Colour in the Cosmos

Professor Ian Morison

Observing colour with our eyes and cameras

Our eyes are all that we can use if we wish to observe the outlines of the constellations, the majestic sweep of the Milky Way or the fleeting trail of a meteor arcing across the sky.  But to use them to view the heavens at their best, a little time is required for them to become dark-adapted.  First, and most obviously, in dark conditions the pupils will dilate so allowing more light to enter the eye.  This happens over a period of 20 seconds or so and will thus almost immediately enable one to see fainter stars.  The typical daylight size of the pupil is about 2.5 to 3mm across but this extends to 5 to 7mm under dark conditions.  Sadly, as one gets older, the maximum size is likely to be nearer 5mm rather than 7 (a factor of 2 in area) so youngsters will definitely be able to see better in the dark!

There is a second dark adaptation mechanism that takes about 20 minutes to come into effect.  Without high light levels reaching the retina, Vitamin A is converted first into retinene and then into rhodoposin that significantly improves the sensitivity of the rods and cones which are the light sensitive receptors in the retina of the eye.  Strong white light can quickly reverse this change, but red light is far less damaging - which is why astronomers use red light to view their star charts.  In daylight we tend to use a region of the retina called the fovea which is densely populated with cones that are colour sensitive but require high light levels to work well.  This is why objects that can have beautiful colours when imaged photographically tend to just appear as shades of grey when viewed through a telescope.  In contrast, the rods are not colour sensitive but are more sensitive to light.  Away from the central foveal region, the cones are fewer in number and the rods are more closely packed.  We can thus see fainter objects by using "averted vision" - directing our gaze to one side of the object of interest. 

So, sadly, our eyes can rarely see any colour when viewing the heavens; we can tell that some stars look orange or yellow and others white or blue-white, that the dust tail of a comet can have a yellow tinge and observe the lovely brown-ochre or orange-red colour of an eclipsed Moon or the iridescent greens, reds and purples of the Aurora Borealis (these latter two will be covered in detail in a later lecture) but, in general, we cannot see any colour in deep sky objects.  Using a 16 inch telescope allows a few objects to show colour - usually green as that is the part of the spectrum where our eyes are most sensitive - but we really need to use cameras to show the "colour in the cosmos".

The days of using film for astrophotography are virtually gone as digital cameras are far more sensitive.  They tend not to be "colour cameras" but work in monochrome so, to provide a colour image, several exposures are taken using appropriate red, green and blue colour filters.  Often this is combined with a monochrome image to give brightness information.  Professional cameras are usually cooled to well below zero C so that long exposures can be made without "electronic noise" becoming a problem.  As we will see, some objects give off very specific colours and, by using filters that allow just their wavelengths to pass it is possible to observe features that would otherwise be lost

The Colour of Stars

Between the bright stars Vega in Lyra and Altair in Aquilla lie a little group of stars whose real name is Brocchi's Cluster but which is usually called the "coathanger". Photographs such as that below show that the stars that make up the cluster have very different colours - from red through to blue.

Brocchi's Cluster - The Coathanger

The colour we see is directly related to the surface temperature of the star    

Blue stars                                   ~ 20,000K
White stars                                 ~ 10,000k
Sun-like stars - yellow                 ~   6,000K
Orange stars                               ~   4,500K
Red stars                                    ~   3,000K

This is because the amount of energy radiated by an object at a particular wavelength depends on the temperature.   As shown in the diagram below, the wavelength at which the emission is a maximum reduces as the temperature increases, so the radiation from a cool star whose surface is  ~3000K actually peaks in the infra-red  part of the spectrum and virtually all the light we see is in the red part of the spectrum.  As the temperature increases so the peak colour moves through the visible part of the spectrum into the ultra-violet.  These will still produce large amounts of blue light so we see these as blue stars.  As we will see, the prodigious amount of ultra-violet light produced by such stars is the cause of much of the colour that we see in the heavens. 

As can also be seen in the diagram below, the total amount of energy increases with temperature - this is an extreme effect as it rises as the 4th power of the temperature so that if the temperature were doubled the power emitted would rise by 16 times!  The total energy is given by the area of the graph in the diagram below.

