Ladies and gentlemen
It seems to me that there are 2 major frontiers, major barriers to our understanding of physics at the present time.
One of these occurs on the sub microscopic scale and we can refer to this as the inner space of fundamental particle physics.
This region we can study in the laboratory using high energy particle accelerators,
although the techniques are becoming ever more complex and costly.
The other frontier occurs at the other end of the scale of length.
It occurs in outer space and concerns the large scale physics.
Such problems as the very origins of space and time themselves, the life history of galaxies, the evolution of the universe.
This region cannot be studied in the laboratory.
We have to extend physics beyond the walls of terrestrial laboratories
and we have simply to observe the inter play of phenomena on a cosmic scale.
The disadvantage of this is that we cannot of course arrange our experiments as in a laboratory.
We cannot adjust the conditions.
This is the major disadvantage.
On the other hand the advantage is that we have at our disposal a range of parameters
far beyond anything which can be achieved here on earth.
So our problem is to extend physics in this indirect fashion
and to extrapolate what we know in the laboratory to the limits of space and time.
Many phenomena occur which are quite different from anything we have previously understood.
The effects of curvature of space time, in general relativity, predicted by Einstein,
are just detectable with the best modern techniques in our own laboratories.
The effects of space curvature can become quite dominant when we examine nature on a large distance scale.
Space and time can, given the concentrations of mass one finds in outer space, close up.
We can create bubbles in space time which are regions in which phenomena are completely removed from our own universe.
There is an event horizon.
I refer of course to what we popularly know as black holes.
Recently there have been very exciting advances in this field.
There has been made a connection between quantum electrodynamics and general relativity,
which seem to me to be a close parallel to the advance we heard about from the lips of its inventor, Professor Dirac,
when he connected quantum theory with the more limited special relativity of Einstein.
We know what advances followed from that link.
And it seems to me that corresponding advances in the understanding of the large scale universe
may follow from the link between quantum physics and general relativity,
which is now being made by such scientists as Stephen Hawking.
These are features of large scale physics which I’m sure will be most fruitful
and we shall be hearing much about these in the years to come.
However in my talk today I wish to be more humble and to consider problems involved,
when matter reaches conditions under compression which make it far different from the matter we know in the laboratory.
Cosmic forces, the gravitation one can achieve inside massive stars is sufficient to compress material until atoms,
the simple atoms are literally crushed out of existence and we achieve a new state of matter
in which the density can reach values as large as one thousand million tons per cubic centimetre.
The possibility of condensed matter in this state was first considered as early as 1932.
Soon after the discovery of the neutron particle by Chadwick.
To my understanding the first discussion was made in Copenhagen,
when news of this discovery reached the Russian scientist who was there at the time, Landau,
and Landau first proposed condensed matter of this kind in a discussion with Niels Bohr and Rosenfeld.
However it was some years later, that the possibility was extended
and the astronomers Baade and Zwicky predicted that perhaps one would find matter of this sort in space
in the debris left behind from the explosion of a supernova.
Theorists attempted to construct models of what a star would be like, if atoms were crushed out of existence
and we had what was essentially a ball of material in which the density approximates that of the atomic nucleus.
These models were discussed in the 1930’s by such scientists as Oppenheimer, Volkoff,
but I think the subject really was of academic interest until quite recently,
because there was no evidence that such material really did exist.
The first evidence that stars of this kind could occur was obtained when we made the discovery of pulsars in Cambridge in 1967.
Now just to remind you of the basic features, which lead us to the conclusion that matter of this enormous density is a reality,
I should just like to run over the basic evidence which the pulsars give us.
May I have the first slide please?
The pulsar, the phenomenon, as you all know is that one receives in the radiation at radio wavelengths,
with the radio telescope, one can receive from certain objects in space a regular succession of pulses as you see displayed there.
Radiation of this kind was of course totally unpredicted and it seemed at first very strange
that there should be objects in the sky which produce radiation in a very regular succession of pulses –
typically one second apart and of duration a few hundreds of a second.
The remarkable feature of these sources, which was realised very quickly,
was the incredible accuracy with which these pulses are maintained.
Careful measurements show that in all cases, except perhaps 1 or 2, where the extent of the effect is not large enough to detect.
