An Introduction to the Stars.
A Point-Form Summary
This section of the course notes, and the associated PowerPoint presentation, makes the following critical points:
when we move from the Solar System (the topic of Physics 015) to the realm of the stars, we are taking an enormous step in scale. The planets, moons, asteroids, comets, and the sun form a compact grouping in which (for example) the gravity of Jupiter has an important effect on the motion of Mars, and asteroids may collide with planets with disastrous consequences. By contrast, the individual stars are separated by huge distances and do not interact with one another
they do affect each other collectively, however: any given star moves in the Milky Way in response to the combined gravitational influence of all the others
moreover, there are circumstances (binary stars, clusters of stars) where there are closer interactions. But in general a single star leads a life of quiet isolation
we can study the motions of individual stars in two ways:
watch slowly changing postions, thanks to sideways motions; or
use the Doppler shift to measure radial velocities (towards or away from us)
from the patterns of motions, we can infer that the sun is travelling at a speed of about 30 km/sec through the general distibution of stars in the solar neighbourhood
with this kind of characteristic speed, a statistical analysis confirms that collisions between individual stars will almost never occur, even given the billions of stars in our Galaxy
the most obvious thing about the stars is that they differ in apparent brightness. Of course, this could be because they are all identical but at a variety of different distances; on the other hand, there may be real differences between the stars. We need to determine the individual distances in order to address that question
astronomers describe the brightnesses of the stars using an unfamiliar scale of magnitudes, which many people find confusing. You do not need to know about magnitudes, but it is a concept you may encounter in your readings
the magnitude scale had its origins in ancient Greece, although it has subsequently been more precisely and mathematically defined, and has the following features:
fainter stars have numerically larger magnitudes;
the magnitude scale can be negative or positive (just as the Celsius temperature scale can be);
there is nothing special about a magnitude of "zero" - a star with this brightness is merely a relatively bright one, like Vega
stars have different colours, which means simply that they produce different proportions of red and blue light. A cool star produces mostly red light; if it were to get hotter, it would produce more light overall, but the balance would shift to the blue
in general, this means that the colour of a star is a good indicator of its temperature. The problem is that the colours can be affected by intervening gas and dust. This is analagous to the way the sun looks red at sunset, when it is low on the horizon and seen through a lot of the Earth's atmosphere. For the stars, however, the problem is caused by interstellar material
on the other hand, if you can spread the light of a star out into a spectrum, the pattern of absorption lines you see will tell you the truth about the temperature. A hot star has characteristically different absorption lines than a cool star. If such a star is deceptively red in colour, there must be intervening gas and dust -- which will also make the star fainter than expected
Associated Readings from the Text.Please look at: Chapter 16, pages 521-539. (You can ignore the mathematical insights.) page 612, for a striking image of the interstellar medium (the gas and dust between the stars)A Change of Scale.As we leave the Solar System and begin our study of the stars, we encounter a complete change of scale. On pages 10-13 of your text, you will find some numbers which make the following profound point: the distances between stars are so vast that separate stars can safely be treated as discrete points which essentially never interact one-to-one. (I hasten to qualify this remark by noting that there are real binary pairs of stars, those locked in a mutual gravitational embrace and thus in close orbit around each other. There are many such, but for the moment we restrict our attention to the immense numbers of single stars.) What exactly does this isolation imply? First of all, I do not mean to suggest that the presence of the other stars is not important! The sun, for instance, moves in a huge orbit around the Milky Way galaxy, an orbit whose shape is determined by the combined gravitational influence of all the other stars. But as the sun moves, it never comes close enough to other stars that they, as individual objects, influence us in any significant way (except for the modest qualification I will offer you two paragraphs further down the page). Consider, by contrast, what we learned about Mars in Physics 015. Its proximity to Jupiter, which is the most massive planet, means that Mars's orbit gets perturbed quite a bit over the millions of years. As a result, Mars suffers dramatic long-term climatic changes. In like fashion, it can be shown that if something as massive as a star were to pass very close to our Solar System -- say, just outside the orbit of Pluto -- its enormous gravitational influence would surely perturb and change the orbits of all of the planets, including that of the Earth, and we might in fact even hurtle off into the depths of space in some new orbit. In fact, however, this is too unlikely to be any kind of a worry. The stars simply do not undergo such close encounters. Please remember, though, that the effects may not be utterly negligible for all time! As we learned, comets may fall into the inner Solar System from the