supermassive black holes

Black Hole Physics and Supermassive Black Holes Athanasios Tzikas Goethe University of Frankfurt, Germany Department of Theoretical Astrophysics June 26, 2016 Abstract This article offers an introduction to one of the most mysterious and intriguing objects in the universe, black holes. In the first part, a description to black hole physics is given, defining the physical and mathematical properties. In the second and biggest part, supermassive black holes are introduced, by describing their char- acteristics, their role in the universe, some ways of observation, as well as, some possible theories of formation. 1

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Black Hole Physics and Supermassive Black Holes

Athanasios TzikasGoethe University of Frankfurt, GermanyDepartment of Theoretical Astrophysics

June 26, 2016


This article offers an introduction to one of the most mysterious and intriguingobjects in the universe, black holes. In the first part, a description to black holephysics is given, defining the physical and mathematical properties. In the secondand biggest part, supermassive black holes are introduced, by describing their char-acteristics, their role in the universe, some ways of observation, as well as, somepossible theories of formation.



1 Introduction to Black Hole Physics 31.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2 General Relativity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.3 Stellar black hole formation . . . . . . . . . . . . . . . . . . . . . . . . . 51.4 Stellar black hole observation . . . . . . . . . . . . . . . . . . . . . . . . 6

2 Supermassive Black Holes 72.1 Definition and characteristics . . . . . . . . . . . . . . . . . . . . . . . . 72.2 Supermassive black holes in active galaxies . . . . . . . . . . . . . . . . . 72.3 Observational evidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.4 Sagittarius A* . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.5 The M − σ relation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.6 Black hole ’feedback’ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.7 Possible theories of formation . . . . . . . . . . . . . . . . . . . . . . . . 172.8 An interesting recent observation . . . . . . . . . . . . . . . . . . . . . . 20

3 Conclusion 23


1 Introduction to Black Hole Physics

1.1 Definition

Physically, a black hole is a region in spacetime, which is empty and dark. Empty, be-cause it has nothing inside it, in other words it lies in vacuum, and dark, because gravityis so strong that pulls the light back. So, we can think of black holes as macroscopicastrophysical objects creating very strong gravitational field that nothing can escape.Mathematically, it can be seen as a singularity in our equations. In other words, equa-tions describing spacetime, diverge at some values and our metric is considered to bephysically singular there. This is indeed remarkable, because we can ”see” black holesas mathematical infinities lying in our own paper. Nevertheless, they are considered tobe the simplest objects, due to the fact that we need only until three degrees of freedomto describe them completely: the mass M, the angular momentum J and the charge Q.This is the most general description that has been found for a black hole, so far, and itwas derived by Kerr and Newman in 1965.

1.2 General Relativity

Einstein’s theory of General Relativity is a classical theory of gravity and gives a connec-tion between gravity, geometry and matter. The word ’classical’ means that it does nottake into account quantum mechanical effects, such as Heisenberg’s Uncertainty Princi-ple. This theory is governed by Einstein’s Field Equation, which is a tensor equation.That means, it remains invariant under coordinate transformation. In geometric or lengthunits, where everything is measured in length, Einstein’s field equation reads:

Rµν −1

2gµνR = 8πTµν , (1.1)

where, Rµν is the Ricci tensor, measuring the local curvature, R is the Ricci scalar, gµν isthe metric tensor and Tµν is the stress-energy tensor, providing us with information aboutthe energy and the momentum of matter. We see that gravity represents a fundamentalcurvature in the fabric of spacetime. According to (1.1), which is written in length units,matter indicates spacetime how to bend, while spacetime indicates matter how to moveinto it. The bigger the energy-mass into a specific region, the bigger the curvature is and,thus, the stronger the gravity is.


Figure 1: Bending of spacetime in 3 different cases.

