Published by the Association Pro ISSI No. 28, December 2011

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Impressum

SPATIUMPublished by the Association Pro ISSI

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PresidentProf. Nicolas Thomas, University of Bern

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Editorial

Do you, dear reader, want to taste the exciting smell of theoretical physics? Go ahead! This Spatium offers you an opulent cocktail of exotic flavours.

To begin with, imagine a proton. It’s about one millionth of a mil-lionth of a millimetre across. With the small size of our proton, a baby black hole brings some millions of tons of mass on the balance. Now, if you find such an object say in the refrigerator of your kitchen, for heaven’s sake, do not touch it, don’t call the police either. Better call the nearest theoretical physicist. He will explain to you with tears in his eyes that you are the first to discover such a lovely baby black hole, some-thing once thought to have been extinct for billions of years. Gener-ations of theoretical physics students will remember your name linked to your seminal discovery.

You then might want to inspect it closer. To this end, your theoretical physics expert recommends that you count the number of hairs on its otherwise bald head. If this count yields a bare zero: look out! Beyond any doubt, this is a veritable baby black hole. Yet, as charming as it may look, its hunger is insatiable: it de-vours everything, from your furni-ture to the flowers in your garden. Not even your old-fashioned TV set will be spared. Your wife will be delighted: the moment has come to buy her a new model.

If, however, your inspection yields a number of hairs greater than zero, it might simply be about an ordi-nary grey mouse seeking shelter from your cat since black holes have

no hair as theoretical physicists love to say. Though remain cautious: your expert instructs you that black holes are not quite black. Hence its colour might be just as grey as that of your intimidated mouse. In any case, do not give up in your efforts to search for black holes: there is one right in your front yard, as your expert says, right in the centre of our galaxy. That one is a bit fatter than yours: it accounts for some 10 million times the mass of our Sun. It helps our daytime star find the right path around the galactic centre, and to return to where it is today within a short time, more pre-cisely in a mere 230 million years from now.

If you are still - or now even more - keen on scenting the fragrances of theoretical physics turn the page and start reading quickly. You can be sure: there is no baby black hole hidden there. Even better: you will find yourself an excellent escort: ISSI’s black hole expert, Dr. Maurizio Falanga, will accom-pany you, and take care of your safety.

Now, it is up to us to thank him for making the present summary of his lecture for the PRO ISSI Associa-tion on 11 November 2010 availa-ble, and to wish you a stimulating journey to the realm of theoretical physics.

Hansjörg SchlaepferBrissagoNovember 2011

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Introduction

How black are black holes? This is the question that the present issue of SPATIUM would like to address and answer. One of the most excit-ing predictions of Einstein’s relativ-ity theory is the existence of black holes. These are very compact ob-jects, which are so dense and whose gravity is so strong that not even light can escape. They can, therefore, only be detected indirectly through gravitational effects on their envi-ronment. After a historical review, the theoretical predictions and the latest astronomical observations of black holes are discussed. Currently, hundreds of black holes are being observed; they are also strongly suspected to exist in the centre of galaxies, including the centre of our own Milky Way.

Gravitation

What causes objects to fall down to Earth? Why do the planets orbit the Sun? What holds galaxies to-gether? All these questions relate to one fundamental aspect of physics: gravity.

Sir Isaac Newton2 was first to pro-pose a mathematical model describ-ing the gravitational attraction be-tween objects. A popular story tells how Sir Isaac Newton was sitting under an apple tree, when an apple fell on his head. This event, accord-

ing to the story, prompted him to conceive the universal law of grav-itation (see Fig. 1). Whether or not Sir Isaac Newton actually sat under an apple tree while pondering the nature of gravity is not known. The fact, however, that all objects fall to-ward Earth was empirically under-stood long before Newton. Galileo Galilei3 had demonstrated earlier that all objects drop down to Earth with the same acceleration, and this acceleration is independent of the mass of the falling object. Sir Isaac Newton was familiar with this con-cept, of course, when he formulated a broader and far-reaching new the-ory of gravitation. His universal law

How Black Are Black Holes?1

Dr. Maurizio Falanga, International Space Science Institute, Bern

1 The present issue of Spatium reports on a lecture for the PRO ISSI Association given by the author on 11 November 2010.2 Sir Isaac Newton, 1642, Woolsthorpe-by-Colsterworth, Lincolnshire, United Kingdom – 1727, Kensington, United King-

dom, founder of classical mechanics.3 Galileo Galilei, 1564, Pisa, Italy – 1642, Arcetri, Florence, Italian philosopher, mathematician, physicist and astronomer.

