The Four 'F's

The title, The Four F,s, has nothing to do with rude words derived from the Anglo- Saxon but represents the Four Forces, in descending order of strength, namely :-

Strong Nuclear Force

Electromagnetic Force

Weak Nuclear Force

Gravity.

I won’t go into the mathematics behind these forces since you’ve all come along for an evening’s pleasure. What I will describe is how they work in the universe.

To begin with, let us consider how these forces were involved in the formation of the EARTH.

About 5000 million years ago the Earth was a mass of gases in orbit round the Sun, rather like a Saturn’s ring, at the distance from the Sun that the Earth is now. Much of the material was hydrogen, oxygen, nitrogen, carbon, and helium, which are either gases or form gaseous compounds. Gravity played a part in gathering this material but would have been insufficient to concentrate these substances on an Earth sized scale and it required electromagnetic force to create compounds in that  oxygen would combine with silicon and  iron to condense and form solid particles and crystals at normal temperatures.

The pressure of the atmosphere upon the Earth’s surface is about 1000g per square cm. The seas, however, are much denser, and the deepest part creates a pressure of around 1000 atmospheres ( a million grams per square centimetre). As one goes into Earth pressure increases steeply owing to the greater density of the rocks. At a depth of 2200 kms the pressure is that of a million atmospheres, at 4000 kms 2 million, and at 13,000 kms, the core, it is 3.7 million., enough to create an inner solid / liquid core.

During Earth’s condensation the pieces of rock and metal coming together carried with them kinetic energy which on impact produced heat. This heat was concentrated towards the centre. As more and more material fell the Earth grew in size with continual cratering. The kinetic energy fuelled the heat while gravity pulled the heavy molten nickel and iron towards the centre and the lighter silicate rocks formed the crust and mantle.

The temperature of the core today is about 4000 - 5000  degrees C., only 1000 degrees cooler than the Sun’s surface, and radioactive decay within has been sufficient to replace heat lost through the crust since Earth’s formation 4.6 thousand million years ago.

If it was possible to burrow towards the centre of the Earth the gravitational pull on the burrower would decrease, since material would be above him as well as below, although, of course, the pressure would increase towards the centre. Only if all the material could be compacted into a smaller volume would the observer experience a greater pull as he approached the centre. This concept of having to compress material to increase the gravitational pull at the surface is essential in order to understand how a collapsed star forms.

While the pressure at Earth’s centre is about 3,7 million atmospheres, that of the planet Jupiter is calculated at 10 million atmospheres. Yet the density is lower as there is eleven times the distance of surface to centre compared to that of Earth. By a coincidence the core temperature is about 55,000 degrees C., eleven times that of Earth.

Radar, infra red and other techniques have suggested that Jupiter is not so much a scaled up version of Earth but a scaled down version of the Sun, but which is just too small and cool in its centre to ignite. The temperature of the visible surface cloud is some minus 100 degrees C. but progressing towards the centre it rises rapidly, and at 3200 kms (4% of the way down), it is 10,000 degrees.

Jupiter is a net emitter of radiation, some three times as much as is received by the Sun. This energy could be due to either a continuing low contraction under gravity, less than a centimetre a year, the energy being released as heat, or additionally / alternatively, the energy may be supplied by the nuclear reaction that keeps the Sun burning, though on a very feeble scale. Gravity is obviously an important force in Jupiter’s history but the electromagnetic one is equally important since it ‘holds the planet up’, ie keeps the atoms as atoms and apart. The weak nuclear force may be involved in the possible (and debatable) fusion reactions which power the Sun.

Now let us consider what goes on in bodies considerably larger than Jupiter. Whereas Jupiter, compared with Earth, is about 10 times the diameter, (1000 times the volume, 300 times the mass and with 2.5 times the surface gravity pull), the Sun is about 10 times the diameter of Jupiter. It also has 1000 times its volume, 1050 times the mass and 2.5 times the surface gravity pull.

