Neglecting the gradient of composition, Equation 6 becomes Δ ln T = 1 3 Δ ln ρ, which gives the 1/3 slope of the evolution of stars in a diagram of T as a function of ρ ( Figure 1). For example, in the case of a perfect gas ( P = ρ μ m H k T, with k the Boltzmann's constant and m H the hydrogen mass), we have α = δ = φ = 1. In this general expression for the hydrostatic equilibrium, all the subtleties of the physics are hidden in the values for α, δ, and φ. Thanks to their gaseous nature, they resist most of their lifetime by adjusting on a thermal structure that provides the pressure needed to exactly counterbalance the gravitational pull, and settle on what is called hydrostatic equilibrium, where the pressure gradient exactly compensate for the gravity: The evolution of stars is a long and desperate struggle against gravity. This review intends to summarize the safe grounds and challenges of massive star evolution modeling and nucleosynthesis, with a focus on the role played by the reaction rates of importance in the modeling. While a full evolution of the entire star for its complete lifetime is not possible in 3D, the hydrodynamical simulations can provide precious recipes for 1D secular evolution modeling. In parallel, the improvement of computational facilities makes it possible to study some physical processes (like convection) from first principles in hydrodynamical simulations. Since a couple of decades, large surveys (either dedicated to massive stars or wide enough to include a significant number of them) are starting to fill this gap and provide observational constraints that highlight the strengths and weaknesses of our massive stars models. However, as they are much rarer than low- or intermediate-mass stars, it has for a long time been impossible to have statistically significant observations of massive stars, and our understanding relied mainly on stellar models. Their intense luminosity makes them dominant contributors to the spectra of galaxies, and tracers of star formation in the early Universe. Massive stars are key drivers of the evolution of the Universe, through the chemical and kinetic imprint they impose on their surrounding.
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