HAO 2011 Profiles In Science: Dr. Boon Chye Low
Contact:
303-497-1553
low@ucar.edu
Dr. Boon Chye (BC) Low graduated in mathematics in 1968 from the University of London, UK, and received his Ph.D. in physics in 1972 from the University of Chicago. He works on the magnetohydrodynamics of the solar atmosphere, with particular interests in the theory of basic physical processes and in the solar corona as an integral natural system. He is also interested in the applied and computational mathematics of magnetohydrodynamic processes, collaborating with Natasha Flyer and Piotr Smolarkiewicz at the NCAR Institute for Mathematics Applied to Geosciences. BC joined NCAR in 1981 as Scientist I, became Senior Scientist in 1987, and served as Acting Director of HAO in 1989.
Summary of Achievements
Overview
BC Low and his collaborators have made sustained contributions to our physical understanding of the solar corona as a hydromagnetic atmosphere. They work on the corona's large-scale evolution in response to the Sun's eleven-year cyclical magnetic-field reversals. Their works focus on the hydromagnetic processes basic to the corona and its couplings downward to the dense chromosphere and photosphere, and upward to the heliosphere.
The study of the Solar-Terrestrial System is not entirely an applied science, for the basic science for application is not all in place. New phenomena from ground- and space-based observatories are a major drive of our research. The discovery and understanding of basic hydromagnetic processes go hand in hand with the application of that knowledge to describe and predict the behaviors of the Solar-Terrestrial System. This kind of work builds the scientific basis for developing the capability of predicting space-weather.
In one hydromagnetic mode the million-degree hot corona behaves as a perfect electrical conductor over most observable length scales. Its magnetic fields of about 10 Gauss or stronger tend to evolve as though they are frozen-into the coronal plasma with no change in their topologies. This property is the means of storing free magnetic energy in the corona; the preservation of field topology demands for a specific measure of irremovable electric currents in the corona. Just this property of an invariant field topology brings the fields to also behave in a different hydromagnetic mode, the intensification of electric current density to unlimited magnitudes in thin sheets so that resistive heating sets in despite the high coronal electrical conductivity. Such a heating process is described by E. N. Parker, University of Chicago, in his book Spontaneous Current Sheets in Magnetic Fields (1994, Oxford University Press), with a realm of challenging basic questions being addressed in current research (A. M. Janse, B. C. Low & E. N. Parker 2010, Phys. Plasmas 17, 092901). This theory is basic to understanding quiescent heating in the corona as well as flares, prominences, and coronal mass ejections, the three major phenomena of coronal activity.
Central to this area of work is the magnetic helicity as a measure of field topology. Although field topology changes during magnetic reconnection via current-sheet dissipation, helicity gets transferred among the sub-systems of magnetic flux such that the net helicity of a coronal structure is approximately conserved, a consequence of the high electrical conductivity. In the course of an eleven-year cycle, new magnetic flux emerges from the solar interior into the corona to eventually reverse the polarity of the global coronal magnetic field typically within about three years into the cycle. Magnetic-flux systems do bodily make their way into the corona creating large scale structures with much reconnection and heating over a broad range of temporal and spatial scales. The flux systems emerge with fresh helicity and, by their coalescence into a growing coronal structure, this emergence results in a build-up of helicity in that structure. The three major coronal phenomena can thus be understood in basic terms: (1) the flare being explosive plasma heating by helicity-conserving dissipation of spontaneous current sheets; (2) the quiescent prominence being the manifestation of a macroscopically stable large-scale, twisted magnetic flux-rope formed by the accumulation of helicity; and (3) the CME being the bodily ejection of such a coronal structure whose accumulated helicity has exceeded a forbidding theoretical threshold. This theory of the corona has withstood the observational tests of three solar cycles of space and ground-based observations (B. C. Low 1996, Solar Phys. 167, 217; B. C. Low 2001, J. Geophys. R. 106, 25141; M. Zhang & B. C. Low 2005, Ann. Rev. Astron. Astrophys. 43, 103).