The respective escape velocities are, if Earth is given as 1. Earth 11.2  kms / second.   Jupiter 60.5 kms / second, ie 5.5 times.  Sun 617 kms / second, ie 56 times.

The SUN. About 99% of the solar system by mass is in the Sun, although c.98% of the angular momentum is in the planets.

The Sun condensed out of the initial gas cloud some 5000 million years ago, under the influence of gravity. Its energy may have originally been provided by contraction, but on its own this would not create the amount of its current output. Kinetic energy by contraction from 300 million kms across to its present size [not given] would, according to fairly accurate calculations done about 1870, last no more than 25 million years. Obviously another source must be present, and the clues to this came with the great discoveries in nuclear physics and atomic structure made around the turn of the 19th century.

Normal and familiar chemical reactions, such as occur when coal is burnt, involve electromagnetic force, ie the force holding atoms together to form molecules, though in this type of action the energy involved is very limited. If the Sun consisted of coal and oxygen it would burn out in a matter of a few thousand years.

The turning point in physics came at the beginning of the 20th century, when forces were discovered within the atom with energies thousands of times greater than in ordinary chemical reactions which relate to the assembly and break-up of molecules, groups of atoms, held together by electromagnetic force.

Under conditions of great heat and pressure (eg. 100 TM atmospheres as at the Sun’s centre) the electron layers or shells of the atoms get crushed and destroyed and a ‘fluid’ mass of nuclei interspersed with negative electrons takes the place of atoms as such. The electromagnetic repulsions between the particles in this condition are much greater than the forces between individual atoms. Indeed this must be since this ‘degenerate matter’ is found under conditions of pressure far greater than individual atoms can stand.

[ there follows a couple of complex diagrams which must have either been drawn on a board or projected on a screen.] : -

Normal matter at fairly ‘low’ pressures, as in the Earth.

Electronic fluid or Degenerate  Matter as in the centre of the Sun.

N u.= nucleus.  e.= electrons spinning round orbits

Electromagnetic force keeping atomic nuclei a fixed distance                                                                       apart by repulsion of like charged negative electrons.

Under these conditions the nuclear reactions that power the Sun occur steadily, and will continue this way for another 5 to 8 TM years. Details of the mechanics of these reactions involve the weak nuclear force.

Eventually, as much of the hydrogen in the Sun is fused into helium by these reactions, the core will heat up and compact down even more, while the extra heat will make the outer layers expand, out as far as Mercury or Venus, and we will then have a red giant. Although the outside will have a temperature of about 2500 degrees C. life on Earth will be impossible, since the Sun will appear to fill around one quarter of the sky.

The centre of the Sun, heated to 100 million degrees C. will permit further fusion reactions in which helium is converted into heavier nuclei up to the size of iron (26 protons, 30 neutrons). Once the bulk of the nuclei have fused to the size of that of iron there is no longer scope for further energy to be derived from nuclear fusion, and its life is now less than 1 TM years. As the nuclear reactions dwindle and fail there is nothing to resist the relentless pull of gravity. Gravity has been pulling patiently for many thousands of millions of years, and finally resistance has collapsed and the bloated Sun can do nothing but shrink. It is this that puts us firmly on the high road to a collapsar, with two stopping points en route.

To introduce the first stopping point we can refer to the 18th century astronomer William Bessel who, while trying to find Sirius’s proper motion, using the parallax method, found that Sirius had a wobble in its expected straight line path. He measured and then calculated its movement as an ellipse which takes 50 years to complete, suggesting a companion similar in mass to the Sun. As, at the time, nothing could be seen in the vicinity of Sirius, it was assumed that the companion was dark and cooled.

The mystery of the dark companion was ended in  the1860’s when Alvin Graham Clark,  a telescope builder, was making a lens for the University of Missippi. He tested it by trying it out on various astronomical bodies, including Sirius, next to which he discovered a tiny point of light, previously unrecorded. Only 1 / 10,000th of Sirius’s brightness, it was certainly not dark, and is now known as Sirius B. After careful study it has been found that the surface temperature of Sirius B is 8000 degrees C., (compared with 10,000 for Sirius A and 6000 for the Sun). However, the fact that for all its high temperature it is so faint implies that it is of small diameter. Calculations indicate a diameter similar to Uranus, with a mass equal to that of the Sun.

