# Lecture 14: Stellar Evolution

Reading Assignment: Arny: Chapters 13, 14, and Cosmos Chpt. 9

The Lives of Stars: How do you figure out the life history of stars? How can we determine the typical history of a person? We could watch a person live out their whole life. But that takes kinda long. We could observe people of all different ages and see what the differences are between them and put together a typical history of a person. We can do the same thing for stars. We can observe a large number of stars all with different ages and see how they differ and work out how they transition from one stage to the next.

## Protostars

The life story begins in the large, roughly spherical clouds that fill interstellar space. The clouds are composed of gas and dust (tiny solid particles of matter).

If the cloud is dense enough its own gravity will cause it to contract. Just as a compressed gas heats up so does a contracting cloud of gas.

The cloud fragments into smaller pieces as it contracts, these smaller pieces continue to contract under their own weight and heat up as they go. We call these pieces Protostars.

The time it takes for a star to contract down to the size of a star is short. The protostar phase lasts for only about a few hundred thousand to a few million years.

As the contraction continues density increases, which causes gravity to increase, which leads to more contraction, which heats up the protostar to greater temperatures.

## Hydrostatic Equilibrium

The gas exerts a pressure outward, which resists the force of gravity. Pressure is a force per unit area. You may recall from chemistry that it is proportional to density and Temperature
(the perfect gas law: P = nkT, n is the number density of particles)

As temperature and density increase so does the outward pressure. Eventually the star reaches a point at which the internal pressure outward will exactly balance the force of gravity inward. This point of mechanical balance is called Hydrostatic equilibrium

If a star does not have more mass than about 0.008M then it will never do anything more interesting than slowing cool from this point on. As it cools the pressure in its interior will drop and it will slowly contract under gravity. Such "stars" are called Brown Dwarfs

## Main Sequence

If a star has sufficient mass, the temperature in its core can reach T = 106 K or greater, It will also be very dense way down in there. These are ripe conditions for nuclear reactions to occur.

When a protostar has collapses down to the point where nuclear reactions first ignite in the core we now call it a star, and find that it is located at some point on the main sequence that corresponds to its mass.

The newborn star will have a luminosity and surface temperature now that will change very little over the course of its lifetime. So it stays put on the H-R diagram for a good long while.

In the centers of stars the conditions are so hot (e.g., in Sun's core, T = 1.5 x 107 K) and dense that atoms have all of their electrons stripped away from them, they are completely ionized. Thus we have atomic nuclei (mostly hydrogen, single protons) all zipping to and fro in the core.

Nuclear Fusion:
produces energy:
In chemical reactions the electrons of atoms and molecules interact and reconfigure themselves into different energy states. When they configure themselves into states that have lower energy than the initial states energy is released: exothermic reactions.

For atomic nuclei the principle is the same; they interact with other atomic nuclei to make new configurations that have less energy than initially (more tightly bound) thus releasing energy in the reaction. (this reaction involves the strong nuclear force which is the strongest of the 4 fundamental forces of nature)
An Example:

41H1 -> 2He4 + energy
2He4 is more tightly bound than 41H1, so energy is emitted. It turns out that the Helium nucleus has less mass than the sum of 4 individual protons. In the reaction 0.7% of the mass of 41H1 is converted to energy:
E = mc2

(In the Sun, 700 million tons of H -> He every second!!)

The reason we need hot temperatures and high densities for nuclear reactions to occur is that the strong nuclear force is a very short range force. The electric force makes protons repel one another. The nuclei (protons) have to be moving very fast and have enough near collisions with each other so that they can get close enough for the strong nuclear force to take effect. Once it does it is far, far stronger than the electrical repulsion that the protons feel.

Iron (Fe) - 26 protons - has the most tightly bound nucleus, so fusion of nuclei up to Fe will release energy.

(Fission of heavier nuclei into lighter one also releases energy, for example 92U238, but these nuclei are very rare and don't contribute any energy to the star.)

By mass, Sun is 70% H, 28% He, and 2% heavier elements: Lot's of raw material to fuse !

Several reactions can occur depending on the temperature of the core. Net Effect: conversion of 4 protons to a Helium nucleus (2 protons + 2 neutrons) plus energy.

This is what is happening inside Main Sequence Stars. Nuclear fusion produces energy to heat the core (and outer layers through heat conduction) and thus maintains the pressure needed to resist the inward force of gravity.

