The fading : red giants and white dwarfs



Nuclear reactions inside a star take only place in the heart of it, because it's only there that temperature and pressure conditions allow them to occur. Hydrogen burning product helium ashes. When there are too many ashes, nuclear reactions are inhibited. At the time where these reactions are stopping, the star has burned between 10% and 20% of its total amount of hydrogen.
At this stage, the star is entering the end of its life.
A summary of the final evolution of stars, dependent upon their mass, is available in the final lexicon.

Around the core itself, a shell of hydrogen will contract, and its temperature will go up. The main effect is the ability to again start nuclear fusion reactions.
The nuclear reactions which happen are quite fast, and the resulting pressure wave will swell the peripheral layers of the star. This phenomenon is called "shell burning".

During this time, the core will continue contracting under the effect of gravity, and it will transfer its energy to the surface of the star, which will inflate further, and so become cooler.
The diameter of the star can increase by a factor of 200, while its cooling is translated into a reddening of its radiation : the star is becoming what is called a red giant.

The Sun as a red giant
Comparison between the Sun, as it is now, and as a red giant in 5 billion years.
Life on the Earth will be, of course, impossible.


An image of Betelgeuse, a red giant in Orion.
It's the only star whose surface can be seen, except the Sun, of course.
The scale provided for comparison clearly shows the gigantic size of this star.


By collapsing, the core gets hotter and hotter. If the temperature can rise up to 100 million degrees, the nuclei of helium are able to merge together to form unstable nuclei of berylium. These nuclei, in their turn, merge to form carbon, which is stable (this reaction is called the "triple alpha" process ). This reaction can only occur if the mass of the star is greater than half of the mass of the Sun.
This very fast phase is called the "helium flash". At this time, the energy is produced as a very high rate, and this allows the star to keep its equilibrium.


If the mass of the star is less than 1.4 solar mass, the process stops when all of the helium is exhausted. The carbon kernel becomes lifeless, the fusion processes are slowing and the star gently begins to switch off.

Considering the requirement over the mass of the core, all this applies to stars whose initial mass is less than a few solar masses.

 The outer envelope of the core is ejected by the stellar winds initiated by the pulsations of the forming carbon kernel. Lit up by the remaining light of the star, the scattered remains of this envelope form what is called a planetary nebula. This nebula will expand away into interstellar space in a few hundreds of thousands of years.

Dumbbell Nebula Helix Nebula NGC3132 Nebula
  NGC6543 Nebula Stingray Nebula  

Some planetary nebulae : from top to bottom, and left to right :
the Dumbbell nebula (source ESO ), the Helix nebula, NGC3132 , NGC6543 and the Stingray nebula, the youngest known palnetary nebula (source NASA/ HST )


The core of the star, having run out of fuel, cannot find the necessary energy to fight against gravity. So it goes on collapsing.

In quantum mechanics, there is a principle, called Pauli's principle which prevents two electrons being in the same state of energy, ie at the same place with the same speed.
When the gravity reduces the available space for electrons -which are totally delocalized, as the core of the star is a fully ionized plasma - they will have to take different levels of energy -ie different speeds. But relativity forbids speeds greater than the speed of light, what implies a upper limitation for the available energy levels. Hence, there comes a time where the volume occupied by these electrons can not decrease any more, in order to obey to the Pauli's exclusion principle.
This effect which brings into conflict with gravity is called a degeneracy pressure.

The star is now a white dwarf, whose temperature is between 5000 and 100,000 K. These white dwarfs can only radiate their residual internal heat, and go on inexorably cooling. When their temperature is cold enough, they become invisible.

Physically, a white dwarf has about the same size as Earth, and a mass between 0.4 and 1.4 solar masses :

a glass of white dwarf matter has a weight of more than 50 tons !

Evolution of a 1 solar mass star
Evolution of a solar mass star on the Hertzsprung-Russel diagram.

At the end of the red giant stage, the star is rapidly becoming a white dwarf, towards the bottom of the diagram.

White dwarf stars are objects with a high rotational speed, because they keep the rotation of the initial star, but are also much smaller (conservation of the angular momentum) .

They can have an electrical and magnetic field strong enough to behave like a particle accelerator, and so radiate in the radio-wave and X-ray part of the spectrum.


The novae phenomenon

Consider a white dwarf as part of a binary system. If the other star, evolving into a red giane, is overflowing its Roche's lobe, it means that its outer layers are within the gravitational field of the white dwarf : the matter of the envelope can be pulled away by the gravity of the white dwarf.

Accretion disk of a binary system
This matter will condense into an accretion disk around the white dwarf and fall upon its surface.
When the temperature and the pressure of this disk is high enough, a global thermonuclear reaction will arise, resulting in a light flash able to radiate as would 10,000 suns :
this is called a nova, and can occur at more or less regular intervals.


The supernovae

In some cases, the fall of this matter is so massive and sudden that the star reaches the Chandrasekar limit, - this name comes from an Indian physicist - whose value is around 1.4 solar masses.
At this time, the star collapses, its internal pressure becoming unable to stop the gravity. This collapse triggers the fusion of carbon and oxygen atoms, and is not regulated by heating or the dilatation of the star.
There comes a chain reaction which will destroy the star in a tremendous thermonuclear explosion.
In the spectrum of this explosion, we won't obviously find any trace of hydrogen, but silicon. This explosion is called a Type Ia supernova, highly luminous phenomenon, but also very regular. All the type Ia supernovae have the same absolute visual magnitude of -19.3, which is about 5 billion times the Sun.

Other supernovae exhibit helium in their spectrum instead of silicon, they are called type Ib, and they could be triggered by collapse of Wolf-Rayet stars.

Some other supernovae don't show silicon nor helium (or only very few traces). They are called type Ic, but their exact nature remains unknown.


References :
Introduction to Cataclysmic Variables (HEASARC / NASA)