Evolution of Massive Stars

Fabrice Fleurot

The main sequence

Galaxies are filled with tenuous hydrogen-helium clouds of the dimensions of tens of light-years, either coming from former stars or made of original Big-Bang matter. When a local instability makes part of a cloud contract, the central density and temperature of what is a new protostar increase by transforming gravitational potential energy into thermal energy. After a few hundreds of thousand years, when this process provides enough energy (at T=107 K), protons can effectively tunnel the Coulomb barrier which normally keeps them apart and commence hydrogen burning, producing primarily 4He nuclei via the proton-proton (p-p) chain. The p-p chain initiates with p+p and d+p fusion reactions and is afterward split into the trhee following branches:
p + p → d + e+ + νe
d + p → 3He + γ

p-p-I: 85%
p-p-II: 15%
p-p-III: 0.01%
3He + 3He → α + p + p 3He + α → 7Be + γ 3He + α → 7Be + γ
7Be + e- + 7Li + νe 7Be + p → 8B + γ
7Li + p → α + α 8B → 8Be + e+ + νe
8Be → α + α
and can be summarized as p(3p,2e+e2γ)4He releasing an energy of 26.73 MeV. Another unprobable reaction occurs 0.0025% of the time with respect to p+p, the so-called pep reaction:
p + e- + p → d + νe .
The '8B neutrinos' of branch III are easier to detect because of their large energies and those detected in detectors such as SNO or Super-Kamiokande.

Whether the original cloud is made of gas stemming from previous generations of stars, it contains heavier (so-called 'metallic') elements produced in the late stages of the evolution of these stars. Population-I stars are defined as such second- or third-generation stars, while population-II stars contain only nuclei dating from the Big-Bang, i.e. mainly hydrogen and helium. A population-I star contains in particular 12C, which, if the temperature is sufficient, induces the CNO cycles. Although the abundance of these three elements is quite low (about 2%) this is a repeating catalytic process that produces most of the 4He in massive stars:

13C (p,γ) 14N (p,γ) 15O (e+νe) 15N (p,α) 12C (p,γ) 13N (e+νe) 13C .
In lighter, colder stars like the Sun, most of the energy is produced by the p-p chain, while heavier stars produce most of their energy from by main CNO cycle. Other secondary CNO cycles exist, which can be neglected in first approach since they do not contribute significantly, though they consume some of the catalysers; and other cycles involve isotopes in very low abundance. The final state of this stage is a mainly-helium core containing about 2% of 14N.

When fusion reactions have started, the hot cloud has become a star. The release of thermal kinetic energy due to hydrogen burning balances the gravitational force and maintains the new-born star at an equilibrium state. Some tens of million years more are needed to stabilise the radiative and convective processes. Such young, hydrogen-burning stars define the Main-Sequence group. The temperature and luminosity of a star are functions of the mass and can be plotted on the Hertzsprung-Russell (HR) diagram. While the heaviest stars burn their hydrogen in a few tens of thousand years, the lightest can shine as long as several times the age of the Universe (e.g. 56 billion years for a 0.5 Mʘ star). As for the Sun, it can burn during nine billion years and is nowadays in the middle of its life.

Hertzsprung-Russell diagram
Stellar evolution summarised on the Hertzsprung-Russell diagram. The yellow circle is the Sun position in this diagram and the blue circle is a 5-Mʘ star. The path followed by evolved stars is shown for both masses with indications of the important phases.

Helium burning stage

After a certain fraction of hydrogen in the star's core has been converted into helium, the energy produced is not sufficient to prevent its gravitational collapse and the burning hydrogen moves outward building a thin, growing shell of hydrogen and producing new helium. As the core collapses slowly, the thermal energy provides shell burning that pushes away the external layers to tens of times the initial radius so that the star leaves the Main Sequence. The energy coming up from the central region is spread out over the larger outer surface. As a result the energy per unit area decreases and the surface cools as the star slowly proceeds along the 'Horizontal Branch' of the HR diagram towards the 'Asymptotic Giant Branch' (AGB). The life time of this stage is of the order of one tenth of that of the hydrogen burning stage.

The core becomes unable to transfer heat fast enough, and as the temperature and the density of the core increase, the star experiences 'helium flashes', or quick helium-burning processes. With the increasing thermal pressure, the core starts expanding, which leads to a cooling and subsequently to a reduction of hydrogen burning in the surrounding shell. Therefore, the outer shells contract rapidly as the core expands. A quiescent helium-burning hydrostatic stage follows.

At 1.5×108 K, the thermal energy is sufficient to allow helium nuclei to tunnel through their Coulomb barrier. The binding energy of two 4He nuclei is negative and the resulting unstable 8Be nucleus releases the two α particles in a very short time (10-16 s). However, this decay time is long when compared to the transit time of two α particles (10-19 s) in the stellar environment. Thus, there is an equilibrium between production and destruction of 8Be so that this element is actually present in the star. Moreover, a resonance in the 12C nucleus at exactly the right energy makes the α radiative capture on 8Be very likely to happen such that 12C can formed in the star. This two-step reaction is known as the triple-alpha process:

4He + 4He + 4He ↔ 8Be + 4He → 12C + γ .
A temperature of 2×108 K then allows 12C nuclei to capture an α particle, producing 16O by the key reaction 12C(α,γ)16O.

