|
||||
|
||||||||||||||||||||||||||||||||||||||||
|
PREPARED NOTES
INTRODUCTION:
The
universe began with a singularity, a point of infinite density.
It is generally believed that our universe resulted from the explosion of
this singularity – the so-called Big Bang.
As a result of the Big Bang, space and energy poured forth from the
singularity and time began.
The universe expanded and cooled and matter condensed out of the mix.
As part of this ongoing process, the Sun and Solar System were formed
over 4 x 109 years ago from a cloud of gas and dust that resulted
from a supernova explosion.
The condensing gas and dust that formed the Sun and the planets contained
all the elements we find today in these celestial bodies.
The planets were formed when matter came together under the influence of
gravity.
Do you live in the Hunter Valley, Central Coast or Sydney areas??? If so, have you been to Koolang Observatory yet??? If not, you should go soon!!! Koolang Observatory is an excellent place to visit for anyone with even a slight interest in astronomy. Expert guides give talks, show the sun, planets and stars through large telescopes, explain what you are seeing & answer your questions. There is also a very good display of many interesting astronomical phenomena. For more information go to the Koolang Website or phone Koolang on 02 49988216.
GETTING STARTED IN PRACTICAL ASTRONOMYNo matter who you are, or what your background in Science, your first glimpse of the Moon or Saturn and its rings or Jupiter and its moons or a Deep Sky object such as the Jewel Box (NGC 4755) through a good quality telescope is absolutely unforgettable. If you, like many people, would like to get started in practical astronomy but are not sure how to do so, then reading this brief section may give you some ideas. If you are really just interested in some casual observation and don't want to spend a lot of money, my suggestion is to purchase a reasonable pair of binoculars. A pair of 7 x 50 or 10 x 50 binoculars offers a good balance of power, image brightness and light weight. Avoid fixed-focus or zoom binoculars, which provide inadequate image quality for viewing sharp pinpoint stars. (Note that a "7 x 50" rating means 7 times magnification and 50 mm aperture for the twin front lenses.) A good planisphere (such as the Chandler Large Planisphere) and the reference book "Astronomy Australia" by Dawes et al for the particular year would also be worthwhile acquisitions. If you are keen to purchase your first telescope I would suggest that a Newtonian Reflector on a Dobsonian mount is a good first choice. If you can afford it a 200mm (8 inch) or 250mm (10 inch) scope is a very useful size. Both of these scopes are capable of producing very beautiful, close-up and detailed images of the Moon, planets and many Deep Sky objects. Both of these scopes are quite easy to re-locate to various sites as needed. You should be able to get a 200mm Newtonian Reflector on a Dobsonian mount for around $800. I know it sounds like a lot of money but it will last you a life time. By way of comparison, it is worth noting that a similar sized refracting telescope will set you back many thousands of dollars for negligible improvement in image quality. If you are serious about purchasing a telescope, don't go to the local toy store, camera shop or similar! Go to a specialist - an expert. I can definitely recommend The Binocular and Telescope Shop, 84 Wentworth Park Road, Glebe NSW 2037, phone 02 9262 1344. This shop is located on the corner of Wentworth Park Road and Pyrmont Bridge Road, Glebe. These people are very experienced astronomers and trained telescope technicians. They know what they are talking about and are very helpful. The link to their Website is given below. The address of the Melbourne shop is 519 Burke Road, Camberwell Vic 3124. (Note: I have no financial or business connection with this shop. It is where I buy all my astronomy tools & supplies.) A very useful reference is "The Night Sky - A Guide to Observing the Sun, Moon and planets" by Steve Massey (New Holland Publishers, Sydney, 2003).
HISTORICAL DEVELOPMENT OF MODELS OF THE UNIVERSEFor excellent notes on the historical development of models of the universe from the time of Aristotle to the time of Newton see the following link: http://csep10.phys.utk.edu/astr161/lect/index.html
You need to be able to do both of the following:
COSMOLOGYCosmology is the study of the nature and evolution of the universe. Underlying current cosmology is the assumption that over very large distances, the universe is homogeneous and isotropic. This is called the Cosmological Principle. To say that the universe is homogeneous means that each region of the universe has the same properties (eg density, temperature) as each other region. To say that the universe is isotropic means that the universe looks the same in all directions. Up until the 1920’s, it was commonly believed that the universe was in a steady state of balance. Galaxies were believed to be stationary relative to one another. This view was one that dates back to Isaac Newton. In 1915 Albert Einstein published his Theory of General Relativity. Today, this is the most powerful mathematical tool that we have for describing the universe. It yields field equations which describe the interactions between all of the matter, radiation and gravitational forces within the universe. When Einstein first used his equations to describe the universe he found that they predicted an expanding universe. As this contradicted Einstein’s expectations, he added a term, called the cosmological constant (L), to his equations to counteract the expansion. Other scientists, notably Alex Friedmann in Russia, Georges Lemaitre in France and Willem de Sitter in the Netherlands continued to develop the ideas of an expanding universe using Einstein’s equations without this constant. This is a good example of what often happens in physics, where theory works ahead of observation and in so doing helps experimental physicists to decide the type of observations they should be attempting to make. If observations are found to support the theory, then the theory becomes more established and accepted by the wider physics community. In the late 1920’s and early 1930’s, Edwin Hubble and Milton Humason showed that the wavelengths of the spectral lines from other galaxies in the universe are red-shifted (ie higher). This phenomenon is called the cosmological red shift and means that as time goes by, clusters of galaxies are getting further apart - the universe is expanding. Hubble & Humason showed further that the greater the distance to a galaxy the greater the red shift. So the further away the galaxy is from us, the faster it is receding. This universal recessional movement is referred to as the Hubble flow. The velocities of recession, v, of remote galaxies are related to their distances from earth, r, via Hubble’s Law:
where H0 is Hubble’s constant, the slope of a plot of recessional velocity v’s distance to galaxy. The actual value of this constant is one of the most controversial issues in modern astronomy because of its extreme importance – it tells us the rate at which the universe is expanding. Values of the Hubble constant range from 40 km/s/Mpc to 100 km/s/Mpc depending on the method of calculation. (NOTE: 1 Mpc = 1 megaparsec, a unit of distance = 3.09 x 1019 km.) This law suggests that the universe is expanding uniformly. It is important to realise that each galaxy, or cluster of galaxies, does not expand as it is held together by its own gravitational forces. It is the intergalactic space between widely separated galaxies, or clusters of galaxies, which expands with time. THE BIG BANGIf we mentally reverse the expansion process, then at some time in the dim, distant past, all the matter, energy, space in the universe must have been located in a very small volume – a singularity (point) of infinite density in fact. It is generally believed that our universe has resulted from the explosion of this singularity – the so called Big Bang. How long ago??? Hubble’s
Law provides a good estimate of the answer.
