The Death of Sun-Like Stars: White Dwarfs

As The Core Contracts, the Envelope Expands

The stars ‘leave’ the main

sequence and become red giants

They are said to ‘climb the

giant branch’ (no real implication of motion in space, of course – just changing properties)

Reconsider the Masses Note that stars of various masses become

red giants of rather similar appearance. But they don’t stay that way for long!

Meanwhile, in the Shrinking Core

The temperature rises, and finally reaches 108 (one hundred

million) degrees. This ignites “triple-alpha burning.” As in the p-p cycle, the fusion takes place in a series of steps.

The net result is that helium nuclei are converted principally to carbon (also oxygen), with a net release of energy.

A Layered Structure Develops - but remember that this is not because

heavy elements settle to the centre!

Unstable Red Giants

As we have seen, main sequence stars have long stable lives -- perfect for life on Earth!

By contrast, in the red giant phase, things are not so

placid. The onset of He burning is very vigorous: the so-called helium flash. The outer properties of the star can change quite erratically. (This is well understood by astrophysicists, but we will not explore the details here.)

The Sun’s Likely Future Behaviour

Eventually, He Fuel Will Run Out! What Then?

The same argument as before would seem to apply:

à the loss of energy generation in the core leads to… àa loss of pressure support, and thus… à gravitational contraction and heating, until… à a new (less efficient) fuel supply kicks in, converting C

and O to even heavier elements, but with reduced life expectancy

For Example:

Suppose we merge Carbon nuclei to form something heavier (say, C12 + C12 à Mg24).

The ‘poor quality’ of this new fuel suggests that it won’t last very long: remember the binding energy curve! And so the cycle should continue, with progressively poorer fuels being used in turn, for ever shorter spans of time…

Instead, Something Amazing Happens!

After the conversion of Helium to Carbon, the Sun will undergo no more significant nuclear reactions at all! But why? Doesn’t this mean that gravity will win, and the sun will dwindle down to a tiny dense object – maybe a black hole? With no nuclear reactions to produce heat, what can prevent such a total collapse?

Meet Wolfgang Pauli

Nobel prize 1945

…and Chandrasekhar

Nobel prize 1983

Following Pauli, Chandra Developed an Amazing New Understanding

…including remarkable ‘new physics’ – with a sad role played by Eddington (seen here with Einstein).

What New Physics? First, Consider the Earth

It is a rock, with a hot interior that will eventually cool off. Even when it is stone-cold, it will not collapse inward, because its crystalline structure gives it permanent rigidity. [See ASTR 101]

The key players in maintaining this structure are

the electrons that surround atoms.

Electrons in Atoms

In everyday molecules and materials, atoms are held “at arm’s length” by their surrounding clouds of electrons.

How About Electrons In Sun-Like Stars?

During the main-sequence phases, the body of

every star contains myriads of free electrons, torn off the fully ionized nuclei thanks to the extreme heat. They play no role in the energy generation and are just ‘part of the background.’

But as the core shrinks, everything is squashed

more densely together. In stars like the sun, the electrons suddenly behave in an unforeseen way.

At Extreme Densities

As the density approaches a million times that of water – unheard of on Earth! – the electrons suddenly resist being squashed together, but the resistance is very much more than you would have expected on classical physics grounds. It is a product of the new (1930s) science of quantum mechanics (the physics of the very small), combined with special relativity.

Pauli Exclusion: A New Kind of Resistance

Even though they are physically tiny, electrons

cannot be arbitrarily squashed closer and closer together. This is not because of their electric charges or physical sizes, but something more subtle.

Among other things, this explains the ways in which electrons distribute themselves around ordinary atoms too!

“Electron Degeneracy”

In a large body (like a stellar core) that is full of densely-packed electrons, this provides a huge new source of resistance against the pull of gravity. This resistance is independent of the temperature of the star.

In other words, the star can now cool off until it is stone-

cold – and yet remain stable against the enormous inward pull of gravity. The ‘degenerate electrons’ prevent its further collapse!

This Explains Sirius B

Enormous Gravity Resisted by Electron Degeneracy

More massive white dwarfs are somewhat smaller (gravity compresses them even more), but they still resist collapse!

Chandrasekhar’s Discovery

Chandra developed a full and correct understanding of this behaviour, but also showed that there is a limit to the mass of stars which may be supported in this way: the ‘Chandrasekhar limit’ (~1.4 solar masses)

There are, of course, many stars more massive than

that! They cannot be supported by electron degeneracy, and gravity might be expected to win out. Are they fated to collapse?

An Unhappy Episode Eddington was very unhappy with that implication, and had no confidence in Chandra’s findings. Speaking immediately after Chandra at an important scientific meeting, he completely undercut him and dismissed his work. Remarkably, Chandra held no grudge. In the long term, he was vindicated and won the Nobel prize decades later (for many important contributions, not just for his white dwarf work).

So We Understand White Dwarfs But Why Do We See Them?

White dwarfs, supported by electron degeneracy,

form deep in the cores of sun-like stars when they are in their red giant phases. In other words, they are located deep within a hugely extended low-density envelope of cool gas.

Do we ever get to see the white dwarf ‘cinder’?

If so, why and how?