The Properties of the Sun:
A Point-Form Summary.
This section of the course notes, and the associated PowerPoint presentation, make the following critical points:
we can straightforwardly determine many of the superficial properties of the sun, but it takes considerably more thought to work out what its interior structure must be
an analysis of the light emitted by the sun reveals its surface temperature, and the absorption lines in the spectrum of the sun allows us to determine its composition. (This is not straightforward: it requires a good understanding of the atomic physics. See sections 24-27 of the
Physics 015 course notes.) At least the outer parts of the sun are (roughly) 2/3 Hydrogen, 1/3 Helium, and just a few percent of everything else.
we determine the mass of the sun from the gravitational influence it has on the Earth and the other planets. (Re-read the section entitled
The Masses of the Other Planets and the Sun
in the Phys 015 course notes to remind yourself how this works.)
to work out the sun's true size, we need to know how far away it is. This reminds us that determining distances in astronomy is critical if we are to understand the true physics. We can do this within the solar system by using radar.
from the sun's known size and mass, we calculate that it is considerably less dense, overall, than the Earth, so it cannot be simply a scaled-up version of a rocky planet
the movement of sunspots reveals that the sun rotates differentially at the surface, which tells us in turn that it is not solid in the outer parts
the fossil record tells us that the Earth has had liquid water oceans for billions of years, so we infer that the sun's temperature and brightness have not changed drastically over that long time-span
to understand its long-lasting stability, we need to have a good understanding of its deep interior structure
fortunately, this is not an impossible problem. The enormous mass of the sun means that its self-gravity -- that is, the gravitational pull of its constituent parts on one one another -- fantastically dominates any imaginable source of support other than very high temperatures. No girders, molecular bonds, or internal crystalline structure could withstand the fantastic pull of gravity, and the sun must have a central temperature of 10-15 million degrees. (See sections 3 and 4 of the
Physics 015 course notes to understand the importance of self-gravity for objects as large as planets and stars.)
as a result of this high temperature, all the elements in the deep interior of the sun are fully ionized -- that is, all the electrons are stripped off the atoms, and we have a sea of free electrons and atomic nuclei rushing about. The interior of the sun, then, acts like a Perfect Gas, with particularly simple laws which describe the structure. This makes the analysis relatively straightforward!
Associated Readings from the Text.Please look at: Chapter 15, pages 496-517.The Sun's Luminosity.The sun is indeed a star, and so close to us that we can study it in enormous detail. In a later lecture I will describe some of its detailed properties, such as the sunspots and so on, but let us for the moment consider it as representative of stars in general. What are its global properties? We begin with a consideration of its total luminosity. In units you may be unfamiliar with, the sun emits four thousand million trillion trillion ergs per second. More familiarly, this is equivalent to the combined light output of four trillion trillion 100-Watt light bulbs. Most of this light just goes streaming off into the emptiness of space, but of course a very small fraction of it does hit the Earth. Indeed, the amount hitting the Earth is roughly equivalent to one kiloWatt -- a thousand Watts -- per square metre when the sun is directly overhead. This is the source of solar power: you can build a solar panel to collect that radiant energy and put it to use in an environmentally friendly way. But it would be naively optimistic to conclude that this would be an easy solution to all our economic needs, providing a nearly limitless source of clean energy. There are important technical limitations. For instance, if you could build a solar panel which is 10% efficient, which would be pretty good engineering, then you would need a panel one square metre in size (and a perfecly cloudless day) to get enough power to light up a single 100-W light bulb -- enough to light a small room. To do more ambitious things, like run an aluminum smelter or a huge factory, much less a whole economy, would require solar panels on really colossal scales. This is not a trivial engineering problem! Let's digress for a moment. It is interesting to realize that essentially all our power reserves stem from the sun, and in some indirect sense are `solar' as well. Consider that: Fossil fuels (oil and coal) are the products of ancient life-forms which used solar energy in converting raw materials to plant structures (or ate and digested those plants). Hydro-electric power depends on the fact that solar heating evaporates water which eventually falls onto high land and, as it rushes down to the sea, turns our turbines. Windmills