Let T0 be the time it has taken the most distant galaxies (at
R from us) to move away from us. Then
T0 = R/v = R/ H0R = 1/ H0.
So the reciprocal of the Hubble constant gives us an estimate of the age
of the universe. It works out to
be roughly 15 billion years. The Big Bang can be understood as the explosion of space at the beginning of time. The four forces (gravitational, electromagnetic, strong and weak) became distinguishable during the first microsecond. In the initial stages (first 300 000 years), the universe resembled a primordial fireball (opaque plasma of electrons, protons and high energy photons). Plasma is the fourth state of matter. A plasma is a mixture of positively charged ions and negatively charged electrons. It is formed when the temperature is so high that electrons and protons are too energetic to come together or stay together in the form of atoms. After about 300 000 years, hydrogen and helium formed and the universe became transparent. Note that in standard Big Bang Theory there is no point asking what conditions were like at or before the Big Bang because time only began after the Big Bang and matter, energy and space only came into being in their current, familiar form after the Big Bang. In fact there is a point in time known as the Planck time (within 10-43 seconds of the Big Bang) when gravity is comparable in strength to the other forces of nature and due to this the laws of physics as we know them do not apply. To deal with the first 10-43 seconds of the Big Bang we need a quantum theory of gravity. (As an aside, there are physicists attempting to use String
Theory to extend our knowledge of events back even before the Big Bang.
For instance see “Before the Big Bang” pp.24-27 in New Scientist 3
June 2000.) It is also worth answering a frequently asked question at this stage. Where did the Big Bang happen? Can we just trace the expanding universe backwards and find the place? The answer is no because there is no need! The reason for this can be explained in many ways but ultimately the simplest explanation is just this: the Big Bang happened where you are right now and everywhere else; in the beginning, all locations we now see as separate were the same location. Another way to answer the question is to realize that if the Big Bang brought our entire universe into creation, it could not have happened at a point inside our own universe, since until the Big Bang happened, there was no universe. Fascinating stuff, isn't it???
EVIDENCE FOR THE BIG BANGThe early universe was extremely hot – at least as hot as the surface of the sun. The hot universe contained many short wavelength photons which formed a radiation field. As the universe expanded the short wavelength photons had their wavelengths stretched to become low energy, long wavelength photons. By the present day, the temperature of this cosmic radiation field should be quite low, just above absolute zero. This cooled down cosmic radiation field was discovered in 1965. It is called the cosmic microwave background and has a temperature of about 2.7 K. This microwave background is almost perfectly isotropic, which confirms Einstein’s assumption that the universe is isotropic. The Big Bang Theory also predicts the correct proportion of hydrogen to helium within the universe. Using the Hubble Law we also obtain an estimate of the age of the universe that is in good agreement with other age predictions.
MATTER & RADIATION IN THE UNIVERSEEverything in the universe falls into one of two categories – matter or energy. The matter in the universe is contained in such luminous objects as stars, planets and galaxies, as well as in non-luminous dark matter. Today when we describe the constituents of matter, we do so in terms of atoms. The atom consists of a nucleus containing protons (positive charges) and neutrons (neutral) surrounded by electrons (negative charges) in orbit around the nucleus. The nucleus is of the order of 10-14 m in diameter and the whole atom is about 10-10 m in diameter. The energy of the universe consists of radiation, that is, photons. The vast majority of photons in the universe belong to the cosmic microwave background. Let us now examine the relative importance of matter and energy in the universe. Einstein’s mass-energy relationship, E = mc2, which describes the equivalence of mass and energy, can be used to express the photon energy in the universe as being equal to a quantity of mass multiplied by the square of the speed of light. The amount of this equivalent mass in a particular volume, divided by that volume, is the mass density of radiation, rrad. Combining E = mc2 with the Stefan-Boltzmann law (see later) we can calculate the value of rrad as 4.6 x 10-31 kg/m3. By determining the total mass of all the stars, galaxies and dark matter in a very large volume of space and then dividing by that volume, we obtain an estimate of the average density of matter (rm) in the universe. This value is currently thought to be in the range 2 to 11 x 10-27 kg/m3. This is equivalent to 1 to 6 hydrogen atoms per cubic metre of space, if the mass of the universe were spread evenly over space. Since the density of matter in the universe today is much greater than the mass density of radiation, we say that we live in a matter-dominated universe. This, however, was not always the case. As we trace the evolution of the universe backwards through time towards the Big Bang, obviously the average mass density of the universe increases, as the volume of space decreases. At the same time, the photons become less red shifted and thus have shorter wavelengths and higher energy than they do today. It turns out that because of this added energy, the mass density of radiation increases more quickly than the average density of matter, as we go back in time. Eventually, we reach a time in the early universe where rrad > rm. Physicists call this state a radiation-dominated universe. The transition from a radiation-dominated universe to a matter-dominated one occurred about 2500 years after the Big Bang. So for the first 2500 years after the Big Bang, radiation dominated the universe. From that point in time onwards, as the universe continued to expand and the wavelengths of the photons became longer and longer, the energy of the photons became lower and lower and matter gained the upper hand. As mentioned previously though, this matter was in the form of a hot, opaque plasma. Then around 300 000 years after the Big Bang another fundamental change occurred in the nature of the universe. Around this time, the energy of the photons became low enough to permit protons and electrons to combine to form hydrogen atoms. This is a major step in the evolution of the universe, since today hydrogen is the most abundant element in the universe. The epoch when atoms first formed is called the era of recombination. As hydrogen continued to form, the universe changed from opaque to transparent, since the hydrogen atoms did not absorb low-energy photons. This occurred around 1 million years after the Big Bang. Photons could then travel throughout the universe with little or no interaction with matter. As a result of this decrease in interaction between matter and photons, the temperature of matter in the universe diverged from the temperature of the background radiation. Today the cosmic microwave background has a temperature of 2.7 K but the temperature of matter in the universe varies over a huge range from a few tens of kelvins in interstellar medium to hundreds of millions of kelvins in the interiors of giant stars. It is worth noting that although we say that the cosmic microwave background is isotropic, it is not completely so. There are tiny variations in the temperature of the radiation field (30 mK) above and below the 2.7 K average value. These minute variations indicate that the matter and radiation in the universe were not totally uniform at the moment of recombination. These tiny nonuniformities in matter are believed responsible for the present-day concentrations of mass, such as superclusters of galaxies. [Top]
