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9.7 Option - Astrophysics: 6. Stellar evolution

Syllabus reference (October 2002 version)
6. Stars evolve and eventually ‘die’	Students learn to: describe the processes involved in stellar formation outline the key stages in a star’s life in terms of the physical processes involved describe the types of nuclear reactions involved in Main-Sequence and post-Main Sequence stars discuss the synthesis of elements in stars by fusion explain how the age of a globular cluster can be determined from its zero-age main sequence plot for a H-R diagram explain the concept of star death in relation to: planetary nebula supernovae white dwarfs neutron stars/pulsars black holes	Students: present information by plotting Hertzsprung-Russell diagrams for: nearby or brightest stars, stars in a young open cluster, stars in a globular cluster analyse information from a H-R diagram and use available evidence to determine the characteristics of a star and its evolutionary stage present information by plotting on a H-R diagram the pathways of stars of 1, 5 and 10 solar masses during their life cycle

Extract from Physics Stage 6 Syllabus (Amended October 2002). © Board of Studies, NSW.
[Edit: 30 June 09]

Prior Learning:
Preliminary module 8.2 The World Communicates (sections 3, 4 and 5).
Preliminary module 8.5 The Cosmic Engine (sections 1, 2, 3 and 4).

present information by plotting Hertzsprung-Russell diagrams for: nearby or brightest stars, stars in a young open cluster, stars in a globular cluster

• To present information in the form of a Hertzsprung-Russell diagram, be aware of the conventions for drawing this special type of graph:
  • the horizontal axis can represent colour, spectral class, colour index, increasing from left to right, or temperature (K), increasing from right to left;
  • the vertical axis can represent absolute magnitude, increasing from top to bottom, absolute luminosity or luminosity relative to the sun, both increasing from bottom to top;
  • both the horizontal and vertical axes use scales that are logarithmic, not linear.
  
  
• Practice both interpreting and drawing examples of Hertzsprung-Russell diagrams with various combinations of horizontal and vertical axes. Identify that, when stars are plotted on the H-R diagram, they fall into recognisable groupings. Learn to recognise the various regions of the H-R diagram where you would expect to find stars at different stages of their life cycle, including main sequence stars, red giants and white dwarfs.
  
  
• Learn the features of the groups of stars named in the syllabus and make a table of comparisons between their H-R diagrams:
  • the H-R plot of nearby, or of the brightest, stars would be expected to show the full range of spectral types;
  • open clusters are generally young, as they tend to disperse with age, so they are populated with young stars on the main sequence, or even still forming, rather than red giants or white dwarfs;
  • a globular cluster will contain main sequence stars up to a turn off point, with no blue giants, but with red giants and possibly white dwarfs, depending on its age.
  
  
• Your teacher may provide you with sample data on one or more of the above groups of stars. Alternatively, sample data may be obtained from astronomy books or internet sites or from past HSC papers or sample questions. Choose the most appropriate combination of axes to represent the data you have been given. Axes must be clearly labelled and the scales must be drawn accurately. Plot points accurately to best represent relationships within the data. Identify and label different groups of stars represented by your data points. Label the H-R diagram according to the group of stars represented.

Windows to the Universe , University Corporation for Atmospheric Research, University of Michigan., USA. An interactive H-R diagram.

describe the processes involved in stellar formation

• Stellar formation begins with the gravitational contraction of a vast nebula of interstellar dust and molecular gas, mainly hydrogen. If the mass of the nebula exceeds the Jeans mass, the gravitational force within it is greater than any thermal pressure outwards, causing the cloud to begin to collapse and form a growing core of matter at its centre.
  
  
• The increasing gravitational attraction of the core causes the contraction to accelerate. Several stars may form together by fragmentation of a very large nebula to form a cluster. The mass of the dust and gas in each contracting region determines both the mass of the star that forms and where that star ultimately enters the main sequence of the Hertzsprung-Russell diagram.
  