The emission curves of bodies with different surface temperatures

Where does the energy come from to make the stars so hot?

Up to the late 1800's, scientists could not understand how the Sun could create so much light and heat. Had the Sun been entirely made of something like coal (along with the oxygen it would need to burn) it would burn itself up in about a thousand years!  Since the Sun had been providing heat and light for at least several thousand years a chemical source of the Sun's energy was clearly impossible.  Around 1870, Hermann von Helmholtz realised that if the Sun were contracting in size, energy, derived from potential energy, could be released.  He knew the mass and size of the Sun and also knew how much energy the Sun is continuously creating and sending out into space.  He calculating how much the Sun would have to reduce in size to provide its observed output, and deduced the Sun would be able to sustain its energy output for around 20 million years.   In the late 1800's people were quite happy to assume that the solar system was less than 20 million years old, so his idea was almost universally accepted as the likely way that the Sun creates its energy. 

However, during the late 1800's, geologists established that many Earth rocks and the fossils within them are definitely millions of years old, so Helmholtz must have been wrong.  In 1905, Einstein published the famous E = mc2 equation as part of his Special Theory of Relativity. One could thus surmise that, as c is very large, a tiny amount of mass (m) might be converted into an enormous amount of energy (E).           By around 1925, Physicists had determined the mass of a proton (a hydrogen nucleus). They had also determined that an alpha particle (a helium nucleus) has a mass slightly less than that of 4 protons. They realised that four Hydrogen nuclei might be able to "fuse" together into a helium nucleus (called fusion) and the mass that apparently disappears could be converted into energy.

This is difficult!  Since the hydrogen nuclei are each positively charged protons, they repel each other.  In order to overcome this mutual repulsion, the protons must be moving toward each other at nearly at the speed of light - and even then quantum mechanical tunnelling must be invoked.  They can only do this if it is very hot - greater than 10 million K.  Due to the great mass of the Sun, the pressure at its centre (called its core) must be very high to oppose the mass of the overlaying layers  of the Sun and calculations show that the core would reach and exceed the required temperature. Thus the source of this energy is a nuclear fusion reactor within the core of the Sun. 

As the dust and gas that made up our Sun collapsed under gravity, the temperature at centre increased and the protons moved faster.  When the temperature exceeded ~10 million K, the proton's kinetic energy became sufficient for two protons on a collision course to get sufficiently close to allow an effect called quantum mechanical tunnelling to come into play.  This allows one of them to overcome the potential barrier due to the electrostatic force between them.

In quantum theory, particles, such as the two protons approaching each other, can be described by wave-functions, which represent the probability of finding a particle in a certain location.  If a particle is adjacent to a potential barrier, its wave function decays exponentially through the barrier and can have still have a small amplitude on the far side of the barrier.  There is thus a very small probability that the particle can "appear" on the other side of the barrier in which case is then said to have tunnelled through it.  Quantum tunnelling thus allows a particle, in this case a proton, to violate the principles of classical mechanics by passing through a potential barrier higher than the kinetic energy of the particle.

Quantum Mechanical Tunnelling

This allows the two protons to come sufficiently close for the strong nuclear force to momentarily bind them together before one of the protons decays into a neutron, a positron and an electron neutrino leaving a deuteron - the combination of a proton and a neutron which is the nucleus of deuterium.  The positron then annihilates with an electron, and their mass energy is carried off by two (sometimes more) gamma ray photons.  This is the first step in what is called the proton-proton cycle outlined below.  The first step in the proton-proton chain is extremely slow, with a proton typically waiting 109 years before carrying out this reaction!  It is thus the limiting step on the chain of nuclear reactions that determines the overall reaction rate.

It is worth pointing out that the slowness of this reaction is vital to our presence here on Earth.  If the reaction rate was just 10 times faster, the Sun would burn up its energy supply in one billion years rather than the ~ ten billion years and there would not have been sufficient time for our human race to evolve!  

The Proton-proton Cycle

The bulk of the Sun's energy comes from the "Proton-proton" or ppI chain. This is a three stage process:

1) Two protons react to give rise to a deuteron comprising one proton and one neutron.  The charge of one of the protons is carried away by a positron (the anti particle of the electron). An electron neutrino is also created.

