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The Birth, Growth and Terminal Ailments of Stars
(Draft) 

 

Stars are simply very large clouds of hydrogen that have fallen together by gravity to very much smaller sizes. And what

happens to them in the end depends on how very large they were at the start. But it's really not so simple as all that. And we're

leaving out all the interesting stuff like why is there gravity at all, why is the hydrogen made of electricity, and why, when things

fall, do they coast? These are the really interesting things, but this is not the place for all that.

 

Long ago J.B.S. Haldane, who gave one of the fascinating lectures of my youth, wrote a charming little essay On Being the

Right Size. I hope you've read it. He was into animals and the problem of how the increase in the complexity of their structures

is related to their increase in size. But the problems are similar for stars, so you can think of this essay as a chapter in his. And

I wrote this stuff up long ago when I was in a more playful mood. It's the first chapter of "Astronomy for Children under Eighty."

 

The first consideration (which we're going to skip for the moment) is whether the star is an early star made of nice clean

hydrogen and helium and spinning slowly in the central bulge of a galaxy, or whether it's a late star, like our Sun, made of dusty

hydrogen and helium and spinning more rapidly in the disc. (And we won't ask yet where the dust is from.) But that is what determines

whether the star could have planets like Jupiter and Saturn only (which are really not planets at all), or whether it could also

have rocky planets like the Earth and Mars. Right now we'll just consider what happens to young stars in general.

 

You remember how things fall, harder and harder, faster and faster. Now when the hydrogen is falling in like that to make a

star, what stops it? Obviously, it runs into the stuff falling in from the other side. If we had tried to make a star out of super

balls, we would have failed, because the balls would have missed each other and coasted on through to the other side. But hydrogen

clouds are very spacy and they do collide. They can't get past the clouds from the other side. So what happens is that the energy of

falling gets scrambled to heat. Now the heat energy can slow down the further collapse but it cannot be used to return the hydrogen

to its former position. It cannot undo the collapse. When the catcher behind home plate catches a pitched ball, the heat in the

catcher's glove does not return the ball to the pitcher. We say that the entropy has gone up. The scrambledness of the energy has

gone up and its useableness has gone down. It's the same in the birth of a star. The entropy goes up. We say, "Entropy tends to a

maximum." It goes up but doesn't go down. Otherwise galaxies and stars could not be born, and living organisms could not exist. We

all live in a cascade of increasing entropy by directing streams of the increase through our forms.

 

Gravitational energy and the kinetic energy of large moving objects, like planets going around stars, are completely free of

entropy. But when the kinetic energy of our falling hydrogen gets scrambled to heat, it gets contaminated with entropy and cannot

prevent the collapse of the star. So as the star gets smaller and hotter and the outer material has fallen as far in as it can fall,

the star, like our Sun, will be round and shiny.

 

But it doesn't end there. The star gets rid of some of its extra energy by shining it away at the surface, and so gradually

the star gets smaller and hotter. Eventually (after several million years), the center of the star gets hot enough (about ten

million degrees centigrade) to fuse hydrogen to helium, and we say that the star has joined the "main sequence." (It's not really a

sequence at all. It's just where the stars that are busy fusing hydrogen to helium fall in the Hertzsprung-Russell diagram. It

just looked like a sequence on the diagram.) 

 

Now when a star converts hydrogen to helium at its center, an enormous amount of energy is released. Seven tenths of one percent

of the rest energy of the hydrogen is released to kinetic energy and radiation. [What we see as matter is just rest energy or

potential energy as Einstein pointed out in 1905. It was suggested much earlier by Swami Vivekananda to Tesla who was a close friend

of Einstein's first wife, Mileva. She was probably responsible for getting it into the appendix of the relativity paper. From

Einstein's 1905 quantum mechanics paper they knew that if something is going away, its energy is reduced. They also knew

from his relativity paper that its mass is also reduced, and by the same amount. These two ideas are put together in the appendix,

(E = m). But you must remember that what we see as matter is just potential energy or you'll never get things straight.]