Fig. 1: Sir Isaac Newton, the apple and gravity. (Credit: www.templatelite.com)

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of gravitation encompasses not only the behaviour of an apple near the Earth’s surface, but also the motions of much larger bodies far away. The essential feature of his theory is that the force of gravity between two objects is inversely proportional to the square of the distance between them. It is universal because all ob-jects in the universe are attracted to all other objects according to this relationship.

Gravity is a universal force ruling the motion of all objects in the uni-verse. It commands planets to orbit around their central star, it makes us stick to the Earth’s surface. Now, we ask ourselves, how fast we would have to accelerate Sir Isaac New-ton’s apple upwardly in order to make it leave the Earth’s gravity field? The escape velocity is defined as the minimum velocity an object must have to escape the gravita-tional field of a celestial body, e.g., the Earth, without ever falling back again (see Fig. 2). Newtonian me-chanics provide us the answer:

where G is the universal gravita-tional constant, M the mass of the celestial body, and r the distance from its centre of gravity. So, our ap-ple requires a velocity of approxi-mately 11.2 km/s (40,320 km/h) to

escape Earth’s gravity. In contrast, from the Moon’s surface 2.3 km/s (8,300 km/h) would be required, as its gravity is far lower than the Earth’s, and from the Sun 600 km/s (2,160,000 km/h) would be needed.

Black Holes

Admittedly, it is a long way from Sir Isaac Newton’s apple falling on his head to objects fast enough to leave the Earth’s gravity. Our Earth has rel-atively low mass, therefore the forces of gravity remain gentle in our daily

life. This, however, changes dramat-ically in the neighbourhood of large masses such as the Sun or huge stars, and even more so in the vicinity of black holes where gravity becomes so strong that nothing, not even light, can escape. For centuries, sci-entists have speculated about such strange worlds, but only the last say forty years have brought clear evi-dence about their existence.

Conceptual Origins

The existence of “dark stars” or “black holes” can be traced back to John Michell4 in the 18th century, and later to Pierre-Simon Laplace5, who speculated that, if a planet or a star were massive enough, the escape velocity would equal the speed of light. Light particles (photons) leav-ing the surface of such a world, would rise, stop, and then fall back down like the projectiles in Fig. 2 preventing it to be seen from the outside. This is a Newtonian view of black holes, which, despite being a nice picture, is an inaccurate descrip-tion of what really happens to light near a real massive body. According to Albert Einstein6, the speed of light is a universal constant. So we must describe the process near that mas-sive body in a different way.

In the early 20th century, he devel-oped the theories that revolution-

4 John Michell, 1724, Thornhill, Yorkshire, United Kingdom – 1793, same, English philosopher and geologist.5 Pierre-Simon (Marquis de) Laplace, 1749, Beaumont-en-Auge, Normandy, France – 1827, Paris, French mathematician and

astronomer.6 Albert Einstein, 1879, Ulm, Germany – 1955, Princeton, New Jersey, USA, theoretical physicist, Nobel prize laureate in

physics, 1921.7 See Spatium no. 18: Einstein in Bern: The Great Legacy, by Rudolf von Steiger, February 2007.

Fig. 2: A Treatise of the System of the World, London, 1728. A virtual can-non shoots projectiles at increasing ve-locity. Below the escape velocity, the bul-lets fall down to Earth at increasing distances. When escape velocity is reached, the bullets will enter an orbit around Earth, and never fall back again. (Credit: Isaac Newton, Philosophiæ Na-turalis Principia Mathematica, 1687).

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ized our view of space and time7. The first is the Special Theory of Relativity, essentially dealing with the question of whether rest and motion are relative or absolute, and with the consequences of Einstein’s conjecture that they are relative. It describes the motion of particles moving close to the speed of light. In fact, it gives the correct laws of motion for any particle at any speed including the cases where New-tonian mechanics are valid. The second is the General Theory of Relativity, which primarily applies to particles as they accelerate, partic-ularly due to gravitation. It constitutes a radical revision of Newtonian me-chanics predicting important new results for fast-moving and/or mas-sive bodies such as black holes.

Einstein’s basic concept was to drop Newton’s idea of a mysterious force (called gravitation) attracting masses, and to generalize special relativity and Newton’s law of universal grav-itation, providing a unified descrip-tion of gravity as a geometric property of space and time, or space-time.