In almost all cases one can measure a slowing down in time of the pulse rate.
It takes generally a long time for anything noticeable to happen,
but if you were to wait in the case of this source I display on the slide,
if you were to wait approximately one hundred million years and make observations again,
the pulse rate would be roughly half what it is today.
Now, in most cases one detects these strange objects with radio telescopes but there is one example, a famous example,
where a pulsar can actually be seen, and I would just like to show you that, because after all seeing is believing.
May I have the next slide? This object that you see is one of the most famous supernovae known to astronomers.
What you see is the remains of a star which has exploded and that explosion was witnessed by Chinese astronomers.
It was witnessed and documented in the year 1054, when the star was visible in broad daylight.
What we see now is an expanding cloud and the object of interest is this star here.
Near the centre of the nebula is a pair of stars and it is the bottom right hand star which is the pulsar.
That star has been known for many years to astronomers, but only after the pulsar discovery was it realised
that this star here is flashing its light with great regularity at a rate of 30 cycles per second.
If one puts a stroboscope inside a telescope, one can display this effect and - may I have the next slide –
with a stroboscopic technique, this is an enlarged picture, these are the 2 stars at the centre of the nebular here.
The bottom right hand star is the pulsar and we see here one frame, another frame taken a few milliseconds later.
This star here has totally vanished.
Its radiation is completely extinguished.
So that star is, we know, flashing at a rate of approximately 30 flashes per second.
Now how does one account in broad terms for this phenomenon.
Well, in the early days, and I won’t bore you with early theories, there were many ideas.
But now the only theory which has stood the test of time,
is that this radiation can only be explained if we have a star which is really acting like a lighthouse beacon.
A star which is rotating rapidly on its axis and producing a well defined beam of radiation.
May I have the next slide please? The type of phenomenon, which we believe accounts best for the pulses,
is a situation perhaps like this: you have some star which produces a well defined beam of radiation.
That beam as the star rotates, circulates around the celestial sphere
and any observer who lies in the right belt of latitude with respect to that star,
will observe a flash each time the star rotates.
This is a rather simplified model: It is probably more realistic to suppose
that the star really is producing a beam along some axis which perhaps does not coincide with the rotation axis,
and that beam produces flashes for any observer in 2 regions of space.
Now the basic problem is to find some star, which can spin sufficiently fast to account for the observed flashes.
This is the fundamental problem.
And the difficulty is to find a star which will hold itself together
at the enormous rate of rotation which this phenomenon demands.
All stars are bound by gravitational forces and if you spin a star on its axis too fast,
then it simply flies to pieces like an exploding fly wheel.
And until the pulsar discovery, the most compact star known to astronomers was the white dwarf star:
That’s a star approximately as large as the earth.
And stars of such matter, stars of such a kind can rotate once every few seconds without disrupting.
But they cannot spin fast enough to account for the most rapid pulsars that we observe.
The only possible candidate is a star in which one finds matter in the neutron state, which I shall be discussing,
and such a star can spin at any speed up to several thousand revolutions per second.
The gravitation is sufficiently strong to hold it together, and that is the only known star, theoretical star,
which could produce the pulsar phenomenon.
Well there is much evidence, and I won’t go into this in detail,
there is much evidence to confirm this conclusion which was reached, it was indeed suggested in the pulse,
when the pulsar discovery was made, that such a star was responsible.
But there were many other possibilities, too.
The conclusion that the star must be a neutron star was confirmed within roughly 2 years of the discovery,
and this theory is now generally accepted.
I want you to understand something about this strange behaviour of matter,
when it reaches the densities one finds in a neutron star.
And to do this I would like to come back to some elementary physics,
because the properties of matter under extreme compression can really be predicted with some precision
from what we already know of the behaviour of fundamental particles.
May I have the next slide? I have sketched on this slide very schematically the behaviour of matter,
common matter under compression.
And we start with matter as we know it, perhaps a lump of iron or something of that kind.
And on a simple model we know that atoms are composed of a nucleus, of heavy particles at the centre,
and we have electrons moving in the region surrounding that nucleus, moving under the laws of quantum mechanics.
