the simulation is compared directly with the chirality of observed filaments, at their observed locations. In our model the coronal field evolves through a continuous sequence of nonlinear force-free equilibria, in response to the changing photospheric boundary conditions and the emergence of new magnetic flux. In total 119 magnetic bipoles with properties matching observed active regions are inserted. These bipoles emerge twisted and inject magnetic helicity into the solar atmosphere. When we choose the sign of this active-region helicity to match that observed in each hemisphere, the model produces the correct chirality for up to 96% of filaments, including exceptions to the hemispheric pattern. If the emerging bipoles have zero helicity, or helicity of the opposite sign, then this percentage is much reduced. In addition, the simulation produces a higher proportion of filaments with the correct chirality after longer times. This indicates that a key element in the evolution of the coronal field is its long-term memory, and the build-up and transport of helicity from low to high latitudes over many months. It highlights the importance of continuous evolution of the coronal field, rather than independent extrapolations at different times. This has significant consequences for future modelling such as that related to the origin and development of coronal mass ejections.

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arXiv2007

Exploring the Physical Basis of Solar Cycle Predictions: Flux Transport Dynamics and Persistence of Memory in Advection versus Diffusion Dominated Solar Convection Zones

The predictability, or lack thereof, of the solar cycle is governed by numerous separate physical processes that act in unison in the interior of the Sun. Magnetic flux transport and the finite time delay it introduces, specifically in the so-called Babcock-Leighton models of the solar cycle with spatially segregated source regions for the alpha and omega effects, play a crucial rule in this predictability. Through dynamo simulations with such a model, we study the physical basis of solar cycle predictions by examining two contrasting regimes, one dominated by diffusive magnetic flux transport in the solar convection zone, the other dominated by advective flux transport by meridional circulation. Our analysis shows that diffusion plays an important role in flux transport, even when the solar cycle period is governed by the meridional flow speed. We further examine the persistence of memory of past cycles in the advection and diffusion dominated regimes through stochastically forced dynamo simulations. We find that in the advection-dominated regime, this memory persists for up to three cycles, whereas in the diffusion-dominated regime, this memory persists for mainly one cycle. This indicates that solar cycle predictions based on these two different regimes would have to rely on fundamentally different inputs - which may be the cause of conflicting predictions. Our simulations also show that the observed solar cycle amplitude-period relationship arises more naturally in the diffusion dominated regime, thereby supporting those dynamo models in which diffusive flux transport plays a dominant role in the solar convection zone.

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arXiv2007

Modelling the Global Solar Corona: Filament Chirality Observations and Surface Simulations

The hemispheric pattern of solar filaments is considered in the context of the global magnetic field of the solar corona. In recent work Mackay and van Ballegooijen have shown how, for a pair of interacting magnetic bipoles, the observed chirality pattern could be explained by the dominant range of bipole tilt angles and helicity in each hemisphere. This study aims to test this earlier result through a direct comparison between theory and observations, using newly-developed simulations of the actual surface and 3D coronal magnetic fields over a 6-month period, on a global scale. In this paper we consider two key components of the study; firstly the observations of filament chirality for the sample of 255 filaments, and secondly our new simulations of the large-scale surface magnetic field. Based on a flux-transport model, these will be used as the lower boundary condition for the future 3D coronal simulations. Our technique differs significantly from those of other authors, where the coronal field is either assumed to be purely potential, or has to be reset back to potential every 27 days in order that the photospheric field remain accurate. In our case we ensure accuracy by the insertion of newly-emerging bipolar active regions, based on observed photospheric synoptic magnetograms. The large-scale surface field is shown to remain accurate over the 6-month period, without any resetting. This new technique will enable future simulations to consider the long-term build-up and transport of helicity and shear in the coronal magnetic field, over many months or years.

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arXiv2006

The impact of meridional circulation on stellar butterfly diagrams and polar caps

Observations of rapidly rotating solar-like stars show a significant mixture of opposite-polarity magnetic fields within their polar regions. To explain these observations, models describing the surface transport of magnetic flux demand the presence of fast meridional flows. Here, we link sub-surface and surface magnetic flux transport simulations to investigate (i) the impact of meridional circulations with peak velocities of <125m/s on the latitudinal eruption pattern of magnetic flux tubes and (ii) the influence of the resulting butterfly diagrams on polar magnetic field properties. Prior to their eruption, magnetic flux tubes with low field strengths and initial cross sections below about 300km experience an enhanced poleward deflection through meridional flows. In particular flux tubes which originate between low and intermediate latitudes within the convective overshoot region are strongly affected. This latitude-dependent poleward deflection of erupting magnetic flux renders the wings of stellar butterfly diagrams distinctively convex. The subsequent evolution of the surface magnetic field shows that the increased number of newly emerging bipoles at higher latitudes promotes the intermingling of opposite polarities of polar magnetic fields. The associated magnetic flux densities are about 20% higher than in the case disregarding the pre-eruptive deflection, which eases the necessity for fast meridional flows predicted by previous investigations. In order to reproduce the observed polar field properties, the rate of the meridional circulation has to be on the order of 100m/s, and the latitudinal range from which magnetic flux tubes originate at the base of the convective zone (<50degrees) must be larger than in the solar case (<35degrees).

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arXiv2002

Inferring X-ray coronal structures from Zeeman-Doppler images

We have modelled the X-ray emission from the young rapid rotator AB Doradus (P = 0.514 days) using as a basis Zeeman-Doppler maps of the surface magnetic field. This allows us to reconcile the apparently conflicting observations of a high X-ray emission measure and coronal density with a low rotational modulation in X-rays. The technique is to extrapolate the coronal field from the surface maps by assuming the field to be potential. We then determine the coronal density for an isothermal corona by solving hydrostatic equilibrium along each field line and scaling the plasma pressure at the loop footpoints with the magnetic pressure. We set the density to zero along those field lines that are open and those where at any point along their length the plasma pressure exceeds the magnetic pressure. We then calculate the optically thin X-ray emission measure and rotational modulation for models with a range of coronal densities. Although the corona can be very extended, much of the emission comes from high-latitude regions close to the stellar surface. Since these are always in view as the star rotates, there is little rotational modulation. We find that emission measures in the observed range of 10^52.8 - 10^53.3 per cubic centimetre can be reproduced with densities in the range 10^9 - 10^10.7 per cubic centimetre for coronae at temperatures of 10^6-10^7 K.

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