 

Regardless of what you might have been taught, the energy released by fusion at the center of a star is not what makes it

hot. The star is heated by gravity. The fusion just keeps it bloated by releasing energy in th core. And the question now is:

why does it keep it bloated for such a very long time? That is because the thermal gradient from the center to the edge of the

star may be only thirty degrees centigrade per mile, and the edge may be half a million miles away. So it may take about a million

years for the energy released at the center to leak out to the edge and get away as radiation. That's why the stars take "such an

unconscionably long time adying." That's why they stay so long on the main sequence. And our Sun is a teenybopper, nearly five

billion years old and only half way through. So after another five billion years, when all the hydrogen is gone in the middle, what

will keep it bloated? Nothing will keep it bloated. The center will then collapse to the density of about two concrete mixing

trucks, with all that concrete and both drivers, squeezed into a one pint jar. And the question is, will that be warm or cold? It

will be hot, so hot that the hydrogen fusion rate around the condensed helium core will be all out of control.

 

At present the fusion rate at the center of the Sun is under the control of a governor. If it fuses too fast, it will bloat the

center and slow down the fusion. And if it fuses too slowly, gravity will compress it and speed it up. But in some five billion

years, when the helium core has collapsed to that awful density, the fusion rate around it will no longer be able to bloat it and

cool it off because the density of the core will no longer be determined by temperature. Then, although the rapid fusion around

the core will no longer be able to bloat the core, what it can and will do is to bloat the rest of the Sun to a red giant. So the Sun

will swell up to a great red balloon with a diameter equal to the diameter of the Earth's present orbit. 

 

In order to understand what happens next, we have to talk about what is known to the astronomers as the solar wind. We see

what looks like a wind blowing away from the Sun. It wouldn't look like a wind at all if you saw it right next to the Sun. It would

just be the Sun's corona at some two million degrees centigrade. So why, from far away, does it look like a wind? And why is the

corona so hot? We'll take the second question first.

 

The material in the immediate vicinity of the Sun, the Sun's corona, is some three hundred times hotter than the surface of the

Sun that heats it. Partly it is heated by the continual turbulence at the surface of the Sun beneath it, and partly by the

continually changing magnetic fields. But also it is heated by the ultraviolet light that knocks the electrons off the atoms.

(Sometimes half of the twenty-six electrons are stripped off the iron atoms.) Since the energy released when electrons rejoin the

atoms is much less than the energy of the ultraviolet radiation that knocks them off, the corona has what we may call a favorable

balance of trade and gets too hot.

 

It is this hot corona, seen from a distance, that we see as the solar wind. If you saw it from near the Sun, it would just be

high speed particles moving every which way. But seen from a great distance, all the particles that reach you would be seen to be

coming from the Sun's direction. That's why you'd see it as a wind.

 

Now when the Sun swells up to a great red balloon, nearly filling the Earth's present orbit, and its diameter has increased

some two hundred times, how much will the surface area have increased? Since the surface goes up as the square of the

diameter, it will go up by some forty thousand times. And what will happen to the solar winds? They will be gravely increased,

and the Sun will thus shed some of its outer garments. Also when the equatorial regions have become so distended that whole atoms

can form there by recapturing their electrons, the energy thus released may puff the surface material away. We think the Ring

Nebula star has puffed away five times as much stuff as we have in the Sun. Photographs with very long exposures show two previous

puffs. But only the last puff can be easily seen. It's only about a tenth of a solar mass but is lit by the ultraviolet radiation of

the central star which is now exposed and which is seven times  hotter than the Sun.

 

We now think that the Sun will lose enough mass by puffs and solar winds so that its relaxed gravitational hold on the planets

will allow the Earth to drift away to about the orbit of Mars where we'll orbit the Sun as a ball of molten rock and iron. Cheer

up, things are sure to get worse. There are no permanent habitats.

 

But we're getting ahead of our story. We've talked only about the outer layers of the Sun. Meanwhile the Sun's helium core will

have gotten smaller and hotter as more and more helium is added to it by the rapid fusion around it. Eventually it will get hot

enough explosively to fuse the helium to carbon and oxygen. And you might think that that would release enough energy to blow up

our great red balloon. But it won't. Not because the energy is insufficient, but because the gravitational field of the dwarf

core is simply too strong and contains the explosion. On the surface of a black dwarf star, with a density comparable to that

of the helium core, you'd weigh as much as one U.S. battleship on the Earth. And think how flat you'd be. When the last bit of

hydrogen has been puffed away at the surface, as we see it in the Ring Nebula, it will be the resulting carbon and oxygen dwarf that

will be exposed at the center. It's the ultraviolet light from the central dwarf star in the Ring that lights up the last puff and

allows us to see it. And the green in the ring is the oxygen coming off the blue dwarf. The earlier puffs, unlit by the exposed

central dwarf, would not have been easily seen.