THE FUTURE OF THE UNIVERSEEinstein’s General Relativity field equations allow for
three different scenarios: u rm < rc an ever expanding (open) universe u rm = rc a balanced, static state (marginally bounded or flat) universe u
rm > rc
universe will reverse its motion and come to a Big Crunch (bounded or closed
universe) where rm = average density of matter throughout space and rc = the critical density of the universe (the value which when substituted into the field equations yields the marginally bounded universe result). Using a Hubble constant of 75 km/s/Mpc we obtain a rc value of 1.1 x 10-26 kg/m3. This density is equivalent to about six hydrogen atoms per cubic metre of space. At present there is much controversy over the values determined for rm. The trouble is obtaining accurate measurements for the amount of dark matter in the universe. Astronomers are convinced that rm is at least 2 x 10-27 kg/m3 which is only about a fifth of the critical density. This would mean we live in an open universe. Our present-day estimates of density are not sufficiently accurate to decide for certain. FURTHER DETAILS OF THE EARLY UNIVERSEBy the end of the Planck time, the energy of the particles in the universe had fallen to 1019 GeV (gigaelectron volts) and the temperature was around 1032 K. At that time there was a spontaneous symmetry breaking event in which gravity was “frozen out” of the primordial fireball. Gravity then remained separate from the other three fundamental forces. The universe continued to expand and cool. At t = 10-35s, particle energy was 1014 GeV, the temperature was 1027 K and a second spontaneous symmetry breaking occurred with the strong nuclear force being “frozen out”. A period of extremely rapid expansion, called the inflationary epoch, is then believed to have occurred, lasting from t = 10-35s to t = 10-24s. During the inflationary epoch the universe increased in size by a factor of about 1050. At t = 10-12s, the particle energy was around 102 GeV, the temperature about 1015 K, and the electromagnetic force separated from the weak nuclear force in a third symmetry breaking event. At t = 10-6s, the particle energy was about 1 GeV and the temperature about t = 1013 K, low enough to allow quarks to remain confined to individual protons and neutrons. This period is called the period of confinement. (Note that quarks are fundamental particle constituents of protons and neutrons.) From around t = 10s onwards, deuterium, a nucleus consisting of one proton and one neutron, began to form but was rapidly broken back down to its constituents by high energy gamma ray photons. From around t = 3min, the background radiation had cooled sufficiently to enable the deuterium nuclei to exist freely and to combine with remaining free protons and neutrons to form helium nuclei. The process of forming nuclei such as deuterium and helium from protons and neutrons is called nucleosynthesis. THE FORMATION OF GALAXIESIt is widely accepted today that there must have been density fluctuations (slight lumpiness) in the distribution of matter in the early universe. Otherwise, the distribution of matter in the universe today would not be as lumpy as it is and galaxies and clusters of galaxies would not exist. Through the action of gravity, these fluctuations eventually grew to become the galaxies and clusters of galaxies that we see today. In the initial stages of formation, a cloud of gas consisting of about 76% hydrogen and the remainder helium, probably surrounded by and interspersed with dark matter (of unknown nature) contains tiny variations in density. Regions of higher density will then gravitationally attract nearby material and thus gain mass. As this contraction occurs, gas particles collide with each other, the temperature increases and much hydrogen is ionised. As the resulting protons and electrons move through the gas cloud they lose kinetic energy by radiating some energy as photons and by electron collisions with neutral hydrogen atoms, which result in the atoms absorbing some energy from the electrons and then re-radiating it as photons. These two processes allow the gas cloud to cool slightly and maintain the temperature at around 10 000K. Since the temperature does not rise, the pressure of the gas does not increase fast enough to prevent the gravitational forces from collapsing (crushing) the cloud. The gas cloud breaks into smaller fragments. The smaller gas clouds then go through the same process and break into even smaller gas clouds. Eventually, a stage is reached where the density of the gas clouds is high enough that photons cannot escape, taking energy with them. Thus, the gas clouds become opaque to photons, the temperature of the clouds rise and the pressure forces build to become comparable to the gravitational forces. At this stage each small gas cloud enters a phase of very slow contraction and radiates at a very reduced rate because of the increased opaqueness to photons. Such an object is called a protostar, and grows in mass as more matter is accreted from the surroundings. A protostar will usually spin, due to the residual gas motion. The matter which accretes to the protostar will form a flattened, spinning protostellar disc of gas around it. The slow gravitational contraction of the protostar will continue until the temperature is high enough for nuclear fusion reactions to commence at its centre. The protostar has then become a STAR. The protostellar disc will continue to undergo its own dynamics, perhaps eventually producing a planetary system around the star. The process just described can account for the formation of a collection of stars – a galaxy - from a gas cloud. Both elliptical and spiral galaxies can form in this way. SPIRAL: If a rotating gas cloud collapses under its own weight, it will have a tendency to form a flattened disk in a plane perpendicular to the axis of rotation. If the rate of star formation is low compared to the time taken for the gas cloud to collapse, most of the gas will end up in the disc before star formation occurs. In such a case most of the stars will form in the disc and a spiral galaxy is formed. ELLIPTICAL: If the stellar birth rate is high, then virtually all the gas is used up in the formation of stars before a disk has time to form. In this way an elliptical galaxy is formed. Note that other theories of galaxy formation exist. The main ones describe the formation of galaxies from the merging of several gas clouds rather than from the gravitational contraction of huge isolated gas clouds. Many questions still exist in galactic evolution. For instance, why did primordial hydrogen and helium in the early universe clump into clouds destined to become galaxies? What is the exact nature of dark matter?