The density of Sirius B is about 35,000 grams per cubic centimetre ; ie 3000 x that of Earth’s core and 350 x that of the Sun’s core. This extraordinary star is known as a white dwarf . Extremely dense, with a fairly hot surface, but due to its small size, very faint.

As in the Sun’s centre, the white dwarf is made up of ‘electronic fluid’ of nuclei (protons + neutrons) with electrons in the spaces, but the particles are much closer together than in the Sun’s centre. On the surface, or in the white dwarf’s ‘atmosphere’, there may be some structured intact atoms with electron shells, uncompressed by overburden like the interior. In this ‘atmosphere’, perhaps only 200 metres thick, fusion reactions using surviving hydrogen can still simmer away.

At the core white dwarf material is extremely dense, 100 million grams per cc. As the electron fluid will compress the resistance to compression is governed by the closeness of the mutually repelling electrons, which are kept ‘apart’ by the electronic force. It is this that even keeps the centre of the white dwarf ‘up’, as it were. Despite the colossal density, the nuclei ‘floating’ in the electronic fluid still represent isolated particles, with a good deal of ‘space’ between. In this classic white dwarf, Sirius B, the nuclei take up only 1 / 4000 millionth of the volume, the rest being a sort of highly compressed electron ‘cloud’, each electron repelling its nearest neighbour. In these conditions, therefore, the nuclei have the properties of gas.

When a white dwarf is formed from a red giant it is very hot indeed, since the kinetic energy of collapse is turned into heat. Surface temperature can begin at 100,000 degrees C., but due to very little continuing nuclear reactions it cools down fairly fast by stellar standards. Whereas a normal star like the Sun is kept from collapsing by its nuclear heat supply, a white dwarf is kept from collapsing by the electron fluid, and will resist further collapse whether hot or cold. White dwarfs will lose heat steadily but still remain as dense bodies. When cold they will be black dwarfs, but still held up by the infinitely enduring electronic fluid resistance to further compression.

But how massive can a white dwarf  be ? In other words, how much compression can the electronic fluid take at the core before it succumbs ?  There is a finality, called the Chandraskhar limit, beyond which the electronic fluid cannot support the pressure at the centre. As calculated by Chandraskhar the mass beyond which a white dwarf cannot exist as such is 1.4 times solar masses, and this is borne out by observation. However, many normal stars have masses of over 1.4 solar masses, such as O, B, A, and many stars of spectral class F. These stars have short lives and early in the history of the universe many of these must have collapsed, but into what?

SUPERNOVA / NEUTRON STAR.

Let us now consider the fate of a large red giant which explodes, then collapses, giving a body of more than 1.4 solar masses at the end. The larger a star the greater its internal temperature at all stages, as compared to the similar but longer stages in a small star, eg. the Sun.

Nuclear reactions in the core of any star produce two massless particles. 1 The photon, a unit of light and light like radiation. 2  The neutrino, an energy carrying massless, chargeless particle. Although  photons travel at the speed of light in a vacuum, inside a star they are continually hitting, being absorbed, and later re emitted by the particles of compressed matter within the star centre, where photons are formed. Thus it can take some millions of years for the photons to progress from the centre to the surface.

Neutrinos, however, although they appear to be massless particles with no charge, they can carry energy. They can pass through entire stars virtually unrestricted. Unlike photons, that can take millions of years, neutrinos can carry energy from the centre to the surface, and beyond into space, in 2 to 3 seconds. In the Sun the energy given out by neutrinos is small compared with that from protons reaching the surface, and the Sun’s core temperature is some 15 million degrees C.