2) A further proton then reacts with the deuteron to give a nucleus comprising two protons and one neutron.  It is thus an isotope of helium called helium-3.  A gamma ray (very high energy photon) is emitted.

3) Two helium-3 nuclei react to give one helium nuclei (also called an alpha particle) and two protons are emitted to take part in further reactions.

This is not quite the end of the story.  The two positrons given off in step 1 of the reactions will quickly meet an electron and annihilate to give 2 (occasionally more) further gamma ray photons.  The pressure generated within the core as a result of these nuclear reactions prevents the star's collapse.

The three steps in the Proton-proton cycle.  Steps 1 and 2 are carried out twice to provide the two 3He2 nuclei required for the third step.

Two further reaction sequences, the ppII and ppIII chains contribute further energy. Though the ppIII chain contributes very little energy in the Sun, it does produce neutrinos of high energy which has proved to be very important in the solar neutrino problem to be discussed later.

The photons - initially gamma rays - work their towards the Sun's surface continuously interacting with matter.  Their direction of motion following each interaction is random so they carry out what is called 'random walk' and, as a result, the energy takes of order 100,000 years to pass through the 'radiative zone' that surrounds the core and extends for ~2/3 of the Sun's radius.  As they work their way outwards, the temperature drops, and as the photons will be in thermal equilibrium with the gas, their wavelengths will increase.

The region, ~1/3 of the Sun's radius in width, between the outer edge of the radiative zone and the surface, is called the 'convective zone' in which the energy is carried outwards by first large and then small convective cells as shown in Figure 2.x. As a result, the Sun's surface, called the photosphere, shows granulations - honeycomb-like variations in brightness. The granulations are brighter in the centre where the convection currents bring the energy to the surface and darker around the edges where material, cooled as it radiated energy into space, returns towards the centre.

A cross section of the Sun showing the regions referred to in the text and their approximate temperatures.

The Solar Neutrino problem

In the 1970's Ray Davis set up a tank filled with 100,000 gallons of tetrachloroethylene (C2Cl4), located 4,900 ft underground in the Homestake Mine in South Dakota.   It was deep underground to prevent cosmic rays (which would be absorbed by the rock strata above) giving rise to false detections. Very rarely a neutrino from the ppIII chain would react with a chlorine nucleus to give a radio-active isotope of argon.  Having left the tank for a month, Davis flushed the tank to extract and detect the argon atoms with, on average, about 10 argon atoms detected per month.  The problem was that only about 1/3 of the expected number of neutrinos were detected.  Remembering that these neutrinos come from relatively rare nuclear reactions in the pplll chain, it could have been due to our lack of understanding of these reactions, but modern experiments have confirmed Davis's results.  He was awarded the Nobel Prize for Physics for this work in 2002.

The Solar neutrino problem is solved

At this point we need to know that in the standard model of particle physics there are three types of neutrino; electron, muon and tau.  Those emitted by the nuclear reactions in the Sun are electron-neutrinos.

At the bottom of a very deep mine at Sudbury in Canada, there is a 12m sphere which holds 1000 tons of heavy water.  This is water which has a deuteron rather than a proton as its nucleus.  Every day of operation about 10 solar neutrinos react with a deuteron, the reaction giving rise to two protons and a very high energy electron.  This travels at a speed faster than the speed of light in the liquid.  It thus produces a shock wave akin to that produced by a supersonic plane.  The shockwave produces 'Cherenkov' radiation which spreads out in a cone. The tank is surrounded by 916 photon detectors which detect the Cherenkov radiation and can even define the direction of the incoming neutrino so it is possible to measure the number of solar neutrinos detected. The Sudbury detector has confirmed that only 35% of the expected number of electron-neutrinos were arriving from the Sun.  In a follow-up experiment, 2 tonnes of high-purity table salt (NaCl) were added to the heavy water in order to provide three times better sensitivity to the muon and tau neutrinos.  It appears that the total number of neutrinos detected with a solar origin does agree well with that predicted for the total number ofelectron-neutrinos that the Sun should produce.  The only way that this could be the case is if the electron neutrinos can change (the word oscillate is used) into one of the other two types en route from the Sun.

