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تسجيل مستخدم جديد2-D Stellar Evolution Code Including Arbitrary Magnetic Fields. I. Mathematical Techniques and Test Cases
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L. H. Li
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A high-precision two-dimensional stellar evolution code has been developed for studying solar variability due to structural changes produced by varying internal magnetic fields of arbitrary configurations. Specifically, we are interested in modeling the effects of a dynamo-type field on the detailed internal structure and on the global parameters of the Sun. The high precision is required both to model very small solar changes (of order of $10^{-4}$) and short time scales (or order of one year). It is accomplished by using the mass coordinate to replace the radial coordinate, by using fixed and adjustable time steps, a realistic stellar atmosphere, elements diffusion, and by adjusting the grid points. We have also built into the code the potential to subsequently include rotation and turbulence. The current code has been tested for several cases, including its ability to reproduce the 1-D results.
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In the second paper of this series we pursue two objectives. First, in order to make the code more sensitive to small effects, we remove many approximations made in Paper I. Second, we include turbulence and rotation in the two-dimensional framework.
The stellar equilibrium is described by means of a set of five differential equations, with the introduction of a new dependent variable, namely the perturbation to the radial gravity, that is found when the non-radial effects are considered in the solution of the Poisson equation; following the scheme of the first paper, we write the equations in such a way that the two-dimensional effects can be easily disentangled. The key concept introduced in this series is the equipotential surface. We use the underlying cause-effect relation to develop a recurrence relation to calculate the equipotential surface functions for uniform rotation, differential rotation, rotation-like toroidal magnetic fields and turbulence. We also develop a more precise code to numerically solve the two-dimensional stellar structure and evolution equations based on the equipotential surface calculations. We have shown that with this formulation we can achieve the precision required by observations by appropriately selecting the convergence criterion. Several examples are presented to show that the method works well. Since we are interested in modeling the effects of a dynamo-type field on the detailed envelope structure and global properties of the Sun, the code has been optimized for short timescales phenomena (down to 1 yr). The time dependence of the code has so far been tested exclusively to address such problems.
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As a massive star evolves through multiple stages of nuclear burning on its way to becoming a supernova, a complex, differentially rotating structure is set up. Angular momentum is transported by a variety of classic instabilities, and also by magnet
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This is a white paper submitted to the Stars and Stellar Evolution (SSE) Science Frontier Panel (SFP) of the NRCs Astronomy and Astrophysics 2010 Decadal Survey. The white paper is endorsed by the American Physical Societys (APS) Topical Group on Plasma Astrophysics (GPAP).
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