Matteo Cantiello

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Stellar Evolution

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The night sky looks still and peaceful, but stars are not eternal. They are born, live and die. This is a tale with gravity as protagonist. The same force that is responsible for the initial cloud of gas to form the protostar, has to be counteracted by the gradient of the internal pressure. Only in this way a star can be in hydrostatic equilibrium. The required energy is  mostly provided by nuclear reactions in the stellar interiors, which turn a small fraction of the rest mass into energy. Thermonuclear reactions in the stellar interior release energy and at the same time synthesize, starting from hydrogen, heavier elements. This process is called stellar nucleosynthesis. Studying stars humans discovered that, aside from hydrogen, all of  the elements we are made of have been synthesized inside stars. A star is a self-regulating system, because the amount of energy released by nuclear burning is exactly the amount  needed to counteract the gravitational force. If the equilibrium is perturbed, the star readjust  its structure, such that the nuclear reactions provide again the right amount of energy.  In this way stars can be stable for long timescales during hydrogen burning (the so-called main sequence). This phase cannot last forever, since the amount of fuel inside of stars is  finite, and energy is released only from the fusion of isotopes lighter than iron. When a sufficient amount of energy can no longer be extracted from the rest mass of the star, the  battle against gravity is lost. Then the final fate of the star depends on the mass of the object: low mass stars end their lives as white dwarfs, while massive stars (more massive than about 8 solar masses)  die in spectacular explosions or disappear forming a black hole.

 

In order to predict stellar nucleosynthesis, the stellar interior has to be modeled. The interior of stars is not quiet. The main reason is that huge amounts of energy are produced in the inner parts of a star, creating strong temperature gradients. This energy eventually escapes from the inside of the star through its surface, transported from below through radiative transfer or convection. Convection, in particular, results in turbulent motions of the stellar plasma; a clear example of this process is visible at the surface of the Sun. In general such motions are able to transport chemical species and angular momentum. In the case of convection the turbulent motions are also able to excite waves, which can propagate and transport energy through the star. In the presence of rotation, further instabilities of the stellar plasma can develop. Rotation also contributes to the generation of magnetic fields, which provide further instabilities and mixing processes. Thermohaline mixing is driven by another instability that may occur in the stellar interior in regions where an inversion in the mean molecular weight is created. Finally, in the case of extremely high temperatures, the production of electron-positron pairs from photons can destabilize the stellar core and induce collapse. This results in the so-called pair creation supernovae (PCSN).

 

It is important to emphasize that modern stellar evolution calculations do not solve the full 3D hydrodynamic equations in the stellar interior. The reason is that this is computationally impossible. The timescale of the evolution of a star (nuclear timescale) is much longer than the timescale of the hydrodynamical processes occurring in its interior (dynamical or thermal timescale). As a consequence a numerical time-step resolving convection or any other hydrodynamical process for the entire stellar evolution would results in almost endless calculations. At least with the actual computational facilities. The trick is to restrict the simulations to 1D, and implement complex hydrodynamical phenomena as diffusion processes. The code is still solving the 1D hydrodynamic equations, but the transport of chemical species and angular momentum resulting from complex instabilities, is implemented through a diffusion scheme. An analytical approach is used to estimate the speed of mixing and angular momentum transport as function of physics parameters. This permits the calculation of a diffusion coefficient for each physical process considered; these coefficients are added together and enter the diffusion equation. Therefore the single processes can be modeled, but it is clear that this approach will neglect possible interactions between different instabilities.