The above-described stages are responsible for the fact that oxygen and carbon are, respectively, the third and fourth most abundant elements in the Universe (after hydrogen and helium), the observed ratio being 12C/16O = 0.4. Most of the heavier elements stem from either of the two nuclei, for example 23Na, 24Mg, 27Al from 12C and 28Si, 32S, 36Ar from 16O. Therefore, all heavier-element abundance in stars is strongly dependent on the 12C/16O ratio, which makes the alpha capture on carbon one of the most important reaction in nuclear astrophysics. Unfortunately, this reaction is poorly known due to a very low cross section and thus has been actively investigated over the last decades.

Near the end of the helium-burning stage the star has built a carbon-oxygen core, surrounded by helium-burning and hydrogen-burning shells and a vast hydrogen mantle.

Further evolution

The star now evolves on the Asymptotic Giant Branch (AGB) where new helium flashes take place. Neutrons are produced by 22Ne(α,n)25Mg and 13C(α,n)16O reactions, 13C resulting from proton capture on 12C. For a low density (108 n/cm3) the slow capture of neutrons by nuclei, followed relatively quickly essentially by β-decay, produces heavier elements eventually reaching 209Bi. This is referred to as the s-process, which may last for millions of years.

During the star evolution on the AGB, the C-O core is collapsing until the temperature is sufficient (7×108 K) for carbon burning to start producing new elements: 12C(12C,p)23Na, 12C(12C,α)20Ne, etc..

The temperature reached in the stars heavier than 8 Mʘ (>109 K) permits nucleosynthesis processes to occur with heavier elements: the neon-, oxygen- and silicon-burning stages produce elements up to the most stable ones, 56Ni and 56Fe.

The star is now at a pre-supernova stage showing approximately a shell structure composed of a nickel-iron core surrounded by layers of burning silicon, neon, oxygen, carbon, and helium, and a vast mantle of hydrogen. Due to convection, these shells tend to mix up.

Pre-supernova core
A pre-supernova is roughly shell-structured from iron-nickel to hydrogen-helium. In reality, frontiers are not that sharp due to convection processes.

Supernova

The ultimate stage of heavy stars (>8 Mʘ) takes place when the iron-nickel core is being built. These elements, being the most stable of all isotopes, can not burn any further. The core builds up until it reaches the 'Chandrasekhar mass' (about 1.4 Mʘ) where the electron-degeneracy pressure is exceeded. The core collapses and, when the thermal pressure reaches the nucleon degeneracy level, bounces at 10-20% of the speed of light. A few-millisecond neutronization phase occurs when electrons are captured on protons, generating a massive burst of electron neutrinos (1% of the total neutrino energy, as much as the total photon energy), which turns the 10-20 km core into a neutron star of the density of an atomic nucleus:
p + e- → n + νe .

The shock wave propagating outwards competes with the matter falling inwards such that it stalls around 100-200 km from the centre within 1 ms. The temperature behind the shock wave is sufficient to generate neutrinos of all flavours by various thermal processes such as pair annihilation, plasmon decay, photoneutrino and Bremsstrahlung. Respectively:

γ + γ ↔ e+ + e- → ν + ν ,
e+ + e- → ν + ν ,
γ + e- → e- + ν + ν ,
e- + A → A + e- + ν + ν ,
where A is a nucleus.

The neutrinos diffuse out of the 'neutrinosphere' (opaque to neutrinos) in a few seconds and a fraction of them heat up the mantle inside the shock wave (called the 'gain region'). The rest is released into space, carrying away 99% of the total energy of the supernova (~31053 ergs). It is currently thought that the re-energization of the shock wave by neutrino heating is the key process that leads to the supernova explosion, which occurs about 0.5 s after the core collapse. If the mass of the core is sufficient (>1.5-2.2 Mʘ), the neutrino flux ends abruptly with the creation of a black hole within 1-2 s of the core collapse.

The shock wave needs a few hours to reach the surface of the star, then the supernova explosion finally becomes visible.

In the case of massive stars, during the last moments of the supernova explosion, the high temperature (109 K) induces the r-process: a neutron high density (1020 n/cm3) makes neutron capture more rapid than β-decay (1 second). This also produces neutron-rich isotopes which eventually β-decay to heavy radioactive nuclei.

The heavy elements produced during the star evolution and the supernova explosion are then released in space in the form of a nebula, while the core remainder becomes a neutron star or a black hole. It is thought that progenitor stars with masses greater than 18-20 Mʘ end up as black holes.

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Further reading: Cauldrons in the Cosmos, C.Rolfs 1988.