This phenomenon is well known to radio astronomers: It is the kind of difficulty we have in our experiments,
and that noise I have frequently heard on a radio telescope.
And it can come from agricultural machinery at a distance of 20 miles.
(laughter).
To return to common matter.
The distance at which one finds electrons from the nucleus
is determined by the most elementary property of fundamental particles,
that particles need to be associated with a quantum wavelength.
And in the very first suggestion by de Broglie,
of course we remember that the quantum wavelength depends upon the speed at which the particle is moving.
The wavelength of a particle is determined by Planck’s constant divided by the momentum of the particle.
Now in ordinary matter the electrons are at a distance roughly speaking of one angstrom from the nucleus,
and this defines the density of common material around us in the world.
The atoms in a solid are roughly as close together as the electron orbits will permit.
And it is the value of Planck´s constant which essentially determines the state of matter as we see it around us.
It is perhaps hard to believe that the common matter is virtually empty space.
There is an enormous amount of empty space within an atom, because the fundamental particles are a great distance apart.
Now what happens when we put such matter under some compression and force it together?
These experiments one can only do on a very small scale in a terrestrial laboratory.
But if you allow cosmical forces to apply an ever increasing pressure to ordinary material,
one can bring about some remarkable changes.
As you squeeze the atoms together, then of course the electrons have less space in which to move.
And from quantum mechanics we see that we have to shorten the wavelength of those particles to fit them into the available space.
And as we shorten the wavelength we must increase the velocity of the particles.
That is the elementary fact of quantum mechanics.
So as we squeeze these atoms together the electrons will move faster.
If we squeeze the matter until it has a density, which we can never achieve in the laboratory,
but say a density of 1 ton per cubic centimetre,
at that density the electrons require such a small wavelength to fit into the available space,
that they’re moving so fast and that they are no longer trapped in orbit about a particular nuclei.
The electrons move freely amongst the nuclei.
All the electrons in any atom one can consider, they are dissociated from one particular nucleus.
This state of matter we call degenerate matter.
A few electrons, degenerate electrons, we understand in the physics of ordinary metals.
But under this compression all the electrons will become degenerate,
and when matter has reached a density of one million tons per cubic centimetre,
then we have the state in which all the electrons move freely through the material.
Now, the electrons need to move very fast to do this.
The electrons have speeds which are approaching the velocity of light itself.
And if we compress the material still further, then a remarkable change takes place.
The matter here is largely composed of positive and negative charged particles, with of course some neutrons present also.
The fundamental particle, the neutron, is basically composed of, in a simple model,
a proton and an electron with opposite charges.
When one creates free neutrons in a reactor such as the reactor we heard about at Grenoble earlier this week,
when one creates neutrons in a reactor,
the normal condition is that that neutron will rapidly change within a few minutes into 2 charged particles.
The proton and the electron, plus other particles to maintain the balance.
This lifetime as I say is short, a few minutes only.
But in matter which is sufficiently compressed,
it is energetically more favourable for protons and electrons to combine to form neutrons.
In other words, the reaction proceeds from left to right.
Nature always chooses, if it can, a state of minimum energy and it is not difficult to calculate
that the energy of compressed material is less when you combine the protons and the electrons into neutron particles.
This is because the high energy that you require to fit electrons into a small volume,
causes the energy on this side to be greater than the energy on this side,
unless you have the conversion of protons and electrons to neutrons.
So progressive compression of this material will eventually lead you to an equilibrium state
in which matter contains mainly stable neutrons.
Always of course one has a fraction of charged particles present, but that fraction will be small in general.
Now, the neutron material has a density which is approximately that of the atomic nucleus.
And so we reach finally a density of one hundred or perhaps even a thousand million tons per cubic centimetre.
And that is the density of this material.
We find it hard to visualise this number.
Physicists are quite happy to juggle large numbers and of course they don’t usually try to imagine what the numbers mean.
It’s not a sensible physical thing to do, but in explanations one likes to know roughly how big things are.
And I can only say that, if one had a spoonful of neutron star material,
a spoonful of neutron material of this kind,
would contain enough matter to build all the ships that are currently sailing the ocean.
Now this is elementary physics essentially, and is the result of an idealised experiment,
where we might just simply compress material on a laboratory bench.