When Einstein applied his theory to gravitational fields, he derived the curved space-time continuum, which depicts space and time as a four-dimensional surface where massive objects create valleys and dips in the surface (see Fig. 3). This

is the theoretical foundation of our understanding of black holes.

Einstein’s theories of relativity have been confirmed to be accurate to a very high degree. Moreover, they predict many unexpected processes of which most have been corrobo-rated experimentally since. The most famous such experiment was on the occasion of the solar eclipse in 1919, when scientists were able to show for the very first time that the light of distant stars is indeed deflected by the Sun’s gravity as the light passes near the Sun on its way to Earth. The total solar eclipse al-lowed astronomers to see the faint starlight near the edge of the Sun which is normally inaccessible due to the Sun’s own intense brightness. The results fully corroborated Ein-stein’s predictions. Another surpris-

ing prediction comes from Ein-stein’s interpretation of planets orbiting a star. Those circular or el-liptical orbits are not due to a cen-tral gravitational force, but rather the planets are travelling on straight lines through curved space. Einstein interpreted gravity as a geometric property of space and time, causing the space-time to be curved around massive objects.

Theoretical Predictions of Black Holes

Einstein introduced the new con-cept of space-time in 1915. Only about a month later, Karl Schwarz-schild8 found the first exact solution for the special case of a single spherical non-rotating mass. This Schwarz schild solution leads to the so-called Schwarzschild radius, des-ignating the size of the event hori-zon9 of a non-rotating body, later called non-rotating black hole.

Schwarzschild had little time to think about his solution: he died shortly after his work was published as a result of a disease he contracted while serving in the German army at the Russian front during World War I. Its interpretation as a region of space, from which nothing can escape, was not fully appreciated for another four decades. Long consid-ered a mathematical curiosity, it was

Fig. 3: Gravity causes space-time to curve around massive objects. Space-time is a dynamic entity, it is dis-torted by matter and it tells matter how to move. (Credit: Time Travel Research Center)

8 Karl Schwarzschild, 1873, Frankfurt am Main, Germany – 1916, Potsdam, German astronomer and physicist.9 The event horizon is the boundary around a massive body at which the gravitational pull of the body becomes so great as to

make escape of matter and light impossible.

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during the 1960s that theoretical work showed that black holes were a generic prediction of Einstein’s general relativity.

The discovery of neutron stars10 sparked interest in gravitationally collapsed compact objects as a possible astrophysical reality. In 1963, a young mathematician, Roy Patrick Kerr11, found an exact so-lution to Einstein’s field equations of general relativity. His solution models the gravitational field out-side an uncharged rotating massive object (later the so-called rotating black hole). This solution is a gen-eralization of the Schwarz schild solution.

The theory of General Relativity predicts that a sufficiently compact mass will deform space-time to form a black hole. The term black comes from the fact that from such a body nothing, not even light, can escape. The term hole comes from the singularity, i.e. a space-time that possesses infinite density. John A. Wheeler12 introduced not only the term black hole, but also the “No Hair Theorem” postulating that all black holes can be characterized completely by only three externally observable classical parameters: mass, electric charge, and angular momentum. All other information (for which “hair” is a metaphor) about the matter which formed the

black hole, or is falling into it, dis-appears behind the event horizon, and remains there permanently in-accessible to external observers (see Fig. 4).

Long before space technology reached the required sophistication, black holes were predicted by physicists, but were perceived as fantastic by-products of theory at that time. Today, however, a wealth of observational data provides strong evidence of their existence even though they are not directly visible, and there is growing con-sensus that super-massive black holes exist in the centres of most if not all galaxies. In particular, there

Fig. 4: According to J. A. Wheeler, all information regard-ing the matter that formed the black hole is lost: “black holes have no hair”. (Credit: C. W. Misner, K. S. Thorne, J. A. Wheeler, Gravitation, W.H. Freeman & Co.).

10 A neutron star is a type of stellar remnant that can result from the gravitational collapse of a massive star. Such stars are com-posed almost entirely of neutrons.

11 Roy Patrick Kerr, 1934, Kurow, New Zealand, New Zealand mathematician.12 John Archibald Wheeler, 1911, Jacksonville, Florida – 2008, Hightstown, New Jersey, USA, US American theoretical

phycisist.

Fig. 5: Linear x-ray versus radio emission from super-mas-sive black holes (top right) down to stellar black holes (bottom left). This is an indication that mass is the only fundamental para meter characterizing black holes. (Credit: A. Merloni, S. Heinz, T. di Matteo, 2003, MNRAS, 345, 1057).

