Dust in the Interstellar Medium:
A Point-Form Summary.
This section of the course notes, and the associated PowerPoint presentation, makes the following critical points:
astronomers once believed that there was negligible gas and dust between the stars, except in isolated large clouds. They were reluctant to believe otherwise since a distributed medium might lead to troublesome obscuration of distant stars -- as indeed it does
the ISM contains both gas and dust. The dust grains are small, but still contain many trillions of atoms so are very different from the gases which are present - typically a single atom
your expectation is that the dust should prevent some of the light of a star from reaching us, either by absorbing it or by scattering it off in some other direction (or both). It can be demonstrated that such effects exist. Indeed, stars a few thousand light years away (well within the confines of our own galaxy) can look very considerably fainter 'than they should' at that distance. We must find a way to correct for such effects if we are going to determine the correct distances to remote stars and galaxies
the scattering of light is best exemplified by the way in which the blue light of the sun is so much more strongly affected than the red light by the molecules of gas in the atmosphere, in a phenomenon known as Rayleigh scattering. This makes the sky blue, and explains the red sun at sunset
in the ISM, the dust is more abundant (relative to the gas) than in the Earth's atmosphere, and the scattering of light is not as strongly dependent on wavelength. This is a consequence of the size of the dust grains (comparable in size to the wavelength of light) but the qualitative result is still the same: blue light is (somewhat) more strongly scattered than the red light. As a result, remote stars will look redder and dimmer than they should
this is easily noted in remote hot stars. Their spectral absorption lines, formed by the atomic physics in the stellar atmosphere, reveal unambiguously that they are hot, and must be emitting a preponderance of blue light. But such stars often look red, thanks to the passage of the lgiht through the ISM. We know what the star's true colour must be (for its spectral type) and then compensate for the reddening and dimming effects
we would like to know more about dust grains, but cannot reproduce the conditions of deep space in any laboratory on Earth; neither can we yet send a probe out to collect samples. So our knowledge of their sizes, shapes, and compositions are all inferential and indirect
we know about the sizes because of the way light of different wavelengths is scattered. We learn about the shapes by noticing that the light of reddened stars is somewhat polarized. This tells us two things: the grains have to be somewhat elongated in shape, and they must be aligned
the only plausible mechanism for aligning the grains is that they must be responding to a weak interstellar magnetic field (which we know exists from other evidence)
there is no absolutely compelling or unique model of what the interstellar grains are made of, but there are some quite plausible models. There is some independent evidence, from the way certain wavelengths of light are absorbed, that at least some of the grains are made of silicates, but there may be carbon or iron flakes as well. The grains are almost certainly coated with icy mantles of some sort
Associated Readings from the Text.Please look at: Chapter 19, pages 603-609.The General Interstellar Medium (ISM).There is no obvious reason why there should necessarily be any material between the stars. It could be, for instance, that when the galaxy formed, all the gas was turned very efficiently into stars, leaving the intervening space essentially completely empty. A century or more ago, however, with the development of the science of spectroscopy and the use of photography, astronomers came to realize that there was certainly some material between the stars, in the form of clouds of gas, or nebulae. (The Latin word for cloud is `nebula.') But the naive hope was that these were simply isolated clumps in a generally empty universe. One way of understanding this point is to imagine a blue summer sky with a few fluffy cumulus clouds in it. You can not see the widely distributed molecules of water vapour between the clouds: the water is conspicuous only where it is condensed into droplets in the fluffy clouds. Yet it can be fairly straightforwardly demonstrated that significant amounts of water vapour are distributed widely throughout the atmosphere, even between the clouds. Early astronomers thought, and indeed hoped, that interstellar space was different -- they acknowledged that there were gas clouds here and there, but assumed that the intervening regions were essentially perfect vacuum, devoid of any significant amount of material whatsoever. Why do you suppose astronomers hoped that interstellar space was essentially empty? The main reason is that if there is a lot of gas out there, there is likely also to be other material (like bits of dust and so forth), all of which might absorb the light from the distant stars and make them look deceptively faint (and possibly of a deceptive colour). This would complicate any astrophysical interpretations, and also mess up distance determinations, so there was a general reluctance among astronomers to accept that the situation was as messy as we subsequently found it to be. In retrospect, this blind trust was quite misplaced. There was lots of evidence, some of it in the form of the pictures I showed in class, for large