Now we witness phenomena of this kind, when we look into the sky.
This basic physics has great relevance to the evolution and the life cycle of common stars.
May I have the next slide please? In a slightly over-simplified way one can sketch quickly
what is likely to happen to most of the stars that we see in the sky.
If we take a common star, like the sun, which is sketched at the top here,
any reasonably small star is of course a nuclear fusion reactor in which we are fusing the simple nuclei
to more complex ones with the release of energy.
The star has the size we see, because it is a balance between the pressure generated inside by the fusion reaction,
which tends to expand the star, and the force of gravity, which tends to compress the star.
So a star is a battle ground between the outward pressure and the inward force of gravity.
And that determines the size at which we see it.
As the reaction proceeds and the fuel is depleted eventually we are left with the ashes of the nuclear fusion process.
And the force of gravity will then squash the star irrevocably and we end up, in the case of a light star,
with a small object in which we have degenerate matter with a density of about one ton per cubic centimetre
and this is the white dwarf star.
And we see many such stars in the heavens.
But if the star is heavier to begin with than the sun, we cannot have such a peaceful passage to old age and retirement.
In the case of a heavy star, what happens is that within the interior, where of course the action takes place,
as the fuel is depleted and gravity compresses it, we can have that conversion of electrons and protons into neutrons.
When this takes place we remove suddenly the cause of the pressure within the star, which maintains it at its equilibrium size.
So it is rather like having a balloon and pricking it with a pin in the case of a heavy star.
As the conversion to neutrons takes place, there is a dramatic decrease of internal pressure
and the inside of the star can simply collapse rather suddenly.
It collapses from the size of a white dwarf to something much smaller in a time of the order of 1 second or less.
So the final evolution of a star can be quite dramatic.
The collapsing fusion products will only reach equilibrium,
when the material has become almost pure neutrons at a density of 1 thousand million tons per cubic centimetre.
In that condition it occupies only a small volume, very close to the centre of the star,
and since the material has really fallen from the edge of a star to the centre,
it is moving very fast under the scale of the collapsing core in a star of the size, say 10 times as massive as the sun.
The collapsing material is falling inwards at nearly the velocity of light.
And when it collides, as it were at the centre here, the situation can be quite complex
but there is an enormous release of energy, and of course that generates a shock wave
which propagates outwards from the centre and will blow off into space the remaining material,
which has not yet had sufficient time to collapse.
Now this is believed, in very brief outline, to be the theory behind exploding stars: the supernova process.
So we expect neutron material to be left behind at the centre of a stellar explosion.
That’s one possible end to a fairly massive star.
Stars that are heavier still can have even more dramatic evolutionary cycles
and finally can collapse into these bubbles of space time that I mentioned, the black holes of general relativity.
But in that case the star would collapse until it disappeared from view entirely
and it is only some quantum effect of the type, which is now being considered, which I mentioned,
which can save matter from collapsing to zero volume.
This is a region of physics which is not yet well understood.
This however is where we are concerned at present.
We expect to find a neutron star.
Neutron material left at the centre of a stellar explosion
and you can regard this ball of neutrons as the ashes of one type of stellar evolution.
The material will be completely inert and it will simply retain the physical properties, which it had at the moment of formation.
But there is nothing left there to burn any longer.
There is no possibility of further fusion reactions.
Well, we can imagine what a cold neutron star might be like.
May I have the lights for a moment.
If we take a neutron star containing roughly the mass of a body as large as the sun,
then when it collapses to the neutron star configuration it will have a radius of some 10 kilometres only.
It will be an extremely small object and the most dramatic feature that one first considers
is of course the intense gravitation which will surround such a region of space.
If that represents the surface of a neutron star, then we have the gravitational acceleration, which I’ll call G neutron.
The gravitational acceleration is approximately 10 to the 11 times stronger than the gravitational acceleration at the earth.
This would be very noticeable if one got close enough to the neutron star to make experiments.
If you lift an object through a height of 1 centimetre and allow it to fall,
then it will reach the surface of the neutron star here.
The velocity after falling1 centimetre is going to be something like 400.000 kilometres per hour.
The weight of a tiny object like a feather would be hundreds of tons.