  
• During contraction, gravitational potential energy is converted into thermal energy. The increasing pressure caused by the rising temperature begins to oppose the gravitational force within the nebula, slowing the contraction process. The contraction process can take from a hundred thousand years for a massive star to several tens of millions of years for a small star.
  
  
• The core continues to collapse until the pressure and temperature build up enough for thermonuclear reactions to start, and the star lights up. A balance then occurs between gravity directed inwards and the pressure of radiation outwards from the nuclear fusion in the core, preventing any further collapse. Radiation and fast particles, the stellar wind, are emitted from the star and push away remaining gas and dust that would have fallen into the star. The star then continues to emit radiation in a stable manner for most of the rest of its life.

outline the key stages in a star’s life in terms of the physical processes involved

• Material accumulating at the centre of a nebula, collapsing under its own gravity, forms an expanding core of hot dense matter. Heat radiated from the core causes the surrounding cloud to become luminous. The luminous cloud with its hot, dense core is known as a protostar. The increasing density of the core begins to slow further in-falling of matter.
  
  
• Eventually the protostar reaches a temperature where molecular hydrogen breaks down to atomic hydrogen, allowing further compression and heating. When it reaches its maximum luminosity it is known as a pre-main sequence star. From then, it continues to shrink, becoming hotter but less luminous.
  
  
• A star is known as a main sequence star when the temperature and pressure are high enough for nuclear fusion to switch on and make the star shine. There is a balance between gravity pulling inwards and energy released by fusion pushing outwards, preventing any further gravitational contraction. Dust and gas not yet accreted into the core are removed by the stellar wind, and the star has a distinct surface.
  
  
• The star now lies on the line of the main sequence of the Hertzsprung Russell diagram, where it remains for about 90% of its lifetime, steadily converting molecular hydrogen into helium by fusion in its inner core. Exactly where the star joins the main sequence depends entirely on its mass. During this time, the star becomes hotter and more luminous. Massive stars burn their fuel quickly, while smaller stars, such as the Sun, burn their fuel slowly and therefore spend a long time on the main sequence.
  
  
• When the helium content at the core is around 12%, fusion of hydrogen stops, and the star moves off the main sequence to become a post-main sequence star. Without the energy of hydrogen fusion, the core of the star collapses and rises further in temperature. The helium in the core then begins to fuse to form heavier elements. In very massive stars, this process turns on slowly, while in medium-weight stars the onset of helium fusion is rapid, giving rise to the “helium flash”. The outer layers of the star are now pushed out and cool. The star becomes a red giant or supergiant.
  
  
• A star’s life ends when it runs out of fuel, that is, when fusion of lighter elements into heavier elements in the core ceases and the star collapses under its own gravity.

describe the types of nuclear reactions involved in Main-Sequence and post-Main Sequence stars

• The proton-proton (PP) chain is the predominant type of nuclear reaction in lower mass, cooler main-sequence stars, i.e. under about 20 million Kelvin. It converts hydrogen into helium in three steps:
  
  
  1. Fusion of two hydrogen nuclei (protons) to form a heavy hydrogen (deuterium) nucleus. One proton decays into a neutron, with the release of a positron, and a neutrino.
  2. Fusion of a proton and a deuterium nucleus to form a helium-3 nucleus, with the release of gamma radiation.
  3. Fusion of two helium-3 nuclei to form a helium-4 nucleus and two free protons, which may participate in further PP chain reactions.
• 
  The net result is that 4 protons have combined to form one helium nucleus.

• The carbon-nitrogen-oxygen (CNO) cycle is the predominant type of nuclear reaction in higher mass, hotter main-sequence stars. It also converts 4 protons into 1 helium nucleus but does so by a different process.
  
  Four successive protons combine with a carbon nucleus to produce, first nitrogen, then oxygen and finally carbon again plus a helium nucleus. The first and the third collisions trigger the decay of a proton into a neutron and a positron, thus increasing the number of neutrons in the nucleus. The second and fourth collisions simply increase the number of protons in the nucleus.
  