amounts of widely distributed interstellar junk. But it took until the 1930s before this was acknowledged, with resignation, after the evidence became incontrovertible.How Might Interstellar Material Make Its Presence Known?In what follows, I will considering the two main components of the ISM: 1 2 dust, and 3 gas. These are distinguished in quite simple fashion, in a way which is easily understood by analogy to our own atmosphere. In the air in the lecture room, we find many free-moving atoms (like argon) and simple molecules (like oxygen, carbon dioxide, nitrogen, and water, each of which consists of no more than two or three atoms). In this gas, we occasionally find intermediate-sized molecules (such as the very complex molecules of aromatic oils used in after-shave lotions or perfume) but these are rare. We also find small solid objects, like tiny bits of chalk dust or bits of pollen, floating in the air. Although tiny, each of these solid bits consists of literally trillions of atoms. So too in the interstellar medium. In the gaseous component, we find single atoms of the common elements -- hydrogen being the most abundant -- or occasional very simple molecules. (In special circumstances, deep within clouds, we find some extremely complex molecules, but they do not survive in the general interstellar medium.) The dust grains, of which we will learn more later, consist of trillions of atoms in the form of small solid flakes. Now, how will each kind of material might make itself known? In simple terms, it might: 1 2 absorb radiation, or 3 emit radiation. Let us explore all these possiblities, beginning with a consideration of the dust.Dust: The Dimming of the Stars.What would happen if interstellar space were filled with something like pieces of soot? Well, depending on the total numbers of soot particles, it is clear that at least some of the light from distant stars would not reach us: any photon which happened to run into a bit of dark soot would not get through. That is, the star would look dimmer than it would if space were truly transparent. The problem is that we so often rely on the apparent brightnesses of stars to determine their distances. (That's not invariably the case, of course. The distances of the nearest stars can be determined by direct parallax measurements. But there are countless others whose distances really depend on a direct intercomparison of their apparent brightness with the brightness of a nearby star of the same spectral type, one whose distance is already known.) If a star looks ``too dim'' because of the presence of dust, we will mistakenly assume it to be farther away than it is. (Driving on a foggy day presents an analogous everyday experience. The droplets of water block some of the light, and everything looks dimmer, with potentially serious consequences. For instance, as you approach a red light, its faintness may persuade you that it is far off. Too late to stop, you shoot straight through the intersection!) Please recall just how important it is for us to work out the correct distances of stars if we are to draw reliable astrophysical conclusions! It is no exaggeration to say that a whole set of determinations -- the mass of our galaxy, the scale of the universe, and so on -- can be undermined if the ladder of distance determinations is undermined by our neglect of the dimming effects of the interstellar 'fog'. Indeed, we will learn that this was a serious problem in the first determinations of the age of the universe, for reasons that will become clear. How might you demonstrate and measure the effect of interstellar obscuration for stars? Here is one (somewhat over-simplified) way of going about this: Find a star which has a spectrum absolutely identical to that of the sun, so that you can assume it is identical to the sun in all respects, including its intrinsic brightness. Determine the distance of this star from its parallax. (The dust will have no effect on the way the angles seem to shift about as the Earth orbits the sun, so the parallax gives the true geometrical distance. ) Knowing its distance and true brightness, calculate how bright it should look. If it looks much fainter than this, you may safely conclude that there is dust between us and it. Is the problem of interstellar obscuration a significant one? You might think not, since we can see distant stars and galaxies! That would seem to suggest that interstellar space is quite transparent. Indeed, dust grains are rare in the ISM. Within the galaxy, there are, on average, only about one thousand of them in each cubic kilometer of space (although there are regions of much higher density). Still, the distances to the stars are so vast that as we look along this enormous line-of-sight the chances are very good that quite a few of the photons flowing our way will bump into a dust grain. In fact it can be shown that along a randomly chosen line of sight, a star a few thousand light years away will be dimmed to about half the brightness one would expect. This sounds surprising, because it makes one wonder how we can see remote galaxies tens or hundreds of millions of light years away! If half the light is lost during a passage of a few thousand light years, how does any light from the remote galaxies reach us? The answer is that intergalactic space is much more transparent than the spaces between stars within a galaxy. When we look out of the Milky Way towards the boundaries of the observable universe, we are looking through a space which approximates what earlier astronomers naively assumed would be the case: a near vacuum, with no