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Ageing Stars Transcript Ageing Stars Transcript Date: Thursday, 2 October 2008 - 12:00AM AGEING STARS Professor Ian Morison What is a star? If a large mass of gas is formed in the space between the stars, gravity will cause it to take on a spherical shape as it reduces in size. As the gas in the centre is compressed it heats up until the pressure produced is sufficient to halt the contraction. If the central temperature has then reached in excess of ~10 million degrees, the protons at it heart will be moving sufficiently fast (and hence have sufficient kinetic energy) so that a pair moving in opposite directions will be able to overcome their mutual repulsion and so get sufficiently close to allow the first stage of nuclear fusion to commence. The fusion process, which converts protons (hydrogen nuclei) to alpha particles (helium nuclei), generates energy which eventually reaches the surface and is radiated away as heat and light - the ball of gas has become a star. This lecture will look at how stars in different mass ranges evolve during the later stages of their life, and describe the remnants left when they die: white dwarfs, neutron stars and black holes. Low-mass stars: 0.05 to 0.5 solar masses For a collapsing mass of gas to become a star, nuclear fusion has to initiate in its core. This requires a temperature of ~ 10 million K and this can only be reached when the contracting mass is greater than about 1029 kg, about one twentieth the mass of the Sun, or twenty times that of Jupiter. In low-mass stars the conversion of hydrogen to helium by nuclear fusion is the same as in our Sun. However, whereas in stars of greater mass nuclear fusion only converts about 10% of the mass of the star (that residing in its core), in the lowest mass stars it is thought that convection currents mix the star's interior and so will allow much of the stars mass to undergo nuclear fusion so increasing the time during which they can carry out the fusion of hydrogen to helium - a period which is significantly longer than the present age of the universe. We thus have no direct observational evidence of what happens when fusion ceases in such stars and can only use computer modelling to investigate what might happen. We will see that in order for helium to fuse into heavier elements, temperatures of order 100 million K are required and this requires sufficient mass in the star's envelope to provide the required pressure to enable such temperatures to be reached. In stars of mass less than 0.5 solar masses there is simply not enough pressure to give the temperatures that would allow helium fusion to begin. So when nuclear fusion, converting hydrogen to helium, finally ceases - and modelling of a 0.1 solar mass red dwarf suggests that this might be after six trillion years - the star will slowly collapse over a period of several hundred billion years to form what is called a white dwarf. Over many trillions of years, the white dwarf will cool until its surface temperature is below that at which significant light is emitted and the inert remnant will become ablack dwarf. No white dwarfs derived from low- mass stars yet exist, but they will be discussed in detail in the following section on mid-mass stars as their evolution also produces white dwarfs which can now be observed. Mid-mass stars: 0.5 to ~8 solar masses All stars in this range will have a common end state in the form of a white dwarf. There is, however, a difference in the process of nuclear fusion from hydrogen to helium in stars above and below ~2 solar masses. For stars whose mass is less than ~2 solar mass stars, like our Sun, the bulk of its energy is produced by what is called the proton-proton cycle. However there is a more complex process called the Carbon-Nitrogen-Oxygen (CNO) cycle that provides 1 to 2% of the Sun's total energy output. In stars greater than about 2 solar masses this process, proposed independently by Carl von Weizsäcker and Hans Bethe in 1938 and 1939 respectively, becomes dominant. It provides a very efficient way of converting hydrogen to helium so the hydrogen in more massive stars burns more quickly so increasing the energy output of the core. As the greater energy output of the star must be balanced by radiation from its surface, the star becomes bluer and has a greater luminosity. The reactions of the CNO cycle are: 12C + 1H → 13N + y 13 13 + N → C + e + ve 13C + 1H → 14N + y 14N + 1H → 15O + y 15 15 + O → N + e + ve 15N + 1H → 12C + 4He The net result of the cycle is to fuse four protons into an alpha particle along with two positrons, two electron neutrinos (which carry some energy away from the star) and three gamma rays. The carbon acts as a catalyst and is regenerated. The two positrons annihilate electrons releasing energy in the form of gamma rays - each annihilation giving rise to two gamma rays. Figure 1: The Carbon-Nitrogen-Oxygen Cycle. When the CNO process reaches an equilibrium state, the reactions of each stage will proceed at the same rate. The slowest reaction within the cycle is that which converts 14N into 15O so, in order for this reaction to have an equal reaction rate, the number of nitrogen nuclei must be significantly larger that those of carbon or oxygen. Thus, over time, the relative amount of nitrogen increases until equilibrium is established. Whilst the total number of the carbon, nitrogen and oxygen nuclei is conserved, nitrogen becomes the most numerous nucleus, regardless of the initial composition. This process produces essentially all of the nitrogen in the universe and thus has great significance for us as nitrogen is an essential element of all life-forms here on Earth. An (perhaps surprising) increase in energy output as a star ages As the proton-proton or CNO cycles convert hydrogen to helium in the core of the star, its mean molecular weight increases. The pressure of an ideal gas increases with the temperature of the gas, but decreases as the mean molecular weight of the gas rises. Assuming (correctly) that the matter in the core acts like an ideal gas, in order for the pressure to remain sufficient to support the overlying layers of the star as the amount of helium increases, the core's temperature must rise. The rate of, for example, the proton-proton chain is a function of the fourth power of the temperature, so that even though the percentage of hydrogen is reducing, the conversion rate of hydrogen to helium gradually increases over time. This, of course, increases the energy output of the star, so its luminosity will increase and, in order to radiate more energy, so will its surface temperature. It is believed that, when formed, our Sun was ~30% less bright than at the present time and that over the next billion years its luminosity will increase by a further 10%. An obvious consequence is that our Earth will eventually become too hot for life (as we know it) to exist on its surface. The Triple Alpha Process Eventually, either by the proton-proton chain or the CNO cycle, the core of the star will be converted into 4He. At this point nuclear fusion stops so that the pressure in the core that prevents gravitational collapse drops. The core thus reduces in size but, as it does so, its temperature will rise. Finally when it reaches ~ 100 million K, a new reaction occurs - the triple alpha process (3[]), so called because it involves three helium nuclei which are also known as alpha particles. This is an extremely subtle process. The first obvious nuclear reaction that would happen in a core composed of helium is that two 4He nuclei fuse to form 8Be. But 8Be is very unstable - it has a lifetime of only 10-19 seconds - and virtually instantly decays into two 4He nuclei again. Only when the core temperature has increased to 100 million K, does it become likely that a further 4He nucleus can fuse with 8Be before it decays. The result is a12C nucleus. It is highly significant to our existence here on Earth that there is such a difference in temperature between that (~ 15 million K) at which the hydrogen fuses to helium and that (~ 100 million K) at which12C can be formed. If this were not the case, and the process could happen at the core temperatures close to that at which the proton-proton or CNO cycles operate, there would be no long period of stability whilst the star remains on the main sequence with a relatively constant luminosity. This, of course, has allowed stable temperatures to exist on Earth for billions of years and so enabled intelligent life to evolve. Figure 2: The Triple Alpha Process. But there is a further real problem in attempting to form 12C. A temperature of 100 million K is required to give the 4He nuclei a reasonable chance to fuse with a 8Be nucleus before it has a chance to decay. The 4He nuclei are thus moving very fast and so have appreciable kinetic energy. It would be expected that this energy would prevent a stable 12C nucleus arising as it would be sufficient to split the newly formed nucleus apart. (If a white billiard ball (4He) approached a red ball (8Be) very slowly they might just "kiss" and remain touching, but if it came in at high speed the energy of impact would split them apart).
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