 

It is now thought that as the Sun loses mass, puffed away at the surface, and its gravitational hold on us is relaxed, that the

Earth will drift away to about the orbit of Mars as a ball of molten rock. Cheer up, things are sure to get worse. There are no

permanent habitats.

 

Little stars like our Sun end up as white dwarfs cooling off to black, made of carbon and oxygen squeezed far beyond the

density of diamonds. So next time you hear "Twinkle twinkle little star", remember! Only little stars go to diamond.

 

Bigger stars get hotter because they fall together harder, and they end up in a different way. Because of the repulsion of

their electrical charges, it is very difficult to push two protons together hard enough to get them to fuse to helium. The

temperature must rise to some ten million degrees. But alpha particles (helium nuclei) have two charges each, so it is very 

much harder to push them together by threes and fours to make carbon and oxygen. So that's as far as smaller stars can go,

because carbon and oxygen nuclei have six and eight charges each, and their repulsion is fierce. But the centers of stars much

heavier than our Sun are hot enough to fuse the heavier elements all the way to iron. And all those nuclear reactions release

energy and delay the collapse of the core. But once the core is iron, any further nuclear reactions absorb energy and simply

hasten the collapse.

 

What the physicists call the free-fall time (the time it takes a cloud or a star to collapse by gravity if nothing stands

in its way) depends only on its density. It doesn't depend on its size, and at the present density of the Sun (nearly one and a half

times the density of water) it's three quarters of an hour. But at the density of an iron core star, it's only three quarters of a

second. In three quarters of a second, the iron core collapses to a neutron star with the density of a hundred thousand U.S.

aircraft carriers all covered with airplanes and sailors on parade squeezed into a one-pint mayonnaise jar.

 

Now the energy released in this collapse is much more than you could think. But try! The energy of an atomic bomb, just the

energy that is released when it blows up, weighs one-thirtieth of an ounce, or one gram. The energy of the Saint Helens explosion

weighed one pound. The energy of the explosion that blew Crater Lake was forty-two pounds. It blew thirty-five cubic miles of rock

to powder and put them in the stratosphere at eighty thousand feet. That was forty-two pounds. The energy which the Sun releases

each second is four and one-half million tons. It's been doing it for some five billion years, and will continue for another five

billion years. But when one of these iron core stars collapses, in three quarters of one second it releases a hundred times as much

energy as the Sun will release in its ten billion years. I knew you couldn't handle it, but I wanted you to try.

 

If you had your hand on a piece of a neutron star as big as a large grapefruit or a small cantelope, your hand would weigh some

five hundred pounds and you would not be able to pull away. It would scrape your bloody fingers off on the stones as it fell

through thr Earth faster than a super ball falls through the air. 

 

What happens to a star in the end depends on how big it was at the start. Jupiter and Saturn are too small to get any smaller.

The Sun is more than a thousand times bigger than Jupiter, but it will go down to the size of the Earth, at some hundred thousand

pounds per pint. Stars big enough to go down to neutron stars go down to some ten or twelve miles in diameter. It is thought that

stars whose collapsed centers are more than three times as massive as the Sun collapse to what are called black holes. If they fall

to less than three miles in diameter, gravity won't let light escape.

 

"Twinkle, twinkle little star" we have, but who will sing of bigger stars which make the heavy elements of which the Earth is

made? Up to iron, the elements are made within the stars. But heavier elements like gold are made in the explosions that follow

the collapse of the cores. And the interesting thing is that the stars that make the heavy elements deliver them abroad, all

through the galaxies, so that late stars like our Sun can have planets like the Earth and Mars. But I didn't tell you the

difference between the early stars in the central bulge and the late stars in the disk of the galaxy.

 

When a great cloud of hydrogen (admixed with some helium) collapses to form a galaxy, most of the cloud is blown away by the

stellar winds of the early stars. And the dusts (the heavy elements) of the early stellar explosions are blown away with it

to what I call the hovering layer (it's now called the halo). Into this hovering layer goes most of the angular momentum (the spin)

of the early stars, carried away by their stellar winds. It is the material in this hovering layer that gradually flattens into the

disc because of the overall spin of the cloud. That is why Jupiter and Saturn, and our Sun when it was young, had so much spin. And

because the disc is dusty, disc stars like our Sun can have rocky planets like the Earth and Mars. And because we're in the disc, we

go round and round the galaxy in an almost circular orbit.