In our previous post I described that the Hertzsprung-Russell diagram:
- Shows a survey of the properties of all the stars in the galaxy
- Provides a means of describing the lifecycle of a single star
In this post I will concentrate on the second of these, and ask “what will happen to the Sun, and what journey has it been on so far?” Some of you may already be aware that the Sun will eventually run out of fuel. Some of you may also be aware that it will become a red giant, and then a white dwarf. We are going to flesh out those statements for you. Some of you may be professors of astrophysics, and to be honest, you are not really the target audience…
We will:
- Explore the balance within stars that dictates their metamorphosis
- See that there are three distinct regions of stars on the Main Sequence, corresponding to different lifecycles
- Identify the Sun on the HR diagram and describe its lifecycle
So let’s begin…
Stars: a dynamic balance
The are some introductory ideas to keep in mind. They will be relevant at all parts of the discussion of star lifecycles, and we will discuss them with reference to the diagram below.
- Firstly, a star is under the influence of its own gravity (green arrows) which is continually trying to shrink it. This tendency is countered by outward pressure (orange arrows) due to the high internal temperatures, and to radiation pressure from photons released by the nuclear reactions in the core. Each stage in a star’s evolution is caused by an imbalance in these two forces.
- Secondly, when a gas shrinks, it rises in temperature, much as a bike pump gets hot when the air is forced through the nozzle with consequent decrease in volume. In contrast, when a separate energy supply causes the temperature of a gas to increase, it expands.
- Thirdly, nuclear energy generation only takes place in the core of the star. The core is surrounded by an outer envelope of material that may be fuel one day, but is not yet… A change that happens to the star as a whole is caused by a change in the core. Funnily enough, these two changes are often in an opposite sense. For example, when the core shrinks and thus rises in temperature, that often causes an expansion of the envelope – take care not to be confused by this.
- And finally, the nature of the nuclear reactions in the core is nuclear fusion. In nuclear fusion, lighter nuclei join together to form heavier nuclei. In the process, a small percentage of the mass of the initial nuclei is converted into energy in the form of photons. A young star is composed mainly of hydrogen. Hydrogen is the element with the simplest atom – a nucleus of hydrogen and a proton are one and the same. The fusion of this hydrogen converts it into helium, via a process called the p-p chain (in very massive stars another mechanism called the CNO cycle is prevalent). We will investigate the p-p chain when we describe the Sun in more detail; for now, it is enough to consider fusion as the conversion of hydrogen to helium with a release of energy.
Keep these four ideas in mind; between them they explain pretty much all of what follows…
The three regions of the Main Sequence
If you have arrived here via our previous post, you will have seen the following picture, the HR diagram.
Apologies, but in the previous post we smuggled past you a feature of this picture that we did not explain. The Main Sequence is partially coloured green (not literally – just in the diagram). The green colouring splits the Main Sequence into three regions, the green intermediate region, and the two grey extremes. Their significance is as follows:
- The green region represents intermediate-mass stars, between 0.8 and about 8 solar masses. These stars spend billions of years on the main sequence. They follow the stages: main sequence, red giant, white dwarf. Our Sun is one of these stars.
- Further down the Main Sequence in grey are the low-mass stars, less than 0.8 solar masses. These have lifetimes older than the galaxy, so have not left the main sequence. Every one of these stars there has ever been is still there! It sort of doesn’t make sense to talk about a lifecycle for them…
- And above 8-or-so solar masses (this limit is not very well established), are the massive stars. As we saw in the first part of this post, despite their larger fuel stores, they burn so fast that they actually have shorter lifetimes. They spend only a few million years on the main sequence. In keeping with their high energy, rock-and-roll lifestyles, their ‘deaths’ are more spectacular than the intermediate-mass stars. They are too big to form white dwarfs. Instead they turn into red supergiants, then after a supernova leave behind a neutron star or a black hole.