Power-point Lecture Presentations
The power-point presentations of BC's lectures:
- Lecture 1: Basic magnetohydrodynamics
- Lecture 2: Coronal heating & spontaneous current-sheet formation
- Lecture 3: The solar wind & related coronal phenomena
These lectures were given at the International Solar/Space Physics Summer School, July 2011 at University of Science and Technology of China, Hefei, China and can be downloaded from http://download.hao.ucar.edu/pub/low/USTC_Lectures/.
Publications
(1) This theory paper corrects a 2005 publication by Craig and Sneyd containing a fundamental misunderstanding of the Parker theory.
Low, B. C. 2010: The Craig—Sneyd Analytic Solutions to the Parker Problem, Solar Phys, 266: 277–291, doi:-10.1007/s11207-010-9619-z.
Abstract This paper follows upon the conclusion by Craig and Sneyd (2005) that the solutions to a linearized magnetostatic problem are counterexamples to the magnetostatic model of Parker (1972), demonstrating a general absence of continuous equilibrium for a magnetic field with an arbitrarily prescribed topology. The analysis presented here shows that Craig and Sneyd had incorrectly rejected an important subset of those solutions in a misunderstanding of the Parker model. The complete set of solutions when correctly interpreted is, in fact, physically consistent with the Parker model. A general discussion of the Parker theory of spontaneous current sheets is given.
(2) This is the third in a series of papers on the Parker theory, investigating topological changes in 3D fields under conditions of high electrical conductivity, with an interesting conclusion that once it is initiated, the spontaneous formation of current sheets is irrepressible. The evolution of a coronal magnetic field to a minimum-energy equilibrium would thus involve perennial formation and dissipation of current sheets, the successive generations of sheets forming with decreasingly small energy contents.
Janse, Å. M.; Low, B. C. 2010: The topological changes of solar coronal magnetic fields. III. Reconnected field topology produced by current-sheet dissipation, Astrophys. J., 722, 1844, doi: 10.1088/0004-637X/722/2/1844.
Abstract In this paper, the third in a series of papers on topological changes of magnetic fields, we study how the dissipation of an initial current sheet (CS) in a closed three-dimensional (3D) field affects the field topology. The initial field is everywhere potential except at the location of the CS, which is in macroscopic equilibrium under the condition of perfect conductivity. In the physical world of extremely high, but finite, conductivity, the CS dissipates and the field seeks a new equilibrium state in the form of an everywhere potential field since the initial field is everywhere untwisted. Our semi-analytical study indicates that the dissipation of the single initial CS must induce formation of additional CSs in extensive parts of the magnetic volume. The subsequent dissipation of these other sheets brings about topological changes by magnetic reconnection in order for the global field to become potential. In 2D fields, the magnetic reconnection due to the dissipation of a CS is limited to the magnetic vicinity of the dissipating sheet. Thus, the consequence of CS dissipation is physically and topologically quite different in 2D and 3D fields. A discussion of this result is given in general relation to the Parker theory of spontaneous CSs and heating in the solar corona and solar flares.
(3) This is a numerical implementation of Piotr Smolarkiewicz's NCAR EULAG 3D time-dependent codes to describe the ideal hydromagnetic evolution of a magnetic field in terms of its flux surfaces, instead of the field as an explicit vector function of space-time. By exploiting the property that current sheets form spontaneously on flux surfaces, this numerical application achieves an exceptional high degree of the frozen-in condition in order to simulate sheet formation to an unprecedented advanced stage before numerical truncation, inevitable at a given computational resolution, artificially destroys the flux surface. This direct simulation has opened a door to a class of high-resolution simulations of hydromagnetic processes.
Bhattacharyya, R., Low, B. C., and Smolarkiewicz, P. 2010: On spontaneous formation of current sheets: Untwisted magnetic fields, Plasma Phys, 17, 112901, doi:10.1063/1.3496379.