MEASUREMENT
OF ASTRONOMICAL DISTANCES: This section is non-examinable but contains useful background information to assist with the study of this topic. There are several different units
used in Astronomy to measure distance (4). ¨ The astronomical unit (AU) is the average distance between the earth and the sun. 1 AU = 1.496 x 108 km. This is used primarily for distances within the Solar System. ¨ The light year (ly) is the distance travelled by light in one year. 1 ly = 9.46 x 1015 m = 9.46 x 1012 km = 63 240 AU. This is used for distances to the stars. ¨
The parsec (pc) is defined as the distance at which 1 AU
perpendicular to the observer’s line of sight subtends an angle of 1 arcsec (1
second of arc). See the diagram
below. 1 pc = 3.09 x 1013
km = 3.26 ly. This unit is used for
distances to the stars. The easiest way to measure stellar distances is to use an effect called parallax. This is the apparent displacement of an object because of a change in the observer’s point of view. Astronomers measure the parallax shift of a star from opposite sides of the earth’s orbit. The direction of a nearby star from the earth changes as the earth orbits the Sun. The nearby star appears to move against the background of more distant stars. This motion is called stellar parallax. The distance, d, in parsecs, to the nearby star is given by:
where p = parallax angle of the star in arcseconds. Note that the parallax angle is half the angle through which the star’s apparent position shifts as the earth moves from one side of its orbit to the other (4). See diagram above.
LUMINOSITY AND BRIGHTNESSThe luminosity of a star is defined as the amount of radiant energy emitted by the star per second (3). Luminosity is usually measured in watts or as a multiple of the Sun’s luminosity (L€ = 3.90 x 1026 W). Note that astronomers use the symbol € to represent the Sun. Knowing a star’s luminosity is essential for determining the star’s history, its present internal structure and its future evolution (4). As the radiant energy leaves the star it spreads outwards in a sphere of increasing radius. The amount of energy passing through each square metre on the surface of the sphere per second is found by dividing the luminosity of the star, L, by the sphere’s surface area. The resulting quantity is called the apparent brightness, b, of the star and is measured in Wm-2.
where d = distance to the star in metres. Note that this is another example of the inverse square law for EM
radiation that we studied earlier. As
we move away from a star (or indeed any light source), the decrease in
brightness is inversely proportional to the square of our distance from the
star.
APPARENT & ABSOLUTE MAGNITUDES:Note that in Astronomy we use the magnitude scale to denote brightness. Hipparchus invented the scale in the second century BC and modifications over time, especially in the nineteenth century AD, have produced what we now call the Apparent Magnitude Scale. Apparent magnitude is a measure of the light arriving at earth and is directly related to apparent brightness. Apparent magnitude describes how bright an object appears to be when seen by an observer on earth (4). In the Preliminary Course, we DO NOT need to know the details of the apparent magnitude scale (or of the absolute magnitude scale). Just be aware that when reading apparent magnitudes, the greater the apparent magnitude, the dimmer the star. A star of apparent magnitude +2 (a second magnitude star) is dimmer than a star of apparent magnitude +1 (a first magnitude star). The limit of vision with the naked eye is about apparent magnitude +6. The Hubble Space Telescope can photograph stars of apparent magnitude +27 (more than 1020 times fainter than the sun) using very long exposure photography. The absolute magnitude is defined as the apparent magnitude a star would have if it were located 10 parsecs (32.6 ly) from earth (4). This quantity measures a star’s true energy output – its luminosity. Again the greater the absolute magnitude figure, the less luminous the star. Absolute magnitude removes the effect of different distances and allows us to compare the luminosities of stars with each other. For instance, the sun appears to be the brightest object in the sky only because it is so close to us compared to all other stars. It has an apparent magnitude of –26.8. If the sun were placed 10 pc from earth, its apparent magnitude would be +4.8. So, the sun’s absolute magnitude is +4.8. The most luminous objects have absolute magnitudes around –10 and the least luminous around +15. We will do more on apparent and absolute magnitudes if we do the Astrophysics Option in the HSC Course.
