Black Holes 3 Essay, Research Paper
Black holes are objects so dense that not even light can escape their gravity, and since nothing can travel faster than light, nothing can escape from inside a black hole . Loosely speaking, a black hole is a region of space that has so much mass concentrated in it that there is no way for a nearby object to escape its gravitational pull. Since our best theory of gravity at the moment is Einstein’s general theory of relativity, we have to delve into some results of this theory to understand black holes in detail, by thinking about gravity under fairly simple circumstances. Suppose that you are standing on the surface of a planet. You throw a rock straight up into the air. Assuming you don’t throw it too hard, it will rise for a while, but eventually the acceleration due to the planet’s gravity will make it start to fall down again. If you threw the rock hard enough, though, you could make it escape the planet’s gravity entirely. It would keep on rising forever. The speed with which you need to throw the rock in order that it just barely escapes the planet’s gravity is called the “escape velocity.” As you would expect, the escape velocity depends on the mass of the planet: if the planet is extremely massive, then its gravity is very strong, and the escape velocity is high. A lighter planet would have a smaller escape velocity. The escape velocity also depends on how far you are from the planet’s center: the closer you are, the higher the escape velocity . The Earth’s escape velocity is 11.2 kilometers per second (about 25,000 M.P.H.), while the Moon’s is only 2.4 kilometers per second (about 5300 M.P.H.).We cannot see it, but radiation is emitted by any matter that gets swallowed by black hole in the form of X-rays. Matter usually orbits a black hole before being swallowed. The matter spins very fast and with other matter forms an accretion disk of rapidly spinning matter. This accretion disk heats up through friction to such high temperatures that it emits X-rays. And also there is some X-ray sources which have all the properties described above. Unfortunately it is impossible to distinguish between a black hole and a neutron star unless we can prove that the mass of the unseen component is too great for a neutron star. Strong evidence was found by Royal Greenwich Observatory astronomers that one of these sources called Cyg X-1 (which means the first X-ray source discovered in the constellation of Cygnus) does indeed contain a black hole. It is possible there for a star to be swallowed by the black hole. The pull of gravity on such a star will be so strong as to break it up into its component atoms, and throw them out at high speed in all directions. Astronomers have found a half-dozen or so binary star systems (two stars orbiting each other) where one of the stars is invisible, yet must be there since it pulls with enough gravitational force on the other visible star to make that star orbit around their common center of gravity and the mass of the invisible star is considerably greater than 3 to 5 solar masses. Therefore these invisible stars are thought to be good candidate black holes. There is also evidence that super-massive black holes (about 1 billion solar masses) exist at the centers of many galaxies and quasars. In this latter case other explanations of the output of energy by quasars are not as good as the explanation using a super-massive black hole. A black hole is formed when a star of more than 5 solar masses runs out of energy fuel, and the outer layers of gas is thrown out in a supernova explosion. The core of the star collapses to a super dense neutron star or a Black Hole where even the atomic nuclei are squeezed together. The energy density goes to infinity. For a Black Hole, the radius becomes smaller than the Schwarzschild radius, which defines the horizon of the Black Hole: The death explosion of a massive star, resulting in a sharp increase in brightness followed by a gradual fading. At peak light output, supernova explosions can outshine a galaxy. The outer layers of the exploding star are blasted out in a radioactive cloud. This expanding cloud, visible long after the initial explosion fades from view, forms a supernova remnant. So, a black hole is an object, which is so compact that the escape velocity from its surface is greater than the speed of light. The following table lists escape velocities and Schwarzchild radii for some objects: The black hole masses ranging from 4 to 15 Suns (1 solar mass = 1 Msun = 2 x 1033 grams.) And are believed to be formed during supernova explosions. The after-effects are observed in some X-ray binaries known as black hole candidates. The velocity depends on the mass of the planet. The scientists believe if our Sun dies, the sun may turn into a black hole. Black holes were theorized about as early as 1783, when John Michell mistakenly combined Newtonian gravitation with the corpuscular theory of light . The concept of an escape velocity, Vesc, was well known, and even though the speed of light wasn’t, Michell’s idea worked the same. He showed that Vesc was proportional to mass/circumference and reasoned that, for a compact enough star, Vesc might well exceed the speed of light. His mistakes were twofold: he subscribed to the corpuscular theory of light, and he assumed that Newton’s law of universal gravitation could apply to such