  This process is cyclic, as a carbon nucleus is present both at the start and at the end, and can initiate the process again. In this sense, carbon acts as a catalyst in the fusion of hydrogen into helium.

• In post-main sequence stars, helium is very plentiful in the core, and three helium nuclei can fuse to form a carbon nucleus through the triple-alpha reaction. This process occurs when the star is at the red giant stage. When the core is mainly carbon, contraction causes the temperature to rise further and helium fuses with carbon to produce oxygen. Further exothermic shell-burning reactions take place in successively deeper shells within the star, converting carbon to neon and magnesium, oxygen to silicon and sulfur, and silicon and sulfur to iron.

discuss the synthesis of elements in stars by fusion

• Only hydrogen and helium were present in the primordial universe. All other elements are synthesised by fusion during the life and death of stars. The mass of the star, and the stage of life of the star, determine which elements are produced.
  
  
• Further helium is produced by fusion of hydrogen in main-sequence stars, either by the proton-proton chain reaction in cooler stars, or by the carbon-nitrogen-oxygen cycle in hotter stars. The rate at which fusion proceeds depends on the temperature and pressure at the core and thus, ultimately, on the mass of the star. These fusion reactions are exothermic: the energy is ultimately released as radiation from the surface of the star.
  
  
• Elements heavier than helium are produced by fusion in post-main sequence stars. Carbon, oxygen, neon and magnesium are produced by the triple alpha reaction, followed by fusion of product nuclei with further alpha particles. In the larger stars “shell burning” can produce all the elements up to iron. These reactions are exothermic and will proceed provided there is enough energy to initiate the reaction.
  
  
• Beyond iron, the reactions are endothermic but inside red giant stars heavier nuclei can still be formed by the slow capture of neutrons. This process can produce elements as heavy as lead.
  
  
• When massive stars explode, forming supernovae, the additional process of the fast capture of neutrons occurs, which is capable of producing all the elements heavier than iron, such as gold and uranium.

analyse information from a H-R diagram and use available evidence to determine the characteristics of a star and its evolutionary stage

• Analyse information from the H-R diagram for any particular star, by observing the position of the star within one of the known groups on the H-R diagram, and by reading the scale value of the star plot on each axis.
  
  
• Determine as many characteristics of the star as possible, and its evolutionary stage by using other evidence available to you, such as:
  
  
• The vertical axis of the H-R diagram may show the star’s mass relative to the sun, its absolute luminosity or its luminosity relative to the sun. The horizontal axis may show the star’s surface temperature, its spectral class or its colour index.
  
  
• Stars fall into distinct groups in the H-R diagram, with common characteristics of luminosity (hence, mass) and temperature (hence, colour), and at a similar evolutionary stage. The regions include:
  • the main sequence (diagonally from bottom right to top left), the red giants (middle to upper right side
  • cool, but very luminous, therefore very large), white dwarfs (bottom middle and left
  • hot, but low luminosity, therefore small) and the supergiants (across the top of the H-R diagram
  • both very hot and very luminous).
  
  Knowing this it is possible to tell what group a star belongs to from its position on the H-R diagram.
  
  
• Stars pass through a common evolutionary sequence, from protostar to main sequence star, to red giant and then, depending on mass, to a white dwarf, a neutron star or black hole.
  
  
• A higher mass star evolves more quickly than a lower mass star.

explain how the age of a globular cluster can be determined from its zero-age main sequence plot for a H-R diagram

• Stars in a globular cluster are believed to be all of approximately the same age, having formed together from a single, large nebula. Theoretically the cluster could contain stars covering the whole possible range of stellar masses.
  
  
• The H-R diagram for a cluster of stars with different masses, which have all just reached the main sequence, having just begun to consume hydrogen, is called the zero age main sequence (ZAMS) plot.
  
  
• When clusters are observed, it is found that the main sequence is missing the larger more massive blue stars. The more massive a star is, the more quickly it burns up its hydrogen fuel and moves off the main sequence. As a cluster ages, the H-R diagram for the cluster appears to ‘peel back’ from the main sequence.
  
