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Black Holes

Black Hole Worm Hole The concept of black hole has its origin in a solution of Einstein's General Relativity for a spherical object with mass M and radius R. If the mass collapses to a radius less than R = 2GM/c2, where G is the gravitational constant and c is the speed of light, then nothing (including light) can escape from inside this radius. It is called the event horizon or the Schwarzschild radius (named after the astrophysicist who solved the equation). Figure 05-02a shows a schematic diagram of the Schwarzschild geometry.

Figure 05-02a Black Hole
[view large image]

Figure 05-02b Worm Hole [view large image]

It is known as the embedding diagram. The two dimensional circles are slices of three dimensional spheres (of the same radius) - the hyperspace. The verticle axis denotes the "stretch" of space in the radial direction. The slope of the curve can be considered as representing the curvature of the space. It is flat (or zero) at the outer edge and becomes infinity at the Schwarzschild radius. This pictorial representation is very similar to a rubber sheet stretched by a rock. The shape of the region inside the horizon is somewhat arbitrary. It is only known that everything plunges inevitably to the central singularity once passing over the horizon. In a more realistic drawing the event horizon would be placed far below the diagram at infinity. The complete Schwarzschild geometry consists of a black hole, a white hole, and two singularities connected at their horizons by a worm hole as shown in Figure 05-02b. A white hole is a black hole running backwards in time. Just as black holes swallow things irretrievably, so do white holes spit them out. White holes cannot exist, since they violate the second law of thermodynamics by allowing some time reversal events such as reassembling a broken glass back to its original whole. The white hole geometry outside the horizon represents another Universe. The worm hole joining the two separate singularities is known as the Einstein-Rosen bridge, but even if it can somehow be generated, it would be unstable and pinch off immediately. Therefore, only the black hole geometry is applicable to the physical world.

Black Hole It is believed that every quasar, active galactic nucleus, and even normal galactic nucleus contains a black hole with a mass of between ten million to several billion solar masses at its core. The difference in appearance is related to the intensity of the activity. Since galaxies rotate, matter falling toward the central black hole will form a rapidly spinning disk of gas - an accretion disk - rather than falling directly into the hole. Kinetic energy released by in-falling matter, and frictional effects within the accretion disk, raise the temperature of the nner parts of the disk to enormous values and provide plenty of energy to power AGN's on all scales from Seyferts to quasars. By a process that is still not fully understood but seems to be related to rotating black hole, the central engine accelerates streams of charged particles to very high speeds. The inner rim of the accretion disk, together with surrounding gas and magnetic fields, forms a nozzle that confines the outward flow of energetic particles into narrow streams that shoot out perpendicularly to the plane of the disk. Figure 05-02c shows a model of the black hole.

Figure 05-02c AGN Model [view large image]

Magnetic Field and Jet Magnetic Field and Spin Magnetohydrodynamics is the branch of physics dealing with the behavior of the combined system of magnet field and ionized gas at low density. A popular theoretical scenario applies such formulation to explain the relativistic jet(s) powered by the black hole. The study found that magnetic field lines are twisted into a helix (as shown in Figure 05-02d) by the differential rotation of matter in the accretion disk. Such field provide a force to expel the ionized particles in a collimated jet from the inner circumference of the accretion disk. The energy to maintain the process is derived from the braking action on the rotation of the disk. In this way, matter can slow down and eventually flow inward into the black hole. Figure 05-02e illustrates a mechanism to extract the spinning energy from a rotating black hole, wherein the surrounding ionized gas and the magnetic field act together to set up a voltage difference between the poles. This is similar to a battery driving electric current around to provide another source of energy for the outflowing jet(s).