BLACKBODY
RADIATION:
If an iron bar is heated over an extended period of time, several interesting observations can be made. While still at relatively low temperature, the iron bar radiates heat, but no difference in the colour of the bar is noted. With increasing temperature the amount of radiation that the bar emits increases very rapidly and visible effects are noted. The iron bar assumes a dull red, and then a bright red colour. As it approaches its melting point the bar becomes a bright yellow colour. If it could be raised to even higher temperatures without melting, the bar would become a blue-white colour. Clearly, with increasing temperature the bar emits more thermal radiation and the frequency of the most intense radiation becomes higher. The relationship between the colour of light emitted by a hot body and the temperature of the body was first recorded by Thomas Wedgewood in 1792. The porcelain-maker noticed that all of his ovens became red hot at the same temperature, regardless of their shape, size and construction. Experiments by many physicists have since shown that any object with a temperature above absolute zero (zero kelvin or 0K) emits light of all wavelengths with varying degrees of efficiency (1). The detailed form of the spectrum of the thermal radiation emitted by most real hot bodies depends to a certain extent upon the composition of the bodies. Physicists found a particularly useful class of hot bodies to assist with the study of the relationship between colour and temperature. This type of body is called a “blackbody” and by definition is a body whose surfaces absorb all the thermal radiation incident upon them and allow none to be reflected. All blackbodies at the same temperature emit thermal radiation with the same spectrum, independent of their composition. The intensities of the colours in the spectrum depend only on the temperature (2). Obviously, blackbodies are hypothetical, ideal bodies. A perfect blackbody does not reflect any light at all. This is the reason why any radiation that it emits is entirely due to its temperature (3). Examples of real bodies which approximate blackbodies include: an object coated with a diffuse layer of black pigment (such as carbon black); an object containing a cavity connected to the outside by a very small hole – such an object is called a cavity radiator (2); stars (including our Sun) and planets (4). Note that a blackbody does not necessarily appear black. The Sun does not look black because its temperature is high (around 5800 K) and so it glows brightly. A room-temperature (around 300 K) blackbody, however, would appear very black (4), as can be seen from the graph shown below. The energy density of blackbody radiation inside a cavity radiator at various temperatures as a function of wavelength is shown below. Note that the intensity versus wavelength plot for the radiation emitted from the hole connecting the cavity to the outside has the same shape. The radiation inside a cavity whose walls are at temperature T has the same character as the radiation emitted by the surface of a blackbody at temperature T (2). This provides a useful means of studying blackbody radiation, since cavity radiators are convenient to handle both experimentally and theoretically.
WIEN’S DISPLACEMENT LAW:As mentioned above, the intensity versus wavelength plot for the radiation emitted by a blackbody has the same shape as the energy density versus wavelength plot shown above. Such a plot indicates that a blackbody of temperature T emits a continuous spectrum with some energy at all wavelengths and that this blackbody spectrum peaks at a wavelength lmax , which becomes shorter with increasing temperature (1). In 1893, before plots such as that above had been obtained experimentally, the German physicist Wilhelm Wien derived a quantitative expression relating the wavelength (or colour) of the radiation emitted by a hot body to the temperature of the body (4). To develop this relationship he used an oven with a small hole as a good approximation for an ideal blackbody. Any radiation that enters the small hole is scattered and reflected from the inner walls of the oven so often that nearly all incoming radiation is absorbed and the chance of some of it finding its way out of the hole again can be made exceedingly small. The radiation coming out of this hole is then very close to the equilibrium blackbody electromagnetic radiation corresponding to the oven temperature. Applying his knowledge of heat and electromagnetism to this situation he came up with what is now called Wien’s Displacement Law:
Wien’s law indicates that as the temperature of a body increases, the wavelength at which maximum emission of radiation occurs is displaced toward lower wavelengths. This is in agreement with the example of the heated iron bar mentioned above, namely that the principal frequency of the emitted radiation becomes higher (that is, the iron bar changes colour from dull red to blue-white), with increasing temperature. Clearly, another way of expressing Wien's law is to say that the wavelength of maximum emission of a blackbody is inversely proportional to its temperature in kelvin. Wien’s law is particularly useful for determining the surface temperatures of stars (4). It is not necessary to know how far away the star is, how large it is or how much energy it radiates into space. All we need to know is the dominant wavelength of the star's electromagnetic radiation. For example, the star Rigel, 815 light years from earth in the constellation of Orion, has a continuous spectrum that peaks at a wavelength of 2.87 x 10-7 m in the UV region of the EM spectrum. Its surface temperature can be found from Wien’s law as: T = 0.0029 / 2.87 x 10-7 = 10 105 K
SURFACE TEMPERATURE OF STARS:Clearly, from the details above, the surface temperature of a star is related to its colour. If a star is very hot, its radiation is skewed towards the short wavelength ultraviolet end of the spectrum. In other words its apparent colour is blue (eg Bellatrix, T = 28 000K). If a star is very cool, its radiation peaks at long wavelengths and its apparent colour is red (eg Betelgeuse, T = 2400K). Stars can be divided into specific spectral classes that summarize not only the colour and surface temperature ranges but also the chemical composition. See the Table below which has been taken from Kaufmann & Freedman p.470 (4).
Be aware that astronomers use the term “metals” to refer to any element above helium in the Periodic Table (4). Clearly, this is different to the term’s meaning in chemistry. Note that in researching the colour-temperature relationship for stars you will also come across something called the B-V colour index (or colour ratio). We will study the details and usefulness of the colour index if we do the Astrophysics Option in the HSC Course. Basically, if the star is hotter than about 10 000 K, it is a very bluish star with a value of B-V less than 1. If a star is cooler than about 10 000 K, its B-V value is greater than 1. After measuring a star’s brightness using UBV photometry, an astronomer can estimate the star’s surface temperature from a blackbody temperature versus colour index graph.
STEFAN-BOLTZMANN LAWWhile on the subject of blackbody radiation, it is worth mentioning the Stefan-Boltzmann Law. This law states that the energy flux, F (in joules per square metre of surface per second), from a blackbody is directly proportional to the fourth power of the object’s temperature, T (measured in Kelvin). Mathematically,
where s = 5.67 x 10-8 Wm-2K-4, is a constant. Both Wien’s Law and the Stefan-Boltzmann Law are useful tools for analyzing glowing objects like stars. Note that you do not need to know the Stefan-Boltzmann Law for the Preliminary Course.
SPECTRA AND
THEIR IMPORTANCE IN ASTRONOMY (NON-EXAMINABLE):
This material is extension material. When a beam of sunlight is shone through a triangular glass prism, the white light is dispersed, producing a rainbow of colours, which can be displayed on a screen. The rainbow of colours is called a spectrum. In 1814 the German optician Joseph von Fraunhofer discovered that the spectrum of sunlight contains hundreds of fine dark lines, now called spectral lines. Fifty years later, chemists found that they could produce spectral lines in the laboratory and use these lines to analyze the kinds of atoms of which substances were made. There are three basic types of spectrum:
Spectroscopy is the systematic study of spectra and spectral lines. Spectral lines are extremely important in astronomy, because they provide very reliable evidence about the chemical composition of distant objects, the temperature of objects and the motion through space of objects.