In certain other stars core temperatures of about 6000 M degrees occur and there comes a point when the nuclear reactions produce neutrinos in huge quantities. Since these carry energy from core to surface and beyond the energy needed to keep the star expanded against gravity leaks out fast. The core then cools within minutes and the star suddenly collapses. The collapse means that gravitation energy converts to heat energy, and this subsequent heating ignites whatever fusible fuel is left, especially in the outer layers. All this ‘fuel’ is burned within months, giving a supernova the brightness of a galaxy.

During a supernova explosion 9 /10ths of the star material is blown away, leaving a small collapsed residue. So, are we left with a white dwarf, or is a further even more collapsed stage possible?. Individual stars have been found with 70 times the Sun’s mass. If this star ended in supernova it must lose some 97% of its mass to produce a white dwarf of under 1.4 solar masses. This reduction is possible, but what if it doesn’t occur to this extent?.

If the supernova residue is, say, 2 solar masses, this will collapse and electronic fluid will contract, contract, then smash. In this situation the gravitational pull will be stronger than the opposing electronic fluid can stand and electrons are driven into protons. When negative electrons are driven into positive protons the charges neutralise and we get neutrons. We now have a neutron star, the neutrons being pulled together until they touch, but kept apart by the nuclear force, and the ‘star’ is then at another stage of its collapse, where the gravity is balanced by the nuclear force. This material - ie neutrons touching - is known as neutronium and has a density of 10 to the power of 15 times that of ordinary matter. For instance, if Earth was converted to neutronium it would be a sphere only about 120 yards across. If the Sun was compressed similarly it would be a sphere some 8 miles across, or if all the matter in the known universe was compressed it would form a sphere smaller than that described by the orbit of Mars.

A neutron star is also a pulsar which emits microwaves from the axis of spin due to a large magnetic field, observable from Earth by regular bursts of radiation. The magnetic pole, where the electrons escape, does not always coincide with the axial  pole (as in Earth) and the energy from these electrons leaves the star as microwave bursts, two per rotation.

The actual composition of a neutron star is still speculative. At the surface there may be a layer of normal matter, mostly iron with  about a half centimetre of gaseous iron atmosphere. Below this crust is a ‘solid’ layer of iron nuclei, even though the temperature is millions of degrees. This layer has density of around 100,000 grams per c.c., and strength 100 million times that of ordinary steel. Gravity is so great that ‘mountains’ would be only 1 cm. high. Going down density increases fast to the close packed neutrons (neutronium), and towards the core there may be even more massive particles called hyperons.

A comparison of escape velocities of the bodies discussed would be :-

Earth.           11.2 km / second.      0.0000373  % of speed of light.

Jupiter          60.5                         0.00020

Sun              617                           0.0020

6

Sirius B (WD)  3400                        0.011

Neutron Star    200,000                    0.67

Even now we are not through !

Nuclear force holding up neutronium can withstand gravitational force which would destroy normal material (and even electronic fluid) but even this force cannot be infinitely strong. In some massive stars up to 70 times the Sun’s mass, the collapse can be accompanied by a gravitational fury so intense that even the individual tightly packed neutrons, held apart by the nuclear force, collapse under the strain. What then is the next stopping point of the collapse ? Apparently none. When nuclear force fails nothing is left to withstand gravity. Gravity, that weakest of  forces, becomes the last obstacle and, as the body shrinks indefinitely and its surface grows correspondingly, it becomes the strongest of all the forces.

Just as no white dwarf can be more than 4 times solar masses, without it collapsing to a neutron star, a neutron star cannot be more than 3.2 solar masses, otherwise it too will collapse. Furthermore, it seems that no star over 20 times solar masses, on collapsing, can throw off enough material to leave a collapsar under 3.2 solar masses.

What happens when this final victory of gravity occurs and the neutronium / neutron star in turn collapses ?  The escape velocity, already two thirds the speed of light will go beyond light’s speed. The size of the shrinking star when the escape velocity equals that of light is the Schwartzchild Radius, and once the collapsar shrinks to within this radius even light cannot leave.

So, as light or any other material comes to a speedy and very permanent end, so does my talk.

Thank you.