Outstanding Issues in Solar Dynamo Theory

The magnetic activity of the Sun, as manifested in the sunspot cycle, originates deep within its convection zone through a dynamo mechanism which involves non-trivial interactions between the plasma and magnetic field in the solar interior. Recent advances in magnetohydrodynamic dynamo theory have led us closer towards a better understanding of the physics of the solar magnetic cycle. In conjunction, helioseismic observations of large-scale flows in the solar interior has now made it possible to constrain some of the parameters used in models of the solar cycle. In the first part of this review, I briefly describe this current state of understanding of the solar cycle. In the second part, I highlight some of the outstanding issues in solar dynamo theory related to the the nature of the dynamo $\alpha$-effect, magnetic buoyancy and the origin of Maunder-like minima in activity. I also discuss how poor constraints on key physical processes such as turbulent diffusion, meridional circulation and turbulent flux pumping confuse the relative roles of these vis-a-vis magnetic flux transport. I argue that unless some of these issues are addressed, no model of the solar cycle can claim to be ``the standard model'', nor can any predictions from such models be trusted; in other words, we are still not there yet.Comment: To appear in "Magnetic Coupling between the Interior and the Atmosphere of the Sun", eds. S.S. Hasan and R.J. Rutten, Astrophysics and Space Science Proceedings, Springer-Verlag, Heidelberg, Berlin, 200

Three-Dimensional Magnetic Reconnection

The importance of magnetic reconnection as an energy release mechanism in many solar, stellar, magnetospheric and astrophysical phenomena has long been recognised. Reconnection is the only mechanism by which magnetic fields can globally restructure, enabling them to access a lower energy state. Over the past decade, there have been some major advances in our understanding of three-dimensional reconnection. In particular, the key characteristics of 3D magnetohydrodynamic (MHD) reconnection have been determined. For instance, 3D reconnection (i) occurs with or without nulls, (ii) occurs continuously and continually throughout a diffusion region and (iii) is driven by counter rotating flows. Furthermore, analysis of resistive 3D MHD magnetic experiments have revealed some intriguing effects relating to where and how reconnection occurs. To illustrate these new features, a series of constant-resistivity experiments, involving the interaction of two opposite-polarity magnetic sources in an overlying field, are considered. Such a simple interaction represents a typical building block of the Sun's magnetic atmosphere. By following the evolution of the magnetic topology, we are able to explain where, how and at what rate the reconnection occurs. Remarkably there can be up to five energy release sites at anyone time (compared to one in the potential case) and the duration of the interaction increases (more than doubles) as the resistivity decreases (by a factor of 16). The decreased resistivity also leads to a higher peak ohmic dissipation and more energy being released in total, as a result of a greater injection of Poynting flux.Comment: To appear in "Magnetic Coupling between the Interior and the Atmosphere of the Sun", eds. S.S. Hasan and R.J. Rutten, Astrophysics and Space Science Proceedings, Springer-Verlag, Heidelberg, Berlin, 200

Dynamical Relaxation of Coronal Magnetic Fields. III. 3D Spiral Nulls

Context: The majority of studies on stressed 3D magnetic null points consider magnetic reconnection driven by an external perturbation, but the formation of a genuine current sheet equilibrium remains poorly understood. This problem has been considered more extensively in two-dimensions, but lacks a generalization into 3D fields. Aims: 3D magnetic nulls are more complex than 2D nulls and the field can take a greater range of magnetic geometries local to the null. Here, we focus on one type and consider the dynamical non-resistive relaxation of 3D spiral nulls with initial spine-aligned current. We aim to provide a valid magnetohydrostatic equilibrium, and describe the electric current accumulations in various cases, involving a finite plasma pressure. Methods: A full MHD code is used, with the resistivity set to zero so that reconnection is not allowed, to run a series of experiments in which a perturbed spiral 3D null point is allowed to relax towards an equilibrium, via real, viscous damping forces. Changes to the initial plasma pressure and other magnetic parameters are investigated systematically. Results: For the axi-symmetric case, the evolution of the field and the plasma is such that it concentrates the current density in two cone-shaped regions along the spine, thus concentrating the twist of the magnetic field around the spine, leaving a radial configuration in the fan plane. The plasma pressure redistributes in order to maintain the current density accumulations. However, it is found that changes in the initial plasma pressure do not modify the final state significantly. In the cases where the initial magnetic field is not axi-symmetric, a infinite-time singularity of current perpendicular to the fan is found at the location of the null

