HAO 2010 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 colleagues in the Institute of Mathematics for 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
Theory of coronal heating and electric current sheets. E. N. Parker (1994, Spontaneous Current Sheets in Magnetic Fields, Oxford U. Press) developed a theory of coronal heating by the spontaneous formation and resistive dissipation of electric current sheets under conditions of high electrical conductivity. Nanoflare observational studies and numerical simulations have demonstrated that this is a promising theory (e.g., Rappazzo, A. F.; Velli, M.; Einaudi, G. 2010, ApJ 722, 65, Antolin, P.; Shibata, K.; Kudoh, T.; Shiota, D.; Brooks, D. 2008, ApJ 688,669). The basics hydromagnetic process proposed by Parker can be clearly described and understood in physical terms, that the continuous state of equilibrium of a magnetic field in a given physical system generally restricts the topology the field may possess. The infinite set of such admissible topologies is generally only a subset of measure zero of the set of field topologies admissible for the field when it is not in equilibrium. That is to say, most naturally occurring magnetic fields have topologies not compatible with continuous equilibrium. Under the approximation of the frozen-in condition, a field rigidly anchored at the boundary of its domain evolves with an invariant topology. The relaxation of such a field to equilibrium in most cases must then inevitably form magnetic tangential discontinuities, i.e., current sheets. These current sheets thin toward zero thickness to eventually dissipate resistively as the frozen-in approximation breaks down. BC Low and his collaborators have made significant progress in their ongoing investigation of the fundamental property that the field topologies of an equilibrium field are restricted.
Basic numerical and analytical MHD. It is a challenge to implement the frozen-in condition in a numerical MHD model to simulate physical conditions characterized by coronal magnetic Reynolds numbers of the order of 1010 or greater. Numerical simulation of the Parker theory of spontaneous current sheets requires the construction of flux surfaces of a 3D magnetic field to reveal the basic effect of these sheets manifesting as magnetic tangential discontinuities across such surfaces. A numerical description of the field as a discrete vector variable presents the prohibitive numerical task of integrating this variable to construct the flux surfaces.
Ramit Bhattacharyya (ASP), Low and Piotr Smolarkiewicz (MMM & IMaGe) have developed a 3D time-dependent MHD code that describes the magnetic field in terms of its flux surfaces that has been demonstrated to be viable for demonstrating current-sheet formation. Using Euler potentials as magnetic flux surfaces is not new, but little work has been previously done with such an approach because the potentials are generally only locally defined for twisted magnetic fields. The new work is thus limited to untwisted fields with globally defined Euler potential fields. The motivation of this undertaking is provided by an earlier work (B. C. Low 2006, ApJ 646, 1288) showing that twisted fields in general can be described by two or more pairs of global Euler potentials, thus opening the door to numerical simulations that can achieve high magnetic Reynolds numbers not possible with traditional approaches.
Interpretation of Hinode data. M. Kubo (National Astronomical Observatory of Japan), Bruce Lites and B. C. Low investigated granular-scale magnetic flux cancellations in the photosphere using accurate spectropolarimetric measurements and G-band images with the Solar Optical Telescope (SOT) aboard Hinode. The particular solar events selected for study show that the cancelling magnetic elements move at velocities distinct from the independently observed surrounding flow. This result suggests that, in addition to the surface flows, subsurface downward convective motions and subsurface magnetic connectivities are important for understanding the approach and collision of the canceling magnetic elements.
Wei Liu, Thomas E. Berger, Alan M. Title, Theodore D. Tarbell (all at Lockheed Martin), and B. C. Low investigated the flare associated with a chromospheric jet observed by instruments onboard Hinode, to interpret this event in terms of a fan-spine magnetic topology resulting from magnetic-flux emergence. The physics of this interpretation suggests that such a field topology may occur universally. This work has led to new theoretical MHD calculations to explore this universality.
Publication:
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.
Publication:
Abstract:
We demonstrate the Parker Magnetostatic Theorem in terms of a small neighborhood in solution space containing continuous force-free magnetic fields in small deviations from the uniform field. These fields are embedded in a perfectly conducting fluid bounded by a pair of rigid plates where each field is anchored, taking the plates perpendicular to the uniform field. Those force-free fields obtainable from the uniform field by continuous magnetic footpoint displacements at the plates have field topologies that are shown to be a restricted subset of the field topologies similarly created without imposing the force-free equilibrium condition. The theorem then follows from the deduction that a continuous nonequilibrium field with a topology not in that subset must find a force-free state containing tangential discontinuities.
