The Miracle of Stars or Why We Are

Michael Bass, Professor EmeritusCREOL, The College of Optics and PhotonicsUniversity of Central FloridaOrlando, FL 32816

© M. Bass

© M. Bass

Cosmologies

Biblical and Mythical.Aristotle’s universe of spheres with the

earth at the center.Copernicus’ sun centered universe.Newton’s universe of absolute motion.Einstein’s universe of relative motion.Einstein plus quantum mechanics and the

Big Bang Universe.

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A scientific cosmology must explain

The night sky is dark.The universe can not be static.Hubble’s law of galaxies rushing apart.The 2.7 K (loosely called the 3 degree)

black body radiation that fills the universe.

The fact that there is 1 helium atom for every 10 hydrogen atoms in the universe.

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There are stars, galaxies, clusters of galaxies, clusters of clusters, and other structures in the universe.

The rotation of galaxies indicates that there is about 10 times more matter than we can see – dark matter and energy.

There are novas and super novas and places in galaxies where stars are continually formed.

There are planets.There is US!

More Facts to Explain

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The Big Bang

The outward rush of the galaxies from one another can be run backwards to an initial beginning.

About 13.5 billion years ago the universe was no bigger that a sub atomic particle, it was very, very hot and it started to expand.

Everything that we see around us was determined in this moment of creation.

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Big Bang Nucleosynthesis

This is a big name for the cooking of atoms during creation.

The Big Bang model explains many observed features of the universe - the He:H ratio, the 2.7 K black body radiation, the Hubble law and so on - but it only explains atoms of H, He, D and Li and these were formed in the first 3 minutes.

For all the other atoms we need stars!!

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Hubble Telescope Ultra Deep Field Image – all spots are galaxies and all galaxies have many, many stars!

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The formation of stars

As the universe expanded turbulences formed as they must.

These gave rise to stars and galaxies of stars. The first stars were probably

supermassive, lived fast, died young and seeded the next generation.

The question we want to address is what does it take to get the kind of stars we need to cook the other atoms that we need to get us.

To do so requires a universe with some very special properties. Stars forming in small

protrusions from the Eagle Nebula

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How do stars cook up elements?

The first stars were formed by the hydrogen (plus a little helium) gas produced in the Big Bang.

Gravity pulled the gas in on itself and collisions heated up the gas.

When a certain temperature was reached nuclear fusion began and so called stellar burning gets going.

The end products of nuclear fusion reactions were higher atomic number elements.

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Star burning

The rate with which a star burns its hydrogen fuel increases with its mass. Massive stars burn up fuel much faster than

smaller stars - makes you glad the sun is a very average star, not a giant.

In such burning stars can produce all the elements through iron that includes carbon, oxygen, nitrogen ...

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The next step

To get past iron you must have temperatures much higher than just nuclear fusion allows.

Thus, to get more massive atoms you must have super novas.

So, stars burn, crash, spew out their remains into the galaxy and seed the formation of newer stars.

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The next generations This process of one generation

of stars seeding the next produces new stars containing more than just Big Bang elements

So too does the residue of star formation.

Therefore, so do the planets that form around the stars, and

therefore so do we. We are star stuff. Spinning cloud

flattening into a disk and condensing into a star and planets

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What is required?

We have pronounced the sequence of events but haven’t explained why it occurs exactly as it must for us to exist.

To do this we will employ our knowledge of modern physics - particularly the Standard Model of Modern Physics The current versions of the theories of Quantum

Mechanics and Gravitation

(You do not have to know quantum mechanics or general relativity to follow this discussion.)

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Fundamental Constants

The Standard Model demands that certain constants be just what they are. About 20 numbers giving such things as the

gravitational constant, the charge on the electron, the speed of light, and etc.

If they aren’t, things don’t happen the way we observe that they do.

We don’t know why these constants are what they are, just that they have to be what they are if things are to make sense.

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A needle standing upright on its point

Why these constants must be exactly what they are is asking why our universe is like a needle standing upright on its point.

The random probability that the several of the 20 constants that must have the precise values needed to explain us is unbelievably small. About one chance in 10234

The anthropic view, the one that says ours is a universe designed for our existence, assumes that a God set the values of the constants just exactly right and then let things go.

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Constants needed for stars

The part of the universe that concerns us is mostly protons, neutrons, electrons and neutrinos. There is much more dark matter but it isn’t us.

These interact through four forces - gravity, electromagnetism, weak nuclear and strong nuclear (in order of increasing strength)

Forces are characterized by strength, range and type of particles they affect.

Particles participate in forces through coupling constants mass for gravity charge for electromagnetism

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Gravity

It is the only universal interaction. every particle having mass feels gravity.

Its range is infinite.Its strength is proportional to the

product of the masses that interact.The proportionality constant, G, is

incredibly small, in units of proton masses, it is 10-38.

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If this constant were any larger stars would live much shorter times than they do they would not last long enough for us to

evolveIf this constant were any smaller

stars would not collapse, ignite, and fuse H into He

and other necessary elements

G

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You need nuclear reactions

As gravity causes the gases of a star to collapse nuclear reactions must take place without nuclear reactions the internal pressure of the

gases can not compete with gravity and the whole mess would collapse immediately into a black hole.

For nuclear reactions to proceed as they must to cook up the elements the proton and neutron can differ in mass by only 2

parts in a thousand and the electron must be ~1800 times less massive than the proton

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Any larger differences and protons and neutrons would not stick together in atoms under the effects of the nuclear forces.

There would be no atoms, no chemistry, no biology and the universe would be very boring.

Neutrinos are particles essential to conserve momentum in nuclear reactions.

It turns out that the neutrino mass can not exceed ~10-9 of a proton mass.

n, p, e and

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The scale of the universe

The universe must be big enough to accommodate us.

To do so the mass density of the universe, must be no larger than 10-40 in units of proton mass.

If it were any larger the universe’s expansion would not have happened.

If it were any smaller the universe would have already expanded out of sight.

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There must be light

Electromagnetism is the force that governs the radiation of light.

It must be present exactly as it is in order to carry energy away from stars so that stars stay in equilibrium long enough to cook the elements and warm our planet.

This balance of gravitational collapse, nuclear burning, and electromagnetic radiation enables stars to last billions of years.

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The demands for electromagnetic radiation to maintain the energy balance of stars requires that the charge on the electron be no more and no

less than 1.6 x 10-19 Coulombs, Planck’s constant be exactly 6.3 x 10-34 J-sec.,

and the speed of light be 3 x 108 m/sec.

Any more or less and stars don’t make it.

e, h and c

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The probabilities if these numbers occurred randomly

For the existence of particles with the necessary masses (in units of the Planck mass, the mass of an elementary particle that would collapse on itself and form a black hole or 1019 proton masses): the proton =1 part in 1019

the neutron =1 part in 1022 the electron =1 part in 1022 the neutrino =1 part in 1027

For the cosmological constant (density of empty space) =1 part in 1060

For the ranges of the forces =1 part in 1080

For the strength of the forces =1 part in 104

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Add ‘em up

The total probability of all of these numbers being just what they must be to have us is the product of all the probabilities or

1 part in 10234

This is so astonishingly small that we are forced to seek some deeper understanding of how so special a universe could come about.

What we have so far is a theory that fixes these numbers so that it agrees with observed facts.

What we don’t have is a theory that explains these numbers.

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Possibilities

Some say it is God’s doing.Some suggest something like cosmological

natural selection where universes that generate many universes generate universes like themselves.

Some suggest simply that in the infinity of possible universes, we exist in the only one in which we could exist.