  
• Hence the age of a globular cluster can be estimated from the expected lifetimes of stars that sit on the main sequence at the “turn-off” point of the globular cluster’s H-R star plot.

explain the concept of star death in relation to:

• planetary nebula
• supernovae
• white dwarfs
• neutron stars/pulsars
• black holes

• Star death occurs when the fusion of elements in the core of the star ceases and the outward pressure of radiation is insufficient to prevent the gravitational collapse of the star. The processes that occur, and the nature of the object that remains, depend on the mass of the star.
  
  
• After a low mass star, less than about 2-5 solar masses, has moved into the red giant stage and the helium flash has occurred, carbon and oxygen build up in the core. The core begins to contract and the star undergoes a series of bursts in luminosity, ejecting successive layers of atmosphere to form expanding shells of material around the core. Viewed from a distance, the shells appear as rings, known as planetary nebulae.
  
  The temperature of the core is insufficient to cause fusion of carbon and oxygen into heavier elements. The extremely hot, dense core simply contracts and cools very slowly, remaining white hot for a long time because the mass is great and the surface area small. The small surface area also means that it has a low luminosity and is therefore very faint. It is known as a white dwarf.
  
  
• In a more massive star, more than about 5-8 solar masses, iron forms by fusion of lighter elements, and is deposited in the core. Collapse of the core is halted only by a quantum effect called electron degeneracy, as electrons resist being forced into the nucleus. However the density and pressure rise until they exceed this outward degeneracy pressure. The core collapses catastrophically and rebounds, producing shockwaves that totally disrupt the star and blast much of its matter into space. During this phase, the star increases dramatically in luminosity, up to several hundred billion times. This event is called a supernova.
  
  If the mass of the core is greater than 1.4 times the mass of the sun, the degenerate core consists of neutrons and is known as a neutron star. Further collapse is now halted only by neutron degeneracy pressure. Neutron stars often have strong magnetic fields associated with beams of radiation from the poles. If the neutron star is rotating, the radiation will sweep around the neutron star like a lighthouse beam. If the Earth is in the path of the beam as it rotates, we detect the beacon as rapid regular pulses of radio waves. Such a rotating neutron star is known as a pulsar.
  
  
• If the core is of sufficient mass, exceeding three solar masses, not even the neutrons can sustain the enormous pressure, and the core continues to collapse. A singularity in space time is formed, known as a black hole. The gravitational field of a black hole is so strong that even light cannot escape.

present information by plotting on a H-R diagram the pathways of stars of 1, 5 and 10 solar masses during their life cycle

The term solar mass refers to the mass of a star compared to the mass of the sun. The sun has 1.0 solar mass.

• In presenting information with a H-R diagram, the emphasis is on conveying information and relationships clearly and accurately. Both axes of your H-R diagram should be correctly labelled and logarithmic scale divisions drawn accurately. Star data must be plotted accurately against the scale on each axis.
  
  
• Label the regions through which stars pass, on the H-R diagram, such as the main sequence stars, the region of red giants and the region of white dwarfs.
  
  
• Draw the evolutionary pathway of each star by showing:
  • where it enters the main sequence from the protostar region
  • where it leaves the main sequence to become a red giant
  • where it turns around as a red giant, or goes to supernova
  • where a low-mass star ends up as a white dwarf
  
  
• The way in which a star evolves is determined solely by its mass. The more massive the protostar, the higher to the left on the H-R diagram it moves onto the main sequence. A small star will enter the main sequence at the bottom right of the H-R diagram and spend a great deal of time there. A very large star of, say, 10 solar mass, will enter the main sequence towards the top left of the H-R diagram and have a short, explosive life.

The following web sites will help you to identify the evolutionary path taken by stars over a range of solar mass.

Basics of the HR diagram Davison E. Soper, University of Oregon., USA. A site that shows where stars of 0.1 to 10 solar masses enter the main sequence.

Stars and Stellar Evolution Cornell University, USA. An interactive site where the evolution of stars of different mass, from 0.1 to 120 solar masses, can be simulated.