PHYSICS TUTORIAL NOTES

 

The Cosmic Engine

 

SYLLABUS TOPIC 8.5

 

 

 

These notes are meant as a guide only and are designed to focus your thoughts on the dot points mentioned in the syllabus. They give a very brief overview of the topic and should be used in conjunction with your class notes, your textbooks and your research from other areas such as the library and the Internet.

 

 

 

Notes compiled by:

CARESA EDUCATION SERVICES

 

 


 

The Cosmic Engine

 

“1. Our Sun is just one star in the galaxy and ours is just one galaxy in the Universe” (syllabus)

 

“Students learn to outline the historical development of models of the Universe from the time of Aristotle to the time of Newton” (syllabus)

 

EARLY ASTRONOMY

 

Observations of the Earth’s place in the universe are as old as mankind itself. The ancients would have been aware of the day as a fundamental measurement of time and a knowledge of the regular pattern of the seasons would have enabled them to plant crops at the best times. Ancient structures such as the pyramids and Stonehenge are aligned in a way to indicate that ancient civilisations had a knowledge of the positions of the Sun and stars at particular times of the year.

 

Around 530 B.C. Pythagoras suggested that the Earth was a sphere. He and his followers proposed that the motion of the heavens was perfect and as such, celestial objects were spherical in shape and could only move in circular paths.

 

Plato (~429-347 B.C.) proposed that the motion of the heavens could be determined by analysing combinations of circular motions with Earth at the centre. Models with the Earth at the centre are called “geocentric”.

 

Eudoxus (~440-347 B.C.) proposed a model where the Earth was the centre of the Universe and the celestial bodies revolved around the Earth in paths represented by 27 concentric spheres that surrounded the Earth. He explained the motion of the Sun and Moon in terms of the motion of three spheres each, and the motion of the five known planets in terms of four spheres each. The outer sphere contained the fixed stars. The Eudoxus model was just that: a model to aid predictions and calculations, he did not believe that the spheres actually existed. He was able to predict the positions of the Sun, planets and stars with a fairly high degree of accuracy.

 

Aristotle (~384-322 B.C.) improved the predictive power of the Eudoxus model by increasing the number of spheres to 55.

 

Aristarchus of Samos (~310-230 B.C.) proposed that the Sun was at the centre of the Universe and that the Earth, Moon and stars revolved around the Sun. Models with the Sun at the centre are called “heliocentric”. He explained night and day by proposing that the Earth was spinning and revolved on its axis once every day. His model explained to a certain extent, the complicated motions of the planets as well as why they varied in brightness. His ideas were rejected because they defied “common sense”. People of the time knew that if you rode a horse then you would feel the wind rushing past you. Obviously if the Earth was moving then the air would be rushing past and produce a constant wind. Also birds would fly backwards as the Earth moved underneath them. Also if the Earth revolved around the Sun then a parallax shift of the positions of the stars should be seen at different stages of the Earth’s orbit. No such parallax was observed.

 

Eratosthenes of Cyrene (~275-194 B.C.) measured the circumference of the Earth. He learned that on the summer solstice the Sun was directly overhead at Syene (now called Aswan – on the tropic of Cancer) at noon and would not cast a shadow. He determined the angle subtended by the Sun at Alexandria at this instant and found that it was 7o12’ away from the zenith. The distance between Syene and Alexandria had been measured as 5000 stadia. Hence the circumference of the Earth was measured as:

360/7o12’ x 5000 = 250 000 stadia.

While the exact length of a stadium has been lost in time it is approximately equal to 1/6 km. This would give a value of about 40 000 km as the circumference of the Earth – accurate within a few percent of today’s value.

 

Ptolemy (~127-151 A.D.), guided largely by the writings of Aristotle, searched for a series of spheres that would explain the observations. Two particular observations that could not be explained by models at this time were (i) retrograde motion of the planets and (ii) differences in a planet’s brightness.

 

Ptolemy developed a model in which the Earth, while being the centre of the Universe, was not the centre of all circular motions. He included three important devices in his theory: the eccentric, epicycle and equant.

(i)                 The eccentric: He proposed that the centre “c” of the circular path of a body could be off centre (eccentric) from the Earth. This could account for the seasonal irregularity that was observed in the Sun’s rate of motion.

 

                 The Eccentric

 

(ii)               The epicycle: The planets were considered to be moving in uniform circular motion about the circumference of a small circle called the epicycle. The centre of the epicycle moves in uniform circular motion in a path around the Earth. The large circle is called the deferent.

 

                                                The Epicycle

This would account for variations in brightness of the planets as well as their retrograde motion.

 

(iii)             The equant: To allow for variations in the motions of the planets (e.g. variations in angular size of the retrograde motion of Mars) Ptolemy introduced the equant. The Earth in this model is off centre, but the motion of the planet is not uniform about c, the centre of the circle, but about a point c’ which is on the opposite side of the centre to the Earth and equidistant from it.

 

 

                                               

                                                                           The Equant

 

Ptolemy’s model was quite accurate in predicting the positions of celestial objects. In addition it explained the retrograde motion of the planets and their variation in brightness. It also satisfied the theological notion of the Earth being at the centre of the Universe.

 

Copernicus (1473-1543) proposed a heliocentric system of more than 30 eccentrics and epicycles. His system made the following assumptions:

(i)                 There is not a precise geometrical centre of all celestial spheres or circles.

(ii)               The Earth is not the centre of the Universe but only of gravitation and the Lunar sphere.

(iii)             All spheres revolve around the Sun and therefore the Sun has the central location in the Universe.

(iv)             The distance of the Earth from the Sun is imperceptible in comparison to its distance from the stars.

(v)               The apparent motion of the sky arises from the motion of the Earth rather than motion of the sky. The Earth with its water and air rotates daily while the sky remains unchanged.

(vi)             The apparent motions of the Sun arise from motions of the Earth, which revolves around the Sun similar to the other planets. Earth has more than one motion.

(vii)           The apparent retrograde motion of the planets arises from the Earth’s motion.

 

Copernicus’ model was able to determine the period of each planet’s motion around the Sun while the sphere of stars was seen to be fixed and immobile. It was also able to determine the size of each planet’s orbit compared to the Earth’s orbit.

 

Although the Copernican system had an overall simplicity to it, it was no more accurate than the Ptolemaic system in predicting the motions of the planets. It was largely rejected because of the theological argument that man’s home should be at the centre of the Universe and also because there was no observable shift for fixed stars. This would imply that the distance to the stars was immense; more than 1000 times the distance between the Earth and the Sun.

 

Tycho Brahe (1546-1601) learned that the sky was unchanging but in 1572 a new star appeared that was so bright it could be seen in the daytime. It faded over a few years and disappeared from view. He had observed a supernova.