It was thought that electron-neutrinos were, like photons, massless.  As Einstein showed, anything travelling at the speed of light would experience no passage of time so there would be no way that an electron neutrino could ever change into one of the other two types. However, if the neutrino does have mass it will not travel at the speed of light so it will then experience the passage of time and thus could "oscillate" into muon or tau neutrinos.  It is thought that on their way from the core of the Sun to the Earth the neutrinos will evenly distribute themselves amongst the three types - thus only 1/3 of the electron-neutrinos emitted by the Sun will remain to be detected - exactly as observed. The neutrino problem is solved!

Fraunhofer Lines in the solar spectrum and the Composition of the Sun

If one observes the Sun's spectrum at high resolution it will be seen to be crossed by a large number of dark lines.  They are named after Joseph von Fraunhofer who independently discovered them in 1814 though they had been observed earlier by William Wollaston in 1802.  Later, Gustav Kirchoff and Robert Bunsen found that the wavelengths of the absorbtion lines seen in the Sun corresponded to those of the emission lines observed when the atoms of a particular element are excited.  This can be achieved by sprinkling a compound of the element into a Bunsen burner flame when, for example, salt gives an orange colour due to a close pair of emission lines called the sodium D lines - very obvious in the spectrum below.)

Before long, Fraunhoffer lines corresponding to all the known elements had been found in Sun's spectrum except for one set of lines.  It was realised that there must be an element in the Sun's atmosphere that had not then been discovered on Earth. It was thus called helium after 'Helios' the Greek name for the Sun

The Fraunhoffer Lines in the Sun's spectrum.

How are these lines formed?  The photosphere will emit a continuous spectrum. The photons will then pass through the Sun's upper atmosphere, the chromosphere, where atoms can absorb photons that correspond to transitions between their energy levels. Thus the lines, called absorbtion lines, will be at just the same wavelengths as the emission lines that we can observe on Earth.

From the analysis of the solar spectrum it is possible to estimate the composition of the majority of the Sun's interior as the outer layers are "mixed" by convective currents as will be described later.  About 71% by mass is hydrogen (91.2% in number of atoms), 27.1% by mass is hydrogen (8.7% in number of atoms), Oxygen 0.97% (0.078% in number of atoms), and carbon 0.40% (0.043% in number of atoms).  The small remainder then comprises all the other atoms detected in the Sun's spectra. 

As the lines that we see in the spectra of stars are highly dependant on their surface temperatures, these are used to classify the stars into 7 spectral types: O,B,A,F,G,K and M.  Here they have been listed in decreasing order of temperature, O the hottest and M the coolest.  Each type is split into tenths, so the hottest stars within a spectral type will be classified as, say, G0 and the coolest within that type G9.  Our Sun is classified as a G2 star and is thus towards the hotter end of the G-type stars.

O-type stars range from ~60,000K down to 30,000 K.  Such stars have a very short lifetime so are relatively rare.

B-type stars are cooler, ranging from 30,000K down to 10,000K. 
A-type stars range in temperature from 10,000K down to 7,500K.
F-type stars cover the range from 7,500K down to 6000K.
G-type stars, the type which includes our Sun, cover the temperature range from 6000K down to 5000K.
K-type stars range from 5000K down to 3500 K.
M-type stars are the coolest with surface temperatures less than 3500 K

From the surveys that currently exist, the percentages of stars in the differing spectral classes are as follows.

Type                  Colour                Proportion
 O                       Blue                        0.003%
 B                    Blue-White                  0.13%
 A                       White                      0.63%
 F                    White-Yellow               3.1%
 G                     Yellow                       8%
 K                     Orange                      13%
 M                        Red                        78%

You will see that the great majority of stars are cool M-type stars and there is a very small percentage of O and B-type stars.  You will also note that only about 7% of all stars are hotter and brighter than our Sun.  It is NOT, as is often stated, an average star.  It may be a typical star, but it is well above average!

The Hydrogen Alpha Line

This is the lovely pinkish-red colour that is seen when hydrogen gas is excited by ultra-violet radiation.  The high energy UV photons lift the electron to high energy states and, as they drop down again to the ground state they emit photons at a series of specific wavelengths called the Balmer Series shown in the diagram below.

