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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.
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
We examine the generation of a magnetic field in a solar-like star and its effects on the internal distribution of the angular velocity. We suggest that the evolution of a rotating star with magnetic fields leads to an equilibrium value of the differ
Atomic diffusion has been recognized as an important process that has to be considered in any computations of stellar models. In solar-type and cooler stars, this process is dominated by gravitational settling, which is now included in most stellar e
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
We investigate the impact of rotation and magnetic fields on the dynamics and gravitational wave emission in 2D core-collapse supernova simulations with neutrino transport. We simulate 16 different models of $15,M_odot$ and $39,M_odot$ progenitor sta