King Frederick II of Denmark offered him an observatory at Uraniborg and an income. He observed the comet of 1577 and by comparing observations from Denmark with observations in other parts of the world he noted that its position against the Moon varied on a particular date but its position against the background stars remained the same. He deduced that the comet was several times further away than the Moon. Up until this time comets were thought to be a local phenomenon like clouds or lightning.

Tycho’s main contribution to astronomy was his many and precise observations. He made better instruments and determined and specified limits of precision of instruments. He developed a compromise between the heliocentric and geocentric models of the Universe. In his system all planets move around the Sun and the Sun moves around the stationary Earth. 

 

Johannes Kepler (1571-1630) was invited to become one of Tycho’s assistants in Prague in 1600. Here he had to determine the precise orbit of Mars. After Tycho died in 1601, Kepler inherited all of his observations. After 1½ years of observations and calculations based on a Sun-centred universe, Kepler concluded that the orbit of Mars was not circular. By using several groups of observations made over 687 days (a Mars year) Kepler was able to determine the Earth’s orbit. He found it to be almost circular with the Sun a little off-centre. He concluded that the area swept out by a line to the Sun is equal for a given time interval.

Kepler then plotted the shape of Mars’ orbit and found that it was not circular. He found that it was an ellipse with the Sun at one focus. Kepler’s two laws were published in 1609. In 1619 he published a third discovery; the square of the period of a planet’s orbit is proportional to the cube of its average radius of orbit, i.e. T2 a r3. This law was found to apply to all planets and even to comets.

Summarising Kepler’s Laws:

  1. The planets move in elliptical orbits with the Sun at one focus.
  2. A line drawn from the planet to the Sun sweeps out equal areas in equal times.
  3. The square of the period is proportional to the cube of the average distance from the Sun.

 

 

Galileo Galilei (1564-1642) observed a new star in 1604. This star that suddenly appeared was a supernova and it awakened Galileo’s interest in astronomy. About 4-5 years later, Galileo learned that a Dutchman, Hans Lippershey, had developed a telescope, so Galileo proceeded to build one for himself. Galileo was the first to use the telescope for astronomy and in 1609-1610 made the following observations:

  1. The Moon: He observed that its surface was not smooth but covered with mountains and craters. He calculated the height of some lunar mountains.
  2. The Milky Way: He saw that it is not a continuous band of blotchy light but thousands of faint stars.
  3. Jupiter: He observed the four large satellites around Jupiter and determined their period.
  4. Venus: He found that Venus shows phases, just as the Moon does.
  5. The Sun: By projecting an image of the Sun onto a screen he was able to observe sunspots. From the movement of sunspots he was able to determine the period of rotation of the Sun.

 

His observations challenged accepted beliefs in the following ways:

  1. The Moon was not perfectly smooth and spherical as all extraterrestrial objects were claimed to be.
  2. Since stars were created so people could see at night there should be no stars invisible to the naked eye.
  3. Satellites revolving around another planet contradict the idea that the Earth is the centre of all celestial motions.
  4. Phases of Venus show that Venus must move completely around the Sun (Copernicus) rather than always be between the Earth and Sun (Ptolemy).
  5. Sunspots show that the Sun is not perfect but disfigured.

 

Isaac Newton (1642-1727) showed that Kepler’s law of periods was the result of an inverse square law; F a 1/d2. He proposed that the force that pulls objects to the ground might also keep planets in orbit around the Sun.

He calculated the rate at which the Moon should be pulling things towards the Earth. The distance to the Moon is about 60 times the radius of the Earth. Assuming that the inverse square law holds then the acceleration of the Moon towards the Earth should be 9.8/602 = 2.7 x 10-3 ms-2. Newton obtained a similar result when he calculated the centripetal acceleration: a = v2/r = rw2.

Whereas earlier astronomers were convinced that the natural path of celestial objects was circular or spherical, Newton proposed that their natural path was a straight line and a force must be acting to get them to travel in a circle. From his second law of motion (F = ma) he realised that the force would be proportional to each of the masses. He combined these two ideas to give the relationship F a m1m2/d2. By putting in a constant of proportionality he determined F = G m1m2/d2.

By assuming G was the same for all bodies, Newton was able to calculate the relative masses of the Sun, Moon and planets. To calculate the actual masses it was necessary to determine G.

 

Henry Cavendish (1731-1810) did this in 1798. He constructed a torsion balance capable of measuring very small forces (around 10-6 N) and used it to measure the force between two large metal spheres. By substituting in Newton’s equation he was able to determine G. The accepted value of G is around 6.67 x 10-11 N m2 kg-2.

 

“Students identify data sources, and gather, process and analyse information to assess one of the models of the Universe developed from the time of Aristotle to the time of Newton to identify limitations placed on the development of the model by the technology available at the time.” (syllabus)

 

The model proposed by Ptolemy was accepted for around 1400 years; longer than any other model. While it is easy for us to criticise this model in the light of today’s technology, it had good powers of prediction and explained things in a way that was intuitively plausible to people of the time. Heliocentric models put forward by people such as Aristarchus relied on the Earth rotating on its axis every day. This denied logic to the people of the time because experience told them that such motion would be felt. Also the air would rush past as a high wind and birds would fly backwards. Also if the Earth was orbiting the Sun then a parallax movement of the stars should be observed. No such parallax could be detected. We know now that the distance to the stars is immense and they would subtend very small angles from different parts of the Earth’s orbit. No technology existed at the time to measure such small angles. The biggest advance in technology that facilitated the progression from this model of the Universe was the invention of the telescope by Lippershey and its application to the study of the heavens by Galileo. While the Copernican model was heliocentric, its predictive power was little better than the Ptolemian model and it still relied on epicycles for the predictions to fit the data. With his telescope Galileo observed

  1. The Moon: He observed that its surface was not smooth but covered with mountains and craters. He calculated the height of some lunar mountains.

Ptolemy

  1. The Milky Way: He saw that it is not a continuous band of blotchy light but thousands of faint stars.
  2. Jupiter: He observed the four large satellites around Jupiter and determined their period.
  3. Venus: He found that Venus shows phases, just as the Moon does.
  4. The Sun: By projecting an image of the Sun onto a screen he was able to observe sunspots. From the movement of sunspots he was able to determine the period of rotation of the Sun.

 

While Galileo’s telescopic observations are generally taken as the major evidence against the geocentric theory some of his work in mechanics is also very important. He conducted experiments in which objects were dropped from the crow’s nest of moving boats. Such experiments showed that the object was moving forward with the boat and would fall vertically down when viewed from the boat but would follow a parabolic path when viewed from the shore. This explained how the air and everything in it is moving with the Earth and would not produce a wind due to this motion.