The formation of the H-α line

Only very hot stars emit much ultra-violet light.  Such stars do not live very long.  They might emit 40,000 times more energy that our Sun, so burn up their "hydrogen fuel" 40,000 times faster but they may only have a mass 10 times greater than our Sun so can only live for a period 4,000 times shorter.   Thus such stars are young and are found in stellar nurseries.   So, whenever we see the red colour associated with H-α we know that there must be young stars about.

Some of the loveliest images of the heavens are associated with star formation regions such as the Orion Nebula in the constellation Taurus.

The Orion Nebula

It is virtually impossible to form a single star as there is not sufficient mass for gravity to enable a cloud of dust and gas to collapse, so stars are formed in groups which we may see at the heart of these stellar nurseries.  But, as the very hot stars die, the ultra-violet light that these emit ceases so we will no longer see H-α emission in the surrounding region.  The groups of stars we observe together are called open star clusters.  The Hyades and Pleiades open clusters in Taurus are two nice examples.

The Pleiades Cluster in Taurus

The brightest stars in the Pleiades Cluster are surrounded by blue nebulosity.  This is because the cluster appears to be passing through a dust cloud.  The nebulosity is  blue both because the light form these very hot O-type stars is blue but also because the dust preferentially scatters light of shorter wavelengths so scatters the blue light more that the red.  (This is not dissimilar to the fact that the sky is blue and that the Sun seen at low elevations appears red - the blue light having been scattered on its passage through the atmosphere.)

The image also shows striations in its structure.  This immediately tells us two things:

1) Something in the dust must be able to have a sense of direction.  This indicates the presence of iron compounds.

2) The iron particle must have something to align with - the galaxy must have a magnetic field!

The evolution of stars to give colourful end results

 As the proton-proton cycle converts hydrogen to helium in the core, its mean molecular weight increases.   A result is that the conversion rate of hydrogen to helium gradually increases whilst the star lies on the main sequence.  This, of course, increases the energy output of the star, so its luminosity will increase and, in order to radiate more energy, so will its surface temperature.   The combined result is that the star slowly moves up and to the left of the main sequence.

It is believed that, when formed, our Sun was ~30% less bright than at the present time and that over the next billion years its luminosity will increase by a further 10%.  An obvious consequence is that our Earth will eventually become too hot for life (as we know it) to exist on its surface.

The Triple Alpha Process

 Eventually the core of the star will be converted into 4He.   At this point nuclear fusion stops so that the pressure in the core that prevents gravitational collapse drops.  The core thus reduces in size, but as it does so, its temperature will rise.  Finally when it reaches ~ 100 million K, a new reaction occurs - the triple alpha process (3α) - so called because it involves three helium nuclei which are also known as alpha particles. This is an extremely subtle process.  The first obvious nuclear reaction that would happen in a core composed of helium is that two 4He nuclei would fuse to form 8Be.  But 8Be is very unstable - it has a lifetime of only 10-19 seconds - and virtually instantly decays into two 4He nuclei again.  Only when the core temperature has increased to ~100 million K, is it likely that a further 4He nucleus will fuse with 8Be to form 12C before it decays.  It is highly significant to our existence here on Earth that there is such a difference in temperature between that (~ 15 million K) at which the hydrogen fuses to helium and that (~100 million K) at which 12C can be formed.  If this were not the case, and the process could happen at the core temperatures close to that at which the proton-proton cycle operate, there would  be no long period of stability whilst the star remains on the main sequence with a relatively constant luminosity.  This, of course, has allowed stable temperatures to exist on Earth for billions of years and so enabled intelligent life to evolve. 

But there is a further real problem in attempting to form 12C.  A temperature of 100 million K is required to give the 4He nuclei a reasonable chance to fuse with a 8Be nucleus before it has a chance to decay.  The 4He nuclei are thus moving very fast and so have appreciable kinetic energy.  It would be expected that this energy would prevent a stable 12C nucleus arising as it would be sufficient to split the newly formed nucleus apart. (If a white billiard ball (4He) approached a red ball (8Be) very slowly they might just "kiss" and remain touching, but if it came in at high speed the energy of impact would split them apart).