Abstract This is a study of the spontaneous formation of electric current sheets in an incompressible viscous fluid with perfect electrical conductivity, governed by the magnetohydrodynamic Navier-Stokes equations. Numerical solutions to two initial value problems are presented for a three-dimensional, periodic, untwisted magnetic field evolving, with no change in magnetic topology under the frozen-in condition and at characteristic fluid Reynolds numbers of the order of 500, from a non-equilibrium initial state with the fluid at rest. The evolution converts magnetic free energy into kinetic energy to be all dissipated away by viscosity so that the field settles into a minimum-energy, static equilibrium. The solutions demonstrate that, as a consequence of the frozen-in condition, current sheets must form during the evolution despite the geometric simplicity of the prescribed initial fields. In addition to the current sheets associated with magnetic neutral points and field reversal layers, other sheets not associated with such magnetic features are also in evidence. These current sheets form on magnetic flux surfaces. This property is used to achieve a high degree of the frozen-in condition in the simulations, by describing the magnetic field entirely in terms of the advection of its flux surfaces and integrating the resulting governing equations with a customized version of a general-purpose high-resolution, viz., non-oscillatory hydrodynamic simulation code EULAG (J. M. Prusa et al., Comput. Fluids 37, 1193, 2008). Incompressibility imposes the additional global constraint that the flux surfaces must evolve with no change in the spatial volumes they enclose. In this approach, current sheet formation is demonstrated graphically by the progressive pressing together of suitably selected flux surfaces until their separation has diminished below the minimal resolved distance on a fixed grid. The frozen-in condition then fails in the simulation as the field reconnects through an effecting numerical resistivity. The principal results are related to the Parker theory of current-sheet formation and dissipation in the solar corona.
Figure 3 caption (A) Computed current sheet formation as a result of a fixed set of magnetic flux surfaces evolving in time to push into each other and meet at contact surfaces across which the field steepens to tangential discontinuity. Shown are the flux surfaces at four different times in the evolution. (B) Numerical destruction of these flux surfaces when that computed evolution has reached the point when the field gradients cease to be numerically resolved.
(4) This observational paper confirms that the rising “dark” streams of bubbles in the dynamic interior of a quiescent prominence (T. E. Berger et al. 2010, ApJ 716, 1288) contain plasmas at near-coronal conditions, an unprecedented first result from the Solar Dynamic Observatory/ Atmospheric Imaging Assembly instrument; see the press release of Lockheed Martin Corporation (http://www.lmsal.com/press/nature2011/). In the context of a coronal evolution leading to a structure that is eventually ejected as a coronal mass ejection, the authors propose the idea that the prominence and its surrounding coronal cavity are a novel form of magneto-thermal convection during its pre-eruption phase.
Berger T., P. Testa, A. Hillier, P. Boerner, B. C. Low, K. Shibata, C. Schrijver, Te.Tarbell & A. Title 2011: Magneto-thermal convection in solar prominences, Nature, 472, 197, doi:10.1038/nature09925.
Abstract Coronal cavities are large low-density regions formed by hemispheric-scale magnetic flux ropes suspended in the Sun's outer atmosphere. They evolve over time, eventually erupting as the dark cores of coronal mass ejections. Although coronal mass ejections are common and can significantly affect planetary magnetospheres, the mechanisms by which cavities evolve to an eruptive state remain poorly understood. Recent optical observations4 of high-latitude 'polar crown' prominences within coronal cavities reveal dark, low-density 'bubbles' that undergo Rayleigh-Taylor instabilities to form dark plumes rising into overlying coronal cavities. These observations offered a possible mechanism for coronal cavity evolution, although the nature of the bubbles, particularly their buoyancy, was hitherto unclear. Here we report simultaneous optical and extreme-ultraviolet observations of polar crown prominences that show that these bubbles contain plasma at temperatures in the range (2.5–12) × 105 kelvin, which is 25–120 times hotter than the overlying prominence. This identifies a source of the buoyancy, and suggests that the coronal cavity-prominence system supports a novel form of magneto-thermal convection in the solar atmosphere, challenging current hydromagnetic concepts of prominences and their relation to coronal cavities.