 

The following websites discuss some of these issues:

http://faculty.fullerton.edu/cmcconnell/planets.html#2

www.astro.utoronto.ca

www-astronomy.mps.ohio-state.edu/ ~pogge/Ast161/Unit3/galileo.html

www.seds.org/messier/xtra/Bios/galileo.html

www-gap.dcs.st-and.ac.uk/ ~history/Mathematicians/Galileo.html

galileoandeinstein.physics.virginia.edu/ lectures/galtel.htm

csep10.phys.utk.edu/astr161/lect/history/galileo.html

es.rice.edu/ES/humsoc/Galileo/Things/telescope.html

www.crs4.it/Ars/arshtml/galileo3.html

www.galileo-galilei.org/galileo-telescope.html

 

 

“2. The first minutes of the Universe released energy which changed to matter, forming stars and galaxies.” (syllabus)

 

“Students learn to: outline the discovery of the expansion of the Universe by Hubble, following its earlier prediction by Friedmann.” (syllabus)

 

COSMOLOGY – THE ORIGIN OF THE UNIVERSE

 

Let’s start with a silly question. “Why is it dark at night?” 

I can hear your answer now. “It is because the Sun is on the other side of the Earth and consequently the Earth obscures the light from the Sun, and the stars are so far away that the light from them is very dim.”

 

Now while the light from each star is very dim, how many stars are there? If the Universe is infinite and stars are distributed more or less evenly throughout the Universe there should be an infinite number of stars. Now while there do not appear to be an infinite number in the night sky there are certainly more than we can count. Observing from a dark region such as out in the countryside, well away from city lights, you will notice that the stars appear more distinct and you can see more of them. Observing the sky through a telescope will reveal even more stars that are not visible to the naked eye. How much light should we get from all these stars?

 

Suppose we consider all the stars on the surface of a sphere of radius 100 light years around the Earth and suppose there are n of them.  Suppose the light intensity from each star is I. The total intensity is nI. If we now go out to a distance of 200 light years there are 4n stars since the surface area of a sphere is 4pr2 and so if we double the radius we get 4 times the surface area. However since the light intensity from the stars decreases according to the inverse square law (I a 1/d2) then we only get ¼ as much light from each star. But ¼I x 4n is nI so we now have a total intensity of 2nI. Similarly when we consider the stars on a sphere of radius 300 light years we get 1/9 I x 9n which is nI and so on.

 

As you can see the further we go out the greater the number of spheres we consider and the greater the number of nI’s that we have to add. If the universe is infinite then we have nI x infinity and the night sky should be infinitely bright. Clearly this is not the case and the question is “Why?”.  This is the question put forward by the German astronomer Heinrich Olbers in the early 1800’s and is known as Olbers’ paradox.

 

Some would argue that it is because dust clouds obscure the light from a significant proportion of the stars. However even if this were the case there would still be sufficient light to make the night sky extremely bright. The dust clouds would also absorb energy from the stars and re-radiate it so these would not reduce the radiation reaching the Earth by very much.

 

In 1917 the Russian cosmologist Alexander Friedmann worked through Einstein’s general theory of relativity and determined that it was not consistent with a static universe and consequently predicted that the universe was expanding.

           

Edwin Hubble suggested a solution in the early 1920’s when he proposed that the Universe is expanding and the frequency of light reaching us from distant galaxies is reduced due to the Doppler effect. According to Planck’s equation E = hf, as the frequency of the light decreases so too does the energy of the photons of light reaching us. Consequently there is not enough energy from distant galaxies to brighten the night sky.

 

Hubble provided evidence to support his hypothesis that the Universe was expanding by studying the spectra emitted by distant galaxies. When energy is put into the vapour of an element, for example by passing an electric discharge through it, the element will absorb energy and then re-emit it at characteristic wavelengths. A prism can separate these wavelengths, and we get a spectrum consisting of one or more stripes of colour on a black background. Such a pattern is known as an emission spectrum and each element has its own characteristic spectrum. Hydrogen for instance has four visible spectral lines of wavelengths 656 nm, 486 nm, 434 nm and 410 nm respectively.

 

When Hubble studied the spectra of galaxies outside the Milky Way he found a lot of them did not display wavelengths consistent with the hydrogen spectrum or indeed any of the elements found in the Sun. Closer examination of the spectra showed that spectra similar to the expected elements were present but all the expected wavelengths had higher values, the wavelengths had somehow got longer. This result would be consistent with the Doppler shift of galaxies that were moving away from us. Since the longer wavelengths move the spectral lines towards the red end of the visible spectrum this phenomenon has been called the “red shift”.

 

Hubble also measured the distance of galaxies by studying the brightness of cepheid variable stars and compared the distance of the galaxies to the amount of red shift displayed. He found that the further a galaxy was away from us then the greater was its red shift and so the faster it was moving away from us.

 

By carefully measuring the rates at which the galaxies are moving away it is possible to extrapolate backwards and work out when all the galaxies would be in the one place.  This time, known as the Hubble constant, has a value of about 20 billion years. Because the gravitational attraction between galaxies has slowed down the rate of expansion it appears likely that the age of the Universe is closer to 15 – 18 billion years.

 

This would also put a limit on the size of the observable universe since light from anything further than 20 billion light years away would not have had time to reach us. A sphere of this size is called the “cosmic particle horizon”. Within the observable universe the concentration of galaxies is sufficiently small that the sum of the light reaching us from them is not sufficient to appreciably brighten the night sky.

 

With all of the galaxies concentrated at one place, gravitational forces would be such that matter would collapse in on itself to a singularity, similar to a massive black hole. In such a situation the laws of physics as we know them would cease to apply and the Universe would be an incomprehensible jumble of space and time in a singularity of infinite curvature until the Big Bang brought space and time into existence.

 

“Students learn to: describe the transformation of radiation into matter which followed the ‘Big Bang’“ (syllabus)

 

The Big Bang was not an explosion in the conventional sense, but an expansion of space at the beginning of time. The temperature immediately after this event was immense; around 1035 K. As the temperature gradually cooled the energy would be converted into pairs of particles of matter and antimatter. (Antimatter is composed of antiparticles i.e. particles with the same mass as their corresponding matter particle, but with opposite values for other properties such as charge and magnetic momentum.) These particles of matter and antimatter would immediately recombine and be converted back to energy. The particles would consist of quarks and antiquarks and leptons and antileptons. The balance between matter and antimatter is known as symmetry. For some reason unknown to physicists the symmetry was broken and more particles than antiparticles were produced.

As the Universe cooled the quarks would combine to form protons and neutrons and as the Universe cooled more the protons and neutrons would combine to form nuclei of deuterium (1 proton + 1 neutron; an isotope of hydrogen) and helium.

Physicists using particle accelerators have succeeded in producing some particle-antiparticle pairs but even the largest accelerators do not approach the energy immediately after the Big Bang.

 

“Students learn to: identify that Einstein described the equivalence of energy and mass” (syllabus)

It is the equivalence of mass and energy that enabled radiation to be transformed into matter. This relationship was discovered by Einstein and is expressed in his equation: E = mc2     where E = energy        m = mass         c = speed of light (3 x 108 ms-1)

This equation quantifies how mass can be changed to energy and energy can be changed to mass.