This post concentrates on the fate of the intermediate-mass stars like our Sun. There are many good sources describing the supernova route of the massive stars, and maybe if enough people ask us, we might add a post of our own, but that time and place is not here. Anyway, we have a vested interest in our own Sun, so here goes…
Energy generation in the infant Sun
The Sun is about 5 billion years old. When it was born onto the zero age main sequence (or ZAMS – see part 1 if you need an introduction) it was about 94 % of its current size, and the vast majority of it was composed of hydrogen, both the core and the envelope. For simplicity, we will assume it was entirely hydrogen. We have previously said that nuclear fusion in the core turns the hydrogen to helium. It is now time to explore this statement more fully.
Firstly, it is important to realise that the core of a star is a fully-ionised plasma (see this post for a description of a plasma). Although we say it is composed of hydrogen, there are no hydrogen atoms (and certainly no hydrogen molecules). All the electrons have been stripped away from the nuclei, and each nucleus is simply a proton. So the core of the infant Sun was a ‘soup’ of protons and electrons in high speed motion, unbound to each other. Although this describes gas-like behaviour, the density of the core hydrogen is greater than that of lead on Earth!
The most common mechanism for nuclear fusion in such a star (and the only one we will consider here) is called the proton-proton reaction, or p-p chain. It is a three-step process. And it’s quite complicated, so you might like to read this in conjunction with the diagram below…
- STEP 1: Two protons from the soup collide. One of those protons turns into a neutron, positron and neutrino (like in beta-plus decay, for radioactivity afficionados). The neutron binds to the proton to form a deuteron (a nucleus of an isotope of hydrogen). The neutrino will likely escape the Sun unhindered. Over a hundred billion of these neutrinos pass through every square centimetre of your body every second. The positron annihilates with one of the electrons in the soup – they both cease to exist, their mass being converted into pure energy in the form of gamma photons.
- STEP 2: Another proton from the soup collides with the deuteron to form a nucleus of helium-3. Excess energy is carried away in the form of a gamma photon.
- STEP 3: A helium-3 nucleus meets another in the soup (which is lucky because the soup is mainly protons and electrons). A suitable rearrangement sees the particles involved return two protons to the soup, while creating a single helium-4 nucleus.
In the diagram, protons are yellow, neutrons are blue, electrons/positrons are green. Apologies for the confusing colour scheme – a proton looks rather like a star! But we’ve rather set ourselves a precedent, and protons seem to be yellow on our website…!
The net process is to take four protons and turn them into a helium-4 nucleus (actually 6 protons were needed, but two of them returned to the soup, so in some ways they acted like nuclear versions of a chemical catalyst). The mass of a helium-4 nucleus is slightly less than the mass of four protons; the overall decrease is mass is converted to energy and is carried away by the various photons and neutrinos produced. That mass loss is what accounts for the power of the Sun; the Sun is losing mass at the rate of 4 million tonnes per second. The fact that it is still here, 5 billion years on, tells you something about how big that makes it!
You will see from the timescales involved that nuclear fusion is extremely difficult to achieve. It requires two protons in the soup to smash into each other. Why so difficult? Well, two protons are both positive. They therefore repel each other, and do so with more and more force as they approach each other. To make them smash into each other and fuse requires enormous temperatures. Fusion is so difficult in fact, that as the diagram shows, a proton typically spends a billion years in the soup before it manages to fuse. In fact, fusion in stars is an extremely inefficient process – it is only because stars are so big and have so many protons that they generate much energy at all. And it is a good thing too that they are inefficient. If they were better at doing their thing, they would have burned up and gone out before life could ever have evolved.
As an aside, fusion may well prove to be a clean energy revolution on Earth. But a lot of effort is going into it, and to say the least, it is a distinctly non-trivial problem. The inefficiency of fusion is the key issue. The Sun can get away with it because of how many protons it has; a Tokamak, say, on Earth cannot take the same approach. To increase the efficiency of the fusion process to make it viable on Earth requires temperatures many times in excess that of the core of the Sun. So you need to put a lot of energy in before you get any out. Oh, that, and the fact you need to prevent your plasma from touching the walls of what you are keeping it in (every school student knows that gases expand to fill their container – plasmas do too).