troublesome 'fog'.Why is the Sky Blue?Many people believe that the sky is blue because we are seeing some sort of reflection of light from the blue ocean. This is quite wrong! Even if the Earth had no oceans at all, and was covered completely with green grass or grey rocks, the sky would still be blue. The blue colour arises from the way light is scattered by the molecules of air (not the dust particles). Light from the sun contains all wavelengths, from blue to red, but as the light enters the atmosphere, the short-wavelength blue light is much more likely to be scattered than the long-wavelength red light. (See page 305 of your text.) This phenomenon is known as Rayleigh scattering, and depends on the fourth power of the wavelength (in fact, the inverse of that number, which is why the shorter wavelengths are more likely to be scattered). I don't care if you remember that dependence, except qualitatively, but let us consider the numbers for a moment. Red light has a wavelength about twice that of blue light. Since two-to-the-fourth-power is sixteen, this means that blue light is scattered sixteen times as efficiently as red light. This strong dependence explains the deep blue of the sky. The Rayleigh scattering arises because of the complex interaction between the electromagnetic waves and the atmospheric particles (the atoms and molecules of gas). The really critical factor is the size of the scattering particles relative to the wavelength of the light. This explains some everyday phenomena: If you glance up at the sun, you discover that it looks yellowish. The light from the sun has to pass through one `atmospheric depth' to reach you. Some of the blue photons are scattered away, but the net effect is not large. You are seeing the true colour of the sun. When the sun is low on your horizon, as at sunset, its light has to pass through a lot of atmosphere to reach your eyes. This means that the cumulative scattering effects are more pronounced. Most of the red light gets through, while much of the blue light is scattered in various random directions. The sun looks quite red. Suppose the sun is high in the sky, but you are not looking towards it but rather in some other direction. Red light from the sun continues on its way essentially unimpeded, but the blue light from the sun gets scattered in various directions, some of it towards you. The sky looks blue in that direction.Expectations for the ISM - and the Reality.As well as the occasional dust grains, the ISM contains atoms and molecules in gaseous form, so you could visualise it as being like a very tenuous planetary atmosphere with small solid particles ('pollution') suspended in it. For that reason, you might expect the passage of photons through the ISM to be rather like that of light passing through the Earth's atmosphere, with blue light more readily scattered than red light according to the Rayleigh scattering law. Does this mean that the remote stars will inevitably look as red as the setting sun, since we are looking through a long path-length of intervening material? In fact, that is not quite what happens. Interstellar space is actually quite dirty, with a surprisingly large amount of dust compared to the gas content. Indeed, if you were to scoop up an enormous volume of interstellar space and condense it until it was as dense as the air in the lecture room, you would not even be able to see your hand at the end of your arm! By contrast, dust-like particles are considerably rarer in the Earth's atmosphere, even in locations like Los Angeles on a smoggy day. (This cleanliness and transparency arises because rain falls through the air and literally washes small grains out of it. There is no equivalent cleaning process in the ISM.) The consequence of the relatively high abundance of dust in the ISM is that there are indeed changes in the perceived colours of the stars, but the effects do not have the strong wavelength dependence that we find in Rayleigh scattering. This is a direct consequence of the typical sizes of the particles relative to the wavelength of light, and indeed this consideration provides the best information we have about the sizes of the dust grains. What we learn is that the particles in the ISM are quite small: they are about a tenth of a micron across (a micron is a millionth of a meter), which is comparable to the wavelength of light. This is very much smaller than a typical water droplet in a cloud, and even smaller than a piece of soot which comes out of a fire, but very much larger than a single atom or molecule. In the end, the 'dust' in the ISM produces effects which are qualitatively similar to that in the Earth's atmosphere -- blue light is scattered more readily than red light as it passes through the ISM -- but the effects are much less dramatic, and a different law is obeyed. To be precise, blue photons are only about twice as likely as red photons to be scattered, rather than the factor of sixteen we saw above. At the other end of the size scale, even larger particles, like droplets of water in a fog, absorb light of all wavelengths indifferently, which is why a fog makes things look grey.The Interstellar Reddening.When we considered the effects of the Earth's atmosphere, we recognized two equivalent ways of thinking about it. The scattered light makes the sky look blue when we look in a direction which is not straight towards the sun. But the same scattering process preferentially removes blue photons from our line-of-sight when we look straight at the sun, so the sun looks somewhat redder - an effect which is most obvious at sunset. When