The Importance of Binary Stars:
A Point-Form Summary.
This section of the course notes, and the associated PowerPoint presentation, makes the following critical points:
about half the visible stars are in binary systems. The sun, being a single star, is not unusual, but binaries and single stars are about equally common
some stars appear close together in the sky, but are unrelated and will gradually drift apart on separate trajectories. They are referred to as (temporary) optical doubles
for some binary stars, we see both companions and watch them orbit one another. These are visual binaries, the orbits of which can take decades or centuries to complete. Patience is needed! The orbit may be seen at a random angle, somewhat complicating the apparent motions and our interpretations of them
for some stars, we see just a single dot of light, but the spectrum reveals that it is a close binary consisting of one hotter star and one cooler one. If we take spectra at later times, we may discover that the absorption lines have shifted since (at various times) one star will be momentarily approaching us while the other is moving away, and vice versa as more time passes. These changing Doppler shifts allow us to study these spectroscopic binaries
some spectroscopic binaries have two nearly identical stars in them, in which case we see doubled sets of absorption lines shifting back and forth thanks to the motions of the stars
occasionally we find a star which has only a single set of absorption lines, but they move back and forth in wavelength. This changing Doppler shift tells us that the star is orbiting something, but the lack of other lines in the spectrum tells us that the other object contributes very little light. It might even be a black hole
some binary stars are so close together that they appear as a single dot of light, but they may vary in brightness because one member periodically passes in front of the other (thereby blocking off some of the light). These are eclipsing binaries
we sometimes see a single star 'wobble' in its path across the sky, a clear sign that it is orbiting a faint companion that is moving along with it. This is an astrometric binary
by studying all these kinds of binaries, we are able to work out the masses of many hundreds of stars of various kinds. These determinations come from simple applications of Newton's laws of gravity. We do, however, have to know how far away any given binary star system is -- without that knowledge, we cannot get the masses
Associated Readings from the Text.Please look at: Chapter 16, especially pages 529-532.Binary Stars Are Not Rare.The sun is a single star (surrounded, of course, by interesting bits and pieces in the form of the planets and so on), but there exist stars in all sorts of more complex arrangements, including great clusters which may contain up to about a million members. We will say more about star clusters later on, but for now we consider the vast majority of stars: the so-called field stars, which look like single points of light in no obvious arrangement. You may be surprised to learn that about half of them are binaries: that is, these apparently single points of light often consist of two stars in mutual orbit about their common centre of mass. To give you some sense of how common this is, let me remind you that the nearby star Sirius has a faint white dwarf companion; and the nearest star to the Earth, Proxima Centauri, is part of a triple system in which one star follows a huge, slow orbit around a pair which are much closer together and orbiting each other quickly. In fact, if you gaze up at the night sky, it is roughly correct to say that every second point of light you see corresponds to a pair of stars bound together under gravity. The sun, being a single star, is not a rarity; but binary systems are common too. This is a great blessing to astronomers, because without the binaries, we would have no trustworthy way of determining stellar masses, and our astrophysics would be much more unreliable. There are several kinds of binary star systems, studied in different ways.Optical Doubles: Not Binaries!.Suppose you look through your telescope at a point of light and discover that, when magnified, it actually consists of two points of light close together. Your first thought might be that this is a binary star, in which case you should see the two stars orbit around each other as time passes. Such behaviour may take decades, but let us suppose you watch patiently - only to discover to your surprise that the two stars gradually move apart in completely different directions in space. Why do they do this? The answer is that the stars are completely unrelated, at very different distances -- perhaps one is 100 light years away, the other 500 light years away -- and only coincidentally, and temporarily, appear close to each other as seen from the Earth by a chance alignment. Such a pair is called an optical double.Visual Binaries.In a visual binary, as in the optical double, we usually see two distinct points of light. In this case, however, we see them gradually orbit one another around their common centre-of-mass. On page 530 of your text, you will see one example in the form of the binary star system Sirius. There are a few things to note: In a binary system, both member stars move around the centre of mass, but it is often easier to visualise the orbit if it is drawn to show the motion of one star with respect to the other, which is plotted as though always at rest. The figure on page 530 correctly shows both stars on the move, but not every representation (in other texts, for instance) will do so. Please remember, though, that in a binary system both stars move - the less massive one having the larger orbit and greater velocity. (This is just as for the Solar System, where you know that the sun "wobbles" back and forth a little in response to Jupiter's motion in its large orbit around their common center of mass.) The blurring caused by the Earth's atmosphere means that the image of any star will be about one second of arc across (do you remember this very small angle?). Through a telescope, we can sometimes notice that a magnified "blob" of light is made up of two separate points (or just looks somewhat elongated), an observation which tells us of the existence of a binary. But binary stars which are very far away and those in which the member stars are actually quite close together in space will inevitably be indistinguishable from a single blob of light and pass unnoticed. As a result of this selection effect, most of the known visual binaries are fairly close to the sun, and contain stars which are fairly widely separated. One consequence of the wide separation of known visual binaries is shown by the dates in the figure on page 530. Known visual binaries may take decades or even centuries to complete a single orbit! (Remember how the period of an orbiting body depends on its distance from the other object. Mercury orbits the sun once every 88 Earth days, while Pluto takes 248 years. ) In other words, finding a binary star is one thing, but working out its complete orbit may take many decades of patient work. Astronomers have been actively studying binary stars for a couple of centuries, fortunately, so