Analysis of shared heritability in common disorders of the brain

ience, this issue p. eaap8757 Structured Abstract INTRODUCTION Brain disorders may exhibit shared symptoms and substantial epidemiological comorbidity, inciting debate about their etiologic overlap. However, detailed study of phenotypes with different ages of onset, severity, and presentation poses a considerable challenge. Recently developed heritability methods allow us to accurately measure correlation of genome-wide common variant risk between two phenotypes from pools of different individuals and assess how connected they, or at least their genetic risks, are on the genomic level. We used genome-wide association data for 265,218 patients and 784,643 control participants, as well as 17 phenotypes from a total of 1,191,588 individuals, to quantify the degree of overlap for genetic risk factors of 25 common brain disorders. RATIONALE Over the past century, the classification of brain disorders has evolved to reflect the medical and scientific communities' assessments of the presumed root causes of clinical phenomena such as behavioral change, loss of motor function, or alterations of consciousness. Directly observable phenomena (such as the presence of emboli, protein tangles, or unusual electrical activity patterns) generally define and separate neurological disorders from psychiatric disorders. Understanding the genetic underpinnings and categorical distinctions for brain disorders and related phenotypes may inform the search for their biological mechanisms. RESULTS Common variant risk for psychiatric disorders was shown to correlate significantly, especially among attention deficit hyperactivity disorder (ADHD), bipolar disorder, major depressive disorder (MDD), and schizophrenia. By contrast, neurological disorders appear more distinct from one another and from the psychiatric disorders, except for migraine, which was significantly correlated to ADHD, MDD, and Tourette syndrome. We demonstrate that, in the general population, the personality trait neuroticism is significantly correlated with almost every psychiatric disorder and migraine. We also identify significant genetic sharing between disorders and early life cognitive measures (e.g., years of education and college attainment) in the general population, demonstrating positive correlation with several psychiatric disorders (e.g., anorexia nervosa and bipolar disorder) and negative correlation with several neurological phenotypes (e.g., Alzheimer's disease and ischemic stroke), even though the latter are considered to result from specific processes that occur later in life. Extensive simulations were also performed to inform how statistical power, diagnostic misclassification, and phenotypic heterogeneity influence genetic correlations. CONCLUSION The high degree of genetic correlation among many of the psychiatric disorders adds further evidence that their current clinical boundaries do not reflect distinct underlying pathogenic processes, at least on the genetic level. This suggests a deeply interconnected nature for psychiatric disorders, in contrast to neurological disorders, and underscores the need to refine psychiatric diagnostics. Genetically informed analyses may provide important "scaffolding" to support such restructuring of psychiatric nosology, which likely requires incorporating many levels of information. By contrast, we find limited evidence for widespread common genetic risk sharing among neurological disorders or across neurological and psychiatric disorders. We show that both psychiatric and neurological disorders have robust correlations with cognitive and personality measures. Further study is needed to evaluate whether overlapping genetic contributions to psychiatric pathology may influence treatment choices. Ultimately, such developments may pave the way toward reduced heterogeneity and improved diagnosis and treatment of psychiatric disorders

Three-dimensional magnetic reconnection regimes:a review

The magnetic field in many astrophysical plasmas -- such as the Solar corona and Earth's magnetosphere -- has been shown to have a highly complex, three-dimensional structure. Recent advances in theory and computational simulations have shown that reconnection in these fields also has a three-dimensional nature, in contrast to the widely used two-dimensional (or 2.5-dimensional) models. Here we discuss the underlying theory of three-dimensional magnetic reconnection. We also review a selection of new models that illustrate the current state of the art, as well as highlighting the complexity of energy release processes mediated by reconnection in complicated three-dimensional magnetic fields.Comment: Accepted for publication in Advances in Space Research. (Based on paper presented at 38th COSPAR meeting, Bremen, 2010.

Coronal heating and nanoflares : current sheet formation and heating

Aims: Solar photospheric footpoint motions can produce strong, localised currents in the corona. A detailed understanding of the formation process and the resulting heating is important in modelling nanoflares, as a mechanism for heating the solar corona. Methods: A 3D MHD simulation is described in which an initially straight magnetic field is sheared in two directions. Grid resolutions up to 5123 were used and two boundary drivers were considered; one where the boundaries are continuously driven and one where the driving is switched off once a current layer is formed. Results: For both drivers a twisted current layer is formed. After a long time we see that, when the boundary driving has been switched off, the system relaxes towards a lower energy equilibrium. For the driver which continuously shears the magnetic field we see a repeating cycle of strong current structures forming, fragmenting and decreasing in magnitude and then building up again. Realistic coronal temperatures are obtained.Publisher PDFPeer reviewe

Current accumulation at an asymmetric 3D null point caused by generic shearing motions

Context. We investigate the dynamical evolution of the reconnection process at an initially linear 3D null point that is stressed by a localised shear motion across the spine axis. The fan plane is not rotationally symmetric and this allows for different behaviours depending on the alignment of the fan plane relative to the imposed driver direction. Aims. The aim is to show how the current accumulation and the associated reconnection process depends on the relative orientation between the driver imposed stress across the spine axis of the null and the main eigenvector direction in the fan plane. Methods. The time evolution of the 3D null point is investigated solving the 3D non-ideal MHD equations numerically in a Cartesian box. The magnetic field is frozen to the boundaries and the boundary velocity is only non-zero where the imposed driving is for stressing the system is applied. Results. The current accumulation is found to be along the direction of the fan eigenvector associated with the smallest eigenvalue until the direction of the driver is almost parallel to this eigenvector. When the driving velocity is parallel to the weak eigenvector and has an impulsive temporal profile the null only forms a weak current layer. However, when the null point is stressed continuously boundary effects dominates the current accumulation. Conclusions. There is a clear relation between the orientation of the current concentration and the direction of the fan eigenvector corresponding to the small eigenvalue. This shows that the structure of the magnetic field is the most important in determining where current is going to accumulate when a single 3D null point is perturbed by a simple shear motion across the spine axis. As the angle between the driving direction and the strong eigenvector direction increases, the current that accumulates at the null becomes progressively weaker.Comment: Accepted by A&A, 8 pages, 9 fig