which generate electricity work because of the strong circulation in the Earth's atmosphere which results from its active climate -- a climate which is driven and controlled by the arrival of sunlight and the redistribution of heat within the atmosphere, both vertically and from one latitude or topographic region to another. Great ocean currents can be used to drive generators, and these are driven by the same sort of physics: they arise fundamentally because of the differences of temperature in various parts of the oceans, thanks again to the different heating effects of sunlight at different latitudes. The rise and fall of the tides can be used in like fashion. As we have seen, this is not purely a solar effect since the Earth's tides are dominated by the much nearer Moon. Still, if we had no moon, the somewhat smaller solar tides would persist and could be used in exactly this way. Finally, consider the nuclear power plants within which the energy released by radioactive elements is used to heat water to steam. The steam is used to drive turbines which generate electricity. Given this description, there seems to be no link to the sun , but when we remember that the radioactive elements used in the reactors were themselves created in an earlier generation of stars, we can stretch the argument a little to affirm that all the power supplies on Earth stem in one way or another from the properties and existence of stars - which in turn would not exist were it not for gravity! Back to business! We have considered the luminosity of the sun; what of the stability of that luminosity? Has the sun varied much in brightness over centuries, millennia, or millions of years of history? The fossil record says no: it shows that there have been liquid oceans on the Earth for at least three billion years. What this means is that the sun has been neither very much hotter nor very much colder over all those aeons. In a way we will see presently, this single piece of information allows us to draw a really profound (and simplifying) conclusion about the structure of the sun.The Mass of the Sun.The mass of the sun, as deduced from Newton's laws, is two thousand million trillion trillion grams -- about three hundred thousand times that of the Earth. We work this out by asking how strong the gravitation of the sun must be to explain how the Earth, as far away as it is and moving as fast as it does, is constrained to move in a near-circular orbit around the sun. Please do not feel compelled to commit a number like the mass of the sun to memory! Once again, it is a big number, so let us put it into a helpful context by comparing it to the luminosity described above. The interesting result is that the sun produces about 2 ergs of energy per gram of material within it every second (on average, that is: some parts of the sun produce lots of energy, some produce none). To put this number in context, ask yourself about the human metabolism. A typical big person might weigh 100 kilograms, and the energy given off over the whole body (which, after all, is warm and radiating away energy) is about equivalent to that of a 100 Watt light bulb. Of course, a light bulb feels hotter than a human body because the energy is more concentrated, but the total given off is about the same, which I hope you will find plausible. What this means is that your body produces about ten thousand ergs per second per gram. (Again, this is an average value. Your fingernails and hair are inert, while other parts are metabolically more active.) In other words, your body is producing, gram for gram, thousands of times as much energy as the sun!! How can that be? The answer is that the sun contains a lot of energy (i.e. it is very hot) but only a tiny fraction of that leaks out. Most of the contained energy is trapped deep inside, below the big, thick, opaque outer parts of the sun. But very little actual energy generation is needed within the sun to replenish the bit that trickles out. It really is a scaling argument again! The sun has very little surface area relative to its huge volume, so only a tiny fraction of its heat energy can flow out. Your body is so much smaller that you lose heat very readily, and must burn up lots of fuel (food) to stay warm. As noted, even smaller warm-blooded animals, like shrews, are worse off still and have to eat voraciously to maintain their body temperatures. T The Size and Density of the Sun. This is easily measured once we know the distance (which we deduce from the delay in the return of radar reflections). We know how big the sun looks, in angular size, and we know how far away it is, so the diameter follows immediately. Combining that with the mass of the sun, we deduce that its average density is about 1.4 times that of water. This tells us instantly that the sun cannot be structured like a scaled-up version of a terrestrial planet - but it takes considerably more thought (as we will see) to go beyond that! For one thing, it must certainly be the case that the central density will be much higher, thanks to the outer material pressing down on the inner parts and compressing them.The Rotation of the Sun.The rotation of the