there is quite an accumulation of measurements and data. In studying visual binaries, there is one messy complication: we may not be looking at the orbit directly `from above.' Imagine, for instance, two stars going around their centre of mass in perfectly circular orbits, so that the distance between them never changes. (This is rather like Jupiter orbiting the sun: their separation is nearly constant. If you prefer, think of the two knobs on the end of a drum major's baton when it is thrown, spinning, into the air.) If you were to look at this system from sideways on, you would see the interesting behaviour of one point of light moving back and forth with respect to the other. If you were looking at some intermediate angle, the path of one star around the other would be more elliptical in appearance, as shown in the following figure. Only if you were looking from 'directly overhead' would you see the true circular shape of the orbit. These ``projection effects'' somewhat complicate our analysis of the orbits of binary stars, but can be dealt with.Spectroscopic Binaries.Suppose now you take the spectrum of a remote star which appears as a single point of light. Let us say that you discover strong helium absorption lines, a sure sign that this is a very hot star, but at the same time notice that it contains other absorption lines suggestive of its being a cool star. How can this be? The simplest answer is that this is a binary, with one cool star and one hot star, and that the light of both is intermixed because the system is too far away to allow you to resolve the separate points of light. How could you check that? Well, if you are fortunate enough to be near the plane of the orbit of the binary, then there will be times at which one star is approaching you and one is going away. The spectral lines for one star will be Doppler-shifted toward shorter wavelengths (`blue-shifted'), while the lines of the other are red-shifted towards longer wavelengths. Moreover, some time later this pattern will be changed: half-way through the orbit, the star that was approaching you is now receding, and vice versa. In other words, you should see the characteristic absorption lines shift back and forth in the spectrum, out of phase with one another. Please note that this behaviour can be recognized even though you cannot tell, through the telescope, that there are two stars there! The blurring of the atmosphere and the remoteness of the system may make it look like a single point of light, but the spectrum tells the tale. Please also note that this sort of behaviour is not restricted to stars of different spectral types! In my example, I imagined a hot and a cool star in a binary system. But there are also binaries with two very similar stars - two stars just like the sun, for instance. In that case, the spectrum will contain two identical sets of absorption lines, one from each star; but they will be separated by the different Doppler shifts of the stars, thanks to their motions. As time passes, the sets of absorption lines will move back and forth in the spectrum.Single-Lined Spectroscopic Binaries.Suppose you get the spectrum of a star and discover only one set of lines (i.e. no hint of, say, a hot and a cool star together). But then suppose that repeated observations reveal that the spectral lines are shifting back and forth in a systematic way. Surely this tells you that you have found a binary system! But why does the second star not show up in the spectrum? The answer is that it may simply be too faint to provide enough light to be noticed. For instance, if you had a bright red giant orbiting a faint white dwarf, you would not notice the inconsequential amount of light given off by the dwarf. Such a system is known as a single-line spectroscopic binary. More interesting examples can be thought of. It may be, for instance, that the unseen object around which a star is orbiting is something really fascinating like a black hole (about which we will learn much more later).Eclipsing Binaries.The next class of binaries is that of the so-called eclipsing binaries. Once again, these are stars in which we cannot distinguish the two separate points of light: they appear as a single spot of light, even through the most powerful telescopes. But they draw attention to themselves by periodically becoming dimmer for a while and then brightening up again, in a way which repeats precisely and regularly, year after year, decade after decade. The explanation is this: when the two stars are separated, the light adds up, but when one star moves in front of the other, the light is somewhat reduced. As we watch the point of light, it varies in brightness according to what astronomers call the `light curve.' By making careful measurements of the time and duration of the eclipses, we can get lots of detailed information about the participating stars -- things like the stellar diameters, for instance.Astrometric Binaries.Astrometry is the science of measuring the precise positions of stars and watching how they change as time passes. Consider a star like Sirius: as it moves through space, its motion can be seen to `wobble' a little. When this was first recognized, it was realized that Sirius must be orbiting something else hitherto unnoticed. That faint companion was subsequently detected (see the figure on page 530 of your text): it turned out to be the first identified white dwarf star - and it is a lot fainter, relative to Sirius, than the figure on page 530 would suggest! It would not have been readily noticed if we had not had an indication, from the behaviour of Sirius, that it existed: that sparked a careful search.Final Remarks: Stellar Masses.Please note that the classes of binary stars I have described are not necessarily mutually exclusive. To give one example: Sirius was found to be a binary because of astrometric work, but subsequent observations allowed the faint white dwarf companion actually to be seen (so Sirius is now also a visual binary). Its spectrum reveals the changing Doppler shift which tells the actual speed with which it moves back and forth in its orbit (so it is a spectroscopic binary as well). But the direction from which we are looking at Sirius means that we will never see it as an eclipsing binary. Similarly, eclipsing binaries first draw attention to themselves because of their brightness variations, but then we can take spectra to measure the forward and backward motions of the stars in the binary by looking at the Doppler shift. And so on. Once we have determined as much as we can about the binary star orbit (things like the velocities with which the stars move) and have some estimate of its distance, we can determine the masses of the stars with straightforward applications of Newton's laws. The numbers in an individual case may be rather uncertain because of difficulties in determining things like the angle from which we are viewing the binary, but statistically speaking, because we have examined hundreds of them in pretty good detail, we have a reasonable idea of what is going on. This gives us the final bit of information we need in developing an understanding of stellar evolution and death - stellar masses. 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.)