a situation. These mistakes happened to cancel each other out, but when the wave theory of light gained favor, the astronomers abandoned these dark stars. In the beginning of the 20th century, Einstein proposed his theory of general relativity. The formula worked out by Michell and rederived, this time without mistakes in the derivation, by Karl Schwarzschild, gives the Schwarzschild radius for any massive body (that is, a body containing mass): RS= 2GM/c2. Vesc for any body smaller than this radius would exceed that of light, and since general relativity forbids this; any matter within RS would be crushed into the center. Thus RS can effectively be thought of as the boundary of a black hole, called an event horizon because all events within RS are causally disconnected from the rest of the universe. There aren t many physical features of a black hole. In an aphorism coined by John Wheeler , “black holes have no hair,” hair meaning surface features from which details of it’s formation might be obtained. There are no perturbations in its event horizon, no magnetic fields. The hole is perfectly spherical and in fact has only three attributes: it’s mass, it’s spin (angular momentum), and it’s electric charge. Of these properties, it is only the mass that concerns astronomers. As a cloud of gas contracts, the interior heats up until the core is so hot and dense that nuclear reactions can occur. This nucleosynthesis of hydrogen into heavier elements generates a tremendous pressure, according to the ideal gas law P=NkT, and this pressure holds the star up against further gravitational collapse. This state of equilibrium, during which a star is said to be on the main sequence, lasts until the hydrogen in the core is used up, about 10 billion years for a star like the sun, whereupon gravity will resume shrinking the star. Exactly what occurs next depends on the complicated interactions between different layers of the star, but generally, the star will explode in a supernova. If there is any remnant of this explosion, its further evolution depends almost exclusively on it’s mass. A remnant below 1.4 M (@) will collapse until it can be supported by electron degeneracy pressure and form a white dwarf. A remnant between 1.4 and 3 M(@) is halted by neutron degeneracy pressure and forms a neutron star. Degeneracy pressure is an effect that results from quantum mechanical interactions when the density of subatomic particles increases. As it depends only on this density, it is non-thermal and will remain no matter how much the star cools down. Still for remnants above 3 M(@), not even degeneracy pressure can counter the force of gravity, and a black hole is born. This was the general base that general relativity gave to astronomers, but just because something is allowed to happen doesn’t mean that it does. Most astronomers resisted such absurd realities. Astronomers are very conservative by nature, and some of the most respected and influential astronomers of the day rejected this idea so soundly that it wasn’t until the 60’s that any actual searches began. At first, the only instruments available were the old familiar optical telescopes. Optical telescopes are just what they sound like, telescopes sensitive to the visible portion of the electromagnetic spectrum . This spectrum can reveal much information regarding the source of the light. The color indicates the temperature of a star. By combining the type of star, identified by observing lots of other stars with similar characteristics, and our models of stellar processes with a measurement of the star’s luminosity, it is possible to calculate the distance to the star. We can even determine the chemical composition of the star by observing any emission or absorption lines in the spectra. Furthermore, these lines are very distinctive, and if they appear in the correct relation to each other but have been Doppler-shifted towards the red or blue ends of the spectrum, a measurement of the star’s speed relative to the earth can be obtained. The only distinguishing feature of a black hole is its gravity, however, and searching for a black hole with an optical telescope is next to impossible. A black hole does not give off any light. It’s too small to observe by blocking out stars behind it. It could act as a gravitational lens, but to do so it would have to be directly in line with the Earth and some bright object, and even then there would be no way to distinguish between a black hole or a very dim star. Still, there was on promising method proposed by Russian astronomers Zel’dovich and Guseinov in 1964. If the black hole was in a binary system with another, normal star, the light curve of the system would give it away. Binary systems comprise about half of all known stars, so it is not unlikely that a black hole might be found next to a normal star. In a spectroscopic binary system, the stars rotate about their center of mass and the light will be Doppler shifted. The light curve of a star is a graph of the intensity or Doppler-shift of light from the star versus time. Here the light curve of the visible companion can yield much information. The period of rotation about the center of mass can be determined by inspection of the Doppler-shifted light curve itself, and the mass of the visible star is given by the type of star and how luminous it is. All that is then needed is a reasonable