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are strong signs of a black hole of more than 4 million solar masses right at the centre of our Milky Way.

Types of Black Holes

According to observation and the-ory, there might be four types of black holes: 1. Super-massive black holes counting

millions to billions of solar masses. It is not exactly known how they form, but it is likely that they are a by-product of galaxy formation. Because of their location close to many tightly packed stars and gas clouds, they continue to grow on a steady diet of matter.

2. Intermediate black holes featuring a few thousand to a few tens of thousands of solar masses. They are thought to emerge from the agglomeration of stellar masses.

3. Stellar black holes having a mass of at least 3 solar masses. These form when a massive star collapses.

4. Miniature (or micro) black holes with masses much smaller than that of our Sun.

Using simultaneous x-ray and radio observational data of black holes, their x-ray luminosity can be re-lated linearly versus radio emission intensity (see Fig. 5). This strong correlation suggests that mass and radius are the only fundamental pa-rameters of black holes as predicted by the General Relativity Theory.

Up to now, no member of the fourth category, the miniature black holes, has been seen. It is thought that they formed in the early uni-verse, but disappeared in the mean- time. S. Hawking13 was one of the first to consider the details of a black hole whose Schwarzschild radius was the size of an atom. Such black holes are not necessarily low mass: for example, it requires 1 billion tons of matter to make a black hole the size of a proton. Rather, the small size means that their behav-iour is a mix of quantum mechan-ics and General Relativity.

Before black holes were discovered, it was known that the collision of two photons can cause pair produc-tion14. This is an example of con-verting energy into mass, in contrast to fission or fusion, which turn mass into energy. Pair production is one of the primary methods of forming matter in the early universe. Hawk-ing showed that the strong gravita-tional gradients near black holes could also lead to pair production. In this case, the gravitational energy of the black hole is converted into particles. If the matter/anti-matter particle pair is produced below the event horizon, then the particles re-main trapped within the black hole. In contrast, when the pair is pro-duced above the event horizon, it is possible for one member to escape to space, while the other falls back into the black hole. Thus, the black hole can lose mass by a quantum mechanical process of pair produc-tion to the outside of the event horizon (see Fig. 6). This process is called Hawking radiation.

Hawking also showed that the rate of pair production is stronger when the curvature of space-time is high. Small black holes have high curva-ture, so the rate of pair production is inversely proportional to the size and mass of the black hole, mean-ing that it is faster for smaller black holes. Thus, Hawking expects mini or primordial black holes, formed in the early universe, to have disap-peared since, thereby resolving the

13 Stephen William Hawking, 1942, Oxford, United Kingdom, British theoretical physicist and astrophysicist. 14 The term pair production refers to the creation of an elementary particle and its antiparticle, for example an electron and its

antiparticle, the positron, may be created.

Fig. 6: Evaporation of a black hole: Virtual particle-antiparticle pairs, gener-ated near the event horizon by quantum uncertainty, might separate: one particle of a pair might fall into the event hori-zon, while the other one can gain enough energy to escape the mighty gravitational field of the black hole and become a real particle: energy of the “black hole” is thus lost by the emission of particles. (Credit: ORACLE ThinkQuest Educa-tion Foundation)

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dilemma of where all those unob-served mini black holes are today.

The resulting Hawking radiation has two fundamental implications:

1. It steadily reduces the mass of the black hole which hence eventu-ally will disappear, and

2. It causes black holes to be not completely black.

The second effect will eventually al-low astrophysicists to observe black

holes directly in the near future thanks to the particles escaping in the form of Hawking radiation. Indeed, some theories predict that micro black holes could be formed at low energy levels such as are attainable now in particle accelerators. This prompted recently popular concerns to be raised fearing that at the Large Hadron Col-lider at the CERN in Geneva black holes could be generated with un-known further consequences. Such low energy quantum black holes, however, would instantly evaporate as

Hawking radiation, either totally or leaving only a very short-lived weakly interacting residue.

Evolution of Stellar-Mass Black Holes

Now that we have the mathemati-cal theory, i.e., the description of gravity and space-time around a massive body, we come to the ques-tion of how black holes form, and where they come from.