Oort Cloud (far out beyond the orbit of Pluto) when a passing star at some intermediate distance perturbs the orbits of some of the far-flung icy remnants found there. So the individual stars nearest the Solar System do have some effect on us, an effect which is fortunately modest -- except that you should perhaps blame those stars for throwing in the comets which lead to the infrequent catastrophic impacts on the Earth every few hundred million years! But the isolation has a more profound meaning. When we try to understand how a single star will change over time, as its nuclear fuel is consumed, we will not need to worry that it will be influenced in any important way by its neighbouring stars and other things in its surroundings. This is a great simplification, as we will see. (By contrast, for the aforementioned binary stars, the complications can be literally life-threatening for the stars concerned.) The vast distances between the stars encourage us to use more sensible units of measurement than the familiar miles and kilometers. Even the astronomical unit, the distance which we use to measure the distances of the planets from the sun, is far too small. Instead, we introduce a new unit: the light year, the distance light travels in a year. This is about 6 trillion miles, or ten trillion kilometers. By the way, many people mistakenly think that this is a unit of time, but it is not. We speak in an analogous way when we describe Toronto as being ``about three hours from Kingston,'' meaning that we can drive there in about three hours. The nearest star is about 4 light years away, meaning that light takes four years to reach us from it.The Isolation of the Stars.Let us think a bit more about the isolation of the stars by considered both their ordered and their random motions. The stars in our galaxy share a general motion like that of an enormous pinwheel, with the stars in the solar neighbourhood moving along together at about 250 km/sec as the galaxy rotates. (As we will learn later, we are very far from the centre of the Milky Way galaxy.) To visualise this, picture all the cars in the westbound lanes of Highway 401 moving roughly in parallel across the top of the city of Toronto. They share an ordered motion of about 100 km/h. Of course, if they moved exactly parallel and at identical speeds, they would never come close together, one to another, or drift farther apart. In fact, however, they have small random motions as well: there are cars changing lanes, speeding up, slowing down, swerving to avoid a pothole on the roadway, and so on. Thus their various separations and relative motions change as time passes. For the stars, a typical random velocity is about 20-30 km/sec. This is about how fast the sun is moving with respect to the other stars in the `solar neighbourhood.' Now the nearest star to us is about 4 light years away, about 25 trillion miles. If that star were directly ahead of us, the sun's motion towards it could bring about a collision in no more than about 30,000 years. Why, then, are there not collisions between stars as frequently as that? (A digression: a speed of about 20-30 km/sec is also about as fast as we can fire space probes out of the Solar System with present technology. This means that it will take tens of thousands of years for such probes to reach even the nearest stars. The implications for interstellar travel are obvious and sobering.) On the highway, of course, drivers take evasive action. If they are travelling faster than the general flow of traffic, they pull out from time to time to overtake, or they put on the brakes as needed to avoid rear-ending another car. But drivers face these problems because the cars are big compared to their separations: one car may be only a few car-lengths away from another. Imagine replacing each car by a grain of sand and you can see that the chances of any sort of collision would be much reduced. There would only be a collision if one grain of sand was moving very precisely towards another, with not the tiniest bit of mis-aiming. The situation in the Milky Way is rather like this: the stars are tiny relative to their enormous separations. Moreover, the other stars are, in general, neither at rest nor directly in front of us. Our motion is taking us towards no nearby star in particular, but even if it were that star would be moving in some random direction as well, so by the time we get to where it is now it will be long gone. We will only suffer a collision if our motion happens to bring us to some remote point in space at exactly the same moment that some other star also moves into that vicinity. So a much more careful statistical calculation is needed to work out how likely it is that any stars will collide in the Milky Way. This turns out to be almost never: over the life of the galaxy so far, it might have happened once or twice at most. (This was a factor in Physics 015 in our discussion of the possible origin of the solar system.) Moreover, it is more likely to happen in the crowded central regions of the Milky Way than here in the outskirts, where the stars are more widely spread out. This long discussion has a pertinent point, already noted but worth restating. The wide separation of the stars, and their effective independence, allows us to consider a star as an isolated body, by and large. And again I don't just mean that we don't have to worry about collisions. I also mean that we don't have to worry about the external surroundings when we try to work out the structure of a star or calculate how its properties will change as it uses up its nuclear fuel (except for close binary stars).What Would You Like to Know?As so many times before, I think it is helpful to write down a `wish list' of things you would like to know about the stars. This