Abstract
Traditionally, stellar structure and evolution have been modelled with a series of concentric spherical shells. This description allows the star to be modelled in 1 dimension, greatly simplifying the calculations. However, as our understanding of stars becomes more advanced, the effects of non-symmetric effects must be included, which necessitates 2 or even 3 dimensional simulations. In this work, I discuss how 2D stellar models can help understand stars, improving our models of their pulsation frequencies, and allow us to place better constraints on their internal convection.
Highlights
The standard technique for modeling stars takes a 1-dimensional approach, and assumes the stars are relatively close to spherical
A more realistic model for gravity darkening was derived (Espinosa Lara and Rieutord, 2011). This model relaxes von Zeipel’s assumption of barotopicity, and is thought to be more applicable to real stars, in cases of extremely rapid rotation. This new model was compared to calculations using 2D models constructed with ESTER (Espinosa Lara and Rieutord, 2011) which calculates the gravity darkening naturally as a result of the stellar structure equations, and the results were in good agreement with the new theoretical model
The equations of stellar structure in 1D have been well understood for nearly 100 years, but almost immediately, it was realized that the effects of rotation, binarity, and magnetic fields would introduce 2D or 3D effects that needed to be taken into account
Summary
The standard technique for modeling stars takes a 1-dimensional approach, and assumes the stars are relatively close to spherical. For conservative rotation laws like these, where depends only on the distance from the rotation axis (cylinderical) or center of the star (shellular), the centrifugal acceleration can be derived from an effective potential V. The best-known of these is the meridional circulation introduced by rotation, but tidal or magnetic distortions can introduce flows (Tassoul, 1978) These currents are expected to be slow, with theoretical velocities on the order of 3 × 10−10 cm s−1 (Sweet, 1950). The effective chemical diffusion depends on the square of the velocity of the meridional circulation, so the contribution to chemical mixing is expected to be small in most cases (Zahn, 1992).
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