Fig. 7: Stellar evolution. Stars are formed within dense clouds of dust and gases. Depending on their initial mass, indicated here as multiples of solar masses, they end as brown dwarfs, white dwarfs, neutron stars or black holes. (Credit: www.ogonek.net)

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15 Subrahmanyan Chandrasekhar, 1910, Lahore, India – 1995, Chicago, US American astrophysicist with Indian roots, Nobel prize laureate in physics, 1983.

16 A white dwarf is a small, very dense star whose mass is comparable to the Sun while its volume is comparable to the Earth.17 Sounding rockets are sub-orbital rockets that carry a payload above the Earth’s atmosphere for a limited period of up to

15 minutes, but which do not place the payload into orbit around the Earth.

During his sea journey from Ma-dras to Southampton in 1930, S. Chandrasekhar15 developed the theory of white dwarfs16. Specifi-cally, he derived a mass limit for a white dwarf, and a universal rela-tionship between the mass and the radius of a star. During most of a star’s lifetime, nuclear fusion in the core generates electromagnetic ra-diation. This makes our Sun shine. The radiation exerts an outward pressure that exactly balances the inward pull of gravity caused by the star’s own mass. When the nuclear fuel is exhausted, the outward forces of radiation diminish, letting gravitation compress the star in-ward. The contraction of the core causes its temperature to rise, allow-ing the remaining material to be used as fuel. At the end phase of this evolution, a massive star can no longer produce energy in its core, and therefore the radiation from its nuclear reactions can no longer keep the star “puffed up”. Gravity then causes the core to collapse. The star’s outer layers may blast away into space, and the core may fall into a collapsed compact mas-sive object.

S. Chandrasekhar predicted that a massive star could collapse into something denser depending on the star’s initial mass. R. Oppenheimer and H. Snyder showed in 1939 that massive stars can collapse into black holes. Consequently, white dwarfs

with masses greater than the Chan-drasekhar limit undergo a further gravitational collapse, evolving into a different type of stellar remnant, such as a neutron star or a black hole.

Fig. 7 depicts the processes whereby a star undergoes a sequence of rad-ical changes during its lifetime. De-pending on the star’s initial mass, this lifetime ranges from a few million years only (for the most massive) to trillions of years (for the least mas-sive, which is considerably more than the age of the universe). Now, depending on the initial mass of the star, it will end up in a different type of collapsed object. For instance, a star with the mass of our Sun will evolve to a red giant, and then col-lapse to a white dwarf. If, however, the initial mass is at least 30 solar masses, a black hole is expected to form when the heavy star collapses into a supernova at the end of its life cycle. So, a black hole forms when a sufficiently massive object reaches a certain critical density, and its gravity causes it to collapse to an al-most infinitely small point. After a black hole has formed, it can con-tinue to grow by absorbing matter from its surroundings. It may even absorb other stars and merge with other black holes thereby forming super-massive black holes of mil-lions of solar masses.

Observational Evidence of Black Holes

The mathematical theory of black holes was firmly established, and their existence as a consequence of star core collapse was also predicted, but no black hole candidate was ever observed up to 1972. This is due to the fact that the footprints of black holes are absorbed by the Earth’s atmosphere.

The Evolution of X-Ray Astronomy

As shown above, a black hole may grow by incorporating matter from its vicinity. Before entering the black hole, this matter is heated up to very high temperatures, say to a million degrees to hundreds of mil-lions of degrees. At such tempera-tures matter is expected to emit x-rays. It was, hence, up to x-ray astronomy to explore the sky for black hole candidates. Since x-rays are absorbed by the Earth’s atmos-phere, such instruments must be taken to high altitude by balloons, sounding rockets17, or satellites.

The era of x-ray astronomy began with a sounding rocket flight car-rying a simple Geiger counter aboard in 1962. Its purpose was to investigate x-rays from the Moon, instead it discovered the first x-rays from an astronomical object outside

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the solar system. The Sun was known to be a x-ray source, but be-cause it is so much closer than other stars, no other x-ray source was ex-pected to be found. It came as a great surprise that it discovered both Scorpius X-1, the brightest x-ray source in the sky, and a com-pletely unexpected diffuse glow of x-rays known as the cosmic x-ray background radiation. During fur-ther sounding rocket flights, Cyg-nus X-1 (Cyg X-1) in the constel-lation Cygnus was discovered ranking amongst the strongest x-ray sources (Fig. 9).

Now, x-ray astronomy was penalized by the fact that the angular resolu-tion of such observatories were in-herently far lower than that of op-tical telescopes as a consequence of the difference in wavelengths. This means that measuring the direction to an x-ray source is much more

difficult than with light or radio waves. Therefore, the optical coun-terpart of those x-ray sources could not be determined at that time.