 

“Students learn to: outline how accretion of galaxies and stars occurred through:

-     expansion and cooling of the Universe

-          subsequent loss of particle kinetic energy 

-          gravitational attraction between particles

-          lumpiness of the gas cloud that then allows gravitational collapse (syllabus)

 

Accretion refers to the gradual accumulation of matter in one place. It usually occurs through gravitational attraction.

Expansion & Cooling:

The expansion of the Universe results in a corresponding drop in temperature, as the energy has to be distributed throughout a larger volume of space. Immediately after the Big Bang the energy was so large that the four force fields (gravitational, electromagnetic, strong nuclear and weak nuclear) were combined into one unified force field. At 10-43 second after the Big Bang, an interval known as Planck Time, the gravitational force separated out from the others. The temperature at this stage was around 10-32K. At 10-35 second when the temperature had dropped to 1027K, the strong nuclear force separated from the other two and at 10-12 second the electromagnetic force and the weak nuclear force separated into two distinct force fields. At this stage the temperature had dropped to 1015K. Quark and antiquark pairs as well as lepton and antilepton pairs were constantly being formed and annihilated at this stage as energy was converted to matter and vice-versa. At 10-6 second when the temperature had dropped to 1013K the quarks were able to stick together to form protons and neutrons. About 3 minutes after the Big

Bang the temperature had cooled to 109K and the protons and neutrons were able to combine to form nuclei of deuterium and helium. Most of the helium in the Universe was formed about 3 minutes after the Big Bang. The universe continued to expand and cool and about 300 000 years later had cooled to around 3000K. At this temperature protons are able to capture electrons to form atoms of hydrogen and helium nuclei could capture electrons to become helium atoms. At this stage matter began to dominate the Universe and the Universe became transparent. The Universe continued to expand and cool over the next billion years.

Loss of Kinetic Energy:

Heat energy is a result of the kinetic energy of particles. As space expanded the temperature decreased as the particles lost kinetic energy. Just as a white dwarf star today is gradually cooling down and losing its kinetic energy as its heat is radiated into space, so too particles would lose kinetic energy as their heat was radiated into the ever-expanding space. (Entropy)

 

Gravitational attraction:

Particles attract each other according to Newton’s law of Gravitation: F = Gm1m2 /d2. While galaxies and stars result from the accretion of matter it is gravity that provides the mechanism for this accretion.

Lumpiness of the Gas Cloud:

Ripples in the radiation caused lumpiness in the gas cloud i.e. some regions had more particles than others. Although the cause of the ripples is not known, their existence has been confirmed by measurements taken by the COBE (Cosmic Background Explorer) satellite. As atoms stuck together the mass of the blob and consequently its surface gravity increased and so it would attract more atoms at an increasing rate. The result was huge clouds of gas that condensed to form groups of billions of stars that we call galaxies.

 

“Students: identify data sources and gather secondary information to describe the probable origins of the Universe” (syllabus)

 

The syllabus deals only with scientific theories as to the origin of the Universe. While many students believe in creationism, note that this is a belief and not a scientific theory as it can’t be tested by scientific means. Many supporters of creationism believe that it can be combined with the “Big Bang” theory described below.

The following copy is taken from “Curriculum Support for teaching in Science 7 – 12, 2001 Vol.6  No.4” published by NSW Department of Education and Training  www.curriculumsupport.nsw.edu.au

 

                                   

 

Identify data sources and gather secondary information:

 

As well as your textbooks and the cosmology section in your school and council libraries you can try the following websites:

http://www.nap.edu/readingroom/books/cosmology/

http://www.lifeinuniverse.org/BigBang

http://www.Pbs.org/wnet/hawking/universes/html/

http://www.Pbs.org/deepspace/timeline/

 


Describe the probable origins of the Universe:

 

After Hubble showed in the 1920s that the Universe was not static but expanding then various scientists tried to explain this observation. The two best-known explanations were the Steady State Theory and the Big Bang Theory.

The Belgian, Georges Lemaitre, put forward the Big Bang Theory, in 1927 when he proposed that the Universe began from a primeval atom. For some reason the “primeval fireball” began to expand and as it expanded matter thinned out, cooled down and gradually condensed into stars and galaxies. In 1948 the British astronomers Hermann Bondi, Thomas Gold and Fred Hoyle put forward an opposing theory, namely the Steady State Theory. This suggests that the Universe has always existed essentially the same as it is today. As the Universe expanded a new atom of hydrogen would suddenly pop into existence in the space between galaxies.

Modern astronomers have largely rejected the steady state theory. While the amount of matter being created would be small (less than an atom per cubic metre per million years) it seemed to contravene the principle of conservation of energy and mass. As telescopes improved, astronomers were able to see further and further into the Universe. With the discovery of Quasars at great distances it was found that the Universe was far from uniform. Also, because of the time it takes the light from quasars to reach us, we are actually seeing what the Universe was like billions of years ago. It appears that a lot more quasars existed in the past than are present today.

In 1950, George Gamow predicted that radiation left over from the Big Bang should still be present in the Universe. Just as the spectra of stars are red shifted because they are moving away from us, so too the energy left over from the Big Bang should still be present in the Universe but at a much longer wavelength than it had originally because of the expanding universe. Calculations suggested that the temperature of the Universe should be in the order of 3 kelvin as characterised by a blackbody spectrum with a peak wavelength of around 1 mm. Arnio Penzias and Robert Wilson confirmed this in 1965 when they discovered this radiation now called the background microwave radiation. Its intensity is isotropic (the same in all directions) and its wavelength is consistent with the predicted temperature of just under 3 kelvin.

 

 “3. Stars have a limited life span and may explode to form supernovas” (syllabus)

 

“Students learn to: define the relationship between the temperature of a body and the dominant wavelength of the radiation emitted from that body.”  (syllabus)

A black body is one that absorbs all radiation falling on it. It is also a perfect emitter of radiation and so its temperature remains constant. If you heat a piece of wire you will notice that as the temperature rises the colour of its glow will change from red, through orange and yellow, to white. Wilhelm Wien found the relationship between the temperature of a body and the dominant wavelength of the radiation emitted from that body.

The relationship:          lmax = W/T  is known as Wien’s Law

where lmax = wavelength in metres,    T = temperature (kelvin)         W = Wien’s constant = 2.89 x 10-3 mK

 Celestial objects resemble black bodies and Wien’s Law gives the relationship between the dominant wavelength of the radiation emitted and temperature.

Note that many wavelengths are present in the emitted light and lmax refers to the wavelength of the most abundant light, i.e. the most intense.

 

 

 

 

 

 

 

 

 

 

 

 

           

            Graph of wavelength against intensity at 5 000K, 10 000K and 20 000K.