sun was first detected by Galileo, who watched sunspots move across its face. We can still do that nowadays, of course, but we can also get a spectrum for the `left edge' and the `right edge' of the sun and determine, from the Doppler shift, that one side is coming towards us at a speed of about 1.3 km/sec, while the other side is going away at this speed. In other words, we can measure the rotation speed directly. This may sound rather uninteresting, but there is an important extra feature about the way the sun rotates. Here is an analogy: suppose you were on the moon, looking down at the Earth. You might notice that Kingston is due north of Santiago, Chile. You would then be very surprised to discover, a day later after the Earth had made one spin on its axis, that Kingston was well to the east of Santiago. Since the Earth spins like a solid ball, we do not see this kind of differential rotation. But the sun does show this (as do the gas giants: Jupiter, Saturn, Uranus, Neptune). The material at the sun's equator goes once around in about 25 days. Material at mid-latitudes, halfway between the equator and the poles, takes about 28 days. This tells us, as it does for the outer planets, that the sun is not solid, at least in its outer parts. (A little more thought, described below, tells us indeed that it must be gaseous throughout.)The Interior Structure of the Sun.The sun is in what physicists call "hydrostatic equilibrium" - that is, it is a fluid body which is not changing in size and shape as time passes: it looks much the same now as it did a billion years ago. Why is it in this state? Your first thought might be that it has some internal rigidity or complex structure that gives it stability, just as your skeleton holds you up and the strengths of minerals gives a mountain structural stability and rigidity. This cannot be the case for the sun. It is so enormous that its own self-gravity would completely overwhelm any structural bonds of the sort that give more familiar objects and materials their strength -- your arm, a tree branch, a mountain. For an object the size and mass of the sun, very simple physical arguments demonstrate that there is only one possible explanation for its equilibrium configuration: it must be terrifically hot inside, so hot that the random motions of the particles provides a sustaining pressure which can counter the pull of gravity. A quick and simple calculation tells us that the sun must have a central temperature near ten or fifteen million degrees. This is a really profound conclusion, for a few reasons. One is that it is nearly independent of the material the sun is made of. If the sun were pure platinum, pure hydrogen, pure oxygen, or some complex mix of many species, roughly the same temperature would still come out from basic physical arguments. The second point is that the conclusion does not require us to understand anything about the sources of energy within the sun! Whether nuclear reactions are going on or not is irrelevant: the only thing that can maintain the massive sun against a rapid inward collapse under its own gravity is the heat within it. (Even before physicists knew about nuclear reactions in stars, they knew it was hot in there!) The third implication is perhaps the most far-reaching. At temperatures of ten million degrees or more, the atoms are moving around so rapidly that collisions between them inevitably knock off all the orbiting electrons around the atomic nuclei, even for the heaviest elements like uranium (in which a nucleus with 92 positively-charged protons can hold on to the orbiting negatively-charged electrons very strongly). In class, I drew an analogy to car crashes. At modest speed, a car crash does little damage. At somewhat higher speed, passengers without seatbelts may be thrown from the vehicle. At extremely high speeds, even the seat belts do not provide enough restraint, and everyone gets thrown out! In the interiors of stars, the atoms move about so vigorously that the positively-charged nuclei cannot hang onto any electrons at all! In other words, the material within almost all of the sun (except the coolest outer parts) is completely ionized. This means that instead of big lumpy atoms consisting of a nucleus and a cloud of electrons, we have little tiny particles moving independently -- the atomic nuclei and the free electrons. These particles are so widely separated, relative to their own tiny sizes, that they obey a particularly simple law called the Perfect (or Ideal) Gas Law . Remarkably, the material at the very centre of the sun is ten times as dense as lead, yet the material there still acts in this particularly simple way. The happy consequence of all of this is that the interior of the sun is very easily understood, far better indeed than the very complex situation within the Earth, with its complications of crystalline structure, strengths of materials, and so forth. We understand the interior of the sun and stars better than we understand the interior of the Earth! This makes the subject of stellar physics surprisingly tractable. 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: |
(Wednesday, 22 April, 2026.)
