From Stars to Nuclei

We recall the basic physical principles governing the evolution of stars with some emphasis on the role played by the nuclear reactions. We argue that in general it is not possible from observations of stars to deduce constraints on the nuclear reaction rates. This is the reason why precise measurements of nuclear reaction rates are a necessity in order to make progresses in stellar physics, nucleosynthesis and chemical evolution of galaxies. There are however some stars which provides useful constraint on nuclear processes. The Wolf-Rayet stars of the WN type present at their surface CNO equilibrium patterns. There is also the particular case of the abundance of Ne at the surface of WC stars. The abundance of this element is a measure of the initial CNO content. Very interestingly, recent determinations of its abundance at the surface of WC stars tend to confirm that massive stars in the solar neighborhood have initial metallicities in agreement with the Asplund et al. (2005) solar abundances 1 Stellar evolution in a nutshell 1.1 Luminosity as a consequence of hydrostatic equilibrium Stars are a privileged place in the universe where microscopic phenomena interact with macroscopic ones. If the long range force of gravity plays the main role in driving the birth of the stars, their life and sometimes their death (in core collapse supernovae), the other three interactions of physics contribute to the processes of production, transfer and loss of energy either under the form of electromagnetic radiation or through neutrinos. During the longest part of their life, stars are in hydrostatic equilibrium. An element of star in equilibrium undergoes a gravitational force balanced by a pressure gradient. In a normal star, pressure depends on temperature and therefore the existence of a pressure gradient implies the build up of a temperature gradient. Higher is the temperature, greater is the quantity of energy contained per 1 Geneva Observatory, CH–1290 Sauverny, Switzerland c © EDP Sciences 2008 DOI: (will be inserted later) 2 Title : will be set by the publisher unit volume in the radiation field. Since the central parts are hotter than the outer ones due to the temperature gradient implied by hydrostatic equilibrium, energy flows from the inner parts of the star to the outer ones and thus the star continually loses energy. Interestingly, more efficiently the energy is evacuated from the central regions where it is produced, hotter become these central regions! Indeed, if the central regions loses energy, the temperature gradient will become weaker and the central regions will slowly contract, making them warmer! Stars (made of perfect gas) are thus systems with a global negative specific heat. This energy has of course to be extracted in one way or another from the stellar material. These mechanisms of extraction of the energy are responsible for the evolution of the star. Stars evolve because they continually lose energy to maintain hydrostatic equilibrium, or in other words to balance the gravitational force. It is interesting to note here that these logical deductions do not involve any particular source of energy. Luminosity is a direct consequence of the hydrostatic equilibrium and not of the nuclear reactions which occur in its stellar interior. Of course nuclear reactions are important and we are going to see how below. 1.2 The main energy reservoirs There are actually two main sources of energy in a star: First, a star can extract energy from the gravitational potential through global (macroscopic) contraction. Second, a star can also release energy by the thermonuclear reactions which take place in its central regions where the temperature and density are adequate for such processes to occur (microscopic contractions). These two processes for producing energy have different characteristic timescales. If the Sun had only the gravitational energy source, its lifetime would be of the order of a few tens of million years, instead a simple estimate gives a lifetime of ten billion years when nuclear sources are taken into account. Only this last value is in agreement with what we know about the past history of Earth and on the apparition of life at its surface. Therefore the presence of the nuclear source is important not to explain the luminosity of stars (stars could be shining even without hosting nuclear active regions), but for explaining why they can shine for very long durations. Beside this energetic aspect, nuclear reactions are of course the process through which chemical elements are transformed in stars. They are thus at the heart of stellar nucleosynthesis and play a key role in the long chain of processes going from the Big Bang to the apparition of living bodies. The evolution of a star can be viewed as a succession of phases where the energy is mainly produced by the nuclear reactions and of phases where the energy is mainly produced by contraction. When the star has burned all the nuclear fuel available in its central regions, in order to maintain the luminosity required by the hydrostatic equilibrium, it has to produce energy via contraction, until new central conditions are reached adequate for the ignition of new nuclear reactions. This succession of contraction periods will increase both the central temperature and density. At a given point (which depends mainly on the initial mass of the Georges Meynet: From stars to nuclei 3 star), the central regions can become sensitive to degeneracy effects. 1.3 Energy production in perfect gas and degenerate conditions Let us recall that degeneracy pressure results from the exclusion principle: only two fermions of spin one half, such as electrons, neutrons, or neutrinos, may locally occupy the same quantum state. Two particles are in two different quantum states if the product of their difference in position ∆x and their difference in momentum ∆p is superior to the Planck constant. An increase of the density restricts the domain for the positions and thus reduces ∆x. The exclusion principle means therefore that certain particles will acquire very large impulses, much greater than that they would acquire by thermal agitation. These particles with large velocities exert a new sort of pressure which is not thermal in origin and which depends only on the density. Depending on the fact that the stellar material is degenerate or not, the two main sources of energy, contraction and nuclear reactions, have very different behaviors. In non degenerate conditions, nuclear reactions are stable and contraction implies an increase of the central temperature. In degenerate conditions, nuclear reactions are explosive and contraction may produce a cooling of the medium. Let us first consider a uniform contraction of a massM . In that case a variation in radius ∆R corresponds to a variation in pressure ∆P and to a variation in density ∆ρ so that we have the following relations: ∆P P = −4 ∆R R , and ∆ρ ρ = −3 ∆R R . The first equality is deduced from the hydrostatic equilibrium equation and the second from the continuity equation. From these two relations, we can write