 

The above graph would apply to all types of black bodies including filaments, hot gases and stars.

Note that as the temperature of an object becomes hotter the dominant radiation (the peak of the graph) increases in intensity and decreases its wavelength.

 

“Students learn to: identify that the surface temperature of a star is related to its colour.”  (syllabus)

 

From Wien’s Law (above) it can be seen that the dominant wavelength of the radiation emitted by a star is related to its temperature. This means that the colour of a star is related to its surface temperature. Consequently, star colours vary from red (cool stars) through orange, yellow and white, to blue stars that are very hot.

 

“Students learn to: describe a Hertzsprung-Russell diagram as the graph of a star’s luminosity against its colour or surface temperature.”  (syllabus)

 

            Between 1911 and 1913 the astronomers Ejnar Hertzsprung (Denmark) and  Henry Russell (America) independently plotted the luminosity and absolute magnitude of stars against their temperature or spectral class. The general pattern is shown in the Hertzsprung- Russell  (H-R) diagram below. On the vertical axis, M refers to the absolute magnitude (not covered in the preliminary course) and L/ refers to multiples of the Sun’s luminosity.                

                                                Hertzsprung-Russell Diagram

 

            Most of the stars (more than 90%) fall in a band that runs from the upper left of the diagram to the lower right. These stars are main sequence stars that obey the mass-luminosity relationship.

            There are two groups of stars above the main sequence and one below it. The two groups above have a greater absolute magnitude (i.e. they are more luminous) than main sequence stars of the same temperature. This is because they are much larger and consist of the supergiants such as Betelgeuse and the giants such as Arcturus. Giants are 10 to 100 times as large as the Sun while supergiants are 100 to 1000 times the size of the Sun. The giants and supergiants have relatively cool surfaces (around 2500 to 3000 kelvin) and consequently appear red. For this reason they are usually called red giants or red supergiants. However, the core temperatures of red giants and supergiants are very much hotter than the cores of main sequence stars as they fuse helium and other elements into still larger atoms.

            White dwarfs are very dense, very dim and very hot stars that have completed their nuclear burning stage. A typical white dwarf would have a surface temperature of around 15000 kelvin while being not much bigger than the Earth. Because of its small surface area it radiates its energy into space at a slow rate and so appears very dim. Because of their hot temperature and low luminosity, white dwarfs are found in the lower left section of the H-R diagram.

Note that neutron stars and black holes do not appear on the H-R diagram. They are not directly observable, even with the largest optical telescopes, so can’t reasonably be plotted on the absolute magnitude/luminosity axis.

                                                           

 “Students learn to: identify energy sources characteristic of each star group, including Main Sequence, red giants and white dwarfs.  (syllabus)

 


Protostar:

Looking at this process on the H.R. (Hertzsprung-Russell) diagram sees the protostar enter the H.R. diagram from the right. As the star gets hotter due to the release of gravitational energy, the star’s position on the diagram moves to the left until it joins the main sequence. At this point nuclear fusion begins and the star remains on the main sequence for billions of years.

 

Main Sequence:

Nuclear reactions take place in the core of the star rather than at the surface. Hydrogen is converted to helium by nuclear fusion and liberates energy in the form of gamma radiation. The photon of gamma radiation will soon collide with another atom, which will absorb the photon and re-emit it, not necessarily as gamma radiation but possibly as two or more photons of lower energy radiation. Thus over a period of millions of years the energy gradually makes its way to the surface where it is emitted as lower energy photons such as light or radio waves.

 

The nuclear reaction proceeds by one of two processes: the proton-proton reaction or the carbon cycle.

The proton-proton reaction takes place where the core temperature lies between 5 and 16 million Kelvin and can be represented by the following series of equations.

 

1H1 + 1H1 " 1H2 + e+ + n

 

            1H2   +  1H1 " 2He3 + g

 

2He3     + 2He3  " 2He4  + 1H1

 

At temperatures above 16 million Kelvin the carbon cycle occurs; i.e. a series of reactions in which carbon acts as a nuclear catalyst.

 

6C12      +          1H1       "         7N13 + g

 

7N13     "         6C13    + e+  + n

 

6C13      +          1H1       " 7N14 + g

 

7N14     +          1H1       "  8O15 + g

 

8O15     "         7N15      + e+ + n

 

7N15     +          1H1       " 6C12  + 2He4

 

The net effect of each type of reaction is that four hydrogen atoms combine to form one helium atom. This is known as nuclear fusion and releases large amounts of energy as mass is converted to energy.

 

Red Giants and Supergiants:

When most of the hydrogen in the core has been consumed the nuclear reaction decreases. Gravity takes over causing the star to collapse further and heat up. As the core heats up, radiation passes through the region surrounding the core, which was previously not hot enough to sustain nuclear reactions i.e. the stellar envelope. The radiation pressure causes the envelope to expand and therefore cool.

 

The energy from the collapsing core heats up the hydrogen at the inner boundary of the envelope, causing it to undergo nuclear fusion. The shell burning of hydrogen increases the total luminosity of the star, which brightens. On the H-R diagram, the star leaves the main sequence. It moves upwards and to the right as it brightens and cools. The expanding envelope in the meantime causes the star to expand to many hundred times its original size, becoming a red giant or supergiant.

 

As the core collapses its temperature rises. At about 100 million Kelvin the temperature of the core is sufficiently high for helium to undergo fusion to form carbon. The reaction, called the triple alpha reaction, involves three helium nuclei forming a carbon nucleus.

 

            2He4  + 2He4 g 4Be8 + n

 

            2He4 + 4Be8 g 6C12 +  g

 

The point at which this begins is called the helium flash.

 

For stars of the Sun’s mass or less the helium fusion is the last nuclear reaction but for more massive stars, as the helium fusion diminishes, the core collapses and heats up causing helium shell burning. As the core reaches about 600 million Kelvin, carbon undergoes fusion to form heavier elements such as oxygen. In this way, massive stars form a series of concentric shells in which the outermost shell consists of hydrogen being converted to helium, the second helium to carbon and so on until at the core, iron is created out of the lighter elements.

 

As these massive stars undergo their series of nuclear reactions, they move back and forth horizontally on the H.R. diagram, passing through a region called the instability strip or Hertzsprung gap each time. This is the region of pulsating variables, i.e. stars that vibrate at their natural frequency in much the same way as gas in an organ pipe. A layer below the surface of the star consists of partly ionised helium. As the star contracts, ionisation increases and the layer more effectively traps the outgoing radiation. Eventually sufficient pressure is built up to push the outer layers of the star outwards so that they cool down and allow the stored radiation to escape. The star then contracts to begin another cycle.

 

During a star’s giant or supergiant stage it loses matter as some of its atmosphere is ejected. What happens to the star at its next stage depends on the mass of the remaining core.