The effects of space curvature, which are normally only just detectable in the laboratory, become quite prominent.
It’s not of course very safe to walk about on a neutron star, even if it’s totally cold,
because the gravitation will cause your weight to be several millions of tons.
And so of course you’ll spread very thinly over the surface.
But we can perhaps attempt to escape such effects by being in orbit in a space craft around a neutron star.
We customarily consider astronauts as weightless, when they are following their geodesic in 4-dimensional space,
and are in orbit about some mass.
Well, this is a possibility.
The space craft would have to orbit a neutron star roughly one thousand times a second in order to maintain a stable orbit.
But we can also consider the effects of space curvature on the astronaut himself.
The fact we tend to forget is that, suppose we have our astronaut here,
supposing he’s just got outside his spacecraft to look around, as of course has been done already in orbit around the earth,
what we have to remember is that it is only the centre of mass of the spaceman which follows this weightless geodesic.
Now the effects of space curvature are quite noticeable,
because in an extended object there is a different gravitational acceleration at your head and at your feet.
And the effect of this is to put a force between your head and your toes.
This is just one phenomenon of space curvature.
And in the particular example of a neutron star and a typical specimen of humanity here,
then this force is something like three hundred thousand tons.
So space curvature becomes not a marginal effect but extremely unpleasant.
Well, I’m not joking entirely here, because in the early days of neutron star physics
it was considered that there might be remnant particles of the original system in orbit about the neutron star.
And this might have led to some of our pulsing phenomenon.
It is not of course possible to have large regions of ordinary material anywhere near a neutron star.
Space curvature simply disrupts the material by immensely strong tidal forces.
Well, on a slightly more scientific level - may I have the next slide please now?
The state of matter under extreme compression is of course an extrapolation of the field of solid state physics.
And solid state physicists have been very busy in attempting to work out all the possibilities of the structure of neutron stars.
There’s still much to be learned here but the general picture seems fairly clear.
We have a ball of neutrons which is roughly 10 kilometres in radius.
But of course near the surface the gravitational compression is not yet strong enough
to compress all the material into the neutron configuration
and we would expect near the surface a shell of the most stable nucleus known, which is FE56.
We expect therefore a skin of iron around the neutron star.
As we descend through that skin we come then to a shell of initially degenerate material,
where the density is still not high enough for many neutrons to be present.
We have a very rigid lattice of material here with probably a melting point of greater than 10 to the 10 degrees Kelvin.
A very rigid material of degenerate electrons flowing between a rigid lattice of positively charged nuclei.
As we descend lower down, more and more neutrons are formed.
The nuclei become neutron rich, the nuclei eventually become unstable and as one proceeds far enough down into the material,
one then reaches virtually pure neutrons.
The properties of this neutron material are interesting, because neutrons are particles we call fermions,
but it is believed that they will behave at any temperature below roughly 10 to the 9 degrees Kelvin, very much,
like helium at room temperature, I’m sorry, helium near the absolute zero of temperature.
The fermions will pair up to form bosons in much the same way as in super conductors, and we shall get a quantum fluid,
a neutron fluid in which the neutrons have essentially paired,
and we get then a liquid which has the quantum properties of liquid helium.
But it does have also the enormously high density.
Now that is generally understood.
As one goes further into the centre and the pressure rises, the problems multiply.
We do not really seem to understand yet the potential,
the neutron potential sufficiently well to predict in detail what is going to happen further in.
There is the possibility that the neutrons themselves form a rigid lattice.
There is the possibility also that rather more exotic states of matter are found.
The pion field can become highly coherent.
One can have what is called a pion condensate in this region here.
But these possibilities at the moment one can barely distinguish,
because one doesn’t understand fully the neutron interaction.
Nearer the centre one gets graver problems.
Hyperons may be long lived particles near the centre of a neutron star,
these are of course the exotic particles of high energy physics,
which normally last a negligible time in a terrestrial laboratory.
It is conceivable that they would be long lived particles at the centre of a neutron star, a sufficiently massive neutron star.
The quantum state of these particles is problematic,
because they are overlapping to such an extent
that the meson fields surrounding the fundamental particles are overlapping and interfering
and the general quantum state of such a situation of course is quite unknown.
