What Is The Sun Doing?
A Point-Form Summary.
This section of the course notes, and the associated PowerPoint presentation, make the following critical points:
a naive thought about the sun suggests that it must do one of two things: (a) if it has no source of internal energy generation, it will presumably lose its heat and turn into a cooler version of itself; or (b) if it has an 'internal engine' supplying fresh energy, it may be able to maintain itself, essentially unchanging, for a very long time
even if it does have an inner 'engine', it is destined to run out of fuel (whatever that may be). This would seem to suggest that option (a), above, is inevitable, and that the sun will eventually die by becoming a cool cinder of some description, like a dying lump of coal
this naive expectation is wrong! Gravity changes everything! In particular, it means that the sun cannot cool down. Paradoxically, the loss of radiant energy (heat and light) has the inevitable consequence of the sun getting even hotter (at least in the deep inner parts)
it accomplishes this by shrinking a little, converting gravitational potential energy to heat (thermal energy). Re-read Sections 3 and 4 in the
Physics 015 course notes to remind yourself how this works, and indeed to remind yourself that this is the reason that the stars are hot in the first place!
we now know that nuclear reactions provide the 'internal engine' that keeps the sun alive for billions of years. Rather more than a century ago, this was not known.
ordinary chemical reactions (literal burning, like wood in a campfire) would provide the sun with a few million years of life at best. It seemed more likely that the Sun was slowly contracting ('Kelvin' contraction), suggesting a maximum possible life of about 10 million years
this estimate was at odds with the timespan probably needed for biological evolution, but no one knew then how to resolve the differences
Associated Readings from the Text.Please look at: Chapter 15, pages 496-517.The Sun's Behaviour: Two Possibilities.It is obvious and incontestable that the sun is radiating away energy. Given that, and the finite supply of energy, there would seem to be two logical possibilities, based on everyday experience. Slow, steady cooling: Think of a pie which has just been removed from the oven. Since nothing now acts to keep it hot, it will cool off gradually as it radiates away its energy. In like fashion, we should consider the possibility that the sun has no internal energy source at all. Perhaps it was just made hot, a long time ago, by some agency that no longer acts, and has been cooling off ever since. (Of course the sun differs from the pie in one very fundamental way: it was never inside an oven and externally heated like the pie was. Instead, it became hot because of the way in which it contracted into a ball under the influence of its own gravity.) But, regardless of the original source of heat, we might ask how long it would take before we might notice any significant change in the sun as it cools down. Is it gradually getting fainter, for example, or changing in colour? Will it turn into a cooler version of its present self, in much the same way as the pie becomes cool enough to eat? A constantly maintained temperature: To understand the other obvious possibility, think about the human body. Although we radiate heat into the air (which is why a crowded room with little air circulation gets very hot), our bodies do not cool down significantly because we have an internal metabolism which processes fuel - the food we eat! - to produce heat and energy, thereby maintaining our internal temperatures. Is the sun like that? Is there some internal energy source which keeps the sun hot for a long time, continuously making up for the heat lost from the surface, so that there are no detectable changes over many years? If we consider the steadiness of the sun over human history or over even longer times, perhaps we can conclude something about the possible energy sources within it. What keeps it going?The Paradoxical Behaviour of the Sun.The two possibilities we have just considered seem to cover everything. Since the sun radiates away energy, surely it either replaces that energy ( and stays hot) or it loses it (and cools down). But bodies the size of the sun do not necessarily act like the everyday objects we are used to, and in fact a bit of simple physics -- which I won't take you through -- yields the following rather surprising conclusion: the sun is incapable of cooling down! In fact, as paradoxical as it sounds, the loss of radiant energy from its surface means that it is destined to heat up still more, at least in the long run. This seems illogical! How can a loss of energy lead to a rise of temperature? To understand this, we really have to recognize the important difference between the pie and the sun -- and the role of gravity. Consider the pie recently pulled from the oven. As it cools down, it maintains its shape and size because it has internal rigidity and structural strength, provided by the electrical bonds between adjacent atoms. It has a well-defined crust, lumps of apple, and so on, and remains recognizably a pie even if it cools down to a very low temperature. As we first saw in Phys 015, this kind of reasoning cannot be extended to objects as large and massive as the sun and the stars. The sun simply cannot slowly turn into a cool version of its present self because of its self-gravity. Here is why: If the sun were to lose a large fraction of its internal heat energy, this would mean that the particles within it would then be rushing around less rapidly and would provide less sustaining pressure to support the weight of the outer layers pressing down on it. The consequent fall in pressure would lead to the sun contracting under the influence of its self-gravity. And here we