In December 1970, NASA launched the first satellite specifically de-signed for x-ray astronomy, UHURU. In 1971, it found that Cygnus X-1 exhibited a rapid var-iability of its x-ray flux with a pe-riod of 5.6 days, see Fig. 10. These variations allowed for gathering of data to assess its accurate position: two independent teams of radio as-tronomers discovered variable radio emissions from within the possible positions of Cygnus X-1. The meas-ured changes in the radio bright-ness occurred at the same time as the changes in x-ray brightness. With the more accurate radio po-sitions, astronomers could finally pin down the exact location of Cygnus X-1. It turned out that the

object was an x-ray binary system18; Cyg X-1 was estimated to have around 10 solar masses orbiting a companion star that was previously catalogued as a blue supergiant star with 30 times the mass of the Sun.

So now, what is Cyg X-1? Astro-physical logics exclude the possibil-ity that it could be a red giant since these stars would be easily seen in the optical wavelength band. Further, it cannot be a white dwarf since the Chandrasekhar mass limit is around 1.4 solar masses, therefore a 10 solar mass white dwarf cannot exist in a stable form. The same applies to the neutron star; the mass limit is around 3 solar masses to be stable. By elim-ination, we are left with a black hole. Cyg X-1 was therefore the first ce-lestial body widely accepted to be a stellar black hole candidate, and it re-mains among the most studied as-tronomical objects in its class.

18 The term binary system refers to two objects in space, usually stars, but also planets, galaxies or asteroids, which are so close that their gravitational interaction causes them to orbit about a common centre of mass.

Fig. 8: X-ray emission observed from the source Cyg X-1 using the EXOSAT observatory. (Credit: ESA/EXOSAT)

Fig. 9: The 30 solar mass blue supergiant star orbits every 5.6 days around an optically unseen, but very bright x-ray object, i.e. Cyg X-1. (Credit: NASA images archive)

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Cyg X-1 is about five million years old, and formed from a progenitor star that had more than 40 solar masses. Hence, the majority of the star’s mass was shed, most likely as stellar wind. If this star had then ex-ploded as a supernova, the resulting force would most likely have ejected the remnant from the binary sys-tem. Hence, the progenitor star may have collapsed directly into a black hole instead.

Black Holes in X-Ray Binaries

We know today that the bright x-ray source Cyg X-1 is a compact star, i.e., a black hole in a binary system orbiting around an optical bright supergiant star. Despite its in-visibility, the presence of the black hole is inferred through its interac-tion with the matter coming from the companion star (see Fig. 10). This in-falling matter is heated by the strong gravitational field of the black hole. It is this process by which astronomers can detect and study the environment of an other-

wise invisible black hole gaining in-sights about the physics of accretion. Most importantly, black holes in x-ray binaries provide a laboratory to test the behaviour of matter under physical conditions that are by far unattainable on Earth.

The matter attracted by the black hole cannot fall directly into it, since it has first to lose its angular momentum. Rather, it forms a rotating accretion disk around the black hole as predicted by N. I. Shakura and R. A. Sunyaev (1973). The rotation of the disk is differen-tial, with the inner portions com-

Fig. 10: An artist’s impression of the stellar mass flow from the star providing the material for an accretion disk around the x-ray source, black hole. Matter in the inner disk is heated to millions of degrees, generating the observed x-rays. (Credit: M. Kornmesser, L. L. Christensen, ESA & Hubble European Space Agency Information Centre)

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pleting an orbit faster than the outer portions. The basic idea behind the accretion disk is that viscosity in the gas disk converts the free energy of differential rotation into thermal energy, which is in turn is expended by radiation. As the energy is re-leased, the gas spirals inward, com-pleting many revolutions before significantly changing its distance from the central source. The amount of energy released by the gas in the disk increases as it draws closer to the centre. This means that most of the energy released by an accre-tion disk comes from the disk’s in-ner edge. In this accretion process energy is lost mainly as x-ray radi-ation making such binary systems some of the brightest x-ray sources in the sky.

Black Holes in the Centres of Galaxies

So far, we have discussed some as-pects of stellar black holes with a few solar masses. Yet, there is grow-ing consensus that black holes exist also in the centres of galaxies with masses millions of times that of the Sun. The earliest radio surveys of the sky were executed in the 1950s. Out of the plane of our Milky Way, most galaxies, identified otherwise as normal-looking galaxies, were found to emit radiation in the ra-dio energy band. However, some of those radio sources coincided with objects that appeared to be unusu-ally blue stars embedded in faint, fuzzy halos in the galactic centres. Because of their almost star-like ap-pearance, they were called “quasi-

stellar radio sources,” which by 1964 was shortened to quasar.