 

White Dwarfs:

Stars up to a size of 4 solar masses on the main sequence will leave a core of about 1.4 solar masses. This is the upper limit for the star to become a white dwarf. As the nuclear reactions die out the star will shrink due to gravity and become much smaller, about the size of the Earth. The reason for this is that the matter becomes degenerate. Because of the large mass and absence of radiation pressure, gravity will cause the white dwarf to collapse. The orbits of the electrons are compressed until they begin to encroach on each other’s space. Since no two electrons can have exactly the same quantum numbers (Pauli exclusion principle) then one of the electrons will gain momentum and so exert an outward pressure to balance the inward pressure of gravity. The degenerate nature of matter in white dwarfs makes them extremely dense with a typical white dwarf being a million times as dense as water. Although white dwarfs are initially very hot they are also quite dim. They radiate their energy into space, but because of their small surface area, this is a very slow process. Over a period of billions of years white dwarfs cool to become black dwarfs.

 

 “Students: gather secondary information to relate brightness of an object to its luminosity and distance.” (syllabus)

 

The brightness of a star describes how much light we receive from the star while the luminosity of a star refers to how much energy it emits in a given time. Just as you can express the luminosity of a light globe in watts, so too you can express the luminosity of a star in watts. The luminosity of the Sun for instance is 4.2 x 1026 watts. As we look at stars from the Earth, one can appear brighter than another either because it is more luminous or because it is closer. The intensity of the energy received from a star diminishes with distance according to the inverse square law: I a 1/d2

 

“Students: solve problems to apply the inverse square law of intensity of light to relate the brightness of a star to its luminosity and distance from the observer.” (syllabus)

 

Canopus, the second brightest star in the night sky, has the same luminosity as Antares. Canopus is about 200 light years from Earth while Antares is about 420 light years from Earth. How many times brighter than Antares does Canopus appear to be?

 

I a 1/d2            I = k/d2            ICanopus = k/2002 = 2.5 x 10-5 k             IAntares = k/4202 = 5.7 x 10-6 k              ICanopus/ IAntares = 2.5 x 10-5 k/5.7 x 10-6 k = 4.4

Canopus is 4.4 times as bright as Antares when viewed from Earth.

 

Sirius, the brightest star in the night sky, is about 22 times as luminous as the Sun and is about 9 light years away. How many light years away from Earth would the Sun have to be so that it had the same brightness as Sirius?

 

Let the luminosity of the Sun be LSun.            Then the luminosity of Sirius is 22 LSun.

When Sirius and the Sun have equal brightness then ISirius = ISun

            (k/dSirius2 )x 22 LSun.= (k/ dSun2 )x LSun.

            22 k LSun./ 92          =  k LSun. / d2                     d2 =  92/22       d = 1.9 light years

“Students: process and analyse information using the Hertzsprung-Russell diagram to examine the variety of star groups, including Main sequence, red giants, and white dwarfs.” (syllabus)

 

Find the positions of the following stars on the Hertzsprung-Russell diagram and hence complete the following table by classifying them as main sequence, red giant, supergiant or white dwarf.

 

Name

Temperature (K)

Luminosity (L/)

Type

The Sun

5800

1

 

Sirius A

10 000

26

 

Sirius B

30 000

2.4 x 10-3

 

Betelgeuse

2900

1.2 x 104

 

Pollux

4500

30.2

 

 

 “4. The Sun is a typical star, emitting electromagnetic radiation and particles that influence the Earth.” (syllabus)

 

“Students learn to: identify that energy may be released from the nuclei of atoms.”   (syllabus)

 

The nucleus of a typical atom can be broken up into protons and neutrons by the addition of energy. However, a strange thing happens. The masses of the protons and the neutrons add up to more than the mass of the nucleus. Similarly, protons and neutrons can combine to form nuclei. In this case the nucleus has less mass than the sum of its protons and neutrons and a large amount of energy is released. We are looking at an illustration of Einstein’s proposal that matter and energy can be converted from one into the other according to the equation E = mc2.

When nuclear particles combine and release energy this is a measure of the energy that is holding the nucleus together i.e. the binding energy of the nucleus. Small atoms can join together so that they have more binding energy per nuclear particle (nucleon) and so become more stable. As they do so they release energy. For instance three helium nuclei can join together to form a carbon nucleus and release energy. This is what happens in the core of red giant stars. Carbon has more binding energy per nuclear particle than helium. Joining together of nuclei is called nuclear fusion.

Large nuclei, such as uranium, can split apart to form two smaller nuclei with more binding energy per nuclear particle, and release energy in the process. This is what happens in nuclear reactors. The splitting apart of nuclei is called nuclear fission.

 

 

“Students learn to:  describe the nature of emissions from the nuclei of atoms as radiation of alpha a and beta b and gamma g rays in terms of:

-          ionising power

-          penetrating power

-          effect of magnetic field

-          effect of electric field       (syllabus)

 

 

 

Nature

Ionising Power

Penetrating Power

Effect of Magnetic Field

Effect of Electric Field

Alpha rays

Helium nuclei. 2 protons + 2 neutrons.

Charge = +2

High ionising power.

Poor penetrating power. Can penetrate only a few centimetres of air.

Deflected by a magnetic field

Deflected towards the negative plate by an electric field.

Beta rays

Electrons.

Charge = -1

Medium ionising power.

Medium penetrating power. Can penetrate about a metre of air.

Deflected by a magnetic field

Deflected towards the positive plate by an electric field.

Gamma rays

Electromagnetic radiation.

No Charge.

Low ionising power.

High penetrating power. Never fully absorbed. Several metres of air or about 4 cm of lead will reduce intensity to about 10% of original.

 

Not deflected by a magnetic field

Not deflected by an electric field

 

“Students learn to: identify the nature of emissions reaching the Earth from the Sun.”  (syllabus)

 

Although the Sun produces electromagnetic radiation of all wavelengths, the visible region of the electromagnetic spectrum is most intense. Most of this radiation is absorbed by the Earth’s atmosphere but light and radio waves are able to penetrate the atmosphere as are short wavelength infra red rays and long wavelength microwaves. X-rays and gamma rays are absorbed by the upper atmosphere and do not reach the Earth’s surface.

 

“Students learn to: describe the particulate nature of the solar wind.”  (syllabus)

 

The solar wind consists mostly of protons and electrons but also some ions of elements. It results from radiation pressure pushing parts of the corona into space and is most prominent at times of increased sunspot activity.

 

“Students learn to: outline the cyclic nature of sunspot activity and its impact on Earth through solar winds.”  (syllabus)

 


 

Sunspot activity on the Sun varies but tends to be cyclic with a period of around 11 years. The graph below was taken from the NASA website: http://science.nasa.gov/ssl/pad/solar/sunspots.htm

 

Graph showing Cyclic Nature of Sunspot Activity

While the activity is cyclic, some cycles show more sunspot activity than others. Records indicate that there was little or no sunspot activity between 1645 and 1715. This corresponds to a cooling of the Earth and a climate change called the “Little Ice Age”.