astronomers study the night sky, they do not usually look `between the stars' in directions where there is nothing much to be seen. Since astronomers look directly at the stars, it makes more sense to think about the reddening effects. To be specific, therefore, let us imagine a star sending one million red photons and one million blue photons towards us along a path through the interstellar gas and dust. For every red photon that is likely to be scattered off to the side, then two blue photons are likely to be scattered. If there is enough dust along the line of sight to scatter one thousand red photons, then about two thousand blue photons will be scattered. If 100,000 red photons get scattered, 200,000 blue photons will be scattered; and so on. You can see what will happen: the proportions of red and blue light are affected. If there is a lot of dust between us and the star, it will as a consequence look redder than it would if the ISM were transparent. This phenomenon is known as interstellar reddening. Since the scattered photons are no longer travelling in our direction, fewer photons in total reach us than would have made it through a clear interstellar space, and the star also looks fainter than expected. Reddening and dimming go hand in hand, and a knowledge of one can tell us about the other.Correcting for the Effects of Interstellar Dust.Imagine getting the spectrum of a distant star. The interstellar dust scatters out many of the very blue photons, some of the yellow photons, and a small fraction of the red photons. Although this changes the general colour of the star, the pattern of absorption lines in the spectrum of the star remains detectable . You can see why this is important. The absorption lines might tell us, for instance, that the star we are looking at is a particularly hot `O' star. But suppose the star looks red to the eye (or, more precisely, that it can be quantitatively measured to be delivering a relative overabundance of red photons and not many blue photons). This is surprising! The absorption lines can only arise in the atmosphere of an extremely hot star: that's an inescapable consequence of the fundamental atomic physics. Clearly, there must be dust along the line of sight, to explain the anomalous colours. How do we correct for it? Well, comparing the colour of the star to that of an unaffected O star allows us to calculate the total reddening effect of the dust, and the relationship between reddening and dimming also allows us to work out just how bright the star would have looked if space were transparent. This allows us to work out its correct distance, undeceived by its misleading faintness.Dust in Dark Clouds.So far we have talked about the effects dust would have if it were widely distributed through all space. But here and there the gas and dust is clumped together in small (or not so small) clouds. When there is a sufficient density of material, the light from remote stars is dramatically obscured. That is, we see a dark patch in silhouette. A couple of examples can be seen on pages 611-612 of your text: here we see the dark clouds in the starry sky. There was a time that astronomers thought that these were literally holes in the distribution of stars, that they were looking through `tunnels' in the galaxy and seeing the empty void beyond. Such silhouetting effects are most noticeable in regions where there is lots of glowing gas, regions like the Orion nebula: see page 610. The dark wisps we see across the face of the nebula are regions of localized higher density where the dust is thick enough to block off much of the light from behind.Dust in Reflection Nebulae.Dust shows up in another way too. Look again at the picture of the Pleiades cluster on page 537 of the text. The stars seem to be surrounded by blue wisps of some kind. The reason is that the stars in the Pleiades cluster are within a cloud of gas and dust, and the light travelling 'sideways' from the stars is scattered and redirected our way by the dust particles -- with the blue photons more strongly affected than the red ones. This give rise to the 'reflection nebulosity' which we see in the Pleiades and elsewhere.Direct Samples? No Way.We have determined, inferentially, that there is dust in the ISM. We would now like to know more about it. What is it made of, what shapes and sizes does it come in? You might think that there would be two obvious ways to try to answer such questions: in a laboratory, simulate the conditions which we find in interstellar space, and test the properties of various materials under those conditions; or send a rocket out into interstellar space to scoop up a sample. Both of these approaches turn out to be utterly impractical. Let us think about why. To address the first of these, let us compare the conditions in the lecture room, in a vacuum tank in a physics laboratory (a `hard vacuum' being the best we can produce on Earth), and in typical interstellar space. (Do not commit the following numbers to memory!) In the lecture hall, there are about ten trillion trillion atmospheric particles per cubic meter, most of which are molecules of nitrogen and oxygen. Their average separation is only about one nanometer - one billionth of a meter. You can understand why it is that these particles are in a constant state of collision with one another. In a vacuum chamber, we can pump most of the particles out. In fact, out of every ten million atoms present in the original gas, we can pump out all but one if we use the best available technology. However, this still leaves about one million trillion particles per