Well, for the moment then the important parts of a neutron star are its rigid shell, which is fairly light,
because the material is not yet too dense, and then the liquid region inside, and this model is generally believed to be correct.
May I have the next picture please?
Now, of course, a neutron star is formed for a real astronomical body
and it is not made ideally under controlled conditions in the lab.
So it is endowed already with stellar properties, which it had originally.
And if we collapse a star, say with properties something like the sun,
where we have a magnetic field of roughly say 100 gauss, 10 to the minus 2 tesla, radius of 10 to the 6 kilometres
and a rotation rate of roughly 1 revolution per month, if we collapse such a star to the neutron configuration,
then it is probable that there will be no leakage of flux.
The magnetic flux in astrophysics is a quantity which is usually conserved
so that we shall arrive finally with an extremely powerful magnetic field at the surface of the star.
Perhaps 10 to the 8 tesla.
And if the star maintains also its angular momentum, if that is conserved in the collapse
and not given to escaping debris from the explosion, then the star can be spinning at up to 10 to the 4 revolutions per second.
These are the properties which must maintain a neutron star and make it detectable.
Because, as I said earlier, a neutron star is not burning, it is only endowed with the energy of collapse,
which his largely turned into rotational kinetic energy and its magnetic flux.
So we expect this lump of matter to cool down steadily in space.
Well, there is some evidence that this general model is more or less correct from observation.
May I have the next slide please?
Occasionally one observes in certain pulsars that the rate of the pulses shows a characteristic jump.
This is the famous pulsar in the crab nebula, the only pulsar to emit visible light.
And here you see the steady slowing down represented as an increase of period with time, calendar time.
Well, schematically what has been observed, is this type of phenomenon
where the pulse rate suddenly shows a small increase over a few days and then relaxes to its previous slightly slower value.
Now how does one understand this kind of phenomenon? I should emphasise that this is grossly exaggerated on the slide.
When the pulse rate changes by perhaps 1 part in 10 to the 8, this is a notable event for pulsar observers.
The pulses are normally so regular that the slightest change becomes a noticeable phenomenon.
How does one explain a sudden change in the pulse rate like this?
Well, clearly you can’t suddenly speed up a star which is spinning on its own in space,
there must be some rearrangement of the material within it to cause this effect.
May I have the next slide?
The type of model, and I’m not saying this is exactly correct,
but the type of model that’s being put forward to account for these phenomena is sketched schematically here.
When the neutron star is spinning rapidly, you expect it to be an oblate spheroid, because of the outward forces at the equator.
So you have a rigid shell of material surrounding a liquid core, and the whole thing will be spinning as a solid body,
although the interaction between the quantum fluid and the outer crust is of some interest.
The linkage here is via, we believe quantised magnetic field lines,
which thread the star and transfer momentum from one part of the star to another.
The momentum transfer probably takes place by the scattering of electrons, the residual few,
small percentage of electrons from this quantised vortex field lines.
As the star spins more slowly, when it loses energy, it wants to revert to a more spherical shape and since the crust is rigid,
it can only do this, when the crust suddenly cracks like the shell of an egg.
So progressively from time to time, as the stored elastic energy overcomes the strength of the material,
then the crust will crack and suddenly become more spherical.
And when it does this, the outer crust will spin a little faster to conserve its angular momentum,
but finally there will be a coupling of momentum between the outside and the inside,
and the star will spin again at approximately its original speed.
Well, effects of this kind are detectable and give us some confidence that the solid state physics,
which has defined our model of a neutron star is mainly correct.
But this is a complex subject and I cannot spend too long on it.
Perhaps the most serious problems are, that we don’t really understand the plasma physics of the space surrounding a pulsar.
It would be nice to know, after all, what it is that generates the radiation that makes these neutron stars detectable.
And this is a major problem which we as yet, about which we understand very little.
Could I have the next slide?
Speaking as a physicists, what we need to do of course is to solve Maxwell’s equations around a rotating magnetised sphere.
And that rotating magnetised sphere might initially have commenced its life in a total vacuum.
It scarcely needs to be stressed that a normal atmosphere surrounding a neutron star one would expect to be non existent.