THE HERTZSPRUNG-RUSSELL (H-R) DIAGRAMEven though in photographs of stars, bright stars appear larger than dim ones, it would be very wrong to assume that this is actually the case. In fact, to determine the size of a star, an astronomer must combine information about the star’s luminosity (determined from its distance & apparent brightness) and its surface temperature (determined from its spectral type) (4). Using the Stefan-Boltzmann law, we can deduce the relationship between a star’s luminosity, radius and surface temperature:
where L = star’s luminosity (watts), R = radius of star (m), s = Stefan-Boltzmann constant and T = star’s surface temperature (kelvin) (4). Clearly then, even a very cool star (low T) can have a very high luminosity, if its radius is sufficiently large. This relationship between luminosity and surface temperature led the Danish astronomer, Ejnar Hertzsprung, in 1911 to discover that a regular pattern is revealed when absolute magnitudes of stars (a measure of their luminosities) are plotted against their colours (a measure of their surface temperatures). In 1913 the American astronomer, Henry Norris Russell, independently found a similar pattern in a plot of absolute magnitudes versus spectral types (another measure of surface temperature). Today, the Hertzsprung-Russell (H-R) Diagram is one of the most important in all astronomy because of its ability to summarize so many trends so succinctly and because of its usefulness in helping us to understand the evolution of stars. Let us now examine the H-R Diagram in detail. The Hertzsprung-Russell Diagram is a graph of the luminosities of stars against their colour or surface temperature. On such a graph each data point represents a star whose spectral type and luminosity have been determined. The most luminous stars are near the top of the graph, the least luminous stars are near the bottom. Hot stars (O & B stars) are towards the left side of the graph while cool stars (M stars) are toward the right (4). The graph below shows only a few stars and is designed to show the general patterns which emerge on an H-R plot. Note
the different possibilities for axes. H-R
diagrams can be plotted as: u
Luminosity
v’s surface temperature (or spectral class or colour index) u
Absolute
magnitude v’s surface temperature (or spectral class or colour index) u
Log10
of the luminosity relative to the sun v’s surface temperature etc
The first important lesson to come from the H-R diagram is the existence of fundamentally different types of stars. The plot clearly shows that stars are found in four main groups: Main Sequence, Red Giants, Super Giants and White Dwarfs. The main sequence stars are represented by a band that runs from bright, hot, blue giant, O class stars in the top left corner down to dim, cool, red dwarf, M class stars in the lower right corner. Between 80% and 90% of all stars are main sequence stars (1). They are in their hydrogen burning phase and remain on the main sequence until the hydrogen in their cores is exhausted (5). Note that here the word “burning” is used to mean “nuclear fusion” – a common piece of jargon used by astronomers. Stars on the main sequence are very stable. The sun is a main sequence star of intermediate luminosity, surface temperature (and radius) and has sufficient hydrogen to keep it on the main sequence for at least another five billion years (5). The masses of main sequence stars are directly related to their absolute magnitudes. The brighter the star, the greater the mass of the star; the dimmer the star, the lower the mass. Red Giant stars are found in the upper right section of the H-R plot. They are 10 to 100 times more massive than the sun and are also about 100 times more luminous than the sun. Since these stars clearly have low surface temperature, their high luminosity can only come from a very large radius. These stars are cool, reddish in colour and gigantic in size (5). Aldebaran in the constellation of Taurus and Arcturus in the constellation of Bootes are examples of Red Giant stars. A few rare stars are considerably bigger and brighter than typical red giants, with radii up to 1000 times that of the sun. These stars are referred to as Super Giants (4). Betelgeuse in Orion and Antares in Scorpius are two examples of Super Giant stars. Giants and super giants have thermonuclear (fusion) reactions occurring in their interiors but the character and location of those reactions can be very different from those occurring in main sequence stars like the sun (4). White dwarfs form the fourth main group of stars on the H-R plot and are located in the bottom left section. These stars are about the same size as the earth and can only be seen with the aid of a telescope (4). They have temperatures of about 10 000 K on average, are very dim and typically whitish in colour (5). Note however, that surface temperatures for white dwarfs do range from 5000 K to 80 000 K and that therefore they can have colours other than white (1). White dwarfs are the remains of giant stars at the end of their life. They have no thermonuclear reactions occurring in their interiors (4).
The following section of notes on H-R Diagrams is extension material only and is not examinable in the current syllabus. In order to assist with the classification of stars on the H-R plot, a system of luminosity classes was developed in the 1930’s, based on subtle differences in the spectra of stars. See H-R plot below and Ref.(1) pp.246-250 for more detail.
Luminosity classes Ia and Ib are composed of Super Giant stars. Luminosity class V includes all main sequence stars. The classes in between provide a useful means of distinguishing giant stars of various luminosities – Class II Bright Giant stars, Class III Giant stars and Class IV Subgiant stars. Class VI consists of Subdwarf stars. There is no luminosity class assigned to white dwarfs, since they represent a final stage in stellar evolution in which no thermonuclear reactions are taking place. Consequently, white dwarfs are referred to only by the letter D (for dwarf). (1 & 4) Astronomers describe stars on the H-R diagram by giving both a spectral class and a luminosity class. The spectral class indicates the star’s surface temperature and the luminosity class its luminosity. For instance, Aldebaran is a K5 III star, which means that it is a red giant with a luminosity around 500 times that of the sun and a surface temperature of about 4000 K. The sun is a G2 V star, which means that it is a main sequence star of luminosity equal to the sun (obviously) and surface temperature of about 5800 K. (4) This two-dimensional classification scheme enables astronomers to locate a star’s position on the H-R diagram based entirely on the appearance of its spectrum. This is very useful, since once the star’s absolute magnitude has been read from the vertical axis of the H-R diagram, the distance to the star can be calculated using a method called spectroscopic parallax. We will study this method if we do the Astrophysics Option in the HSC Course. (See Ref.(1) pp.248-250 for more detail.)
