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7–1 Stellar Structure and Evolution The life of stars is a continual struggle between gravity which tries to collapse a star and other forces which hold the star up. At different points in a stars life, it is different processes which hold a star up against gravity. In following a star’s evolution we will follow its path in the H-R Diagram (how its temperature and luminosity vary). Stellar Birth Stars form from large clouds of dust and gas called molecular clouds. Typically, a molecular cloud of several thousand solar masses starts to collapse. As it collapses, small fluctuations cause it to subfragment into hundreds to thousands of smaller collapsing regions—each forming an individual star. Thus, roughly hundreds to thousands of stars are created from each collapsing cloud creating a cluster of stars. In what follows, we will examine a single protostar (a single subfragment of the cloud): Evidence for theory of stellar birth Each protostar begins life as a large cold (10K to 100K) cloud. Where would it be on the HR-diagram? As it collapses, it shrinks in size leading to a release of gravitational energy. Some of this energy is radiated away, but some also goes into heating up the forming star. As it shrinks and heats up would you expect it to become more or less luminous or can you tell? Evidence for interstellar material is seen from a variety of sources. Emission nebula: Gas clouds near hot stars. Atoms in cloud are excited by absorbing light from the nearby star. Appear pinkish in color due to emission of hydrogen balmer lines. Reflection nebula: Starlight reflected off dust particles in the nebula. What path does it take on the HR diagram? Because the dust scatters blue light most effectively, they appear bluish in color. 7–2 Dust clouds: Dust in an interstellar cloud can obscure light from stars behind it. Often can be seen as dark patches in the milky way. Energy Production in Stars How is energy produced in the sun? Earth is 4.5 billion years old so energy source for the sun must be able to power it at least that long: Chemical reactions (combustion)? Young stars are often associated with nebulae indicating that they are regions of star formation. While most of the initial formation of stars is obscured behind dust and gas around the star, the last leg to the main sequence can be seen. At its present luminosity, the sun could shine for only about 30,000 years if its energy were produced by chemical reactions. Gravitational energy? Gravitational energy could supply the sun’s luminosity for about 30 million years. Better but not enough. Nuclear reactions? Where does the excess mass go? Nuclear reactions provide the only energy source powerful enough to power the sun. Nuclear fusion of hydrogen into helium in the Sun can fuel the sun for about 10 billion years. Nuclear Reactions The mass of the elements per nucleon (proton or neutron) varies slightly. For example, 4 hydrogen nuclei (1 proton each) are slightly more massive than one helium nucleus (2 protons and 2 neutrons). Thus, fusing four hydrogen atoms into one helium atom results in a loss of mass (about 0.7% of the total mass). 7–3 Hydrogen Fusion Main Sequence Stars Because nuclei are positively charged, they repel each other. As a protostar collapses, the gravitational energy released heats up the star until the core becomes hot enough for hydrogen fusion to begin. For fusion to occur, this repulsive force must be overcome and the nuclei brought close together. Thus, fusion can only occur at very high temperatures (~15,000,000K) where the nuclei are moving fast enough to overcome the repulsion. At this point the energy generation by fusion counteracts gravity. The protostar has reached the main sequence. What if the star were compressed? Because of this fusion depends sensitively on the temperature: Release of gravitational energy would heat up interior... What if the star were expanded? Mass-Luminosity Relation This sensitivity of fusion reactions to the temperature creates a stable situation with fusion just counteracting gravity. Luminosity α Mass3.5 Different masses of stars will find their own stable configuration along the main sequence: Massive stars: How long will a star live? Star’s lifetime α Fuel Available Rate of Energy Production A star’s available fuel goes as the mass of the star. Its rate of energy production is the luminosity. Low mass stars: ==> Star’s lifetime α M α M = 1 L M3.5 M2.5 ==> High mass star’s live brief lives. Position of a star on the main sequence depends mostly on its mass. Why are most main sequence stars low mass red dwarfs? 7–4 Life on the main sequence Eventually, stars will exhaust their fuel of hydrogen, having fused the hydrogen into helium. Star’s spend about 90% of their lives on the main sequence burning hydrogen into helium. What happens to stars at this point? Stars are quite stable during this time maintaining nearly the same temperature and luminosity. The evolution of stars after life on the main sequence follows different paths depending on the mass of the star. ==> remain at the same point in the H-R Diagram. This explains why most of the stars we see are main sequence stars. However, stars do evolve slightly during their lives on the main sequence: Evolution of medium mass stars (0.4 to a few solar masses) With no more fusion taking place one might expect gravity to win and collapse the star into a black hole. Helium nuclei have more charge than hydrogen, thus it takes higher temperatures to fuse helium. However, as the star collapses another mechanism comes into play to counteract gravity: Electron degeneracy pressure. ==> after hydrogen is exhausted, the core is not hot enough to fuse helium. Thus, energy production in the core ceases: Recall that electrons can only have certain permitted energies in atoms. The same is true of electrons confined to the volume of the star. According to the Pauli Exclusion principle, no two electrons can occupy the same state. In a low density gas, the Pauli Exclusion Principle is not very important because few levels are occupied and electrons can change energy freely. The regions around the core still contain hydrogen. As they are heated, hydrogen fusion begins in a shell around the helium core. However, as the gas is compressed to higher density, more and more energy levels are occupied. 7–5 If the gas is compressed enough, all of the lower energy levels are occupied by electrons and the gas becomes degenerate. In a degenerate gas some electrons must occupy higher energy levels because there are no lower energy levels available. Even at low temperatures (even absolute zero), these electrons will have considerable energy, moving about quickly. This energy and motion creates an outward pressure—electron degeneracy pressure. This electron degeneracy pressure is what halts the gravitational collapse in white dwarf stars. Because it does not depend on the temperature or the production of energy, electron degeneracy pressure can hold a white dwarf star up indefinitely. However, massive stars cannot do this. Thus, they cannot end their lives as white dwarfs. However, there is a limit to the size of a star which can be supported by electron degeneracy pressure. As mass is added to a white dwarf star, it shrinks in size. When a white dwarf star reaches a mass of 1.4 solar masses it shrinks to a radius of zero. Masses greater than 1.4 solar masses cannot be supported by electron degeneracy pressure. What happens to stars more massive than 1.4 solar masses? If the star is not too massive (perhaps up to a few solar masses), it may shed enough mass during their lives to get under the 1.4 solar mass limit. Evolution of low mass stars (<0.4 solar masses) What happens to these stars? We’ll see later. But first we’ll take a detour to examine the evolution of low mass stars. As we found earlier, these stars live long lives on the main sequence. They also have the advantage that they are convective throughout their interiors. Allows it to burn all its hydrogen, not just that in the core of the star—lives even longer than one would otherwise expect. In fact, their expected lifetimes are longer than the age of the universe. Thus we would not expect to see any which have fully evolved yet. What is expected to happen when they run out of hydrogen? 7–6 As with heavier stars, the core will start to collapse and heat up. However, unlike heavier stars, no hydrogen left: The star will continue to collapse. However, being of such a low mass it never becomes hot enough to ignite helium. Thus, after its hydrogen burning phase, no further fusion takes place and the star continues to cool off Being under 1.4 solar masses, the collapse is eventually halted by electron degeneracy pressure. Stars will end up as white dwarf stars as well.