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1 Stellar Evolu,on Stars spend most of their lives on the main sequence. Evidence for this is provided by the fact that 90% of stars observable from Earth are main- sequence stars. Stellar evolu,on during the main- sequence life-,me, and during the post- main- sequence phase, is driven by the fact that stars convert hydrogen into helium in their cores. Stars expand and become more luminous while they are on the main- sequence. This is because the conversion of hydrogen into helium changes the chemical composi,on in the core. According to the ideal gas law (see on- line notes for equa,ons of stellar structure), the pressure is given by P = k/(m H μ) ρ T where k = Boltzmann s constant, m H is the mass of a hydrogen atom, μ is the mean molecular weight (measured in units of the mass of a hydrogen atom), ρ is the gas density and T is the temperature. In a pure hydrogen plasma, where the gas consists of unbound electrons and protons, the value of μ=1/2. Each hydrogen atom provides two par,cles, an electron and a proton, but the electron is essen,ally massless so the average mass of the gas par,cles equals (1/2) x the mass of the hydrogen atom (or proton)). Given that μ is measured in units of m H, we have that μ=1/2. For a pure helium plasma, each helium atom contributes 3 par,cles (2 electrons, 1 helium nucleus). The electrons are essen,ally massless, and the helium nucleus has a mass essen,ally equal to 4 hydrogen atoms. The value of μ=4/3 in this case. So we see that μ increases as a star converts H to He, and this causes the central pressure P to decrease.

2 As the central pressure decreases due to the increase of μ, the stellar core contracts and the central temperature increases. This increases the luminosity of the star because the nuclear reac,ons occur at an increased rate when the temperature increases. The 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 composi,on of the Sun over its life-,me so far.

3 Main sequence life-,mes We know empirically that the luminosity, L, and mass, M, of a star are related by L is propor,onal to M 3.5. If we consider that during the main sequence a star burns a fixed frac,on, 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,me spent on the main sequence. This can be rearranged to give the main sequence life-,me t = (f M c 2 ) / L We know that L is propor,onal to M 3.5, so we see that t is propor,onal to M In other words, high mass stars have main sequence life,mes very much less than low mass stars. This is because the ho`er temperatures at the centres of high mass stars cause them to burn their hydrogen much more rapidly than low mass stars do. The table below lists the main sequence life,mes for stars of differerent spectral type.

4 Evolu,on of stars less than 0.4 M sun Low mass stars are oben referred to as red dwarfs because of their low surface temperatures and red- ish appearance (Wien s displacement law). They are fully convec,ve in their interior, and these convec,ve mo,ons mix the helium and hydrogen in the star throughout its life,me. As helium builds up in the core it is mixed into the rest of the star, and fresh hydrogen is mixed into the core. A consequence of this is that almost all of the hydrogen in these stars is converted into helium. The central temperatures of red dwarfs is lower than in the Sun, so nuclear reac,ons occur more slowly. This, combined with the convec,ve mixing, causes the main sequence life-,me of these stars to be 100 s of billions of years. The age of the universe is only 13.7 billion (13.7 x 10 9 ) years. The end- state of these stars is a helium star that is unable to convert helium to heavier elements. In the absence of nuclear reac,ons this star will slowly cool and contract un,l electron degeneracy pressure prevents its further collapse.

5 Post- main sequence evolu,on of solar type star When a solar type star gets to the end of its main sequence life all of its core hydrogen as been converted into helium. At this stage only a thin shell of hydrogen at the outer edge of the core con,nues to undergo hydrogen burning this is called shell hydrogen fusion. As nuclear reac,ons cease in the inner core, the core cools and begins to contract as the pressure there decreases. As we know, contrac,on converts gravita,onal energy into heat (Kelvin- Helmholtz contrac,on) and the core temperature increases. Heat radiates out of the core into the surrounding region, and the increase in temperature there increases the rate of shell hydrogen fusion, making the shell of burning hydrogen eat into the surrounding ma`er. Helium produced by H burning sinks down into the core which con,nues to contract and heat up. Over a,me 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 contrac,on, the star s outer layers expand drama,cally because the increasingly large shell of hydrogen fusion causes the luminosity to increase. The envelope expansion causes the surface temperature to decrease to 3500 K and the star now glows with a dis,nc,ve red colour. A red- giant star has now been formed. Weaker gravity at the surface of the red- giant allows substan,al 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.