find the paradox. The very act of contraction of the sun would lead to the conversion of gravitational potential energy into heat, so the loss of energy from the surface of the sun would actually lead to its heating up rather than cooling down! Why a heating up? It is because only some of the converted energy gets radiated away -- about half of it, in fact, in the ideal case. The rest of that released energy stays in the sun, raising the temperature. In short, any time a large self-gravitating object loses a lot of its internal energy, it will shrink and heat up. To appreciate the paradoxical nature of this, imagine feeling too hot and pulling off your woollen sweater. This strategy is successful, and you feel cooler since some of your body heat can now radiate freely and be carried off by air currents. You would be very surprised to discover that removing your sweater had the unwanted effect of making you feel hotter! But that is, in a sense, what happens to a star. If it succeeds in radiating away a lot of its internal heat, it loses the pressure support which is provided by the rapidly-moving particles within it, contracts, and gets even hotter as a result. Is this what the sun is doing? Maybe not -- we have to consider the alternative. It could be that the outward-flowing energy is being constantly replenished by an internal source, permitting the sun to maintain an equilibrium (unchanging) form over many millennia. Is that the case?The Ultimate Fate.Please note that even if the second possibility is correct right now -- that is, even if the sun is in equilibrium, with some internal energy source maintaining its present temperature -- the sun's fuel supply is limited, so eventually it must succumb to the sort of process described as the first possibility. In short, eventually gravity must win out. We will learn later what this is what happens to the sun after its fuel is consumed.Is the Sun Slowly Shrinking? Kelvin Contraction.As we noted before, the fossil record tells us that the sun has not changed much in luminosity over several billion years. This allows us to put some constraints on the possible energy sources within it -- and to consider, and then to reject, the possibility that it has no energy source at all other than a slow contraction under the influence of its own self-gravity. (Something else must be going on inside the stars.) But this rejection is a modern development. About a hundred years ago (before the discovery of the phenomenon of radioactivity, Einstein's theories, and a knowledge of the structure of the atom), the phenomenon of slow contraction was indeed thought to explain how all the stars behave! A British physicist named Lord Kelvin argued and believed that the gradual release of the sun's gravitational potential energy explained its continued heat and luminosity -- hence the name "Kelvin contraction." Moreover, most astronomers agreed with him. What led them to change their minds? Well, let us first ask how we might test Kelvin's proposition. You might think that this shrinkage would be obvious and directly measureable, but in fact it amounts to only about 1 cm per year, an immeasurably small rate. Remember that the sun is about 1.5 million kilometres in diameter, so this is clearly not a directly testable proposition. But before we discover what it is that dooms Kelvin's idea, let's remember that he was right in one context: Kelvin contraction was an important source of outflowing energy while the sun was forming. Here is the basic physics again: the sun started as a distended low-density cloud of gas in space this cloud then condensed (`collapsed') under the effects of gravity to form a denser lump, getting hotter as it did so because of the release of gravitational potential energy, but also radiating away some of that accumulating heat into the depths of space. (That's why young proto-stars glow at infrared wavelengths.) To start with, this collapse was quite rapid, with the atoms and dust particles `raining in' towards the middle and accumulating fairly quickly. But why did the collapse ever stop, leaving a ball of the size of the sun? Why did it not collapse down to a very dense, much smaller body? It is because the lump eventually got so dense that it became opaque: that is, the heat energy within it could not easily be radiated away to empty space since each photon emitted had a good chance of running into another atom. This made it hard for the gas to get rid of its heat energy, so a great sustaining pressure was provided from the random rapid motions of the atoms whizzing around. This pressure brought the collapse virtually to a halt. Everyone came to understand, and we still agree, that this explains how the sun first formed, fairly rapidly, as a hot ball, but Kelvin believed that this process was still important at the present day, although acting more slowly. As I will describe in the next section of the notes, we now understand that there are continuing thermonuclear reactions deep within the sun. But if some mysterious agency could instantaneously shut off all these reactions, the sun would not instantly die out. Instead, slow Kelvin contraction would take over again, and continue to keep the sun hot for a long time. But for exactly how long? Well, we now know that this is its fatal problem. The sun could only last about ten million years in a state of slow contraction. That was not a problem in Lord Kelvin's time, a century ago, because no one knew just how old the Earth was - radioactive age dating had not been developed (indeed the phenomenon of radioactivity was unknown). There were some very crude calculations made about the age of the Earth, using arguments based on the time it would take for rainwater falling on the continents to leach out minerals from the rocks and soil to produce the salinity we see in the oceans today. Such