Figure 05-02d Magnetic Field and Jet [view large image]

Figure 05-02e Rotating BH

See more detail in "Magnetohydrodynamics (MHD) and the Formation of Jet(s)"

Figure 05-02f is a HST (Hubble Space Telescope) image of NGC4261, which is a radio galaxy. The image strongly suggests that it is a black hole fitting the description of the theoretical model. Infrared observation of
NGC1068 in 2004 was able to resolve the inner region down to a few parsec. Figure 05-02g penetrates the dusty central region and shows the structures on arcsec scales. The picture on the right is a model for the nucleus of NGC1068. It contains a central hot component (dust temperature > 800K, yellow) marginally resolved
Black Hole NGC4261 Black Hole NGC1068 along the source axis. Its finite width and the dashed circle indicate the currently undetermined extent. The much larger warm component (T=320K, red) is well resolved. The arrows indicate the projected orientation of the two interferometer baselines and the angular resolution L/2B, where L is the wavelength and B is the projected baseline. The image shows that the active galactic nuclei are arranged like a thick doughnut. This model requires a continuous injection of kinetic energy to maintain such cloud system. The mechanism is currently unknown; thus a better understanding of the physics of these spectacular objects is needed.

Figure 05-02f NGC4261
[view large image]

Figure 05-02g NGC1068
[view large image]

The quasar 3C273 is a 2-billion-solar-mass black hole encircled by a doughnut of gas (accretion disk) and with two gigantic jets shooting out along the spinning axis. The Schwrzschild radius for this object is about 6x109 km. Such supermassive black hole can be created while matter is still at quite low density (~ 10-3 gm/cm3). Since the tidal force at the event horizon of a black hole is inversely proportional to the square of its mass, its effect on a space visitor would be un-noticeable, although he would soon be in dire trouble as he plunges irrevocably toward the central singularity. However for a stationary observer, it takes an infinitely long time for the asronaut to approach the event horizon (due to gravitational time dilation) and the view of the asronaut would gradually disappear (due to gravitational red shift of light). The effect on the astronaut visiting a stellar black hole (mini-quasar) would be more violent due to the drastic increase of the tidal force.
Black Hole 2 In a November, 2004 announcement by NASA, a black hole catalogued as SDSSp J1306 appears to be about one billion times as massive as the sun. It is 12.7 billion light-years away. A similarly massive and distant black hole was studied in the same year with the European Space Agency's XMM-Newton X-ray satellite. The object, SDSSp J1030, is 12.8 billion light-years away. These two results seem to indicate that the way supermassive black holes produce X-rays has remained essentially the same from a very early date in the universe. How such massive and energetic structures formed so quickly (only after one billion years of the big bang) remains a major puzzle for scientists. Mergers of smaller galaxies and their black holes may have played a role. Researchers suspect that black hole formation and galaxy development go largely hand-in-hand, but they cannot say which comes first. Figure 05-02h is an artist's conception of a supermassive black hole with matter swirling into it.

Figure 05-02h BH, Supermassive

In 2009, radio observations of 4 early galaxies (1 to 2 billion years after the Big Bang) including J1148+5251 shows that the mass ratio of central bulge to black hole is about 10 times smaller than the more recent data indicating the black hole probably came first.

Black Hole 5 A 2012 update on the supermassive black hole J1148+5251 reveals that while matter swirls inward from the accretion disk toward the black hole, intense radiation creates outflow of gas at the same time. The process is shown schematically in Figure 05-02i. The orange wavy lines represent photons emitted during the accretion process. Most of them escape the galaxy, but some imping on clouds of gas (blue) and the radiation pressure drives the gas out. The stars and dark are too heavy to be affected by the radiation. It is suggested the elliptical galaxies may lost their gas component in this way. The Milky Way has a mild imitation of such process in the form of the 30-kpc arms.

Figure 05-02i BH Gas Outflow

Black Hole Cannibalism On 28 March 2011, the Swift satellite designed to look for gamma-ray bursts (GRBs) detected a burst with unusually long duration of more than a month. The new source, called Swift J164449.3+573451, is now believed to be generated by the tidal disruption of a star moving too close to a black hole. The left portion in Figure 05-02j shows the level of X-ray flux recoded by various detectors over the past 20 years with observational duration indicated by horizontal bars. The data indicate the gradual buildup of intensity until it suddenly flared up more than 200 times in few hours. The right portion in the same diagram is the follow-up to show the flux variation for the first 7 weeks of the most recent observation. Time interval of the variation (in luminosity) can be used to calculate the size of the

Figure 05-02j Black Hole Cannibalism [view large image]

source since each part of the source would have to be in contact with others on such a time scale t to coordinate the variations; thus the size r c t. For the most rapid variability of t 100 s, r 3x1012 cm, which is about 50 time bigger than the Sun and about 1/2 the size of Mercury's orbit.
Under the assumption that the central object, i.e., the black hole, dominates the variability, r can be taken as the Schwarzschild radius of the black hole, then its mass M rc2/2G 107 Msun, which is in close agreement with the estimate from the relationship between the black hole mass and galactic bulge luminosity. The unusually high luminosity may be related to the onset of relativistic jet pointing to the direction of observation and moving at a velocity of 99.5% of the speed of light.