The increase in sunspot activity results in the increase in solar flares with the consequent increase in solar wind. This bombards the Earth with a barrage of charged particles. Most of the charged particles are trapped by the Earth’s magnetic field and are deflected towards the poles where they react with the atmosphere to cause the Aurora Australis and the Aurora Borealis. Satellites are very susceptible to the effects of solar winds and the increase in charged particles can damage the controls and communication equipment on board. Astronauts in the space shuttle and space stations have to take extra precautions at times of high solar activity. The increase in magnetic activity on Earth can cause circuit breakers on power grids to trip and cause widespread blackouts.

 

“Students learn to: describe sunspots as representing regions of strong magnetic activity and lower temperature.”  (syllabus)

Sunspots were first observed by Galileo in 1611. They appear as dark spots on the surface of the Sun and Galileo used them to determine the period of the Sun’s rotation. They are cooler than the surrounding region and represent regions of strong magnetic fields. They usually come in pairs of opposite polarity. They are constantly being formed and disappearing and typically last from a few days to several weeks.

 

“Students: perform a first-hand investigation to gather information to compare the penetrating power of alpha, beta and gamma radiation in a range of materials” (syllabus)

 

This experiment can be done as a computer simulation if you have a suitable program. Otherwise it is usually performed as a teacher demonstration so that pupils do not handle radioactive sources. The following is a report of a possible teacher demonstration.

 

Purpose: To compare the penetrating power of alpha, beta and gamma rays.

Equipment: Geiger counter, stopwatch, metre rule, alpha ray source (americium-241), beta ray source (strontium-90) and gamma ray source (cobalt-60).

Method: Jessica was chosen to do the timing while the teacher handled the Geiger counter and radioactive samples. Jessica reported one-minute time intervals by calling “start” as she clicked the stopwatch, and then carefully watching the stopwatch and calling “stop” when exactly one minute had elapsed. The teacher and Jessica began by taking five readings of the background radiation i.e. turning the Geiger counter on for one-minute intervals and recording the count with no radioactive sources nearby. Jessica recorded the results in her practical book.

The teacher then placed the window of the Geiger counter on the zero mark of the metre rule. She then placed the gamma ray source at one-centimetre intervals from 0 to 10 centimetres, taking three readings of the radioactive count for one minute at each interval. The true count was obtained by subtracting the background count in each case. Jessica again recorded the results in her practical book.

The procedure was repeated for the beta ray source and then the alpha ray source.

Results:

Background radiation(counts per minute)

Count 1 = 11

Count 2 = 15

Count 3 = 10

Count 4 = 14

Count 5 = 9

Average = 11.8 = 12 (nearest whole number)

 

Gamma ray source: cobalt-60

 

Distance (cm)

Count 1

Count 2

Count 3

Average Count

Average-Background

1

1176

1280

1294

1250

1238

2

460

496

430

462

450

3

297

276

285

286

274

4

184

171

176

177

165

5

109

126

98

111

99

6

76

69

68

71

59

7

48

44

49

47

35

8

38

34

36

36

24

9

28

28

25

27

15

10

19

24

22

22

10

 

Beta ray source: strontium-90

 

Distance (cm)

Count 1

Count 2

Count 3

Average Count

Average-Background

1

257

268

271

265

253

2

86

81

92

86

74

3

48

51

45

48

36

4

25

28

27

27

15

5

25

24

24

24

12

6

21

22

19

21

9

7

18

17

19

18

6

8

16

17

16

16

4

9

16

14

14

15

3

10

14

15

13

14

2

 

Alpha ray source: americium-241

 

Distance (cm)

Count 1

Count 2

Count 3

Average Count

Average-Background

1

98

76

97

90

78

2

24

29

31

28

16

3

16

14

17

16

4

4

11

14

12

12

0

5

15

9

11

12

0

6

14

10

9

11

-1

7

11

14

10

12

0

8

8

17

14

13

1

9

12

10

14

12

0

10

15

14

8

12

0

 

Because the radioactive samples were different strengths as indicated by their widely different original counts, the radioactivity was converted to a percentage of its original value i.e. a percentage of its count at a distance of 1 cm.

           

Distance (cm)

Percentage of original value

Alpha

Beta

Gamma

1

100

100

100

2

21

29

37

3

5

14

22

4

0

6

13

5

0

5

8

6

0

4

5

7

0

2

3

8

0

2

2

9

0

1

1

10

0

1

1

Table showing percentage of original count and distance

 

From the table it appears that alpha rays have the least penetrating power, gamma rays the highest penetrating power with beta rays intermediate between the two.

 

 

 “Students: identify data sources, gather and process information and use available evidence to assess the effects of sunspot activity on the Earth’s power grid and satellite communications” (syllabus)

 

Identify Data Sources: As well as your textbooks and your school and local libraries, try some of the websites below.

 

http://www.ips.gov.au/Main.php?CatID=8&SecID=2&SecName=The%20Sun%20and%20Solar%20Activity&SubSecID=2&SubSecName=Sunspots

 

http://www.radioelectronicschool.com/downloads/elusive.pdf

 

http://www.ga.gov.au/media/releases/1008798949_3676.jsp

 

http://www.aig.asn.au/solar_outbursts.htm

 

http://au.dir.yahoo.com/Science/Astronomy/Solar_System/Sun/Sunspots/

 

http://www.space.com/scienceastronomy/power_outage_031031.html

 

http://www.atnf.csiro.au/education/teachers/Sun.html

 

http://www.smh.com.au/cgi-bin/common/popupPrintArticle.pl?path=/articles/2003/10/30/1067233288580.html

 

http://www.frekenbox.com/log/comments.php?id=M67_0_1_0_C

 

http://www.sfgate.com/cgi-bin/article.cgi?file=/chronicle/archive/2000/07/15/MN50119.DTL

 

http://msnbc.msn.com/id/3077823

 

Assess the effects of sunspot activity on the Earth’s power grid and satellite communications.

Sunspot activity results from magnetic storms on the Sun, which produces a solar wind of charged particles streaming towards Earth. The charged particles can disrupt communications with satellites and high-flying aircraft. The increased magnetic activity can cause circuit breakers in power grids to trip and cause widespread blackouts. The charged particles are trapped by the Earth’s magnetic field where they are deflected towards the poles where they cause the auroras.

 

 

LIFE CYCLE OF A STAR

 

There is a vast amount of empty space between the stars of the galaxy. The Sun’s nearest neighbour, Alpha Centauri for instance is over four light years away. However, the space between the stars is not completely empty. It contains small amounts of hydrogen and helium as well as fragments of heavier metals expelled by the supernova of dying stars. While the density of matter in interstellar space is very low (about one molecule per cubic centimetre), because the volume is so large the amount of matter is immense.

