Download Stellar Evolu1on Stars spend most of their lives on the main

Stellar Evolu,on Stars spend most of their lives on the main sequence. Evidence -­‐> 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 conversion of hydrogen into helium in their cores. Stars expand and become more luminous while on the main-­‐sequence -­‐> 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/(mH μ) ρ T. k = Boltzmann’s constant, mH = 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 par,cles, an electron and a proton. The electron is approx. massless, so average mass of the gas par,cles = (1/2) x mass of the H-­‐atom (or proton). Given that μ is measured in units of mH -­‐> μ=1/2. For a pure helium plasma, each He-­‐atom contributes 3 par,cles (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. Stellar core contracts and central temperature increases as the central pressure decreases due to the increase of μ -­‐> increases luminosity of the star because nuclear reac,ons 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 composi,on of the Sun over its life-­‐,me so far. 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 M3.5. 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 c2. 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 c2) / L We know that L is propor,onal to M3.5, so we see that t is propor,onal to M-­‐2.5. High mass stars have main sequence life ,mes very much less than low mass stars. This is because the hober 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 ,mes for stars of differerent spectral type. Evolu,on of stars less than 0.4 Msun Low mass stars-­‐> oden 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 109) 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. 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 -­‐> core cools and contracts as pressure decreases. Contrac,on converts gravita,onal energy into heat (Kelvin-­‐Helmholtz contrac,on) 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. Helium produced by H burning sinks down into core. Core 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. Envelope expansion causes the surface temperature to decrease to 3500 K -­‐> the star 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. 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 -­‐> He nuclei have twice the charge of H nuclei. -­‐> Central temperature of star needs to be higher to fuse helium. Contrac,on 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 -­‐> helium begins to fuse. Helium fuses via the triple-­‐alpha process (see on-­‐line supplementary lecture notes), and results in forma,on 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 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. Quantum mechanics plays a role when the maber 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 collec,on 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 1st 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 reac,ons so that a stable equilibrium can be reached. The igni,on of He in the star’s centre occurs when degeneracy pressure supports the core -­‐> the rising temperature does not ini,ally change the pressure. The rising temperature due to igni,on of He fusion leads to more and more rapid He fusion -­‐> leading to explosive igni,on 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 1011 ,mes the luminosity of the Sun. Only a modest effect is seen at the surface of the star -­‐> most of this energy goes into hea,ng the core and removing the degenerate state. Ader 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 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 ledward 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 led as the luminosity decreases and the temperature increases ader 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. Ader helium fusion stops the core consists of carbon and oxygen atoms. These cannot undergo fusion reac,ons in the core of a sun-­‐like star because the temperatures never get high enough. The core contracts again because it lacks a heat source to compensate for energy that it radiates. Contrac,on of the core is eventually stopped by electron degeneracy pressure. Contrac,on heats the core up -­‐> radiates heat into the surrounding star, hea,ng up region just outside the contrac,ng 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 asympto,c 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 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. 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). Sudden increases 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 ~ 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 forma,on of a cooling white dwarf.