Finishing Off Black Holes:
A Point-Form Summary.
This section of the course notes, and the associated PowerPoint presentation, makes the following critical points:
a brave astronaut who chose to fall into a black hole would suffer a quick demise. But any signals that he or she sent back to us would reach us with ever-increasing delays and with ever-reduced energy, so that we would never even see the astronaut reach the periphery of the black hole
searches have been made for black holes, but not (as you might have thought) by looking for regions where light is disappearing in some sense
one search method relies on the fact that a black hole lined up between us and a remote star will actually make the star look temporarily brighter because of the gravitational focussing of the light. This will only happen rarely, and briefly, so one has to monitor the behaviour of millions of stars to see many such events. The best way is to intercompare a whole series of images taken of a rich field of stars, like a nearby galaxy. This is the basis of the MACHO project
any single focussing event will never be repeated (the black hole drifts between us and the star, then goes on its way). So such studies can only give us statistical estimates of the properties of the black holes lurking in interstellar space
an alternative approach is to recognize that many stars are in binary systems, and in some of these one star may already have undergone a supernova explosion and turned into a black hole. In that case, the other star will be seen to be in orbit around a massive object which emits no light. If the unseen object is too massive to be a neutron star, it must be a black hole
there are too many stars in the sky to monitor carefully in the hope of detecting this behaviour. Fortunately there is a suggestive lead: in a close binary, the companion star may be expanding as it evolves, or have a strong stellar wind, so that it transfers material towards the black hole. As in a nova, this would lead to the formation of a hot accretion disk and the emission of X-rays
the strategy, then, is to look in the direction of sources of X-rays. If we see a bright star in that location, we monitor it to see if it is 'wobbling' about some unseen object - possibly a black hole. Indeed it was in this way that the first really persuasive black hole candidate was found: Cyg X-1
supermassive black holes may exist in the cores of galaxies. The evidence may be in the form of the motions of stars, which allows us to identify a million-solar-mass black hole in our own Milky Way galaxy. For more remote galaxies, we cannot do this kind of work; but there are indirect arguments that there are billion solar mass black holes in some galaxies. We will encounter them when we discuss quasars
black holes may not represent the permanent repository of any material that fell into them. Hawking has shown that the formation of virtual particles (a consequence of quantum mechanics) may lead to the slow 'evaporation' of black holes. For big black holes, of stellar mass and above, this happens on such a long timescale that it is really not relevant, but if black holes of smaller mass exist (perhaps created during the Big Bang) their evaporation would have observable consequences
Associated Readings from the Text.Please look at: Section S4, pages 489-490. Chapter 18, pages 583-588. Chapter 19, pages 619-621. Chapter 22, pages 687-688.Exploring a Black Hole.Suppose we could determine, somehow, that there is a black hole sitting in space, fairly close to the Earth and within practical reach of a space mission. We announce this to the world and solicit volunteers who are willing to be launched in that direction. We choose one brave person, and send her on her way with instructions that she is to continue sending back signals (radio waves) describing what she sees and experiences as she nears the hole. Let us suppose, to be specific, that she will comment on her impressions and feelings once every ten seconds. What do we learn? You should not be surprised, considering the number of times the subject has arisen, to be told that the astronaut falling towards the black hole will experience strong tidal forces. For instance, if our brave astronaut falls feet-first towards the hole, she will discover that the atoms in her feet are pulled more strongly than the atoms in her head. As she nears the hole, the difference in these forces can become so large that she is literally ripped into tiny pieces. The astronaut would experience all of this in short order, accelerating rapidly towards the hole because of the strong gravity and suffering a prompt demise. The remarkable thing, however, is that an external observer would never see this happen, or hear her final remarks! The reasons are complicated, and have to do with the way in which time passes in the vicinity of strong gravitational fields (or, in modern parlance, in the strongly-distorted space-time which we find near the black hole). The important elements are that: The signals which she sends out at the agreed-upon constant rate (once every ten seconds, in our example) seem to become more and more widely-spaced out from our point of view, because our clocks no longer run in synchronization. The consequence is that we hear less and less frequently from the astronaut, just as letters from a once-dear friend may become less and less frequent with the passage of years as your interests drift apart and other things fill your lives. (But there is an important difference! The astronaut is scrupulously keeping her word, reporting every ten seconds by her watch. She does not slack off, but your receipt of the messages gets ever less frequent because of relativistic effects.) In other words, everything that happens to the astronaut