Publications:
(3) Low, B. C. 2010, “The Craig – Sneyd analytic solutions to the Parker Problem”, Sol. Phys., 266, 277, DOI: 10.1007/s11207-010-9619-z.
Abstract:
This paper follows up on 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.publications:
(4) Janse, Å. M., Low, B. C., and Parker, E. N. 2010: “Topological complexity and tangential discontinuity in magnetic fields”, Plasma Phys, 17, 092901, DOI:10.1063/1.3474943.
Abstract:
This is a study of the topological magnetostatic problem. A magnetic field embedded in a perfectly conducting fluid and rigidly anchored at its boundary has a specific topology invariant for all time. Subject to that topology, the force-free state of such a field generally requires the presence of tangential discontinuities (TDs). This property proposed and demonstrated by Parker [Spontaneous Current Sheets in Magnetic Fields (Oxford University Press, New York, 1994)] is explained in terms of (i) the overdetermined nature of the magnetostatic partial differential equations nonlinearly coupled to the integral equations imposing the field topology and (ii) the hyperbolic nature of the partial differential equation for the twist function α of the force-free field. The mathematical analysis elucidates a basic incompatibility between preserving a complex field topology and attaining equilibrium, if analyticity is assumed. Physics avoids this incompatibility via TD formation as a natural consequence of perfect conductivity. The study relates TD formation to topological complexity in two-dimensional and three-dimensional fields, as well as the topological connectivity and geometric shape of the field domain. Mathematical points made are given physical interpretations, but important topological concepts for understanding spontaneous TDs have remained incomplete. As an application, examples are presented to define twisted and untwisted potential fields found in simply and multiply connected domains, clarifying a confusion in several recent publications. Appendix A treats the expression of the frozen-in condition by a continuum of conserved, total generalized helicities. Appendix B reports briefly on concurrent developments showing that a published objection to the theory of spontaneous TDs is based upon a misunderstanding of the theory.Publication:
(5) Kubo, M.; Low, B. C.; Lites, B. W. 2010: "Granular-scale Magnetic Flux Cancellations in the Photosphere", Astrophys. J., 712, 1321, doi: 10.1088/0004-637X/712/2/1321.
Abstract:
We investigate the evolution of five granular-scale magnetic flux cancellations just outside the moat region of a sunspot by using accurate spectropolarimetric measurements and G-band images with the Solar Optical Telescope (SOT) aboard Hinode. The opposite-polarity magnetic elements approach a junction of the inter-granular lanes and then collide with each other there. The inter-granular junction has strong red-shifts, darker intensities than the regular inter-granular lanes, and surface converging flows. This clearly confirms that the converging and downward convective motions are essential for the approaching process of the opposite-polarity magnetic elements. However, the motion of the approaching magnetic elements does not always match with their surrounding surface flow patterns in our observations. This suggests that, in addition to the surface flows, subsurface downward convective motions and subsurface magnetic connectivities are important for understanding the approach and collision of the opposite-polarity elements observed in the photosphere. We find that the horizontal magnetic field appears between the canceling opposite-polarity elements in o-nly one event. The horizontal fields are observed along the inter-granular lanes with Doppler redshifts. This cancellation is most probably a result of the submergence (retraction) of low-lying photospheric magnetic flux. In the other four events, the horizontal field is not observed between the opposite-polarity elements at any time when they approach and cancel each other. These approaching magnetic elements are more concentrated rather than gradually diffused, and they have nearly vertical fields even while they are in contact each other. We thus infer that the actual flux cancellations are highly time-dependent events at scales less than a pixel of Hinode SOT (about 200 km) near the solar surface.Bhattacharyya, R., Low, B. C., and Smolarkiewicz, P. 2010 “On spontaneous formation of current sheets: Untwisted magnetic fields”, Plasma Phys, in press.
Wei Liu, Thomas E. Berger, Alan M. Title, Theodore D. Tarbell, B. C. Low, "Chromospheric jet and growing loop observed by Hinode: evidence of fan-spine topology resulting from flux emergence”, Astrophys. J., submitted August 2010.