Figure 4 caption Simultaneous observations from several space observatories of the quiescent prominence on the northwest solar limb on 22-June-2010 studied in this publication; additional observational data and detailed information available at http://www.lmsal.com/press/nature2011/.
(5) Solar observations above the photosphere generally have no direct information on the magnetic field. The field's presence in a dynamical phenomenon is generally inferred from its interpreted influence on an observed event. This observational paper explains a flare and flux-emergence event, observed by Hinode and other complementary instruments, in terms of magnetic reconnections that have produced a spine-fan topology in a 3D helmet-like magnetic field in the corona.
Liu, Wei , Thomas E. Berger, Alan M. Title, Theodore D. Tarbell, and B. C. Low 2011: Chromspheric Jet and Growing "Loop" Observed hy Hinode: New Evidence of Fan-Spine Magnetic Topology Resulting From Flux Emergence, Astrophys. J. 728, 103, doi:10.1088/0004-637X/728/2/103.
Abstract We present observations of a chromospheric jet and growing "loop" system that show new evidence of a fan-spine topology resulting from magnetic flux emergence. This event, occurring in an equatorial coronal hole on 2007 February 9, was observed by the Hinode Solar Optical Telescope in the Ca ii H line in unprecedented detail. The predecessor of the jet is a bundle of fine material threads that extend above the chromosphere and appear to rotate about the bundle axis at ~50 km s-1 (period 200 s). These rotations or transverse oscillations propagate upward at velocities up to 786 km s-1. The bundle first slowly and then rapidly swings up, with the transition occurring at the onset of an A4.9 flare. A loop expands simultaneously in these two phases (velocity: 16–135 km s-1). Near the peak of the flare, the loop appears to rupture; simultaneous upward ejecta and mass downflows faster than free-fall appear in one of the loop legs. The material bundle then swings back in a whip-like manner and develops into a collimated jet, which is orientated along the inferred open-field lines with transverse oscillations continuing at slower rates. Some material falls back along smooth streamlines, showing no more oscillations. At low altitudes, the streamlines bifurcate at presumably a magnetic null point and bypass an inferred dome, depicting an inverted-Y geometry. These streamlines closely match in space the late Ca ii H loop and X-ray flare loop. These observations are consistent with the model that flux emergence in an open-field region leads to magnetic reconnection, forming a jet and fan-spine topology. We propose that the material bundle and collimated jet represent the outer spine in quasi-static and eruptive stages, respectively, and the growing loop is a two-dimensional projection of the three-dimensional fan surface.
Figure 5 caption Multiwavelength observations of a flare jet interpreted to be the result of magnetic flux emergence and formation of a 3D helmet-like magnetic field with a fan-spine topology.
(6) In this theory paper Phil Judge and his collaborators propose a limb-effect along a fold in a current-sheet (magnetic-flux) surface extending vertically from the chromosphere, as an alternative to current interpretations of spicules; see Judge's profile webpage.
Judge, Philip G., Alexandra Tritschler, and Boon Chye Low 2011: Thermal Fine Structures and Magnetic Fields in the Solar Atmosphere: Spicules and Fibrils, Astrophys. J., 730, L4, doi:10.1088/2041-8205/730/1/L4.
Abstract The relationship between observed structures in the solar atmosphere and the magnetic fields threading them is known only for the solar photosphere, even then imprecisely. We suggest that some of the fine structures in the more tenuous chromosphere and corona—specifically some populations of spicules and fibrils correspond to warps in two-dimensional sheet-like structures, as an alternative to conventional interpretations in terms of tube-like structures. The sheets are perhaps related to magnetic tangential discontinuities, which Parker has argued arise naturally in low-β conditions. Some consequences of this suggestion, if it can be confirmed, are discussed.
