Thursday, February 3, 2011

Stellar Objects Part 5: Black Holes

Stellar Objects Part 5: Black Holes

Black Holes are the puzzles of the universe. The physics of matter and energy break down at their mysterious event horizons, presenting theorists with fertile ground from which many of our current cosmological theories are growing.

This is a NASA image of the youngest known black hole, only 30 years old. This image is a compilation of data from several sources including the Chandra X-ray observatory. The black hole is the yellowish-white spot labeled SN 1979C within the galaxy M100, which is about 50 million light years away.

Researchers think this black hole is the result of the recent collapse of a star of about 20 solar masses.

A black hole is a concentration of mass so great that the force of gravity it creates is so intense that nothing can escape it, not even light. A common misconception is that black holes will eventually suck everything in the universe up. However, only when something, including light, gets close enough will it be unable to escape a black hole. Stars have been observed in stable orbits around black holes, just as if they were orbiting a star of the same mass.  You might be wondering why light, which consists of massless photons of electromagnetic radiation, is affected by gravity at all. The answer is not that photons are interacting with gravity but that gravitational fields, especially strong ones, bend the fabric of spacetime itself. The traveling photons respond to and follow the curvature of spacetime. Spacetime is so strongly bent inward toward a black hole that photons cannot escape if they come very close. This idea will be fleshed out more as we go.

This is a NASA concept drawing of what a black hole might look like closer up. It is essentially an invisible black sphere made visible by gases swirling around it that are so hot they emit radiation. The blue curved lines are possible magnetic lines along which hot gases may be dragged.

Composition of A Typical Black Hole

There are theoretically four basic types of black holes. These types are based on four known black hole solutions to Einstein's theory of general relativity. Two kinds rotate. An electrically charged rotating black hole is a Kerr-Newman black hole. A rotating black hole of zero charge is a Kerr black hole. A nonrotating charged black hole is a Reissner-Nordstrom black hole. And a nonrotating black hole of zero charge is a Schwarzchild black hole. Most black holes rotate because the stars that formed them were spinning. In other words, angular momentum is conserved. The charged black holes can be thought of simply as theoretical solutions because physicists do not expect real black holes to have charge. No astronomical objects with any appreciable electrical charge have ever been observed and no such thing as a black hole electron has ever theoretically stood up. We will simply compare nonrotating and rotating black holes from here on in.  All black holes consist of an event horizon, which is an envelope surrounding a central singularity. The singularity is a geometrical point of zero radius. Many theorists are uncomfortable with this notion and perhaps a solution, combining quantum mechanics, which describes particles not as physical points but as regions of maximum probability, combined with relativity might reveal a better description of the singularity. The event horizon is not a physical shell but is better thought of as "the point of no return" where nothing, not even light, once it ventures this close, can escape. In the image above, the black shell is the event horizon. It is impossible to observe or directly test the singularity within it.

A photon sphere exists just outside the event horizon. It operates like this:  A photon can escape from just outside the event horizon if it is traveling straight outward away from the black hole. The directions close enough to straight out that allow a photon to escape form a cone called an exit cone. Photons traveling outside the cone will fall back into the black hole. Photons pointed outward that are right on the boundary of the cone neither escape nor fall back in but instead orbit the black hole. This is the photon sphere.

A rotating black hole has an additional feature, an ergosphere, which is ellipsoidal in shape and touches the event horizon at the two poles of the black hole. This is not a physical boundary but a theoretical region outside the event horizon in which spacetime is dragged along in the direction of the black hole's spin with respect to the rest of the universe. Within this region objects are dragged along as well. Any object near the black hole will tend to start moving in the direction of rotation. As we explore how the ergosphere works, it is important to remember that objects do not break the light speed barrier, but the fabric of spacetime itself can and does. An object close to the event horizon, within the ergosphere, would have to move faster than the speed of light in the opposite direction to just stand still. In other words, within the ergosphere, spacetime is moving faster than the speed of light. The outer edge of the ergosphere is called the stationary limit. Here objects moving at the speed of light are stationary with respect to the rest of the universe because spacetime itself is dragged at exactly the speed of light. Spacetime outside the stationary limit is also dragged but slower than the speed of light. Objects within the ergosphere, because they have not reached the event horizon, can still escape the black hole, and in fact an object traveling on a tangent to the black hole and entering its ergosphere should be able to gain energy from the black hole - this is called the Penrose process. The object being boosted can theoretically reduce the black hole's energy by as much as a third and rob it of its angular momentum, dissolving the ergosphere with it. The result is a nonrotating black hole. The Penrose process may be a possible source for gamma ray bursts, the most energetic phenomena observed in the universe, and it is also really the only possible source of a nonrotating black hole.