The optical spectra of quasars pre-sented a new mystery: their emis-sion lines were at odds with all ce-lestial sources then familiar to astronomers. The puzzle was solved by Maarten Schmidt, who in 1963 recognized that the pattern of emis-sion lines of the brightest known

quasar 3C 273 could be understood as coming from hydrogen atoms with a red shift of 16%. This implies that their emission lines were shifted toward longer, redder wavelengths by the expansion of the universe. With this red shift, 3C 273 is placed at a distance of slightly more than two billion light-years. This was a large, though not unprecedented, distance. Bright clusters of galaxies

Fig. 11: The heart of our galaxy is a veritable soup of stars, gas, and dust. In partic-ular, there is strong evidence of a black hole of more than 4 million solar masses at the centre of our Milky Way called Sagittarius A*. (Credit: Kassim, LaRosa, Lazio, Hyman, 1999, NRAO Very Large Array)

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for instance had been identified at similar distances. However, 3C 273 is about 100 times more luminous than the brightest individual galaxy in those clusters, and nothing so bright had ever been seen so far away.

It came as an even bigger surprise when it was seen that the bright-ness of quasars can vary significantly on timescales as short as a few days. This in turn implies that the total size of those quasars cannot be more than a few light-days across. Later research revealed that they reside in the centres of their host galaxies. So, quasars are objects of very high luminosity located in the very cen-tres of galaxies, and are powered by

gas spiralling at high velocity into an extremely large black hole. The brightest quasars can easily outshine all the stars in the host galaxy, which makes them visible even at distances of billions of light-years. Quasars are therefore amongst the most distant and luminous objects known so far.

The Black Hole in the Milky Way

Quasar 3C 273 was the first extra-galactic black hole detected in 1963, and it stimulated researchers to look right into the centre of our own galaxy to search for a strong radio source there. The prescient applica-

tion of the then speculative black hole model for quasars led Lynden-Bell and Rees in 1971 to anticipate that our galactic centre would also contain a super-massive black hole. Subsequently, Balick and Brown (1974) found a compact radio source indeed which was named Sgr A* (to distinguish it from the more extended emission of the Sgr A, and to emphasize its unique-ness) eight years after its discovery. More precise high-resolution ob-servations in 1981 with the Very Large Array (VLA) at the European Southern Observatory (ESO) in Chile revealed that it is located near the dynamical centre of the galac-tic nucleus. All these observational signatures make it clear that Sgr A* is a very unusual object, rendering it a prime suspect for the location of a putative super-massive black hole (see Fig. 11).

Over 16 years of observation cam-paigns of the region right in the centre of our galaxy have confirmed the existence of a super massive black hole there. 28 individual stars have been tracked orbiting a com-mon, invisible point (Fig. 12). Usu-ally these stars would be obscured by gas and dust, though ESO’s in-frared telescopes were able to peer deep into the black hole’s lair. Judg-ing by the orbital trajectories of these stars, astronomers have not only been able to pinpoint the black hole’s exact location, they have also deduced its mass which amounts to 4 million solar masses. At exactly this location is the compact radio source Sgr A*. All the stars there are moving extremely rapidly: one of them even completes a full orbit within 16 years.

Fig. 12: Yearly location of stars near Sagittarius A* orbiting the common, in-visible compact radio source. (Credit: A. Ghez, UCLA Galactic Center Group)

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Flares From Our Galactic Centre Black Hole

The fast motion of stars and gas around the galactic centre suggested that something very massive must be hidden there. Indeed, Sagittarius A* is believed to be powered by a super-massive black hole. Long-term monitoring has led to the dis-covery of several near-infrared and x-ray flares from this object. This is extremely exciting because it’s the first time that the super-massive black hole right in our front yard could be observed devouring chunks of material. During time spans of just a few minutes, x-ray emissions from Sgr A* became 45 times brighter than normal, before

declining to pre-flare levels a few hours later. These events have pro-duced compelling evidence of a sig-nificant modulation in the x-ray light-curve with a quasi-period of around 17-22 minutes (see Fig. 13). These periods are rather intriguing because simple considerations place the regions where this emission is generated at roughly 3 Schwarz-schild radii above the event horizon for a black hole mass of 4 106 so-lar masses. The energy released in the flare corresponds to a sudden in-fall of matter with about as much mass as a comet or an asteroid. Sev-eral models have been invoked to explain these quasi-periodic mod-ulations. Recent magnetohydrody-namics simulations of Sgr A*’s disk

