The Oldest And The Coldest

This is a post about white dwarfs. White dwarfs are not short people from Northern Europe; rather they are the the end state of stellar evolution for many stars; ‘dwarf’ as they form from so-called ‘dwarf’ stars and ‘white’ as most of them are hot enough to look ‘white’.

In particular, there is a lot that we can learn from old white dwarfs, such as SDSS J1102+4113.

White dwarf stars are bizarre objects.

Despite often being referred to as such, white dwarfs are not really ‘stars’ as such. Rather, they are what most stars will eventually turn into. The distinction is subtle, but important. During its life, a normal star shines because hydrogen is being converted into helium in its core. The mass of a helium nucleus is slightly less than the mass of the hydrogen atoms that it is fused from. The difference is released as energy, following Einstein’s famous relationship. This, incidentally, is the same underlying principle as a hydrogen bomb – a star can be considered as an extremely large H-bomb! However, unlike a ‘conventional’ thermonuclear explosion, a star has sufficient mass that the inward force of its gravity overcomes the outward force of its energy-release.

In fact, stars are doubly-stable against collapse. Nuclear burning is heavily dependent on both pressure and temperature. If a star burns too hot and fast, its core heats up and expands, as the outward force of the radiation exceeds the inward force of its gravity. But, as the core expands, its internal pressure falls, and this reduces the nuclear reaction rate. As a result, the core cools and shrinks again. But if the core shrinks too far, the opposite process happens – the star’s core pressure rises. This higher pressure drives up the nuclear reaction rate, releasing more energy, heating the core and – yes! – making it expand.

In the jargon of the field, we say that stars exist in ‘hydrostatic equilibrium’. Basically, during their main sequence life spans, all stars settle out into a comfortable balance between expansion and contraction. The balance point, the amount of nuclear burning required to keep the star in a steady state, will be different depending on mass. Higher-mass stars need to burn brighter to hold themselves up against their gravity, and lower-mass stars burn more gently. Nonetheless, however, stars can remain in equilibrium for billions of years. Our Sun, for instance, has burned for around 5,000,000,000 years and we expect it to carry on burning for something like another 5,000,000,000 years. Long after we’re gone, the Sun won’t look much different from how it does today.

However, hydrostatic equilibrium depends on one thing – an available supply of nuclear fuel. The hydrogen supply in a star is large but finite. Eventually, it will run out. When it does, the star has an energy crisis. In the very largest stars, this sets in motion the chain of events that will lead to a supernova detonation. Lower-mass stars end their lives somewhat more gently. The core shrinks until the pressure becomes high enough to start burning helium. The resulting fresh release of energy causes the rest of the star to bloat up, into a red giant. Red giant expansion is dramatic – when our Sun eventually goes off the deep end, it is expected to swell up at least as far as the orbit of Venus and quite possibly as far as the orbit of Earth. (Whether or not the Earth will actually be ‘swallowed’ is a side-issue, and actually not that straight forward – red giants lose a huge amount of mass through stellar winds, and the decline in gravity may allow the Earth to escape actually being consumed. We don’t really know for sure at the moment, however. Red giant winds are complicated, and not wholly understood.)

Cycles of pulsation and powerful stellar winds eventually disperse the outer atmosphere of a red giant. For a short time – a few thousand years – the dying star is wreathed in a so-called ‘planetary’ nebula. This phase is brief, however. Such nebulae quickly fade away into the Interstellar Medium, becoming another part of the extremely tenuous gas that exists between stars.

The former star’s core is left behind, however.

Now exposed to space, this object is very different from what it once was. All nuclear fuel has gone. No further burning can occur. The core shines, but it only shines because it’s hot. As it ages, it too will fade away, cooling from a blazing blue-white down through yellowish, then orange-ish and eventually to a dull, sooty red. (There’s an odd parallel here – white dwarfs behave very like brown dwarfs in this sense, ‘cooling like a rock’. I find it strange and weirdly elegant that the end-state of normal stars should echo what happens when star formation miscarries!)

Now, I mentioned hydrostatic equilibrium before. The question you’ll be asking now is, without fusion, what holds the core up against its gravity? And that’s an excellent question. The answer is something called electron degeneracy. I shan’t go into the maths here, but electron degeneracy is an odd consequence of quantum mechanics. The electrons in the star’s core find themselves confined by the enormous weight of the matter around them. The equivalent electron wave finds itself compressed into a smaller and smaller space. However, when particles are confined on the quantum scale, the reduction in their available variation in position forces an increase in their range of momentum. (Effectively, this is just the stellar restatement of Heisenberg’s Uncertainty Principle.) This creates a new pressure – electron degeneracy pressure – that is independent of an active thermal energy source.

But, electron degeneracy can only take over at extremely high densities. As such, the star’s dead core will shrink a long way before it stabilises. In fact, as an example, Sirius B – the nearest white dwarf – is known to be about the same size as the Earth! Inside that volume it contains nearly as much mass as the Sun.

(Another odd brown dwarf parallel – brown dwarfs are also supported by electron degeneracy pressure. In their case, they’re too small to burn hydrogen.)

Now, onto the subject of cool white dwarfs.

White dwarfs have no active energy source, so as we said earlier, they ‘cool like a rock’. This implies, therefore, that we can date a white dwarf by how ‘red’ its spectrum is. The redder its light, the colder the emitting object and thus (in the white dwarf case) the older it is. On the face of it, this might not sound very useful, but actually for astronomy, this would be extremely important.

If you find the coldest white dwarf, colder than any other observable object, then you’ve potentially found one of the oldest stars in the sky. Consider. We know roughly when star formation started, a few million years post-Big Bang, but we don’t know exactly when. Find the coldest white dwarf, and you can put limits on that age. (“This WD is 13.5 billion years old. Therefore, the Universe was forming stars at least 200 million years after the Big Bang” – and so on.) Find the oldest, coldest WD orbiting inside the galactic disk, and you’ve effectively dated the galactic disk! Find the oldest WD visible in the galactic halo, and you’ve effectively dated the halo! Etc., etc.

Do these sorts of things, and we can figure out what order the various components of the galaxy formed in. That’s crucial to reconstructing the process underlying galaxy formation. That has implications for everything, for the entire visible Universe. Also, it has more local consequences. If you see a white dwarf from some time in the past, it means stars could form at that time. If you don’t see any, then they couldn’t. If you see lots of WDs in a certain date range, then clearly it was party time for protostars! And all of these things can give us clues about star formation, a process which retains many enigmatic aspects even now.

(Another – another! – weird brown dwarf parallel: these arguments apply to old, cold brown dwarfs as well.)

So, hopefully I’ve made the point that identifying old, cold WDs is quite definitely Serious Business(TM) and not just stamp-collecting. Currently there are only a few such ‘cold’ WDs known. This is a field that has undergone a lot of development over the last decade, and continues to develop fast. Future instruments such as JWST or E-ELT will certainly bring new discoveries. Although it’s not specifically my field, I shall watch this one with interest!


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