Approaching the Event Horizon

Imagine that we are several light years away from a black hole, a safe distance, and from this vantage point we notice a derelict spacecraft that is about to be sucked in. We are bewildered by what we see. It seems to be slowing down as it gets closer! It should be speeding up because the increasingly intense gravitational field is drawing it in. The reality is that the spaceship is approaching the speed of light away from us as it falls inward. Yet it seems to us that it is taking forever to fall in. How can things speed up and slow down at the same time? We are witnessing Einstein's theory of general relativity in action. As the force of gravity approaches infinity, time itself slows to a complete stop from the perspective of an independent observer. For a rat, say, marooned on the derelict spacecraft, time would tick along as usual and it would not sense a thing (that is, until it becomes spaghettified - this is Stephen Hawking's word - as it falls closer into the black hole it will simply be crushed and its body will experience such an intense gravitational gradient that its tissues, then its cells, and then even its atoms will be torn apart).

To us watching it, the spacecraft slows to a stop as it approaches the boundary of the black hole called the event horizon.  Even though the event horizon is not a physical barrier, physicists can describe the event horizon as a mathematical membrane with physical properties. For example it behaves as though it contains heat, as if it were a hot material of some kind. And its temperature is inversely proportional to the mass of the black hole. Stephen Hawking came to an interesting conclusion about this heat. Like any hot body, the black hole should radiate energy and particles into space. This radiation comes from just outside the event horizon and not from within the black hole. This means that the radiation, called Hawking radiation, doesn't violate the theory that nothing, not even light, can escape. Over time an isolated black hole should radiate away all its mass and disappear. This is a teaser; we will build on this idea shortly.

For us, the event horizon is simply a black disk; we see the spacecraft's approach slow to a stop and then it simply hangs there suspended, an effect called gravitational time dilation.  At the same time, the spacecraft has been getting redder and dimmer as it approaches the horizon because all processes acting on this spacecraft (light in this case) slow down from our perspective. Eventually it will become less and less visible to us and disappear all together, an effect called gravitational redshift.  We are now left alone wondering what happened to it. We can get some clues by examining how black holes work.

The Nuts and Bolts of Black Holes

Lets start by refreshing our concept of spacetime. We experience a four-dimensional universe consisting of three spatial dimensions and one dimension of time. These dimensions operate together, weaving a fabric that influences the behaviour of all objects. The fabric of spacetime can be visualized as the elastic surface of a trampoline (keep in mind that we are making a two-dimensional model of a four-dimensional system). A massive object, a large star for example, indents the fabric, or bends spacetime. The curvature of spacetime is directly related to the mass of the object. Planets might orbit around it and they are held in place by the curvature created by the star (and they too contribute their own curvatures).  At the event horizon of a black hole the curvature of spacetime is infinite. If we use the trampoline analogy, the indent in the trampoline fabric would be infinitely long, extending right through Earth across to the farthest reach of the universe, and theoretically, beyond. Mathematically, and thanks to four dimensions operating rather than two, the distortion of spacetime created by a black hole is a much more complicated geometry than an infinite spike.