The scale height of the atmosphere in the intense gravitational field that I have mentioned,
would be roughly 1 centimetre for some reasonable temperature, so that one really expects no atmosphere.
One would expect a neutron star to be surrounded virtually by a vacuum.
But a vacuum does not generate electromagnetic radiation very easily, and we must have some type of plasma surrounding this star.
Well, the basic ideas I can only sketch, because as yet there is no exact solution to this problem.
When one spins a magnetised sphere in vacuo, that of course on a laboratory scale is a purely classical experiment.
The magnetised sphere, if it is spun in the simplest symmetrical fashion
with the magnetic axis aligned with the rotation axis, will generate polarisation charges within itself,
and charge will redistribute and the sphere will be surrounded by what we call a quadruple electrostatic field.
That is well understood.
But when we try to extend the simple solution to a neutron star, the numbers get slightly out of control.
The electric field between the pole and the equator of a neutron star is obtained
by integrating a field strength of perhaps 10 to the 14 volts per metre.
One can then have something like 10 to the 11 megavolts electric field between the pole and the equator of a neutron star.
And this means that the surface electric effects at the star will produce forces on any charged particles one has,
which can exceed even the immense gravitational fields which I’ve discussed.
So the possibility is that particles are literally wrenched from the surface of a neutron star, and flung into space by electrostatic forces.
When this happens one runs into the usual astrophysical situation,
which is that charged particles in space tend to move with the magnetic field.
The situation of the frozen in magnetic field which one so frequently finds.
So that charged particles which are in space surrounding the neutron star
are essentially tied to the magnetic field lines and will spin with it.
Now if one attempts to solve this problem, one can write down the equations of electrodynamics
and leave out of the equations any effects of the inertia, or the mass of the system.
This is a reasonable approximation close to the star, and one results with the sort of situation I have here,
one generates a plasma surrounding the star in which the charges are virtually separated into 2 regions
depending on the sense of rotation.
One can have a region of positive charge near the equator.
One can have a region of negative charge around the poles.
And this generates a plasma with which we’re not familiar.
When we create plasma in the laboratory, the charge balance is always perfect or nearly perfect.
The idea of a plasma in which the charges are completely separated is rather unusual to us.
Well, we have this atmosphere in which the charges as I mentioned are,
as it were tied down to the magnetic field like beads on a wire, and as the star rotates the atmosphere must rotate with it.
But one soon reaches a grave problem, because in the case for example of the neutron star in the crab nebular,
at something over one thousand kilometres from the star, one reaches a region
where the material tied to the magnetic field is trying to sweep through space at the speed approaching velocity of light.
Now this runs into relativistic physics and the situation is not understood,
but probably the kind of effect that happens is that at this critical radius,
which we call the velocity of light cylinder, material can no longer be tied to the star and must escape.
So one probably has an efflux of particles as a stellar wind probably at a speed close to the velocity of light,
beyond that distance, and within that distance one has material which co-rotates, spins with the star and forms a closed system.
Well, somehow within this type of model we have to explain the generation of the radiation, which makes these objects detectable.
Just one feature while we have the slide present.
Some of these magnetic field lines intersect the velocity of light cylinder
and they are the field lines which come from the magnetic poles.
From here particles can always escape from the star because they are threaded on lines which never return to the star.
So near the poles one can have escaping particles along these so called open field lines,
which intersect the velocity of light cylinder.
Now we have a wealth of information available.
In fact we have too much information available.
There are too many facts about pulsars to be explained and I would just like to show you some of the features
which observers can feed in to this situation in an attempt to understand the physics of this complicated relativistic plasma.
May I have the next slide?
This is an expanded version in time of a succession of pulses from the first pulsar to be discovered.
The time scale here is some 10’s of milliseconds from one side to the other
and you see successive flashes of radiation are displayed one beneath the other,
and you see the profile of the flash of radiation from this particular neutron star.
It is like a lighthouse in which somebody is tampering with the mechanism.
Each time it goes around one gets a flash of slightly different character.
And the situation can change dramatically from one second to another second.
These peaks here in the emission are reminiscent of an alpine range and this kind of irregularity is typical of all pulsars.
Could I have the next slide please?
One can measure also such features as the polarisation of the radiation and an important feature,
which shows up clearly in this example of a pulse.