may help us to direct our discussion in a profitable fashion. I would say that if you really wanted to understand how the stars work, you would want to determine: the distance . This is essential, if we are to say anything of real physical interest - like the total amount of energy being emitted, which tells us about the energy sources within the stars. Think of the sun, for instance: we have to know whether it is like a small bonfire just above our heads or some enormous energy source at a very large distance. the brightness, both apparent and absolute (or intrinsic ). In other words, we have to measure how much energy is being received here on the Earth from each star (its apparent brightness). Then, knowing how far away it is, we can correct for the effects of distance - even a bright star will look faint if it is farther away than average! - to work out how much energy the star pumps out in total, its absolute or intrinsic brightness. the temperature. As you know from the Wien displacement law, the colour of the star should give us an indication of this. Red stars are cooler in general than blue stars (although we will encounter complicating factors!). Determining the colours requires finding out the relative abundance of blue and red light, which really means nothing more than measuring how bright a star looks when it is observed through different filters. the entire spectrum. This represents an extension of the simple notion of measuring a star's brightness through different filters: we now want to see how much light is given out at each wavelength, in finer detail. As you know, analysis of the spectrum leads to a lot of other inferences. the motions of the stars through space. The `sideways' (transverse) motions result in changes in the apparent stellar positions, something we can keep track of over the decades and centuries. The `radial' (towards-or-away) motions are measured from the Doppler shift of the absorption lines in the spectrum. the masses of the stars. We derive the mass of the Sun from Newton's laws by observing how a small `particle' like the Earth is constrained to move under the influence of the Sun's gravity. For the stars, we must do something similar: we need to find a `test particle' whose motion is influenced by the star. We will see later how this is done. (Remember that we cannot see planets and asteroids orbiting around even the nearest stars!) the size and shape of a star its rotation rate. As is explained in the discussion on page 167 of your text, the rotation rate of a star can be deduced from the spectrum by an analysis of the widths of the absorption lines in its spectrum. Thus, even though the star looks like a fuzzy blob of light in which we cannot distinguish one side from the other, we can determine whether it is rotating, and at what speed, just from a consideration of the light we receive. its average density (from a knowledge of its mass and its size) its composition (from a study of its spectrum) its internal structure the energy sources within it (what keeps it hot) whether it is active (i.e. does it flare up, for instance) how and if it is changing at present as it slowly uses up its fuel how it will end up (die) when its fuel runs out its age how it formedEven More Questions.There are still some questions to be added, although they pertain not to the inner workings and nature of the stars themselves, but to other matters. Thus we add: do any other stars have planets around them? how do they interact with other stars? are they all separate, or are they found in pairs, groups and clusters? what is the large-scale structure? how are the stars distributed in space? You can see that there are many questions, and the path to the answers to some of them is quite complex. How, for instance, would you ever hope to know anything about the internal structure of a remote star? You will learn that there are ways.In the Absence of....When we drew up a list of things we would like to know about the stars, I pointed out that the distance is very important. Until we know it, we don't know how massive the stars are (except the sun), how much energy in total they are putting out, and so on. But there is still a surprising amount we can learn even without a knowledge of distances at all, quite a few of which I alluded to in my `wish list.' Let us consider some of those aspects a little more closely.Positions and Motions.For centuries, astronomers measured the positions of stars in the night-time sky, to various degrees of precision. (Remember the work of Tycho Brahe, for instance.) Even the non-scientific ancients - the `people in the street' - knew about the motions of the planets, since they shift about dramatically with respect to the field of background stars. This, of course, is the origin of the name planets, or `wanderers.' But careful scrutiny had shown, even as early as the time of Hipparchus in about 150 BC, that the patterns of stars themselves slowly change as the decades and centuries pass. If you come back to Earth many thousands of years from now, for instance, the familiar constellation of Orion will have a somewhat different form, thanks to these slow changes. This is because the individual stars are also drifting about in space. As I noted earlier, a typical star moves through space at a fairly rapid pace of about 20-30 km/sec. (Incidentally, that is also about as fast as the Earth moves in its orbit about the sun.) The reason that the stellar patterns change so slowly from our point of view, of course, is that the stars are so very far away. The true motion of a star carries it partly along our line of sight (with a speed which is called the radial velocity ) and partly across it (the transverse velocity ); see the discussion and figure on page 167 of the text. The