seems to take very much longer from our point of view. Time seems to `slow down' for her, from our perspective. (But, I emphasise, not from hers! She experiences a quick and painful demise.) Secondly, the photons which reach you - the bursts of radio waves which constitute her radio messages - are having to climb out from deeper and deeper in the `gravitational potential well,' the pit that the black hole creates in curved space. Each photon loses a lot of energy in doing so, and the photons which reach you are strongly red-shifted to the extent that, eventually, you receive effectively no measurable energy at all. Remarkably, then, what we observe is rather like the analogous situation I described in class. Imagine being at a movie theatre when the power fails. Two things happen to the projector. (i) the motor which makes the strip of film move through the machine stops working; and (ii) the lamp fades away. As a result, the action on-screen slows to a standstill, but the light fades away so rapidly that eventually we see nothing beyond some last, faint frozen frame in a slow fade to black. Although the causes are much more complex, this is very much like what we would see as our brave astronaut plunges in.Searching for Black Holes.The theory of black holes is fascinating, but you might think that they must be forever beyond our ken since they emit no radiation. How can we ever tell that they are present? If we can't find them, how can we test or have any confidence in astrophysical theories that suggest that they must exist? The solution is to recognize that black holes compress matter in a certain location, but do not remove its gravitational infuence. Since gravitation influences light and ordinary matter, it makes sense to ask what the detectable effects would be on photons and atoms. There are various aspects to this question, as we will see.Not a General Inflow.The first point, one we have seen before, is that a black hole would not `suck in' all surrounding matter. (The average person believes this, but the average person is wrong.) So we do not look for regions in space where a lot of matter is moving into some dark apparently empty spot.Gravitational Focussing: MACHO.A gravitating lump can make light change direction. We saw earlier that the sun, passing between us and remote background stars, can bend the rays to a small but detectable extent. Of course, when we study that effect, we are looking at light which `skims' the outer surface of the sun, half a million miles from the very center. At this distance from the center, the sun's gravitation is weak. Light passing near the Scharzschild radius of a black hole will experience a much stronger bending effect. Of course, any light which is moving straight towards the black hole will simply fall into it, so some photons are lost to the outside world, but light rays which `just miss' will suffer a strong change of direction. Interestingly, these effects would lead to a temporary brightening of a star, thanks to what is called gravitational focussing. If a black hole should pass directly between us and some remote star, it can be shown that we would see a brief up-and-down in the star's brightness, a phenomenon which might last for some hours or days, depending on the speeds and distances of the hole and the star. There is a project which has been underway for some years now, one with the interesting title of `The Search for MACHOs' (A MACHO is a MAssive Compact Halo Object, a dense star or black hole located in the halo of our own galaxy.) Astronomers in Australia have been taking, night after night and year after year, images of the nearby galaxies the Large Magellanic Cloud (LMC) and the Small Magellanic Cloud (SMC). Each of these galaxies contains millions of stars, so the idea is to see if any of them vary up-and-down in brightness in a way which seems to suggest that a black hole has passed between us and them. There are problems with this approach: There are many kinds of variable stars, and any star which changes in brightness may be one of these. There are, in fact, ways of distinguishing them, but many of the detections are bound to be false alarms. One has to study millions of stars over hundreds of nights to detect even a few cases, so there is a great glut of data, and processing it takes a lot of time and effort. Perhaps most discouragingly, the discovery of one good candidate can never be pursued further. Any black hole will pass between us and a distant star only once, and there is no way to explore the circumstances or learn more about the black hole. Only statistical statements can be made about the numbers and kinds of black holes one detects in space. It is worth pointing out that the MACHO project has succeeded in identifying many episodes of star brightening which are almost certainly due to the passage of a compact object - a black hole or a neutron star, or perhaps a `Jupiter-like' object. But it would be better to find a black hole in some circumstance which allows us to study it in detail.Black Hole Binaries.The black hole left behind after a star's death continues to exert a gravitational influence on its surroundings. In particular, if the original star was in a binary pair, the other star should continue to orbit a now-invisible location in the sky. This sounds like a good prescription: find a star which is `wobbling' back and forth, as shown by minute changes in its position; or find a star which is moving towards and away from us, as shown by ever-changing Doppler shifts in its spectral lines. This will tell us that the star is in a binary, and by analysing the motions we should be able to work out the mass of the `other' object. If that turns out to be big - say, five times the mass of the sun - but the object