6 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 helium nuclei have twice the charge of hydrogen nuclei. Therefore the central temperature of a star needs to be higher in order to fuse helium. Contrac,on of the core of a star as it becomes a red giant, assisted by the addi,on of helium sinking onto the core from the shell of burning hydrogen, eventually causes the temperature to exceed 100 million K, and helium can begin to fuse.

7 Helium fuses via the triple- alpha process (see on- line supplementary lecture notes), and results in forma,on of C and O.

8 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 condi,ons 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 rela,on between pressure, density and temperature. When the ma`er at the centre of the star becomes very dense then quantum mechanics begins to play a role. The Pauli exclusion principle states that no two electrons can simultaneously occupy the same quantum state. When confined to a,ny volume, a collec,on of electrons (as is present in the hot plasma at the centre of the red giant) are subject to this principle. Electrons have spin ±1/2, so two electrons can occupy the same energy level, but no more. So, if we consider that the electrons in the plasma can occupy different energy levels, only two electrons can occupy the ground state, only two electrons can occupy the 1 st excited state, etc 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.

9 When helium fusion ignites, the rise in temperature would normally cause the core to expand slightly, reducing the rate of nuclear reac,ons so that a stable equilibrium can be reached. But the igni,on of He in the star s centre occurs when degeneracy pressure supports the core, so the rising temperature does not ini,ally change the pressure. Consequently the rising temperature due to igni,on of He fusion leads to more and more rapid He fusion, leading to the explosive igni,on known as the helium flash. This breaks the electron degeneracy so that the core becomes supported by the pressure of an ideal gas. The helium flash is over in a couple of seconds, but releases an amount of energy per second that is 10 11,mes the luminosity of the Sun. Only a modest effect is seen at the surface of the star, however, because most of this energy goes into hea,ng the core and removing the degenerate state. Paradoxically, aber the helium flash the red giant actually decreases in luminosity even though the core is now burning helium. This occurs because the now non- degenerate core expands, and this expansion cools the hydrogen burning shell, decreasing its luminosity. The hydrogen shell s,ll 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 lebward on the H- R diagram.

10 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 leb as the luminosity decreases and the temperature increases aber 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,me the star occupies a region of the H- R diagram called the horizontal branch.

11 Aber helium fusion ceases the core consists mainly of carbon and oxygen atoms. These are unable to undergo fusion reac,ons in the core of a sun- like star because the temperatures never get high enough. Consequently the core contracts again because it lacks a heat source to compensate for the fact that it radiates energy out into the rest of the star. Contrac,on of the core is eventually stopped by electron degeneracy pressure. The contrac,on heats the core up, and this radiates heat into the surrounding star, hea,ng up the region just outside the contrac,ng core. When the temperature here reaches 100 million K then helium fusion begins in a thin shell surrounding the C and O core (this helium has been created largely by the hydrogen burning shell). This is called shell helium fusion.

12 Shell helium fusion once again increases the star s luminosity, and this causes the stellar envelope to expand and cool again the star goes through a second red giant phase when it ascends the asympto,c giant branch in the H- R diagram. Stars on this branch are usually referred to as AGB stars. When a star first becomes an AGB star it 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 convec,ve, and the convec,on 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.

13 Planetary nebulae The last stage in the evolu,on of a solar- type star is the forma,on 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). The sudden increase in luminosity causes the overlying hydrogen envelope to be pushed away from the star in a series of pulsa,ons. 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 radia,on coming from the hot (100,000 K) degenerate core, radia,on pressure drives the envelope away from the star, eventually leaving behind a white dwarf star consis,ng of C and O and supported by electron degeneracy pressure. The white dwarf contains approximately 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.

14 The diagram shows a summary of the life of a solar- type star from the main sequence to the forma,on of a cooling white dwarf.

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