radial velocity of a star is straightforward to determine. We can measure the Doppler shift of features in the star's spectrum to work out how fast it is moving towards or away from us, in real values like kilometers per second. Please note that there is no need to make two observations: we get the spectrum once, and the Doppler shift reveals the speed. (It is a common misunderstanding to think that you have to get the spectrum at some second time later on, and then look for differences of some sort. This is simply not so.) Moreover, you can do this just as easily for a remote star as for a nearby star: all you require is that the star be bright enough to allow you to get a good spectrum. The motion across the sky, by contrast, shows up as a change in position, a change in the direction in which we see the star, relative to its neighbours. This change is called the `proper motion.' Of course you should be careful not to be confused by the motions we see every night! The rotation of the Earth carries the entire pattern of starry constellations across the sky, but this has nothing to do with the motions of the stars themselves. The proper motions of the various stars are very small, and only recognizable after decades or centuries of observation as we see one star drift with respect to its fellows! Indeed, the very largest proper motion known is that of `Barnard's star,' which moves about half a degree (the apparent diameter of the full moon) every couple of centuries, relative to the patterns defined by the more remote background stars. In other words, if Barnard's star were conveniently located just beside the right-hand end of the belt of Orion (which it isn't), it would be seen to move across to the other side within a couple of thousand years. It is not possible to convert the proper motion of a star to a true velocity in kilometers per second unless you know the distance. In general, nearby objects have larger proper motions than their remote counterparts, as an everyday example will make plain. Imagine looking up into the sky at an airplane which is crossing the sky from one side to the other, taking perhaps two or three minutes to do so. Suddenly a fly whizzes across your field of view, passing from left to right in a matter of seconds. How can it do that? Is it travelling faster than the jetliner? No; it is merely very much closer, so that even its moderate speed carries it through a large angular distance (or simply a large angle) in very short order. Similarly, the very remote stars, even if moving fairly quickly, would not appear to shift in position much as the years pass: the patterns stay the same. But relatively nearby stars may appear to drift about with respect to that background, since all stars are moving through space in various directions. Indeed, if all stars moved at approximately equal speeds, the ones which are closest would seem to change position most quickly - a consideration we will come back to later in an important context: the search for stellar parallax.The Motion of the Sun.Perhaps surprisingly, these measurements of position and velocity allow us to work out where the sun itself is going (relative to its neighbours). Let me remind you that the stars in the `solar neighbourhood' are, by and large, all moving in roughly the same direction. They are all orbiting the centre of our Milky Way galaxy. But each star is moving at random to some extent, and the sun has its own `peculiar velocity', as it is called, which is causing it to pass through the general distribution of nearby stars. Reconsider the analogy I used earlier. The stars are moving more-or-less in parallel, just like the cars on the westbound lanes of Highway 401 as they pass Toronto. But a given car, perhaps a sports car in the middle lane of a three-lane stretch of the highway, might have a little extra velocity at a given moment. If so, it will slowly overtake the cars which are in the inner and outer lanes. The driver of the sports car will see the cars on either side falling back as she proceeds. Moreover, she will be catching up to the cars directly ahead of her in the center lane, and pulling away from the cars behind her - an effect which her passenger could measure with a hand-held radar gun and the Doppler effect. Something similar applies to the sun in its motion. We discover that there is a part of the sky called the solar apex where, on average, the absorption lines in the spectra of the stars are Doppler-shifted to shorter wavelengths, indicating that we are catching up to those stars. (Any single star has its own random motion which may be large enough to cancel out the effect, so we have to look at average values.) In the opposite direction, the so-called solar antapex, the average velocity of the stars is a bit positive: that is, the distance between us and them is increasing as we slowly leave them behind. Moreover, the stars which are off to the sides seem, on average, to be slowly drifting backwards, just as the speedy sports car driver would see cars fall behind on either side. This shows up in the proper motions. In this way, we are able to identify where the sun is moving, and at what speed (about 30 km/sec) relative to the nearby stars. In fact, the discovery of the direction, relying only on the proper motions, was made by Herschel about 200 years ago, long before the distances of any of the stars had been directly measured. (He did not have the technology to measure Doppler shifts.) The sun is moving approximately in the direction of the star Vega.The Apparent Brightnesses of the Stars.In measuring the apparent brighnesses of the stars, astronomers use what is called a magnitude scale, but you don't need to learn it or use it to understand the material in the rest of the course. Your textbook wisely