The evolution of a 1 solar mass star (e.g. the Sun!) on the Main Sequence
The hydrogen burning in the core goes on for about 10 billion years, before anything too dramatic happens, so the Sun is currently roughly half way through its prime. However, during that 10 billion years there are subtle changes occurring that affect its internal structure.
To explain these subtle changes will require us to zoom in a long way to the HR diagram, so far that it would be almost unrecognisable. So here is a version to orientate us…
The dot within a circle is the symbol for the Sun, and is placed on the ZAMS; it represents the Sun ‘at birth’. The grey rectangle shows the area that we are about to zoom in to. Ready…?
The new expanded HR diagram is shown above. The birth of the Sun is shown in blue at bottom-left.
After ‘ignition’, the temperature of the core increases. As this temperature rise continues, the core expands further into to envelope, which is to say that hydrogen (protons) that was just outside the core before is now fusing and is therefore by definition part of the core. This fresh fuel supply causes the luminosity to increase. The Sun migrates upward on the HR diagram; the second position shown represents the Sun today, five billion years old. These slow changes turn the main sequence into a band rather than a line. This graceful ageing process will continue for another five billion years. And then the hydrogen runs out…
The Sun beyond the Main Sequence
Well that might have been a bit melodramatic. The hydrogen in the core runs out; there is still plenty left in the envelope, if only it can be accessed.
So what happens when the core hydrogen does run out? Remember at the top of the page we said that stellar evolution is a constant battle between the inward pull of gravity and the outward push of pressure due to temperature and radiation? Well, if the hydrogen runs out, the core stops producing energy, so that outward push is decreased. And gravity (temporarily) wins. The (temporarily) victorious gravity causes the core to shrink. But as we know (see introductory section) a shrinking gas gets hotter. The increase in temperature of the core will have little effect on the central portion of the core (where the hydrogen really has run out), but the outer shell of the core is still burning. This burning hydrogen shell then expands into the envelope because of the rising core temperature, causing fresh energy generation. In turn, this causes the envelope to expand. As the envelope expands, it cools. The decrease in surface temperature and increase in size roughly balance so the luminosity does not change much (see the part of the diagram between 10 and 11 billion years). The star is now in the ‘hydrogen shell burning’ stage. The core is composed of the helium formed form the hydrogen burning, surrounded by a shell of burning hydrogen.
As the core shrinkage accelerates, so does the star’s evolution. The density of the core becomes quite extreme under the shrinkage – 10 tonnes of mass in a teaspoonful. The envelope expands more and more rapidly, and the star becomes a red giant (see the enthusiastic red arrow labelled ‘RGB’ for ‘red giant branch’, two diagrams previously. Also, apologies to readers of our ‘Primer on colour’, this ‘RGB’ is different from the ‘RGB’ you found there! Terminology, eh?). As a red giant, the Sun’s envelope will consume Mercury and Venus, and life on Earth as we know it will become impossible.
The standard texts now say that the red giant becomes a white dwarf etc etc… But there is a whole lot more to it than that.
With the helium core at such high density, the electrons are forced so close together that quantum effects become important. In particular, the collapse is halted by a phenomenon called ‘electron degeneracy pressure’ whose origin resides in the exclusion principle – it is not possible to have electrons so close together in the same energy states. It is technically complex to understand electron degeneracy, so don’t worry if you don’t. The point to take out of this is that the electrons in the soup in the core no longer behave like a normal gas, and in consequence the temperature of the (non-burning helium) core increases dramatically. As the core temperature hits a hundred million degrees, the helium itself starts to fuse (into nuclei of carbon and oxygen). Helium fusion occurs via a process called the triple-alpha process (we won’t cover this here – you have already been subjected to the p-p chain, and can look it up if you wish). This sudden onset of helium fusion is known as the Helium Flash, shown as number 3 in the diagram below.