So why is 12C so common?   This problem was pursued with great vigour by Fred Hoyle.  As he then stated: "Since we are surrounded by carbon in the natural world and we ourselves are carbon-based life, the stars must have discovered a highly effective way of making it, and I am going to look for it".

He realised that the excess energy that was present in the reaction (and thus expected to break up the newly formed 12C nucleus) could be contained if there happened to be an excited state (called a "resonance" by particle physicists) of the carbon nucleus at just the right energy above its ground state.  This is because, due to the quantum nature of matter, though atomic nuclei usually exist is their ground state, it is possible for them to absorb energy (such as an interaction with a gamma ray photon) and jump into an excited state.  This will later decay back to the ground state with the emission of a gamma ray of the same energy.  This is analogous to an atom absorbing a photo of energy which lifts an electron to a higher energy level.  The electron will then, in one or more steps, drop back down the energy levels emitting photons as it does so.

Hoyle realised that a stable carbon nucleus could only result if it had an excited state that was very close in energy to that of the typical kinetic energy of 4He that fuses with it.  This would thus lift the resulting 12C nucleus into an excited state from which it could drop back to the ground state by the emission of a gamma ray photon and so reach a stable state.

Some experiments in the late 1940's had suggested that such an excited state might exist, but Hoyle had been told that these were in error.  Hoyle argued that there must be an appropriate excited state otherwise we could not exist and pestered the particle physicists at the California Institute of Technology (Caltech), led by William Fowler, to repeat the experiments.  Fowler did so (it is said only so that Hoyle would go away) and found that there was indeed an excited state within 5% of the energy predicted by Hoyle!   Hoyle was essentially using the "anthropic principle" - which says that our existence as observers puts constraints on the universe in which we live.   William Fowler received the Nobel Prize in part for this work.  Many believe that Hoyle also should have won the Nobel Prize for this incisive observation.

In stars like our Sun, the nuclear fusion process continues largely by the addition of alpha particles (the helium-4 nucleus).

So         C12         + He4   gives O16
            O16                + He4  gives Ne-20
            Ne-20     + He4   gives Mg-24
            Mg-24    + He4   gives Si-28

As the number of protons in the nuclei increases, the incident alpha particle has to be travelling at ever higher speeds.  This requires higher temperatures.  Stars like our Sun do not have sufficient mass to increase the central temperature above that where Silicon can be formed so this is the heaviest element that such stars can produce.  (This explains why silicon is quite abundant.)

You will note that, as a result, carbon and oxygen are two of the commonest elements.  There is a process that occurs in more massive stars that produces nitrogen so giving, with hydrogen, the elements that make up the major part of life-forms here on Earth.

Variable Stars

In the latter stages of their life, stars become less stable and may well oscillate in size.  As the stars size increases, so its surface area will increase tending to increase its luminosity but, at the same time, the surface temperature will reduce.  As the emitted energy per unit area increases or decreases as the fourth power of the temperature, the star's luminosity actually falls as the size increases. The changes in colour and luminosity that result will cause the star to become a "variable star". 

During this phase of their life the stars often have intense solar winds and so lose much of their outer envelopes into space.

Planetary Nebula

Finally it appears that the star becomes so unstable that the outer parts of the star are blown off to form what is called a planetary nebulasurrounding the core remnant.   Planetary nebulae are some of the most beautiful objects that we observe in the universe and many, such as the Ring and Dumbell Nebulas may be observed with a small telescope.  Sadly, the range of colours that are seen in colour photographs cannot be seen by our eyes though, observed with a 16 inch telescope, the Dumbell Nebula appears a bright green colour. Planetary nebulae are relatively common with over 1500 known, but it is expected that many more, perhaps over 50,000, will exist in the galaxy but hidden by dust.  The name "planetary nebula" is, of course, inappropriate, as they have nothing to do with planets, but many do have a disk-like appearance.  They are large tenuous shell of gas which are expanding outwards at velocities of a few tens of kilometres per second.  They also contain some dust and have masses of typically one fifth to one tenth of a solar mass.  Of order 10 planetary nebula are thought to be formed each year so that, as each may contain about half a solar mass of material, the interstellar medium is being enriched by several solar masses per year.

