Statistics – Computation
Scientific paper
Jun 2009
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009phdt.........3f&link_type=abstract
Proquest Dissertations And Theses 2009. Section 0883, Part 0606 244 pages; [Ph.D. dissertation].United States -- Virginia: Geor
Statistics
Computation
Sun, Hydrodynamics, Numerical Modeling, Corona
Scientific paper
Explaining the nature of the million degree solar corona is a question that
has been challenging astrophysicists for over 60 years. While many theories have been proposed to explain the nature of the heating mechanism, there is as yet no single answer to this question. An important step toward finding a solution would be to first determine where in the atmosphere the heating is occurring, for this would narrow the different theoretical possibilities for its cause. >From an observational standpoint, recent measurements by instruments on the Solar and Heliospheric Observatory (SOHO) and Transition Region and Coronal Explorer (TRACE) spacecraft revealed that many coronal loops in active regions on the sun are nearly isothermal in their coronal parts. Loop modeling using pseudo-stereoscopic methods applied to SOHO EIT data indicated that temperature gradients were much smaller than predicted from scaling laws. From these and other observations, some authors conclude that the heating results from processes operating in the chromospheric and transition regions. On the other hand, many observed loop properties may be explained by assuming that the heating mechanism is due to the idea of tangled magnetic fields combined with a growing instability that becomes turbulent and releases impulsive energy through magnetic reconnection. Some authors claim that these energy releases occur at higher altitudes in the corona and are responsible for supplying the majority of coronal heating. Clearly, current observations along with numerical modeling results are interpreted differently depending on the researcher and vigorous debate continues over the nature of the heating process and whether it is located near the chromosphere/lower transition region or in the corona.
In this work we attempt to determine if there are observational discriminators derived through computer modeling that can distinguish where the heating occurs. To accomplish this we first use an astrophysical magneto-hydrodynamics computer code to model a solar flux tube having the physical conditions of a one million degree quiet sun corona. A series of experiments is then performed in which energy of various durations and peak intensities is injected at different locations along the flux tube. These experiments are evolved over time and the differences in the temperature, density and velocity profiles are observed. In performing the simulations, the details of the energy transport processes including thermal conduction, convection, radiative cooling, and the nature of the heating sources are studied. The purpose in examining these processes is that they give insight into the validity of various assumptions used by other authors in their analytical models of the corona. It is expected that the determination of the positional and temporal characteristics of the heating will lead to an understanding of the exact physical process responsible for the heating.
Most work currently being done in coronal modeling is accomplished with limited one-dimensional codes that do not include a magnetic field. The primary justification for using such codes is that thermal conduction is constrained to operate only along the magnetic field lines. Our work uses a two-dimensional code and includes a magnetic field. This is more physically realistic and allows for the examination of any interaction between the plasma and the magnetic field. In the course of performing these experiments, a major computational goal was to develop the computer code needed to correctly model conduction only along the field lines and quantitatively compare the effects of isotropic vs. magnetic field-aligned thermal conduction on the evolution of the plasma in the flux tube. The results indicate that assuming all conduction is along the loop axis in one-dimensional loop models is more accurate than assuming isotropic conduction in multi-dimensional models. However, there are differences between the one-dimensional and two-dimensional models.
Our work has produced three main results. First, we developed the techniques and computer code to model physically correct conduction as a vector quantity in multi-dimensional magnetohydrodynamic codes. Secondly, the results of our calculations under solar coronal conditions indicate that one-dimensional models are more accurate than two-dimensional models with isotropic conduction. Finally, there are differences in the dynamics of coronal loops depending on where energy release occurs but that there are currently no observations capable of detecting these differences.
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