General relativity not only tells us that black holes are possible, it actually predicts that a black hole will form whenever mass gets packed in tightly enough to create a gravitational collapse. One way to make a black hole is to let a massive star reach its natural conclusion. Aging stars collapse in on themselves when they exhaust their nuclear fuel. The outward pressure created by nuclear fusion is no longer there to balance the star's tremendous gravitational pull inward. If the star is not too massive, it will collapse into a core of atomic nuclei floating in a sea of electrons. It remains supported from further collapse by electron degeneracy pressure. These are white dwarf stars, described in the article, "Introduction to Stars." If the star is more massive, nuclei themselves collapse into neutron plasma or even quark plasma, and the remaining core is prevented from complete collapse only by neutron degeneracy pressure (or quark degeneracy pressure). These are neutron stars, discussed in the article, "Neutron Stars." Now, when a star is very massive, its gravitational pull inward is so intense when it collapses that no intra-atomic force can hold up against it. All particles of matter become infinitely squeezed together, into what is called a singularity. At this point, any information about the matter that goes into a black hole is lost forever. And this is where we once again pick up on Stephen Hawking radiation.

Hawking Radiation

Hawking radiation is related to thermal radiation and it is predicted to be emitted by black holes due to quantum effects, which will be described shortly. This radiation should, over time, reduce the mass of a black hole until it eventually evaporates away entirely, if it does not consume as much matter as it loses. Micro black holes should emit more net radiation than larger black holes. In fact the smallest black hole possible, a Planck-size black hole, should evaporate as instantly as it forms. One way of explaining Hawking radiation is as follows:  The radiation doesn't come from the black hole itself but is the result of virtual particles being sufficiently energized by the black hole's gravitation into becoming real particles of radiation. This is how it works in more detail:  Virtual particles, according to quantum dynamics, arise spontaneously near the black hole due to quantum fluctuations of spacetime, as particle-antiparticle pairs. Normally these pairs instantly annihilate each other when they form and disappear as a result. But one of the pair may fall into a black hole while the other one escapes. In order to preserve the total energy of the system, the particle that falls into the black hole must have negative energy (this idea will be expanded upon soon), with respect to an outside observer. As a result the black hole loses energy and therefore mass and again, with respect to an outside observer, it will appear to have just emitted a particle (this is the leftover one of the pair and as a result it becomes real). Hawking radiation differs from thermal radiation in that thermal radiation contains information about the body that emitted it and Hawking radiation depends only on the mass, momentum and charge of the black hole. In September 2010, researchers at the University of Milan claimed to have observed Hawking radiation experimentally for the first time.

Black Hole Information Paradox

A black hole's information loss can be is summed up by the no-hair theorem. This theorem holds that every black hole can be completely characterized by only three externally observable parameters: mass, electric charge and angular momentum. Any other information (and this is where the "hair" metaphor comes in) about the matter that goes into one is permanently inaccessible to external observers. This is called the black hole information paradox. The problem is with all the other information about the matter that goes into a black hole and is irreversibly lost, such as baryon number and lepton number. Quantum dynamics is built on the principle that information like this can't be lost from a system. In other words, quantum dynamics is based on the principle of time reversibility. For example, if a particle interacts with another particle, it may be absorbed or reflected or even broken apart into its constituent particles. But you can always run the sequence of events backward and reconstruct the process that occurred. Events that occur at the event horizon of a black hole are, in contrast, irreversible. They are lost and cannot be reconstructed. This illustrates an epic battle between quantum dynamics and general relativity. Both theories must be satisfied or one or the other or both must be modified to explain black holes (and still explain all other phenomena in the universe). And the finger is pointed at gravity. I explored this idea in more depth in the article, "Our Universe: A Baby Picture." When enormous mass is concentrated in an extremely tiny volume, the normally weak gravitational force (so weak in fact that this force is ignored all together when working with particle physics) becomes as significant as the other fundamental forces. In this sense, black hole theories might become a platform from which to build the as yet elusive concept of quantum gravity, which would marry the two theoretical systems of quantum dynamics and general relativity.