avoids the use of the magnitude scale, except for a brief mention on page 526, because people often find it quite confusing. For completeness, though, and because you may be referring to other textbooks, let me tell you the main points: The magnitude scale runs opposite to what you might expect. The fainter the star is, the numerically larger its magnitude is. (This is what perplexes most people!) The reason is largely historical, because of the way the ancients use to divide the visible stars into six classes: the brightest few of them were of the `first magnitude,' the next were `second magnitude,' and so on. This arose in response to the way people noticed the stars coming into view after sunset. When the sky is twilit, one notices only the brightest few stars; later, stars which are somewhat fainter can be seen in the slowly-darkening sky; and so on. In this way, the ancients subdivided the stars into six broad classes. Actually I personally do not have any problem with this kind of scale, and not merely because I am an astronomer. It seems to me to make good semantic sense to think of a `problem of the first magnitude' as being more important or outstanding than something which is of the second magnitude, for instance. (If you prefer another analogy, where lower numbers are more important than higher ones, you could consider something like the sport of golf, where a low score is better than a high score. In basketball, the reverse is true, but this does not make either sport nonsensical, or any more nonsensical than they are already.) Among the first magnitude stars (at least as they were originally defined) are stars like Sirius and Vega. But the moon is even brighter, and the sun much brighter still, so if the moon and sun are to be measured on this scale they need to have magnitudes which are less than one. In fact they are so bright that the magnitudes are about -10 for the full Moon and -26 for the Sun. (Naturally the brightness of the moon varies, depending on its phase.) You should note that there is nothing special about a star which has a magnitude of zero - it is simply something which is brighter than Vega but not nearly so bright as the Moon. People find this confusing too: they seem to think that a star with magnitude zero should be extraordinarily faint or even invisible, or distinctive in some other way. To understand that, it may help if you think of the Celsius temperature scale, which allows both positive and negative values. (T = 0 is cold, but it can certainly get very much colder! Indeed, it is `five below' outside as I write these words.) On the Celsius scale, zero degrees has a special meaning: it is the temperature at which water freezes. But the zero-point can be quite arbitrary, as it is for the astronomical magnitude scale. You may know, for instance, that there is nothing special about `zero degrees Fahrenheit.' The magnitude scale actually measures ratios of brightness. (Technically, then, it is a logarithmic scale. Another example of this is the decibel scale which is used in discussions of the intensity of sound.) By design, every 5 magnitudes difference between two stars represents a brightness ratio of a factor of 100, so a first magnitude star is one hundred times as bright as a sixth magnitude star . An example may help. Consider the following: the Sun has an apparent magnitude of -26. (This extraordinary brightness, of course, is because of its proximity to us. The sun is not a particularly remarkable star.) This is: 100 times as bright as a hypothetical object of magnitude -21 (if such a thing existed in the sky), which in turn is 100 times as bright as a hypothetical object of magnitude -16, which in turn is 100 times as bright as an object of magnitude -11 (which is a little brighter than the full moon), which in turn is 100 times as bright as an object of magnitude -6 (which is somewhat brighter than Venus gets at its very brightest), which in turn is 100 times as bright as an object of magnitude -1 (which is about as bright as the star Sirius). Putting this all together, you will find that the Sun looks about (100) x (100 )x (100) x (100) x (100) = (ten billion) times as bright as Sirius. The reason, of course, is that the Sirius is about one million times farther away. (If it were as close to us as the sun is, Sirius would in fact considerably outshine the sun. Sirius is intrinsically quite a bright star.) As I noted, you don't have to understand the magnitude scale to follow the course from here on! But perhaps I should point out to you that the diagrams we will be studying (such as the one on page 533 of the text) are on this kind of scale, even if not labelled as such: notice that the scale on the left of the figure is not linear. It shows the luminosity of stars relative to that of the sun, so that steps of constant size along the vertical axis correspond to equal changes in the ratio of brightnesses. Rather than use these ratios explicitly, astronomers simply use magnitudes. Permit me one last remark in our defence! There is a very good reason for using such scales. They allow us to display and deal with numbers which cover a very great range of values (what a scientist would call a large `dynamic range.') Here is an analogy: imagine trying to construct a diagram in which you plot the mass against the length of every kind of living creature on Earth. If you use a linear scale, stretching from zero (for the tiny bacteria) to some large values (to accommodate the blue whales and elephants), you will find that the smallest animals are all plotted in a complicated blob of crowded points near the origin (the zero values on the graph). If, instead, you use a logarithmic scale, expressing all values relative to some standard -- "ten times as tall as a man", "one one-hundredth