Stellar Evolution Stars spend most of their lives on the main sequence. Evidence: 90% of observable stars are main-sequence stars. Stellar evolution during the main-sequence life-time, and during the post-main-sequence phase, is driven by the conversion of hydrogen into helium in their cores. Stars expand and become more luminous while on the main-sequence. Why? -> The conversion of H into He changes the chemical composition in the core. According to the ideal gas law (see on-line notes for equations of stellar structure), the pressure is given by: P = k/(m H μ) ρ T. k = Boltzmann s constant, m H = mass of a hydrogen atom, μ = mean molecular weight (measured in units of the mass of a hydrogen atom), ρ = gas density, T = temperature. μ=1/2 in a pure hydrogen plasma, which consists of unbound electrons and protons. Each H-atom provides two particles, an electron and a proton. The electron is approx. massless, so average mass of the gas particles = (1/2) x mass of the H-atom (or proton). Given that μ is measured in units of m H -> μ=1/2. For a pure helium plasma, each He-atom contributes 3 particles (2 electrons, 1 helium nucleus). The electrons are ~ massless, and the He nucleus has a mass ~ 4 H-atoms. -> μ=4/3 in this case.
μ increases as a star converts H to He -> causes the central pressure P to decrease (see equation of state on previous slide). The stellar core contracts and the central temperature increases -> increases luminosity of the star because nuclear reactions occur at an increased rate when the temperature increases. Increased luminosity causes the star s envelope around the core to expand and the surface temperature to increase. During its main-sequence life so far, the Sun has increased its luminosity by 40%, increased its radius by 6%, and increased its temperature from 5500 K to 5800 K. The diagram below shows the change in the chemical composition of the Sun over its life-time so far.
Main sequence life-times We know empirically that the luminosity, L, and mass, M, of a star are related by L is proportional to M 3.5. If we consider that during the main sequence a star burns a fixed fraction, f, of its mass of hydrogen, then the total amount of energy released E = f M c 2. The luminosity of the star can be expressed L = E/t where t is the total time spent on the main sequence. This can be rearranged to give the main sequence life-time t = (f M c 2 ) / L We know that L is proportional to M 3.5, so we see that t is proportional to M -2.5. High mass stars have main sequence life times very much less than low mass stars. This is because the hotter temperatures at the centres of high mass stars cause them to burn their hydrogen much more rapidly than low mass stars do. The table lists the main sequence life times for stars of differerent spectral type.
Post-main sequence evolution of a solar type star When a solar type star reaches end of its main sequence life all of its core hydrogen has been converted into helium. Only a thin shell of hydrogen at the outer edge of the core continues to undergo H-burning > this is called shell hydrogen fusion. As nuclear reactions cease in the inner core -> core cools and contracts as pressure decreases. Contraction converts gravitational energy into heat (Kelvin-Helmholtz contraction) and the core temperature increases. Heat radiates out of the core into surrounding region. Increase in temperature increases rate of shell hydrogen fusion -> the shell of burning hydrogen eats out slightly into surrounding hydrogen envelope. He produced by H burning sinks down into core. Core continues to contract and heat up. Over time of 100 s of millions of years the core contracts to be about 1/3 of its original radius, while the central temperature increases from 15 million K up to 100 million K. During the core contraction, the star s outer layers expand dramatically because the increasingly large shell of hydrogen fusion causes the luminosity to increase. Envelope expansion causes the surface temperature to decrease to 3500 K -> the star glows with a distinctive red colour. A red-giant star has now been formed. Weaker gravity at the surface of the red-giant allows substantial mass loss in the form of a stellar wind. The mass loss is strong enough that it could deplete the star s mass completely in 10 million years.
The image to the right compares the size of the Sun as a red giant with its current size. The Sun will expand by a factor of about 100 as it becomes a red giant, achieving a radius of ~ 0.5 AU. Fusion of helium the triple-alpha process Fusion of helium requires a larger Coulomb barrier to be overcome because He nuclei have twice the charge of H nuclei. -> Central temperature of star needs to be higher to fuse helium. Contraction of the core of a star as it becomes a red giant, assisted by helium sinking onto the core from the shell of burning hydrogen, causes the temperature to exceed 100 million K, at which point helium begins to fuse.
Helium fuses via the triple-alpha process (see on-line supplementary lecture notes), and results in formation of C and O.