NOTE: The photons produced in the core take millions of years to leak out from the core out to the photosphere where they then stream away freely into cold, dark space.

Solar Neutrinos:
The reaction that converts 4 protons to a He nucleus involves the conversion of protons into neutrons. This reaction looks like this

p+ -> n + e+ +
e+ is called a positron, it is what we call antimatter. It annihilates with electrons (e-) and produces a photon with energy equal to the sum of their masses (E = mc2).
neutrinos () have very little (if any) mass, and travel near the speed of light. They hardly react with anything. They can escape directly from the core, unlike photons. Hence we can observe them to probe directly the conditions in the core of the Sun.

To do this we build giant tanks filled with a liquid compound akin to cleaning solution and put them far underground. Since neutrinos hardly react to anything we expect to detect only 1 neutrino per day interacting with the liquid in the tank! We actually detect significantly fewer.

Most probable solution is that neutrinos have some (non-zero) mass which allows them to mutate from one kind of neutrino to another. We can only currently detect electron neutrinos, which are those produced in the center of the Sun.

## Death of Stars: Low Mass

For stars with masses 0.2M < M < 4M (which is the majority of them) They will live quietly and contently, not changing much, for several billion years on the main sequence. (The Sun will live 10 billion years on the main sequence, it's about 5 billion years old now).

There comes a time when all of the available hydrogen in the core is used up and has been converted to helium. The core is then made almost entirely of helium. The nuclear reactions in the core stop, and the core cools.

This causes gravity to take over again (after quite a long respite) it contracts the star which will heat it again. A shell of hydrogen gas surrounding the core will then begin to heat up and reach sufficient temperature and density to start fusing hydrogen to helium.

This shell of burning hydrogen heats up the envelope of the star which increases the outward pressure which expands the envelope. The surface cools and the Star bloats up to become a Red Giant. The surface temperature is low but the star is huge and thus has a large Luminosity. Earth is fried!

The hydrogen burning shell rains down "helium ash" onto the helium core, thus increasing its mass and causing it to contract and heat. Eventually the helium core reaches T = 108 K and helium begins fusing

32He4 -> 6C12 + energy
This reaction is much faster than the hydrogen reaction and this doesn't last for very long ~ 106 years. During this time the core can reach sufficient temperature to have the additional reaction of
6C12 + 2He4 -> 8O16 + energy
A core composed of Carbon and Oxygen forms and begins to contract because the Temperature is too low for further fusion. Just as before the contracting core will heat the envelope and cause it to expand out further making an even bigger and cooler Red Giant.

## Planetary Nebulae and White Dwarfs

The star is now very unstable. The outer layers of the star will begin to be ejected (~ 0.2M*). The outer layers will "sluff off" forming a Planetary Nebula (they have nothing to do with planets, the name is kept for historical reasons). This is an expanding shell of chemically enriched ionized gas.

The Planetary Nebula and winds from the star will cause the star to loose mass, revealing the hot Carbon/Oxygen core. In the end all that is left behind is just this white-hot cinder (the core of the Red Giant) that is composed of mostly Carbon and Oxygen, with a little hydrogen and helium still mixed in. This is called a White Dwarf.

The White Dwarf will have a mass less than 1.4M, even if the star had 4M when it was born. It's size is about that of Earth (R ~ 6000 km). So it is incredibly dense! If you brought 1 cm3 of white dwarf matter to the surface of Earth it would weight as much as a 1-ton truck.

Electron Degeneracy Pressure:
What provides the pressure to hold a white dwarf up under its considerable weight? It's a quantum mechanical effect...

The electrons in the star are moving very fast, and they are prevented from slowing down (cooling down, losing energy) by a law in quantum mechanics known as the "Pauli exclusion principle". This says that no two particles may share the same quantum states. Once the lower energy states get filled (become degenerate) the remaining electrons must maintain their fast speeds and hence high temperature and pressure. This pressure provides the hydrostatic balance needed to keep gravity at bay.

The atomic nuclei (positive ions) in the star are not degenerate and are able to lose energy (cool). The white dwarf shines as the atomic nuclei cool. There are no nuclear reactions.

After about 1010 years, the nuclei cool down and the luminosity of the star becomes very low. The star is now what is sometimes called a "black dwarf". The Universe may not be old enough yet for any black dwarfs to exist. The star will still be supported by the electron degeneracy pressure and the size will remain the same.