The Ring Nebula

White Dwarfs

At the centre of a planetary nebula a central white or blue-white star is observed.  They are not very bright so that relatively large telescopes are required to see them visually.  (The author has once, under perfect conditions using a 16 inch telescope, observed the star at the centre of the Ring Nebula.)  This star is approaching the final stage of its life when it will become a "white dwarf".  Once nuclear reactions have ceased, what is left at the centre of the star, now devoid of its outer layers through a combination of the intense stellar winds and the ejection of a planetary nebula, and composed mainly carbon and oxygen will contract under gravity.  The fact that contraction finally ceases is due to the quantum-mechanical effect known as degeneracy pressure.  In 1926, R.H. Fowler realised that as electrons would obey Fermi-Dirac statistics, the Pauli exclusion principle would mean that no more than two electrons could occupy a given energy state.  As the allowed energy levels fill up, the electrons begin to provide a pressure - the electron degeneracy pressure - which finally halts the contraction. 

A further consequence of being supported by electron degeneracy pressure is that there is a limiting mass which cannot be exceeded.  This depends on the composition of the star; for a mix of carbon and oxygen, it turns out to be ~ 1.4 solar masses. This result was published in 1931 by Subramanyan Chandrasekhar when he was only 19!  In 1983, Chandrasekhar rightly received the Nobel Prize for this and other work.  In a later lecture we will what happens when the mass of the collapsing stellar remnant exceeds the Chandrasekhar Limit.

White dwarfs range in size from 0.008 up to 0.02 times the radius of the Sun.  The largest (and thus least massive) being comparable to the size of our Earth whose radius is 0.009 times that of the Sun.  The masses of observed white dwarfs lie in the range 0.17 up to 1.33 solar masses so it is thus obvious that they must have a very high density.  As a mass comparable to our Sun is packed into a volume one million times less, its density must be of order one million time greater ~ 1 million grams per cubic centimetre.  (A ton of white dwarf material could fit into a matchbox!)

Exciting the surrounding gas

 As white dwarf's can have very high surface temperatures, the produce copious amounts of ultra violet radiation.  It is this radiation that excites the gas that has been blown of the explosion that has given rise to the planetary nebula and stimulates them to emit the spectral lines that make them appear so beautiful.

The Discovery of White Dwarfs

The first white dwarf was discovered by Wilhelm Herschel in 1783; it was part of the triple star system, 40 Eridani.  What appeared surprising was that its colour was white (which is normally indicative of bright stars) but had a very low luminosity.  This is of course totally due to its small size so although each square metre is highly luminous there are far fewer square metres!

The second white dwarf to be discovered is called Sirius B, the companion to Sirius, the brightest star in the northern hemisphere.  Friedrich Bessel made very accurate measurements of the position of Sirius as its proper motion carried it across the sky. The motion was not linear and Bessel was able to deduce that Sirius had a companion.  Their combined centre of mass would have a straight path across the sky but both Sirius and its companion would orbit the centre of mass thus giveing Sirius its wiggly path.  Due to the close proximity with Sirius, Sirius B is exceedingly difficult to observe as it is usually obscured by light scattered from Sirius within the telescope optics.  A very clean refractor has the least light scatter, and it was when Alvin Clark was testing a new 18-inch refracting telescope in 1862 that Sirius B was first observed visually. 

The future of White Dwarfs

The surface temperatures observed for white dwarfs range from 4000K up to 150,000K so they can appear from orange to blue-white in colour.  Their radiation can only come from stored heat unless matter is accreting onto it from a companion star.  As their surface area is so small it takes a very long time for them to cool; the surface temperature reduces, the colour reddens and their luminosity decreases.  The less the surface temperature the less the rate of energy loss, so a white dwarf will take a similar time to cool from 20,000K down to 5,000K as it will from 5,000K to 4,000K.  In fact, the universe is not old enough for any white dwarfs to have cooled much below 4000K; the coolest observed so far, WD 0346+246, has a surface temperature of 3,900K.