 

A disturbance of some kind will cause a huge cloud of this interstellar matter to begin to collapse under the influence of its own gravity. The disturbance could be a large star passing nearby or the shock waves from a supernova; the exact reason is unclear. As the collapse occurs, the potential energy is converted into kinetic energy, i.e. heat. Thus the cloud collapses and heats up. If the mass of the cloud is sufficiently large (greater than 0.07 Solar masses) then the temperature becomes hot enough to initiate the nuclear fusion reaction in which hydrogen is converted to helium with the liberation of huge amounts of energy.

 

Looking at this process on the H.R. (Hertzsprung-Russell) diagram sees the protostar enter the H.R. diagram on the right. As the star gets hotter due to the release of gravitational energy, the star’s position on the diagram moves to the left until it joins the main sequence. At this point nuclear fusion begins and the star remains on the main sequence for billions of years.

 

Nuclear reactions take place in the core of the star rather than at the surface. Hydrogen is converted to helium by nuclear fusion and liberates energy in the form of gamma radiation. The photon of gamma radiation will soon collide with another atom, which will absorb the photon and re-emit it, not necessarily as gamma radiation but possibly as two or more photons of lower energy radiation. Thus over a period of millions of years the energy gradually makes its way to the surface where it is emitted as lower energy photons such as light or radio waves.

 

The nuclear reaction proceeds by one of two processes: the proton-proton reaction or the carbon cycle.

The proton-proton reaction takes place where the core temperature lies between 5 and 16 million Kelvin and can be represented by the following series of equations.

 

1H1 + 1H1 " 1H2 + e+ + n

 

            1H2   +  1H1 " 2He3 + g

 

2He3     + 2He3  " 2He4  + 1H1

 


At temperatures above 16 million Kelvin the carbon cycle occurs; i.e. a series of reactions in which carbon acts as a nuclear catalyst.

 

6C12      +          1H1       "         7N13 + g

 

7N13     "         6C13    + e+  + n

 

6C13      +          1H1       " 7N14 + g

 

7N14     +          1H1       "  8O15 + g

 

8O15     "         7N15      + e+ + n

 

7N15     +          1H1       " 6C12  + 2He4

 

The net effect of each type of reaction is that four hydrogen atoms combine to form one helium atom.

 

When most of the hydrogen in the core has been consumed the nuclear reaction decreases. Gravity takes over causing the star to collapse further and heat up. As the core heats up, radiation passes through the region surrounding the core, which was previously not hot enough to sustain nuclear reactions i.e. the stellar envelope. The radiation pressure causes the envelope to expand and therefore cool.

 

The energy from the collapsing core heats up the hydrogen at the inner boundary of the envelope, causing it to undergo nuclear fusion. The shell burning of hydrogen increases the total luminosity of the star, which brightens. On the H-R diagram, the star leaves the main sequence. It moves upwards and to the right as it brightens and cools. The expanding envelope in the meantime causes the star to expand to many hundred times its original size, becoming a red giant or supergiant.

 

As the core collapses the temperature rises. At about 100 million Kelvin the temperature is sufficiently high for helium to undergo fusion to form carbon. The reaction, called the triple alpha reaction, involves three helium nuclei forming a carbon nucleus.

 

            2He4  + 2He4 g 4Be8 + n

 

            2He4 + 4Be8 g 6C12 +  g

 

The point at which this begins is called the helium flash.

 

For stars of the Sun’s mass or less the helium fusion is the last nuclear reaction but for more massive stars, as the helium fusion diminishes, the core collapses and heats up causing helium shell burning. As the core reaches about 600 million Kelvin, carbon undergoes fusion to form heavier elements such as oxygen. In this way, massive stars form a series of concentric shells in which the outermost shell consists of hydrogen being converted to helium, the second helium to carbon and so on until at the core, iron is created out of the lighter elements.

 

As these massive stars undergo their series of nuclear reactions, they move back and forth horizontally on the H.R. diagram, passing through a region called the instability strip or Hertzsprung gap each time. This is the region of pulsating variables, i.e. stars that vibrate at their natural frequency in much the same way as gas in an organ pipe. A layer below the surface of the star consists of partly ionised helium. As the star contracts, ionisation increases and the layer more effectively traps the outgoing radiation. Eventually sufficient pressure is built up to push the outer layers of the star outwards so that they cool down and allow the stored radiation to escape. The star then contracts to begin another cycle.

 

During a star’s giant or supergiant stage it loses matter as some of its atmosphere is ejected. What happens to the star at its next stage depends on the mass of the remaining core.

 

Stars up to a size of 4 solar masses on the main sequence will leave a core of about 1.4 solar masses. This is the upper limit for the star to become a white dwarf. As the nuclear reactions die out the star will shrink due to gravity and become much smaller, about the size of the Earth. Although white dwarfs are initially very hot they are also quite dim. They radiate their energy into space, but because of their small surface area, this is a very slow process. Over a period of billions of years whit dwarfs cool to become black dwarfs.

 

Stars above 4 solar masses, i.e. where the core will be above 1.4 solar masses, undergo a massive explosion at the end of their supergiant stage. This explosion, called a supernova, causes an increase in brightness of up to 20 magnitudes. While the mechanism of the supernova is not fully understood it results in the expulsion of a large proportion of the star’s mass into space to form interstellar dust from which new stars are formed. The core that remains is destined to become either a neutron star or a black hole.

 

If the mass of the star on the main sequence lies between 4 and 10 solar masses then a core of 1.4 to 3 solar masses will result. This is above the Chandrasekhar limit for the formation of a white dwarf and the sub-atomic particles will be compressed so tightly due to gravity that protons and electrons will combine to form neutrons. As the neutron star collapses its rate of rotation increases so that it spins very rapidly (conservation of angular momentum) and its magnetic field strength is compressed so that is in the order of 100 million tesla at the surface. It is thought that these two factors contribute to the pulsar effect often associated with neutron stars. If the plane of rotation is inclined to the plane of the magnetic field and if electrons were drawn into the field from a nearby star then electrons would spiral along the lines of force and emit electromagnetic radiation. As the star rotates the pole of magnetism would sweep across the line of sight once each rotation, causing the electromagnetic radiation, which is beamed outwards from the pole to appear as pulses.

 

The supernova of a star above 10 solar masses would leave a core of more than 3 solar masses. The matter in this would compress to such an extent that its gravity would be so strong that even light could not escape from it. Such an entity is called a black hole; black since no light or matter can get out and hole in that matter can fall into it.

 

While the exact process for the evolution of galaxies is not known it appears that they evolve from quasars. These are huge energy sources located billions of light years from the Earth. Because they are so far away we can only see what they were like billions of years ago. They emit vast amounts of energy in the light and radio regions of the electromagnetic spectrum. It has been suggested that their energy source is matter being sucked into a supermassive black hole at the centre of the quasar and releasing energy on its way.

 

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