(7) The topology of a coronal magnetic field anchored with footpoints in the dense photosphere has been described in terms of relative helicity for almost 3 decades; a seminal construction that successfully treats the well-known complication of the free gauge of the magnetic vector potential involved in the concept of helicity (M. A. Berger and G. B. Field, J. Fluid Mech. 147, 133, 1984). The new theory paper here culminates the development of an alternative theory of an absolute helicity, initiated by Low in 2006. By a unique decomposition of a given field into a linear sum of two fields, this absolute helicity of the given field is defined as a measure of flux entanglement between the latter two fields without invoking the free gauge. A conceptual obstacle encountered in the 2006 paper has been removed. All the fundamentals are now in place and a general theory has been constructed that unifies the classical, relative, and absolute helicities in terms of the Largangian and Eulerian descriptions of fluids. This development opens up new basic questions for hydromagnetic research.
Low B. C. 2011: Absolute magnetic helicity and the cylindrical magnetic field, Phys. Plasmas, 18, 052901, doi:10.1063/1.3587083.
Abstract The different magnetic helicities conserved under conditions of perfect electrical conductivity are expressions of the fundamental property that every evolving fluid surface conserves its net magnetic flux. This basic hydromagnetic point unifies the well known Eulerian helicities with the Lagrangian helicity defined by the conserved fluxes frozen into a prescribed set of disjoint toroidal tubes of fluid flowing as a permanent partition of the entire fluid [B. C. Low, Astrophys. J. 649, 1064 (2006)]. This unifying theory is constructed from first principles, beginning with an analysis of the Eulerian and Lagrangian descriptions of fluids, separating the ideas of fluid and magnetic-flux tubes and removing the complication of the magnetic vector potential's free gauge from the concept of helicity. The analysis prepares for the construction of a conserved Eulerian helicity, without that gauge complication, to describe a 3D anchored flux in an upright cylindrical domain, this helicity called absolute to distinguish it from the well known relative helicity. In a version of the Chandrasekhar-Kendall representation, the evolving field at any instant is a unique superposition of a writhed, untwisted axial flux with a circulating flux of field lines all closed and unlinked within the cylindrical domain. The absolute helicity is then a flux-weighted sum of the writhe of that axial flux and its mutual linkage with the circulating flux. The absolute helicity is also conserved if the frozen-in field and its domain are continuously deformed by changing the separation between the rigid cylinder-ends with no change of cylinder radius. This hitherto intractable cylindrical construction closes a crucial conceptual gap for the fundamentals to be complete at last. The concluding discussion shows the impact of this development on our understanding of helicity, covering (i) the helicities of wholly contained and anchored fields; (ii) the Eulerian and Lagrangian descriptions of field evolution; (iii) twist as a topological property of solenoidal fields versus the linkage properties of open and closed discrete curves treated by Gauss, Caligarneau, Berger, and Prior; and (iv) the change of absolute helicity by resistive diffusion. These are important hydromagnetic properties of twisted magnetic fields in the million-degree hot, highly conducting corona of the Sun.
Figure 7 caption Fluid tubes and magnetic-flux tubes. Projected on a plane are six arrowed field-lines of a given 3D magnetic field B, permeating a perfectly conducting fluid. A toroidal subvolume of fluid of an infinitesmal cross section is identified by each of the six representative unarrowed fluid lines contained in that subvolume. The fluid lines are separate, closed, and unlinked in 3D space, appearing to partially coincide only as a result of projection. Breaks in the drawn field and fluid lines at crucial spots help with the three-dimensional sense of the sketch. The publication treats a Lagrangian description of this fluid by a permanent partition of the fluid into an exhaustive set of disjoint but contiguous, unlinked fluid tubes of this kind. The evolution of the fluid and magnetic field is then described in terms of the motions of these partition tubes and the two conserved magnetic fluxes associated with each tube, an axial flux along the tube and a net flux through the doughnut hole of the tube. This construction unifies the different concepts of magnetic helicity.