Enter, Once Again, String Theory

Let's re-imagine that we are watching the derelict spacecraft falling into a black hole. Remember that to us it appears to slow down to a stop because all physical processes working on it stop. Lets now focus on one of the ship's atoms as it slows. Think of this mental game as analogous to watching one of those nature films where the film is slowed down to the point that a hummingbird's wings become separate and visible. First the atom looks like we expect it to look, like a whirling cloud of negative charge.  Soon the electrons slow down enough to become visible. As they freeze, the protons and neutrons in the nucleus become visible, and a moment later, we can see the individual quarks that make up these nucleons. As the quarks themselves now slow down we begin to make out the strings from which they are composed. They are minute, Planck-size to be exact, and as their vibrations slow down, more and more of them become visible. When higher modes of vibration freeze out, the strings become identical to each other. An electron string looks the same as a quark string and so on. According to the mathematical calculations done for this scenario, the strings and all the information they once carried simply become smeared across the event horizon. And here is where our loss of information could be explained. When time from our perspective is slowed to a stop, even the fundamental strings of matter stop vibrating and it is within these vibrations that information about the various particles exists. From the perspective of the atom we are studying, all of its functions are carrying on as usual, just like the derelict spacecraft rat as it approaches the event horizon. However, like the rat, the atom is also experiencing an ever-increasing gravitational field and its velocity is approaching the speed of light. As it does so, its mass is increasing as well. According to general relativity, its mass will continue to increase to infinity and its volume will decrease to zero. According to quantum mechanics, its mass will approach a maximum possible mass called Planck mass and its volume will decrease to a minimum possible Planck volume. We can see here how the two theories approach each other but do not offer a cohesive picture. There are other competing theories about black hole operation and indeed about the nature of matter itself, but I especially like the simplicity of string theory here.

Huge and Tiny Black Holes

Physicists speculate that the very early universe contained many extremely massive stars, which have since collapsed into black holes as massive as hundreds of solar masses. These heavy black holes may have been the seeds of immense galactic black holes consisting of millions to billions of solar masses and spewing out massive amounts of radiation. These monsters will be explored in the article, "Quasars." The recent (2011) discovery of a truly gigantic black hole with a mass equivalent to 6.6 billion Suns places a new upper limit on black hole size. It is inside the galaxy M87 about 50 million light years away.

Physicists are also fairly confident that micro or Planck-size black holes also exist. In fact, they pop into existence and just as instantly evaporate every time two Planck-energy particles collide. This occurs in the case of cosmic radiation. These extreme-energy collisions may also be a clue to understanding the ultimate structure of particles.

How To Observe a Black Hole

Black holes do not emit light, with the possible exception of Hawking radiation from the event horizon, so phenomena such as gravitational lensing (light is bent in the direction of extreme gravitational fields) and stars that appear to orbit an invisible body are used to locate massive black holes in space. This latter technique recently revealed that the Milky Way harbours a supermassive black hole, called Sagittarius A*.  This is a CHANDRA image of Sgr A* (white dot) based on data from a series of observations.

This is not an optical image but a radio image. The bright dot near the center is a very concentrated radio source. Physicists think that the radio emissions are not centered on the black hole itself but rather from a region around it close to the event horizon.  The radio emissions most likely come from gas and dust heated to millions of Kelvins as it accelerates into the black hole.  The mass of this black hole is just over 4 million solar masses confined within a 44 million km diameter sphere (the size of the sphere reflects the measurement of the event horizon, not the singularity within it; as well, a larger horizon means a singularity of greater mass and vice versa). It is believed to emit a small amount of Hawking radiation as well. Many astrophysicists now suspect that a supermassive black hole lurks within the center of most if not all large galaxies.

Matter falling into a black hole sometimes results in spectacular effects.  Moving like water spiraling down a drain, matter collects in an extremely hot and fast-spinning disc called an accretion disc before it is swallowed by the black hole in its center. Friction within the disc causes the angular momentum of the particles to be transported outward allowing the matter to fall inward. This causes a release of potential energy that increases the temperature of the matter. Many accretion discs are accompanied by relativistic jets that are emitted from the poles of the black hole, and which carry away tremendous amounts of energy.

This NASA image shows how extragalactic relativistic jets form from a galactic black hole like Sgr A*.

Particles are spewed out from the vicinity of the black hole at speeds up to 99.98% the speed of light and they traverse distances longer than the diameters of galaxies. What accelerates these particles to near light speed and what kinds of particles make up the jets is still largely unknown. But some physicists believe that magnetic fields in the accretion disk may be responsible for expelling charged subatomic particles outward at near the speed of light and as the charged particles interact with the magnetic field, they emit radiation, in the case of Sgr A*, powerful radio waves.

In this NASA image, matter from an orbiting companion star is drawn toward a black hole, forming an accretion disc (blue).