arguments were very uncertain, so Kelvin's idea was not easily refuted. It was thought possible, a century ago, that the Solar System really was only a few million years old. One argument against Kelvin contraction, by the way, was the Theory of Natural Selection (or Evolution) proposed by Charles Darwin. Kelvin himself discounted Darwin's theories because he thought the solar system could be at most ten million years old, and he felt sure that the great diversity of species we see around us could not all have evolved from primitive ancestors in such a short time. Although Darwin did not do so at the time, he could have completely turned the argument around! He could have (and perhaps should have) said that his theory and its evident successes imply that the Earth has to be much older than ten million years - as indeed it is. Eventually, of course, we developed techniques for dating rocks and minerals, and proved as a consequence that the Earth and Sun are much older than the brief lifespan allowed by Kelvin contraction. You may be interested to know that we can set some very modest limits on any changes in the size of the sun by considering eclipses. If the sun had been much bigger in the past, then the ancient Romans (say) would not have seen total eclipses because the moon would not have been big enough to cover the full face of the then-larger sun - they would have seen annular eclipses instead. Since we know that they did see total eclipses, we can be confident that the sun has not shrunk very significantly in size over the last few thousand years at least. But this doesn't help us very much: the Kelvin contraction would not show up over such a short span of time anyway. Thus we have no direct measurements which rule it out. The timescale argument is the critical factor.An Important Point About The Original Heat.As I have said several times already, gravity made the sun hot through the release of gravitational potential energy as particles `fell toward' each other in the originally-condensing sun. We will see later that this extreme heat allowed the nuclear reactions to begin. Most people (and many textbooks!) get this the wrong way around! They usually say that the sun is hot because it has nuclear reactions going on within it. This is backwards. Here is the correct way of considering it: The sun was made hot because of its contraction under self-gravity and the consequent release of gravitational potential energy. This would have been the case even if there were no nuclear reactions at all. This extreme heat allowed the nuclear reactions to start, in a way we will soon describe. The energy produced by these reactions now maintains the sun's heat (but did not originally produce it). Consequently, even if there were no such thing as nuclear reactions, we would still expect the universe to be full of hot star-sized lumps with typical lifespans of tens of millions of years, slowly contracting just as Kelvin hypothesized. In short, there would still be stars (but they would not be very long-lived). It is interesting to remember that the slow evolution of life to complex forms takes an enormously long time and depends on a steady and reliable energy source. Moreover, the heavy elements needed for planets and living creatures are the product of late stages of nuclear reactions within massive stars. A universe full of Kelvin-contraction stars would probably not contain advanced living species to observe the skies and speculate about origins.Another Possible Heat Source: Chemical Reactions.As a kid, I was taught that the sun was a `great ball of burning gases.' This always made me wonder how it could be burning in the vacuum of space, with no air to support the fires. Of course, the same argument could be applied to us here on the Earth! How can we light a campfire when we are surrounded by the vacuum of space? The answer to that, of course, is that the Earth has both the fuel and the oxygen `on board.' There is likewise no reason why the sun could not be (say) half coal and half oxygen with enormous fires raging. But this cannot be the principal energy source for the sun. Chemical reactions are merely those in which atoms and molecules find themselves in new arrangements, with some net release of energy. (For instance, carbon atoms and oxygen atoms combine to form carbon monoxide or carbon dioxide waste gases when a charcoal briquette burns in a barbeque). The total energy available through such processes is far too little to explain the longevity of the sun. So what can we conclude? Neither slow gravitational contraction nor ordinary chemical reactions can explain the sun's longevity, and some other more abundant source of energy must be invoked. That is the subject of the next section of the notes. Previous chapter:Next chapter0: Physics 016: The Course Notes, spring 2005. 1: The Properties of the Sun: 2: What Is The Sun Doing? 3: An Introduction to Thermonuclear Fusion. 4: Probing the Deep Interior of the Sun. 5: The Sun in More Detail. 6: An Introduction to the Stars. 7: Stars and Their Distances: 8: The HR Diagram: 9: Questions Arising from the HR Diagram: 10: The Importance of Binary Stars: 11: Implications from Stellar Masses: 12: Late in the Life of the Sun: 13: The Importance of Star Clusters in Understanding Stellar Evolution: 14: The Chandrasekhar Limit: 15: Supernovae: The Deaths of Massive Stars, 16: Pulsars: 17: Novae: 18: An Introduction to Black Holes: 19: Gravity as Geometry: 20: Finishing Off Black Holes: 21: Star Formation: 22: Dust in the Interstellar Medium: 23: Gas in the ISM: 24: The Size and Shape of Our Galaxy: 25: The Discovery of External Galaxies: 26: Galaxies of All Kinds: 27: The Expanding Universe: 28: Quasars and Active Galaxies: 29: The Hot Big Bang: 30: The Geometry of the Universe: 31: Closing Thoughts: Part 1:Part 2:Part 3: |
(Monday, 20 April, 2026.)