estimation of the inclination i of the system, and several important things can be calculated. The mass function f(M) = M2^3 sin i / (M1 +M2)^2 gives a relation between the masses of the two bodies, and the semi-major axis a1=AM2/(M1+M2)^2 sin i (where A is the separation of the centers of mass) gives the size of the orbit, which can also be related to the rotational velocities of the stars. A spectroscopic binary with no visible companion would be a candidate for a black hole, and if the dim star’s mass is determined to be greater than that of the visible star, it would be a promising candidate. However, this method consists of many uncertainties. Although there were no hard cases for black holes any scientist s search, there arose another way a black hole might show itself. If the black hole were in a gaseous nebula, the gas would fall into the black hole. The inherent magnetic fields of the gas create turbulence, generating heat, which is in turn transformed into electromagnetic radiation. The luminosity of the gas could oscillate rapidly due to the turbulence, and such rapid oscillations would give the black hole away. Another Soviet scientist, Schwarzmann, developed the “Multichannel Analyzer of Nanosecond Pulses of Brightness Variation” in an effort to detect these oscillations, but that method also proved fruitless. X-ray novas are a special class of X-ray binaries where the system contains a late-type optical companion (a star near the end of its life) and a compact object, which can be either a neutron star or a black hole . Usually the spectrum of the companion in this type of system is very weak compared to that of the gas, but in X-ray novae the fraction of light from X-ray heating is negligible, and we have an excellent opportunity to study the system in detail. If the accretion disk is due to a black hole, then understanding the companion star in detail will also allow understanding of the processes of X-ray emission. Several X-ray satellites detected Muscae 1991 and calculations began to pinpoint an optical companion. To do this, the exact position of the X-ray source must be known. If there is a star in the visible range at that same position, it is most likely related to the X-ray star, and the light curve can then be studied in detail. In this case, a companion was found. The similarities of Muscae 1991 with one of the best black hole candidates, V616 Mon, make it seem realistic that it might be a black hole. The evolution of the light curves, the decay rate in magnitude of the novae, and variations in brightness on the order of a day are all similar in the two systems. The spectrum of the nova, its various emission lines and other spectroscopic details, also does not resemble a classical nova in the same stages, but instead resembles that of the black hole candidates Cen X-4 and V616 Mon. As it is not a classical nova, the distance to Muscae 1991 must be estimated from a known linear relation of the width of the NaD line to distance. This gives a result of 1.4 kpc (kiloparsecs), which returns some typical values for low mass X-ray binaries and justifies confidence in its validity. Using this distance and the spectral features of the binary, the companion star seems to be a late main sequence star, which is in agreement with current theories of low-mass X-ray binaries. What this all boils down to is that the binary X-ray nova Muscae 1991 behaves very similarly to other black hole candidates in the galaxy, and gives a picture of the nova as a burst of gravitational potential energy released as matter from the disk accreted onto the compact object. The large amounts of energy released in the nova as X-rays indicates the companion is at least a neutron star and possibly a black hole, but no obvious conclusions can be made as to Muscae 1991’s containing a black hole. Cygnus X-1 is accepted as a black hole by most astronomers, there is still nothing about it that demands unequivocally to be accepted as such. Cygnus X-1 is the best X-ray astronomy can give us. But X-rays and visible light are not the only ways of probing the sky. Radio astronomy was also discovered accidentally. In the 1930’s, a technician trying to clear up intercontinental phone calls discovered radio waves coming from the Milky Way. Curiously enough, nobody really seemed to care very much; an amateur built the world’s first radio telescope. A modest 9 meters in size, it had extremely poor resolution, and the larger dishes that were to slowly follow did not fare much better. As in X-ray astronomy, the astronomers couldn’t do anything really useful with cosmic radio waves until they could identify an optical counterpart. Since radio waves are on the order of meters long, diffraction effects would require unreasonably large dishes to acquire any decent resolution. To counter this, astronomers came up with radio interferometry. At first the bodies that shone most brightly in the sky could not be associated with an optical counterpart. As radio telescopes improved, the error boxes for these sources shrank until, in 1953, a team at Cambridge had a sufficiently accurate estimate that other astronomers at the Palomar 5-meter optical telescope could identify the radio source Cyngus A with an optical source. This source turned out to be a galaxy, and once it’s redshift, and hence distance, were measured, it was found that this galaxy’s radio luminosity