Also see the following for some good H-R Diagrams: H-R plot for nearest stars to us H-R plot for temperature-luminosity information H-R plot for mass-luminosity information
ENERGY SOURCES IN STARSThe Sun: The Sun gains its energy from nuclear fusion reactions in which four hydrogen nuclei (protons) combine to form a single helium nucleus, releasing energy in the process. The energy released comes from the conversion of some of the hydrogen nuclei mass into energy according to Einstein’s equation, E = mc2. The total mass of four hydrogen nuclei is actually greater than the mass of a single helium nucleus. This difference in mass is called the mass defect of the helium nucleus and is the amount of mass converted to energy and given away by the helium nucleus to stabilize itself during its formation. This energy given away to stabilize the nucleus is called the binding energy of the nucleus. Note that two of the four protons mentioned above actually decay into neutrons during the fusion reaction. Thus, the helium nucleus contains two protons and two neutrons. The fusion reactions occur only in the dense, hot core of the sun, since fusion requires temperatures of around 107 K. Note that for this reason fusion reactions are often referred to as thermonuclear reactions. Astronomers are notorious for referring to fusion reactions as “burning”. So they speak of “hydrogen burning” instead of hydrogen fusion and “helium burning” instead of helium fusion, and so on. All stars on the Main Sequence are in their hydrogen-burning phase. Two different fusion mechanisms are responsible for the helium production and consequent release of energy. For stars whose core temperatures are above 18 million K, the carbon (or CNO) cycle is the main mechanism, while for stars whose core temperatures are below this, the proton-proton chain reaction predominates. We do not need to know the details of these reactions in the Preliminary Course. Red Giants: When the hydrogen has been exhausted in the core of a Main Sequence star, hydrogen burning ceases. This leaves a core consisting almost entirely of helium, surrounded by a shell through which hydrogen burning works its way outward in the star. The core shrinks and becomes hotter, while the star's outer layers expand and cool. The result is a Red Giant star. When the core temperature reaches about 100 million K, the fusion of helium (helium burning) begins there. This process, also called the triple alpha process, converts helium to carbon and oxygen. In a more massive red giant, helium burning begins gradually whereas in a less massive red giant, it begins very suddenly, in a process called the helium flash. White Dwarfs: When an old, low mass, star undergoes a helium shell flash, thermal pulses occur during which more than half the star’s mass may be ejected into space. This exposes the hot carbon-oxygen core of the star. Ultraviolet radiation from the exposed core ionizes and excites the ejected gases, producing a planetary nebula. (A nebula is an interstellar gas cloud.) No more nuclear reactions take place in the exposed core. It becomes a degenerate (non-contracting), dense sphere about the same size as the earth. It is called a White Dwarf. It gives off thermal radiation, which causes it to glow. As it cools, it remains the same size but becomes less luminous, eventually fading into obscurity as a black dwarf.
NUCLEAR RADIATIONThe fact that energy can be released from the nuclei of atoms was mentioned above. Energy can be released from nuclei by three processes – nuclear fission (the splitting of heavy nuclei to form lighter nuclei), nuclear fusion (the joining of light nuclei to form heavier nuclei, as happens in stars) and natural radioactive decay of the nucleus. Without delving too much into the realms of nuclear physics, which is another story, it is worth mentioning a few facts about the three types of natural radioactive nuclear emissions. Nuclei can emit a,
b or g
radiations. u Alpha
(a)
particles:
These are doubly charged helium nuclei, consisting of a nucleus containing two
protons and two neutrons. Their
double positive charge gives them very good ionizing ability.
Alpha particles therefore interact strongly with matter and have very
poor penetrative power. They are stopped by a few centimetres of air or a few sheets
of paper. Alpha particles are the
most massive of the natural radiations. u Beta
(b)
particles:
These are rapidly moving electrons. Due
to their single negative charge, they have a smaller ionizing ability than alpha
particles and interact less strongly with matter.
They therefore have a higher penetrative ability, being able to pass
through matter hundreds of times thicker than can an alpha particle with the
same energy. b particles can
penetrate about a metre of air. u Gamma
(g) rays: As
you are already aware, gamma rays are electromagnetic waves.
They have no charge and therefore interact with matter to a much smaller
extent and have a much lower ionizing ability than the other two natural
radiations. Gamma rays have a much
greater penetrative ability than alpha or beta particles and are capable of
penetrating many centimetres of concrete.
It is the relatively larger mass of the alpha particle that enables it to suffer less deflection as it passes through both magnetic and electric fields.
THE VISUAL APPEARANCE OF THE SUNIf you study photographs of the Sun, it appears that the Sun has a sharp well-defined surface. This seems strange, since we know the Sun is gaseous throughout its volume because of its high internal temperature. The Sun appears to have a surface because all of the visible light comes from a relatively thin layer of gas called the photosphere. The photosphere is actually the bottom layer of the solar atmosphere and is about 500 km thick (4). The gases in the photosphere radiate energy with a spectrum approximating that of a blackbody and with a temperature of 5800 K (4). Above the photosphere are the chromosphere and corona, which are transparent to visible light. Below the photosphere is the solar interior, which consists of the central core with a temperature of about 1.55 x 107 K and two other regions above the core, which do not concern us here. The total radius of the Sun is 696 000 km (4). NOTE: NEVER look directly at the Sun. It will damage your eyes and can cause permanent blindness. Never attempt to view the Sun with optical equipment (eg binoculars, telescopes) unless it is fitted with appropriate filters, by someone who really knows what he/she is doing!!!