M87 Jet In another 2011 report, the jet from M87 has been observed in great detail with the Very Long Baseline Array (VLBA), which has resolution 400 times finer than the HST. Since black hole is not a clean eater, about half of the food (the in falling star) is left behind in the accretion disk close to the black hole. Interaction of the rotating "crumbs" and magnetic field produces the jet. The observation finds a jet of high-energy particles starts as a broad flow at a distance about 14 to 23 times the

Figure 05-02k M87 Jet
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Schwarzschild radius of the black hole. The jet becomes more cylindrical and faster with distance from the black hole. Figure 05-02k (a) is a schematic diagram showing different sections of the jet that have different particle densities observed at different frequencies, from about 200 GHz
(more dense) to 5 GHz (less dense); diagram b shows the actual jet obtained with the VLBA at a frequency of 15 GHz (yellow is brightest, blue is faint). The orientation of the disk is vertical in these pictures. This observation is in broad agreement with the magneto-hydrodynamics description in earlier study. The discrepancy is in the distance of 100,000 Schwarzschild radius from the black hole predicted by theory and observed in quasars. One of the explanations ascribes the difference to viewing direction.

Black Hole Correlations Black Hole Formation M87 used to hold the title of harbouring the most massive black hole with a mass of 6.3x109 Msun. The record was broken in 2011 with the detection of 2 super massive black holes in NGC 3842 (within the Abell 1367 cluster) and NGC 4889 (within the Coma cluster) both with a mass of about 1010 Msun. These giant galaxies all sit at the bottom of the cluster's gravitational potential well collecting a lot of the material falling inward. Estimate of black hole mass depend on

Figure 05-02l Black Hole Correlations

Figure 05-02m Black Hole Formation [view large image]

either the measurement of stellar (or gas, or maser emission from molecular clouds etc.) velocity dispersion or V-band galactic bulge luminosity Lv. The data points usually fall on (or near) a straight
line of a logarithmic plot (see the formula for the solid black line in Figure 05-02l, b). However, the super massive black holes doesn't seem to follow such relationship (Figure 05-02l, a and b). The deviation is explained by proposing that the super massive black hole was formed by merger of black holes while the lighter variety was grown by accretion of cold gas (Figure 05-02m). BTW, the BCG (in Figure 05-02l) is the abbreviation of Brightest Cluster Galaxies, and MW denotes Milky Way.

The discovery of a 2 billion solar mass supermassive black hole at a mere 770x106 years after the Big Bang (Figure 05-02n) has
Supermassive Black Hole Formation presented astronomers with a problem to explain how could it be created so soon and so big? It is known that the acquisition of material by the black hole is always balanced by ejection of some of the in-falling matter. It has been calculated that a black hole sucking in matter continuously at its maximal rate would double its mass Mbh every 50x106 years, i.e., Mbh=M0x277/5~ 4x104M0, where M0 is the initial mass. This is too slow for a seed black hole of stellar mass to grow into billion-sun in 770x106 years (Figure 05-02o,a).

Figure 05-02n Supermassive Black Hole [view large image]

Super Black Hole Formation Two different theories has been proposed to resolve the problem. They all try to make the basic component from solar-mass black hole to middleweight one with mass of 105 to 2x106 Msun, i.e., to bump up M0. One theory suggests that black hole at the center of a star cluster could grow quickly enough to middleweight seed hole (Figure 05-02o,b). The other one involves collapse of primordial gas cloud (Figure 05-02o,c). The former scenario predicts more leftover middleweight seed holes to survive into the present age. Since only a few hundred such holes among 2x105 galaxies have been found so far, it seems that the odd is against the bottom-up version at least for now (see also related observation in Baby Galaxy).

Figure 05-02o Supermassive Black Hole Formation

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