The helium flash In a solar-type star the fusion of helium begins in an explosive event called the helium flash. The helium flash occurs because of unusual conditions in the centre of the star. During the main sequence, the centre of a star acts like an ideal gas it heats up when compressed, and there is a simple relation between pressure, density and temperature. Quantum mechanics plays a role when the matter at the centre of the star becomes very dense. The Pauli exclusion principle states that no two electrons can simultaneously occupy the same quantum state. A collection of electrons in a small volume (as is present in the hot plasma at the centre of the red giant) are subject to this principle. Electrons have spin ±1/2 -> two electrons can occupy the same energy level, but no more. The electrons in the plasma occupy different energy levels. -> Only two electrons can occupy the ground state. -> Only two electrons can occupy the 1 st excited state, etc. This forces electrons to have higher energies than predicted by the temperature of the gas, leading to a phenomenon known as electron degeneracy pressure. As the helium core of the red giant tries to contract just prior to the onset of helium burning, it is prevented from doing so by the electron degeneracy pressure.
When helium fusion ignites, the rise in temperature would normally cause the core to expand, reducing the rate of nuclear reactions so that a stable equilibrium can be reached. The ignition of He in the star s centre occurs when degeneracy pressure supports the core -> the rising temperature does not initially change the pressure. The rising temperature due to ignition of He fusion leads to more and more rapid He fusion -> leading to explosive ignition known as the helium flash. This breaks the electron degeneracy so that the core becomes supported by ideal gas pressure. The helium flash lasts a couple of seconds, but releases energy equivalent to 10 11 times the luminosity of the Sun. Only a modest effect is seen at the surface of the star -> most of this energy goes into heating the core and removing the degenerate state. After the helium flash the red giant decreases in luminosity even though the core is now burning helium. -> The now non-degenerate core expands, and this cools the hydrogen burning shell, decreasing its luminosity. The hydrogen shell still provides most of the luminosity of the star during the red giant phase. The decrease in luminosity causes the star s envelope to contract, allowing the surface temperature to increase. This causes the star to move down and leftward on the H-R diagram.
The H-R diagram for a solar-mass star shows the star ascending the giant branch to become a red-giant. It then moves down and to the left as the luminosity decreases and the temperature increases after the helium flash (shown by the *). Core helium fusion only lasts for 100 million years (compared with 12 billion years for the main sequence). During this time the star occupies a region of the H-R diagram called the horizontal branch.
After helium fusion stops the core consists of carbon and oxygen atoms. These cannot undergo fusion reactions in the core of a sun-like star because the temperature never gets high enough. The core contracts again because it lacks a heat source to compensate for energy that it radiates. Contraction of the core is eventually stopped by electron degeneracy pressure. Contraction heats the core up -> radiates heat into the surrounding star, heating up region just outside the contracting core. When temperature there reaches 100 million K -> helium fusion begins in a thin shell around the C and O core (this helium has been created largely by the hydrogen burning shell). This is called shell helium fusion.
Shell helium fusion increases the star s luminosity -> causing stellar envelope to expand and cool again > the star goes through a second red giant phase when it ascends the asymptotic giant branch in the H-R diagram. Stars on this branch are called AGB stars. An AGB star consists of an inert, degenerate C+O core, a helium fusing shell, and a hydrogen fusing shell, all within a volume just larger than that of the Earth. This is surrounded by a hydrogen-rich envelope that expands to be as large as the Earth s orbit around the Sun. Expansion of the envelope allows expansion and cooling of the underlying hydrogen burning shell, causing H-fusion to cease (see the diagram). AGB stars have strong winds that cause mass loss at a rate of 10-4 solar masses per year, and surface temperatures of ~ 3000 K. The stars envelope is convective, and the convection can dip into the core and dredge-up heavy elements such a C, N and O. This allows the interstellar medium to be enriched with heavy elements as the AGB star loses its envelope.
Planetary nebulae The last stage in the evolution of a solar-type star is the formation of a planetary nebula. Here, the AGB star goes through a series of thermal pulses generated by a series of helium flashes that occur in the helium burning shell (when the helium is used up in the shell, it contracts and heats up, allowing helium from the over-lying hydrogen burning shell to ignite). Sudden increases in luminosity causes the overlying hydrogen envelope to be pushed away from the star in a series of pulsations. The expansion and cooling of the envelope allows heavy elements to condense into small dust grains, and when these are exposed to the intense UV radiation coming from the hot (100,000 K) degenerate core, radiation pressure drives the envelope away from the star, eventually leaving behind a white dwarf star consisting of C and O and supported by electron degeneracy pressure. The white dwarf contains ~ 60% of the original stellar mass. The other 40% is ejected into the interstellar medium. The white dwarf is the burnt out remnant of a main sequence star, and gradually cools while remaining supported by electron degeneracy pressure.
The diagram shows a summary of the life of a solar-type star from the main sequence to the formation of a cooling white dwarf.