cubic meter - a `vacuum' which is a trillion times denser than interstellar space! Our inability to do any better than this has an immediate consequence: if we want to understand the physical processes happening in the near-vacuum of the ISM, there is no way we can carry out realistic experiments in our laboratories. In interstellar space there are only about a million particles per cubic metre; on average, they are separated by about 2 centimeters (an enormous distance compared to the size of the atoms). In addition to the gas particles (simple atoms and molecules), the interstellar medium also contains dust which makes up about one percent of the total mass. (Please notice, by the way, that this fraction does not mean that one in every hundred `lumps' in space is actually a dust particle, with the other ninety-nine being atoms or small molecules. In that case, we would say that the ISM is one percent dust by number.) Instead, the dust particles are very rare indeed. In fact, as we have seen, there are only about 1000 of them per cubic kilometer of space. This point is important, so let me emphasise it with a simple analogy. Suppose you took a huge scoop of sea water and somehow determined that it contained life forms of two sorts: blue whales and microscopic plankton. If you could also work out that one percent of the total mass was in the form of whales, this certainly would not imply that there is one whale for every ninety-nine plankton. The whales would be very rare. Likewise, in the ISM the massive dust particles are rare. The scarcity of the dust grains explains, in part, why we would find it difficult to scoop up reasonable samples. For other reasons, however, that prospect really is hopeless. We would need to send a rocket way out past the planets to get a true sample of the ISM, uncontaminated with the sort of rubble and dust which we find within the Solar System; and we would have to bring this sample back home, taking care that it did not get contaminated as we did so. This is ridiculously beyond any practical capabilities we possess at present. (There is, however, an interplanetary probe now in space with the goal of collecting bits of material from a comet which it will come close to.) I have already explained how we know about the sizes of the grains. -- they scatter blue light more effectively than red light, a phenomenon which is controlled by the size of the grain relative to the wavelength of light. But how can we ever hope to draw any other sensible conclusions about the physical nature of the dust in the ISM? There are ways.Shapes and Orientations: The Polarization of Light.In Physics 015, in discussing the nature of light, I demonstrated the behaviour of polarizers, and used the phenomenon of polarization as evidence for the wave nature of light. Here, we will turn the argument around. If we see polarized light, what can we infer about the material through which the light has passed? When we look at the light of remote stars, we discover that it is somewhat polarized - not a great deal, but measureably. Moreover, the amount of polarization is highest in those stars which are the most reddened, so the inference seems inescapable that the dust grains are the cause. What does this tell us? There are some immediate implications: The dust grains cannot be perfectly spherical, with no features which distinguish one part from another. If the grains were perfectly spherical, then there would be no way for light passing by to `know' which polarization of light should get through and which should not. Careful analysis of the observations seems to imply that the grains must be somewhat elongated, like little stubby footballs (although probably not so symmetric as that: they are probably quite irregular). The grains must also be aligned, with the vast majority of them pointing in nearly parallel directions, over quite a large region of space. If they were individually oriented at random, then there would be no net polarization: one grain would tend to cut out a bit of the left-to-right wave; the next might cut out a bit of the up-and-down wave; and so on. So the grains cannot be oriented completely at random. This second thought seems to pose a real problem. If the dust grains are so widely spread out (only a thousand of them per cubic kilometer), how can we possible arrange for them to be lined up, like a lot of little parallel footballs floating freely in space, over distances of trillions of miles? What could possibly influence them in this way?Controlling the Grains: What Doesn't Work.In class, I invited speculation as to what might control the grains. Before we look at the correct answer to which we worked our way, here are some other thoughts: One guess might be that gravity is responsible for aligning the grains. (After all, it plays such an important role in all of astronomy.) Is it possible, for instance, that the grains all align themselves along the direction of the local gravitational field, pointing towards a nearby massive star or the center of the Milky Way? Perhaps the grains are in the middle of a gentle `wind' of atoms moving through space, a wind which provides a pressure which tends to line them up? Just to explore these possibilities a little further, in preparation for my saying that they do not explain what is going on, think of the following analogy. Visualise a bomb dropped from an aircraft. Before it is released, the bomb is horizontal (at least, that is how they are usually mounted in the bomb bays). You have perhaps seen films which show the bombs tipping over into a vertical position once they