It might be a good idea to read what follows in conjunction with the diagram above.
After the Helium flash there is a new source of ‘fuel’ in the core, so the core expands and the condition of electron degeneracy is removed. In turn, the core temperature falls, the envelope shrinks, and the surface temperature rises at nearly constant luminosity. This is the horizontal branch (the part about being a red giant that nobody ever tells you about).
There is now energy production from two sources: the core is hot enough to sustain helium burning in the centre of the core, and there is hydrogen shell burning in a shell surrounding the helium. The star now settles in a fairly stable “clump” at the end of the horizontal branch. This clump is like a miniature Main Sequence, but burning helium as well as hydrogen.
Now, you might well ask ‘The hydrogen ran out before and we ended up with a red giant. Does anything big happen when the helium runs out?’ Well, yes. The core is now starting to resemble the layers of an onion. The central part of the core is mainly carbon and oxygen, with helium outside it, and hydrogen surrounding that.
Much like what happened when the hydrogen ran out, as the helium is exhausted the energy generation slows down, gravity ‘wins’ and the carbon/oxygen inner core shrinks. Once again, the core temperature increases; this time it makes the helium burning move outwards in a new shell. It is fed by fresh helium formed in the hydrogen-burning shell above. The outer layers swell (as before) and cool to place the star on the asymptotic giant branch (AGB). AGB stars are more luminous than RGB stars because they are powered by two shells instead of one.
It is as though the star has had two attempts at being a red giant, it tried first on the RGB, and then mastered it on the AGB.
By the time the star is on the AGB branch, the carbon and oxygen core is comparatively stable – the inward pull of gravity is not sufficient (because it’s ‘only’ a 1-solar-mass star) to cause ignition of the carbon and oxygen mixture.
The outer envelope is now so enormous that large parts of the star are no longer tightly held on by gravity. The outer envelope starts to drift away. The surface temperature increases, not because anything is getting hotter, but because the cool envelope is drifting away, leaving hotter parts exposed as the surface. The core, meanwhile, is so hot that its u-v ionises the escaping envelope, and the envelope glows in the radiation as a planetary nebula. Planetary nebulae are some of the most beautiful objects in the galaxy; a cool selection can be found in the Hubble space telescope gallery.
As an aside, the word ‘nebula’ can be confusing to modern users. It comes from the Latin for ‘mist’ or ‘cloud’ and seems to have been coined in the 17th century. By this stage, the invention of the telescope had allowed for the discovery of planetary nebulae, diffuse nebulae, supernova remnants and galaxies. But ‘discovery of’ is not the same as ‘differentiation between’, so they were all labelled as ‘nebulae’. Only much later were the natures of the objects ascertained, and then some of them retained the name ‘nebula’, while others were reclassified. So when you see the word, depending on the source, you may need to decode it in either a modern or older sense. For example, Hubble’s publications that contained his ‘law’ spoke of ‘extra-galactic nebulae’, whereas we would call them galaxies. (And each of those galaxies would contain nebulae!). To further confuse the issue, ‘planetary nebulae’ have nothing to do with planets; they are round, and looked like planets in early telescopes, hence their non-ideal name.
As the envelope drifts off and becomes admired as a planetary nebula, what becomes of the core? Well, it glows by virtue of its high temperature – it is a white dwarf. But no further reactions are taking place within it, and it cools slowly, as its residual heat is emitted. Eventually it ceases glowing, and leaves the HR diagram forever, although still there in space, forgotten by most, but not now by you…
Acknowledgements:
Again, James Kaler’s book “Stars” is the source of much of my knowledge. In particular, my diagrams of evolutionary tracks on the HR diagram are adaptations of similar diagrams from his book. And you really should read his book…
‘If how bright a star looks depends on how far away it is, how do we know how bright any star really is?’ is a really good question and potentially your next step. It requires a knowledge of star spectra (for which Kaler is again excellent) and distance measuring in the universe for which Kitty Ferguson’s ‘Measuring the Universe’ is a really accessible source.