the size of a man" -- the scale is `stretched out' for the smaller values, so the plotted points can be seen rather than all jammed together near one corner, indistiguishable. It may be interesting, for example, to know that millipedes are ten times as long as ants but only fifty times heavier; but if the data points are indistinguishably muddled, as they would be on the linear scale, you can't see anything useful, such as trends or relationships. The use of a logarithmic scale `blows up' (magnifies) the small values in a way which allows you to keep the large values on the plot at the same time.Colours, Temperatures - and Dust!.If I tell you that one star looks brighter than another, I have to be careful to tell you the wavelength or colour at which I made the observation. To understand why, imagine two stars side-by-side which look exactly the same brightness to your eye. If one of them is a cool star, it will give off lots of red light and only a little blue light; if its companion is hot, these proportions will be reversed. Consequently, if you look at them through a red filter (a piece of coloured glass which allows only red photons to slip by), the cool star will look brighter than its companion; conversely, the hot star will look brighter through a blue filter. In other words, your perception of relative brightness may depend on the particular wavelength of observation because of the different temperatures of the stars. The important point is that we can turn this reasoning around! We can measure how bright any given star looks through various filters to determine the relative proportions of red and blue light, and thus determine its temperature. These procedures can be made quite quantative, using standard filters and detectors. In short, astronomers define colours in mathematical terms, not merely in vague subjective terms of how things 'look to the eye.' Once again, however, the book wisely refrains from using this particular astronomical tool (which is related to the magnitude scale discussed earlier). Those of you using other texts may encounter expressions like `B-V', which is the arithmetical construct which is indicative of stellar colour. Once we have a mathematical definition of colour, it is possible (and indeed important) to calibrate the relationship in terms of other things. In practice, this means that we want to work out what precise colour, as measured through the filters, corresponds to what stellar temperature. The sun, for instance, has a surface temperature of about 6000 Kelvins. What colour does this correspond to? Sirius is hotter, and thus bluer: but by how much? Astronomers have established such calibrations, so in principle the colour of a star is a quantifiable and reliable indicator of the temperature of its surface layers (which is where the observed light is emitted). It is considerations of that sort that go into the construction of diagrams like the ones shown on page 533. If the space between the stars was truly empty, we would be able to do this regardless of the distance of the star (the only requirement being that you must be able to collect enough light to make a reliable and precise measurement of the colour). A blue star should still look blue from a great distance, just as a red car looks red whether it is parked in front of you or a mile down the road! All photons travel unimpeded through empty space, and their relative numbers - the ratio of the numbers of blue and red photons, and thus the colour of the light - will not change. But there is an important exception, best understood by consideration of an everyday example. The sun often looks red at sunset. Is this because the sun is cooling off at the end of the day? No! It is simply because we are seeing it low in the sky, along a path which passes through a lot of the Earth's atmosphere, including water droplets, smog, dust, and what-have-you. This makes the sun look deceptively red. In like fashion, stars can have their colours modified by gas and dust in the interstellar medium (ISM). In other words, an intrinsically hot [blue] star can look deceptively red. The colour of that star may indeed mislead us into thinking that is is actually a cool star! How can we resolve the ambiguity and tell that we have been misled? The answer is to rely on the spectrum, which always tells the truth. As we will learn, the pattern of absorption lines in the spectrum of a star depends not only on the compositions of the stars - which turn out to be remarkably similar - but even more importantly on their temperatures. Suppose, therefore, that we have a hot star, with its characteristic pattern of absorption lines. The interstellar medium (ISM) will remove many blue photons, and proportionally fewer red photons, as the light makes its way towards the Earth. This changes the overall balance of photons, but the pattern of absorption lines will still be discerned. So here is the answer: we examine the spectrum of the star to determine its temperature, and then measure the colour of the star to see if it accords with expectation. If the star appears considerably redder than expected, this tells us of the presence of absorbing material along the line of sight to that star. This may seem like a quibble, but if there is dust and junk between the stars they will appear not only redder but also fainter than they should, and our estimates of their relative distances may go completely to pieces. (Imagine driving a car in a fog. The traffic lights ahead may look very faint and suggest that you are a long way from the intersection when in fact you are already dangerously close to it.) Since distance estimates are so important in astronomy, these complicating factors become very important. 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.)