EMISSIONS FROM THE SUNThe most obvious emissions from the Sun that reach Earth are light and heat. Other less obvious forms of electromagnetic radiation are emitted by the Sun and do reach Earth. As mentioned above, the photosphere radiates like a blackbody with a temperature of 5800 K and therefore emits EM radiation of all wavelengths. The radiation peaks in the visible region of the spectrum. It has been verified by direct observation from space-craft that charged particles are also emitted from the Sun and make their way to Earth. A continuous stream of particles passes the Earth at speeds up to 700 km/s (1). This stream of particles is called the Solar Wind and consists mainly of protons and electrons, with some atomic nuclei. Another type of particle that is emitted from the Sun and literally passes through the Earth is the neutrino. Neutrinos have no charge, an extremely small mass (almost zero) and interact only very weakly with matter. Experiments are in progress today to detect and accurately measure the neutrino flux from the Sun, in order to gain valuable information about the nature of the Sun’s core, where the neutrinos originate.
SUNSPOTS
& THE SUNSPOT CYCLE
A sunspot is a dark
region of irregular shape in the photosphere.
Typical sunspots are a few tens of thousands of kilometres across.
They can occur in isolation or in clusters called sunspot groups (4).
Sunspots are not permanent features of the Sun and last from a few hours
to a few months (4). Using Wien’s Law and
photometric analysis of sunspots, the temperature of the center of a typical
sunspot is found to be 4300 K (4). Clearly,
this is much lower than the average temperature of the photosphere of 5800 K. In 1908, the American astronomer George Hale found that sunspots were places in the photosphere where very high magnetic fields were concentrated. Magnetic fields of around 0.4 T have been detected in sunspot areas (4), which is about 6000 times more intense than the Earth’s magnetic field measured at its poles. Thus, sunspots can be thought of as regions of the photosphere of lower temperature and very strong magnetic activity. The number of sunspots varies with a period of about 11 years. This is called the sunspot cycle. During the 11-year cycle the number of sunspots increases from a minimum to a maximum and then decreases again to a minimum. Sunspot minima occurred recently in 1965, 1976, 1986 and 1996 (4). Sunspot maxima occurred in 1968, 1979 and 1989 (4). This 11-year sunspot cycle is related to a 22-year cycle called the solar cycle, during which the Sun’s magnetic field reverses. The sunspot cycle has a direct impact here on Earth. Sunspot groups are the sources of solar flares, huge bursts of energy stretching perhaps 100 000 km in length (1). EM radiation of all wavelengths is released, from radio waves through to gamma radiation (1). Charged particles are also accelerated to high speeds, many escaping into interplanetary space as solar cosmic rays (1). These charged particles, mainly protons and helium nuclei, enhance the solar wind and may reach Earth in 30 minutes or so, disrupting radio communications, causing power blackouts and difficulties for anyone navigating by magnetic compass and causing auroral displays (1). An aurora is a high altitude, natural light display, occurring most frequently above 60° north or south latitude. It is named according to its location - aurora borealis (northern lights) or aurora australis (southern lights). Extensive auroral displays are usually accompanied by disturbances in the Earth’s magnetic field and interference with radio, telephone, and telegraph transmission. Note that there are several links in the Cosmic Engine section of my Links Page that provide information useful for answering Syllabus point 8.5.4 Column 3 dot point 2 on "the effects of sunspot activity on Earth's power grid and satellite communications".
NOTE: The remaining sections of notes are extension material only and are not examinable in the current syllabus.
THE FORMATION OF THE SOLAR SYSTEM (Not Examinable)Our Solar System consists of nine planets: Mercury, Venus, Earth, Mars Jupiter, Saturn, Uranus, Neptune & Pluto in orbit around the Sun. Many of these planets have natural satellites (moons). There is an asteroid belt consisting of rocky objects of various sizes between the orbits of Mars and Jupiter. Beyond the orbit of Neptune there is a belt of asteroids of rock and ice and short period comets called the Kuiper Belt. Pluto and its moon Charon are actually located on the edge of this belt. The Nine Planets has more information. Our Solar System formed from matter created in ancient stars that existed billions of years ago. One or more of these stars ended their life as a supernova (exploding star) and cast the matter from the star, including many heavy elements, into the surrounding space. Thus, the interstellar gas clouds became enriched with heavy elements. One such slowly rotating gas cloud containing hydrogen, helium, traces of heavy elements, ice and dust particles, contracted under its own gravity, via the process described previously for the formation of galaxies. At the center of the cloud, a protostar formed and the gas cloud flattened into a spinning disc around the protostar. Eventually, after about 100 million years, hydrogen fusion began and the new star (the sun) began to shine. Over that same 100 million year period, the solar system formed from the material in the spinning protostellar disc. The four inner planets, the terrestrial planets, formed through the accretion of dust particles into planetesimals (small asteroid-like objects with diameters of about 10 km). Under the action of gravity these planetesimals coalesced into protoplanets (about the size of the moon). These protoplanets then collided to form the terrestrial planets. The four large outer planets, the Jovian planets, began to form by the accretion of planetesimals. Due to the abundance of ice as well as rock grains in the outer solar system, objects much larger than any of the terrestrial planets formed in the outer regions. Slow moving gas atoms were captured by the strong gravitational attraction of these massive rock and ice objects. The accretion of gas happened slowly at first and then more rapidly as time went by. Eventually, huge planets formed. These planets had extremely thick, hydrogen-rich atmospheres, surrounding rocky cores and were about five to ten times the mass of the earth. That of course just leaves the planet Pluto. How did it form? Possibly it began in the same manner as the other Jovian planets with the accretion of rock and ice to form firstly a planetesimal and then a protoplanet. Perhaps because it was so far out in the protostellar disc, there was insufficient gas to accrete to this core and so a small, rock and ice mass formed. At some stage, Pluto was probably involved in a rather catastrophic collision with another body, which tore off enough of the planet to form Pluto’s moon, Charon.
THE
EARTH’S MAGNETIC FIELD
|