is invisible, we may be able safely to conclude that it is a black hole. This sounds easy, but is not very practical. There are literally millions of stars in the sky, and we cannot monitor all of them in precise detail to see if any are wobbling about in unexplained fashion. (It takes a lot of telescope time and patience to do this correctly for even a handful of stars!) We should try to think of a good way of finding a short-list of candidates beforehand, so that we have some reasonable chances of quick success. X-rays provide this, as described on pages 586-588 of your text. If one star in the binary pair has become a black hole and the other then expands or blows off material as a strong stellar wind, then matter can fall into the black hole. (Please note: once formed, the black hole does not instantly start to `suck material' from the other star. Material will only be transferred once the second star is puffed up, in the course of its own evolution, that the atoms feel the black hole's gravity as strongly as that of the parent star. They then fall toward it in the fashion I described when we considered Novae a few lectures ago.) Just as in the novae, the material which is spilling towards the black hole forms an accretion disk (shown on page 587 of your text), and for exactly the same reason: the conservation of angular momentum means that the atoms cannot simply fall straight in. As new atoms arrive, they run into the disk and, because they are falling under the influence of the strong gravitational field of the black hole, they arrive with enough speed and energy to lead to collisional heating which results in the emission of energetic X-rays. Please note that the X-rays do not come from inside the black hole. Nothing - no matter, no light - can come out in this fashion. The X-rays merely alert us to a region of space in which there are energetic collisions between gas particles, and suggest that there may be an accretion disk surrounding some compact object, possibly a black hole (but also possibly a neutron star, for instance). Once the tentative identification is made, a detailed study is carried out, one which tells us exactly how the visible star moves. We may discover, for instance, that its orbital motion implies that it is feeling the gravitational influence of a body nine times the mass of the sun - far too massive to be a neutron star or white dwarf. If this massive body is invisible, it cannot be a conventional star and much almost surely be a black hole. (Some likely candidates have been found.)Supermassive Black Holes.As we saw earlier, there are circumstances in which the formation of a black hole seems particularly inescapable -- namely, when we find a huge agglomeration of stars in a moderately-sized volume. The example I gave was with reference to a location like the centre of a galaxy, where we might find as many as a billion stars slowly drawing together under their mutual gravity. Once they are within a volume comparable to that of the Solar System, black hole formation is inevitable. Interestingly, the motions of stars near the centre of our own Milky Way have shown unambiguously that there exists a black hole of about one million solar masses there. This may sound huge, but it is really only a tiny fraction of the total mass of the Milky Way (one hundred billion solar masses or more). We will learn, however, that there may be billion solar mass black holes in the cores of many galaxies, and that these explain the phenomena of quasars.The Fate of Black Holes.On pages 489-490 of your text, credit is given to Steven Hawking for first recognizing that black holes must eventually `evaporate.' In fact, this attribution is not quite correct: the original idea came from a Russian theorist, and Hawking's first study along these lines was intended to disprove this notion, which he did not believe. In due course, however, he realised its fundamental correctness, and developed the theory much more fully than anyone else, so is rightly to be credited with the way it is understood at present. Steven Hawking is a remarkable scientist who has received a great deal of attention for his science as well as for his overcoming a debilitating illness (`Lou Gherig's disease') which has rendered him essentially immobile and unable to speak. Much of what he has carried out has had to be done entirely in his head, some of it intimidatingly complex mathematics, and he is a fine example of the ability of the human mind to transcend physical limitations. The explanation which I provided you with in class is nicely summarised on pages 489-490 of your text, but the point I especially wanted to make is the following: Gravity does not always win! For the most massive stars, gravity leads to a lot of matter being compressed into black holes here and there, but still that matter may be returned, bit by bit, to the universe at large until the black holes are gone. But this `victory' over gravity is probably irrelevant: as I told you, a black hole of one solar mass would only evaporate over a timespan which is 10**60 times (a trillion trillion trillion trillion trillion times) longer than the universe has already been in existence! On the other hand, small black holes (of the mass of a mountain, say) would evaporate over a relatively short period of about ten billion years - about the age of the universe since the Big Bang (as we will learn). The evaporation of a black hole undergoing Hawking radiation actually speeds up as it goes, and would end in a shower of gamma rays. The fact that we don't see a lot of this going on now seems to suggest that the dense conditions in the early universe did not produce large numbers of these mid-sized black holes. 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.)