was millions of times brighter than that of an ordinary galaxy. The first radio galaxy had been found. Now that the technology was in place, more and more of these galaxies were discovered and they began to be studied in great detail. The results troubled astronomers; radio galaxies had two lobes of radio emissions with the dim optical galaxy in the center. These lobes stretched out millions of light-years, indicating a stable source of emission, and conservative estimates of the energy involved in their production was on the order of 10^61 ergs, as much energy as would be released in ten billion supernovas. Radio galaxies were among the first in what are today classified as AGN – active galactic nuclei. Other types of AGN include Seyfert galaxies, N galaxies, BL Lacertae objects, and quasars. They all demonstrate violent behavior that can’t be associated with the ordinary behavior of stars and interstellar dust, whether it be matter and energy ejected from the nucleus to luminosities of truly astronomical proportions. While all these objects were regarded as puzzles, it was really the quasars that could not be explained by any astronomical processes at all. Of course they do exist, and astronomers rushed to find explanations for them. It was in this storm of hypotheses that the idea of a super-massive black hole lost it’s exotic nature and became the most reasonable explanation. In fact, many of the other realistic explanations also support this idea, for they could evolve into a super-massive black hole . If there are a lot of star-star collisions occurring, the stars will lose enough energy such that they become bound in a binary which fairly rapidly decays, if they do not coalesce directly with each other. Such models of AGN could have two natural results without invoking black holes: supernova explosions, or clusters of pulsars. The supernova explosions are only as efficient as regular nuclear burning in stars, and must occur at a rate of about 5 to 10 a year. Furthermore, these supernovas cannot be ordinary stellar supernovas but rather a sort of ‘hypernova’ , wherein neutron stars must pass through the cores of super-massive stars, due to calculations of the energies released. If the cluster evolves into a cluster of pulsars, it is the rotational energy of the pulsars that powers the quasars. Through horrendously complicated interactions of particles and strong electromagnetic fields, this energy could be released into the universe, but both this and the supernova model have another serious flaw; there is no directionality of the radiation that could result in the observed jets of quasars and other AGN. To correct this would require a flattened cloud of gas that would either hasten the death of the cluster and it would collapse into a black hole, or the luminosity would be so great that the resulting wind of radiation would drive the gas into space, thereby destroying the model entirely. Other models involve the rotational energies of massive uncollapsed bodies. Known as super-massive stars, magnetoids, or spinars, they are all basically the same; a massive, spinning flattened disk (a super-massive rotating star will evolve into a disk). One way these spinars could liberate energy is by gravitational contraction, releasing up to a few percent of their rest mass as energy. However, to remain stable against collapse, a very large ultraviolet radiation pressure must be present, and such radiation is not found in radio galaxies, though they might be in high-redshift quasars. A pulsar is a rotating neutron star with skewed magnetic poles . Radiation is emitted in the direction of the magnetic poles, and if this beam passes earth, it has the same effect as a lighthouse. The incredible angular momentum of a pulsar makes its pulses extremely regular, to a degree of accuracy elsewhere found only in atomic clocks. As such, the orbit of a binary pulsar can be scrutinized in extreme detail, and has been. The results are amazing; the period of the stars is declining and their orbit is slowly decaying to exactly the degree predicted by general relativity. A better proof of gravitational radiation could hardly be imagined. The first person to attempt to detect this radiation was Joseph Weber. He eventually came up with the first bar gravity-wave detector. This was a long aluminum cylinder, 2 m by 1/2 m, that should be compressed with an incoming gravity wave. To detect this compression he wired piezoelectric crystals, which respond to pressure by generating an electric current, to the outside surface of the bar. Although it didn’t work, other bar detectors were built that used a device called a stroboscopic sensor to filter out random vibrations. This was an ingenious device, but it too proved to be a non-contributor in the advancement of learning more of the galaxy. Just as X-ray astronomy went from simple detectors in the noses of rockets to full fledged X-ray telescopes housed in orbiting satellites, and radio astronomy went from crude dishes to continent spanning arrays, gravity wave detectors may show a completely new spectrum. And, just as X-rays brought a completely new universe into focus, one can hardly imagine what a gravitational view of the universe will reveal. At the very least, we will have definitive proof or denial of black holes, but we may find that black holes are some of the more subtle features of the universe.