Colour in external galaxies

Let us look at two images of distant galaxies as see if some of what we have learnt within our own galaxy holds true elsewhere:

        M81 in the Ursa Major Cluster

 I think that the most obvious thing about this image is the fact that the central part of the galaxy appears orange in colour whilst the spiral arms have a bluish tinge.  As has been mentioned before, hot blue stars do not live very long - but are very bright.  It thus appears that the central region of M81 is largely composed of old stars whilst the spiral arms contain numbers of blue stars which, as they burn up their hydrogen relatively quickly, must be young - indicating that the spiral arms are where star formation is currently in progress, specifically in the regions giving off H-α light that are seen in the spiral arms at the upper left and lower right.  As a single blue star can emit greater than 10,000 times the light of our Sun, it does not need many to give the spiral arms a bluish colour that we observe.

The central region of M51 - the Whirlpool Galaxy

This Hubble Space Telescope Image of the centre of the Whirlpool Galaxy shows a small nucleus and spiral arms which are delineated by giant dust clouds.  Within these clouds of gas and dust are regions of star formation where hydrogen is being excited the ultra violet radiation from young stars and is emitting the pink-red H-α spectral line.  There is quite a burst of star formation in progress! 

Starburst Galaxies seen in visible (left) and UV radiation (right)

Galaxies in which rapid star formation is in progress are called Starburst galaxies.  As there are large numbers of very hot stars emitting ultra violet radiation, the regions of star formation show up very well in images taken by U-V telescopes!

A little Metaphysics

Several aspects of the way that both the energy is produced in the Sun and also how the key element for life, Carbon, is created depend crucially on the fine tuning of the way in which our Universe works.  There are many other such examples.  How is it that our universe is just right for life to exist?  Obviously, if it wasn't, we would not be here discussing this problem but there is no fundamental reason why it should be so.   The laws of physics do not define the many constants of nature that have to be "just right" for us to be here.

There are two possible reasons.  The first is that our universe was "designed" by its creator specifically so that it could contain intelligent beings, a view taken by some scientist-theologians.  A second view is that there are many universes each with different properties, the term "multiverse" has been applied to this view.  We have no knowledge of what lies in the cosmos beyond the horizon of "our" visible universe.  Different regions could have different properties and these regions could be regarded a different universes within the overall cosmos.  Our part of the cosmos is, like baby bear's porridge, just right.

String Theory: another approach to a multiverse

Theoretical physicists do have a fundamental problem.  Einstein's General Theory of Relativity that relates to "gravity" is a classical theory, whereas the other forces are described by quantum mechanics.  A "theory of everything" has yet to found that can bring together all the fundamental forces.  One approach that is being actively pursued is that of "String Theory".  The early string theories envisioned a universe of ten dimensions, not four, making up a 10-dimensional space-time.  The additional six beyond our three of space and one of time are compacted down into tiny regions of space of order 10-35 m in size and are called strings.  These are the fundamental building blocks of matter.  Different "particles" and their properties, depend on the way these strings are vibrating - rather like the way a string of a violin can be excited into different modes of vibration to give harmonically related sounds.  As these strings move they warp the space-time surrounding them in precisely the way predicted by general relativity.  So string theory unifies the quantum theory of particles and general relativity.

In recent years five string theories have been developed each with differing properties.  In one there can be open strings (a strand with two ends) as well as closed strings where the ends meet to form a ring.  The remaining four only have closed rings.   More recently Ed Witten and Paul Townsend have produced an 11 dimensional "M-Theory" which bring together the five competing string theories into a coherent whole.   This 11th dimension (and it not impossible that there could be more) gives a further way of thinking about a multiverse. 

We can think of a simple analogy: take sliced load and separate each slice by, say, one centimeter.   On each of these slices add some ants.  The ants could survive, at least for a while, eating the bread of what is effectively a 2 dimensional universe.  To them the existence of other colonies of ants on adjacent slices would be unobservable.  But we can see that all of these exist within a cosmos that actually has a third dimension.  

In just the same way, rather than being individual regions of one large spatially linked cosmos, it could be that other "universes" exist in their own space-time - hidden from ours within a further dimension.

©Professor Ian Morison, Gresham College, 15 November 2007