Here you see a very rapid pulsar in the southern skies.
The total pulse lasts a few milliseconds only.
And here is shown the direction of the electric vector in the radiated field,
and from the leading edge of the pulse to the trailing edge it shows a very characteristic rotation.
The radiation in this case at radio frequencies is approximately 100% linearly polarised.
And that of course gives us some strong clues as to the kind of radiation process,
which must be taking place in the plasma close to the star.
The properties of pulsar radiation change so quickly,
that attempts have been made to display in a more elaborate way the character of the pulses.
May I have the next slide please?
Here you see a plot in colour of a succession of pulses, and one is displaying different characteristics.
This slide was sent to me by the operators of the large radio telescope at Arecibo in the United States, Puerto Rico.
And here is a sample of pulses, one under the other, and the first slide shows you how the intensity varies.
The intensity is adjusted on a colour scale there with white being most intense and violet least intense,
so that this is essentially the pulse profile measured across here.
You then get various polarisation parameters plotted out successively
and you can see that it really is a very complicated situation.
Apart from the changing intensity and polarisation, there are features in the radiation which appear to drift.
It shows up quite nicely on this band of radiation here.
A polarisation feature, which in this case lasts a few milliseconds,
drifts across the pulse as if it were somebody in the lighthouse moving something across the lens which is forming the beam.
This phenomenon is well known, it occurs in many examples and is called the phenomenon of drifting sub pulse features.
Well, we do not understand these at all.
All we can do is make some guesses as to the correct explanation.
And to finish I will just mention very briefly the kind of model on which astrophysicists are currently working.
May I have the next slide please?
The type of model which appears to fit a fair quantity of observational data is that we have a neutron star
with a rotation axis which is vertical, and a magnetic axis, which is oblique.
As one rotates this system, then the overall character of the plasma surrounding the star
will be much the same as in my simplified sketch earlier.
But of course one has now a fluctuating magnetic field, fluctuating at the rotation rate of the pulsar
and this adds further complications.
But the kind of model, which seems to fit the observation,
is that we have charged particles escaping along the field lines which can reach to infinity.
So those particles can escape from the star altogether.
And if some mechanism can be found to create particles in bunches,
then as they accelerate outwards along this curving magnetic field near the pole, magnetic pole of the star,
they will launch radiation which is akin to the synchrotron radiation one is very familiar with in high energy particle beams.
This will generate radiation which points, beams of radiation which point,
along the general direction of the magnetic axis and this can lead to the kind of pulse shapes, which we certainly observe.
But pictures of this kind are drawn with much imagination and what we have to do is work out in some detail
why the electric charges should be bunched, and just how many one needs, of course, to make the radiation fields.
These sort of calculations are fairly straightforward.
And whether the radiation has the right polarisation.
It turns out that this synchrotron type radiation does have the sense of polarisation
to account for the drifting angle of polarisation, which I mentioned earlier.
But some arrangement, where electrons move extremely coherently, as in a radio transmitter,
some arrangement of that kind is essential to explain our radiation.
As I said earlier, pulsars are not burning any fuel, they are as it were a freely running electrical dynamo
and the radiation they emit must come from purely electrodynamic processes.
May I have the last slide please?
Theories as always tend to become exotic and the kind of exotic idea which is being mentioned now is
that one perhaps has a pair creation process, electron, positron pairs - this process occurring near the magnetic pole of a star.
The sort of situation would be as follows: the star is rotating about a vertical axis
and charged particles in the magnetosphere are escaping from the polar cap region where such escape is possible.
The escaping particles can perhaps leave at a rate which is not easily maintained
by a flux of further particles from beneath the star.
That is a statement which I could amplify, but unfortunately it would take us too far from the general scope of this lecture.
But one might end with a near vacuum with zero charge and escaping charges higher up.
In this case one will build up across this gap the voltage which occurs between the pole
and the equator of the star which as I mentioned can be something like 10 to the 10, 10 to the 11 megavolts.
A very powerful field exists here
Well, a stray particle in that field will be accelerated rapidly to relativistic speed, it will emit gamma radiation
and in the powerful magnetic field that exists here, that gamma radiation can create positron electron pairs.