Fig. 13: Near-infrared flare observed from our own galaxy super-massive black hole, Sgr A*. Quasi-periodic modulations are indicated with arrows. (Credit: F. Me-lia “The Galactic Supermassive Black Hole”, Princeton University Press)

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have demonstrated disk instabilities that enhance the accretion rate for several hours, possibly accounting for the observed flares. Falanga et al. (2007) carried out ray-tracing cal-culations in a Schwarzschild metric to determine the light-curve pro-duced by general relativistic effects during such a disruption (see Fig. 14). This figure also shows how an ob-server from Earth would observe space-time around the black hole located in our galactic centre.

Outlook

Since the beginning of x-ray astron-omy in the 1960s, the steady in-crease in the capability of space ob-servatories has led to the detection of high-energy radiation from ob-jects of all scales in the universe, from compact sources such as black holes to the diffuse hot plasma per-vading galaxies and clusters of gal-axies. Thanks to this advancement, we now know that the basic phys-ical processes behind the emission of energetic radiation in most cos-mic sources pertain to two main categories: accretion physics and particle acceleration mechanisms.

So, accreting black holes are ideal laboratories for studying both phys-ical properties of accretion onto compact objects and effects of gen-eral relativity in the strong gravita-tional field regime. New x-ray and black holes phenomena are fre-quently discovered, which have no explanation in terms of established theory. New missions exploiting all electro-magnetic wavelengths are still needed to resolve new myster-ies from massive black holes. At the same time, experiments like those executed at CERN in Geneva will resolve the mysteries of micro black holes, e.g., the enigmatic evapora-tion from mini black holes.

Fig. 14: The view of matter orbiting in an accretion disk at the edge of the event horizon for a non-rotating black hole. The first figure is for an observed in-clination angle of 30 º, the second and third for 60 º and 80 º, respectively. (Credit: Fa-langa et al, ApJ, 2007)

Maurizio Falanga grew up in Basel. After his electronics apprenticeship in 1990 under Edi Blatter, a Basel, Switzerland, based radio and tele-vision marketing company, he re-ceived the “Eidgenössische Matura Typus C” in Zürich, 1993. He then enrolled at the University of Basel in theoretical physics and astron-omy. He concluded his studies with the diploma in 1998. In 2002, he received his Ph.D. degree in astro-physics from the University of Rome La Sapienza. His Ph.D. thesis work included theoretical general relativistic ray-tracing calculations to reproduce the light curve emit-ted by matter orbiting in the strong-field regime around a black hole, or from a neutron star surface. He then was a Postdoctoral Fellow, at the

Service d’Astrophysique (High En-ergy Division), Paris until 2006. Thereafter, Maurizio Falanga was a Research Scientist, at the Unité Mixte de Recherche, University of Paris. His research interests are focused on accretion and emission in neutron stars, white dwarfs and black holes, physics of the pulsar magnetosphere, x-ray polarization, accretion wind models, radiative transfer, star atmos-pheres, magneto hydrodynamics, plasma instability, type I x-ray bursts, numerical simulations, mapping super-massive black holes. Maurizio Falanga has published over 100 pa-pers in his research fields. At the same time, he was supervising un-dergraduate and Ph.D. students. Falanga has given numerous lectures for example at the Vatican High School in Rome, or for a variety of associations in Switzerland, Italy, and France.

He is a member of the INTEGRAL Users Group of ESA, and a mem-ber of the Large Observatory For X-ray Timing (LOFT) Science Working Group (Dense Matter, Strong Gravity). LOFT is a me-dium-class mission selected for the assessment phase of the ESA M3 Cosmic Vision call. He has also served on numerous Time Alloca-tion Committees for orbiting mis-sions like INTEGRAL, Chandra or XMM-Newton. He is also a mem-

ber of the Editorial Board for Ad-vances in Astronomy Journal, and for Astronomy Studies Develop-ment Journal.Since 2009, he has been Science Program Manager at the Interna-tional Space Science Institute (ISSI) in Bern, Switzerland. Apart from the programmatic responsibilities at ISSI, he continues active research in high-energy astrophysics.

The Author

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