are released. The bombs then fall that way thereafter, nose downward. Why does this happen? You may have reasoned that the nose drops because that is the heaviest part of the bomb. But that is not correct. You must remember that heavy and light things fall equally under the influence of gravity: there is no tendency for the heavier nose of the bomb to `get ahead' of the less-massive tail. Indeed, if there was no atmosphere, the bomb would continue to fall in the orientation it had when you released it. No, the reason a bomb falls nose-first is that it is designed to do so when acted upon by the air resistance it encounters as it falls through the atmosphere. Bombs are streamlined and have little fins on their tails to encourage and control this behaviour, which helps the bomb stay on course towards its target. This example shows that a combination of atmospheric influences (like a `wind') and motion under gravity can be important in certain contexts - but not for dust in the ISM. We can rule out such effects quite easily, as follows: Gravity would not make the dust grains line up. Any individual grain sitting in a random orientation in space will maintain that orientation (unless something collides with it). There will be no tendency for any grain to turn towards the largest mass in the vicinity. Nor can stellar winds explain the effect. (I remind you that stellar winds are streams of particles emitted from the surfaces of stars. The Earth, for example, is under constant bombardment by charged particles from the sun, an effect which causes the Northern Lights.) While it is true that a strong stellar wind would have some effect on grains in the star's immediate vicinity, the problem is that our observations tell us that all the interstellar grains in some huge region of space have to be aligned, which requires a coherent influence over a vast volume. The wind from each star would affect only the grains in the vicinity of that star, so there is no way to understand the large-scale alignments needed to impose the observed polarization effects.Controlling the Grains: What Does Work.What other influence can act over such wide distances? Let me give you a hint. Think of all the compasses in all the boy-scout and girl-guide kits in Canada. They are all pointing the same direction, even though they are not interacting with each other in any way. Yes, the actual answer is that the grains have certain magnetic properties, and they tend to line up in the weak interstellar magnetic fields in a way which is analogous to compasses on the Earth all pointing in parallel. So the implications are two-fold: There must be a generally-distributed weak magnetic field (about a millionth as strong as that of the Earth) in interstellar space. As it happens, there are other ways of demonstrating this as well, so we know this to be the case. Moreover, the grains themselves must have certain magnetic properties, so that they `line up' like the boy scout compasses. These properties allow us to determine what the grains could be made of, within certain broad constraints. With respect to the composition of the grains, I should emphasise that there is no absolutely right model! Moreover, there is no absolute guarantee that every dust grain is like every other one. No doubt there are a range of sizes and probably of compositions as well.The Composition of the Grains.Putting this all together, astrophysicists have suggested that the grains could consist of one or more of the following: iron-rich materials? (which is probably what you first thought of when the magnetic fields were mentioned). You can visualise a grain as a small sliver of some iron-rich mineral. graphite? (i.e. a form of carbon. Ordinary `pencil lead' is graphite.) silicates? (i.e. silicon oxides) perhaps some mixture of these? and the grains might well be surrounded with a `mantle' (coating) of some icy substance like frozen methane (CH 4 ), ammonia (NH 3 ), or water (H 2 O). These suggestions are reasonable in one important sense: carbon, silicon, oxygen and iron are all quite abundant elements. If someone were to suggest a model in which grains contained a large amount of europium or yttrium, say, (both of which are quite rare elements), you would be dubious! The main point of the discussion, then, is that although we don't know the composition precisely, there are reasonable models incorporating some of the more common elements. There is yet more evidence that we can appeal to. If we look in detail at the way the light from a remote star is dimmed as it passes through the interstellar medium (comparing it to the light from a similar undimmed star nearby) we make the following important discovery: There is very little extinction (dimming) at large wavelengths -- that is, the red light passes through fairly readily. But at shorter (bluer) wavelengths, the extinction increases, as we have already described. There is an extra amount of dimming, a `bump,' at a particular wavelength in the ultraviolet part of the spectrum. That is, light at this wavelength is very readily absorbed. This feature is called the `silicate bump' because laboratory experiments show that silicates have this optical behaviour (although there could be other explanations too). At this stage, you may feel dissatisfied with the sketchiness of our knowledge, but consider: we are able to make certain confident remarks about the size, shape, orientation, and (within limits) composition of tiny grains which are now and perhaps for ever beyond our grasp. I think this is remarkable! 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.)