An example of this system may be Cygnus X-1, one of the strongest X-ray sources observed from Earth. This black hole probably has a mass of about 9 times that of the Sun and the radius of its event horizon is thought to be about 26 km. The other star, the one being "eaten," is a supergiant called HDE 226868.  Cygnus X-1 might be the black hole remnant of a star that was once more than 40 solar masses that has since blown up in a supernova.

How Dangerous Are Black Holes?

The closest black hole is V 4641, just 1600 light years from Earth on the way to the center of the Milky Way in the direction of the constellation Sagittarius.  This relatively small black hole is part of an X-ray binary system and it is believed to be between 3 and 10 solar masses. Despite its size, it is unusually energetic, emitting occasional but very powerful radiation bursts, much like a quasar does. As a result some astronomers call it microquasar (these are briefly discussed in the Quasar article). Its jet is oriented at an angle toward Earth but, fortunately for us, not directly at Earth. There are currently no black holes close enough to Earth to worry about.

On the other hand, there has been some public concern that the Large Hadron Collider (LHC) might create a microscopic black hole that might in turn swallow the Earth. The Standard Model of particle physics holds that the LHC energies are too low to create a black hole but string theory suggests that extra spatial dimensions exist and it might be possible to create a micro black hole within one or more of these tightly folded up dimensions. Yet, even if a micro black hole were to pop into existence, it would be expected to almost instantly decay as it released its energy via Hawking radiation. Even if such miniature black holes were created and they were stable, the safety assessment group at the LHC remind us that these micro black holes would also have been produced by cosmic ray collisions with the special matter in neutron stars and white dwarfs where the creation conditions are very similar to the those in the LHC, and the stability of these stars gives us good evidence that they aren't dangerous.

Can We Use Black Holes?

There has been much speculation about using a black hole to space-jump. Perhaps we could enter the ergosphere of one where spacetime is dragged around at ultra-relativistic speeds and use it as a slingshot to another part of the universe. There are two problems with this idea. First, your spaceship must be traveling at very close to the speed of light to enter the ergosphere on a tangent and avoid the event horizon and we have no technology yet to achieve anything close to this velocity. Second, objects even in the near vicinity of black holes experience enormous gravitational forces that can rip apart stars let alone space ships. I have read about the possibility of a black hole connected to a white hole via a wormhole (a white hole is a black hole antithesis where matter is shot outward. There is some speculation that when a black hole forms a big bang occurs at the core and a new universe is created. This expanding universe is in effect a white hole and the cosmological horizon is its event horizon). This idea too has all the problems associated with trying to enter or come near a black hole. But, before we toss out the baby with the bath water, there actually are theoretically possible wormholes based on general relativity. None have yet been observed. You can explore them in the article, "Wormholes."

A sea of tiny Planck-size black holes may have been created during the birth of the universe. Total gravitational collapse of matter is required to make a black hole, and this in turn requires very high densities of matter. Shortly after the Big Bang, when baryonic matter first appeared, the density of matter would have been very high. Uniform density alone is not enough to make a black hole, however. For a non-stellar black hole birth, a perturbation is required, much like star formation itself requires. Different computer models of the early universe vary widely in the size of these initial perturbations of matter but they, to varying extents, were expected to exist. Once Planck-size black holes formed they would be expected to grow very rapidly feeding on the molecular gases around them, and many would be able to grow into the behemoth matter-gobbling black holes called quasars, of which the early universe had many more than the universe does today. These black holes might predate the first stellar black holes created as the first massive stars went supernova. NASA's Fermi Gamma-ray Space Telescope, launched in 2008, is searching for the Hawking radiation signature of evaporating primordial black holes (with the caveat that if Hawking radiation doesn't exist, these black holes would be virtually impossible to detect if they existed).

Black holes express the mystery that lies beyond the absolute limits of nature. They extend beyond our current understanding and it is up to us to build theoretical frameworks that can scaffold us to a more complete understanding of them (and find ways to test those theories!). To astrophysicists and physicists this presents an opportunity for the most fun kind of play. And as our understanding of how black holes work advances, so will our understanding of how physics itself works.

Next up: Quasars.

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