Now, by imposing spherical symmetry, staticity and vacuum, we get the simplest so-lution of a BH from Einstein’s equation, which is called Schwarzschild Solution:

ds2 = −(

1− 2M


)dt2 +

(1− 2M



dr2 + r2dθ2 + r2 sin2 θdφ2 (1.2)

This line element describes the spacetime around a spherical and static black hole of massM, which lies in vacuum. By referring to the mass M of the black hole, we mean theenergy-mass that has been transformed from an initial compact stellar mass, into energyof warped spacetime. There is no compressed matter of mass M that lies inside the blackhole. It is only vacuum. Furthermore, we can see that we have one physical singularityat r = 0, and one coordinate singularity at r = 2M . The coordinate singularity can beeliminated in other coordinate systems, while the physical singularity remains a completemystery to us. The surface around the black hole with radius

Rs = 2M, (1.3)

is called Event Horizon, and is the point of no return. The escaping velocity of an object,orbiting around this surface, is equal to the speed of light. Therefore, If an object passesthrough the Event Horizon it cannot come back, due to the strong gravitational pull.This radius, Rs, is also called Schwarzschild radius and represents the radius of the staticand spherical black hole.


Another solution, more realistic, is the Kerr Solution, which describes the spacetimecreated by an axially symmetric, stationary and rotating black hole in vacuum, with anangular momentum J:

ds2 = −(

1− 2Mr


)dt2 − 4Mrasin2θ



δdr2 + ρ2dθ2 +


ρ2sin2θdφ2, (1.4)


ρ2 = r2 + a2cos2θ,

δ = r2 − 2Mr + a2,

A = (r2 + a2)2 − a2∆sin2θ,

a = J/M.

The line element (1.4) is written in Boyer-Lindquist coordinates. For this solution theEvent Horizon is not at r = 2M , but it depends on the Kerr parameter, α, which showshow fast the black hole is spinning. There is an upper limit for the rotation of a blackhole and, thus, for the parameter α.For α = M , we have the maximum rotation with Jmax = M2, and the horizon lies atdistance RH = M .For α = 0, we conclude to Schwarzschild metric (1.2) and, thus, the horizon is at RH =Rs = 2M . Therefore, Kerr solution could be seen as a generalization of Schwarzschildsolution. Nevertheless, both solutions are asymptotically flat, meaning that for very largedistances, r →∞, spacetime behaves as a Minkowski spacetime.

1.3 Stellar black hole formation

We should not forget to mention that the most usual birth of a stellar black hole, whichhas a mass of M ∼ 10M�, occurs with the death of a massive star with initial stellarmass

Mstar > 15M� (1.5)

When the fuels of the star run out, its core collapses upon itself in a supernovae explosion.The remaining core is becoming denser and denser, when it comes to a point that evenlight cannot escape its gravitational pull. What is finally left behind is a dark remnantwith huge amount of energy, the known black hole. It should, also, be mentioned that,depending on the initial stellar mass, after a supernovae explosion, a black hole can becreated directly, or, a neutron star can be formed first and, then, it may follow its pathinto a black hole. According to Tolman-Oppenheimer-Volkoff (TOV) limit, which givesthe upper limit of a star composed by degenerate neutron matter is 1.5 to 3 solar masses.Therefore, a neutron star with Mstar ≥ 3M�, could collapse into a black hole. The TOVlimit corresponds to an initial stellar mass of 15 to 20 solar masses or more for the creationof a black hole.


1.4 Stellar black hole observation

We are unable to detect black holes directly, since they emit no light. Therefore, theobservation becomes indirectly. Most of the times, stellar black holes are followed bya companion star, orbiting around them. When the star runs out of hydrogen in itscore and begins to expand, creates an accretion disk of matter/gas around the blackhole. As matter/gas spirals, transforms its kinetic energy into thermal energy, due tothe vast collisions between particles and, therefore, the material is heating up to milliondegrees, emitting enormous radiation, particularly at X-ray wavelengths. In other words,we observe the influence that the strong gravitational field has on the matter/gas aroundthem. Strong gravity means high acceleration and, hence, high frequency emission fromcharged particles, before entering the Horizon. Almost 50% of the energy of the matteris transformed into radiation. These stellar black holes are, also, called X-Ray Binaries,because we detect their X-rays. Next, by studying the Doppler shifts of the companionstar-spectrum, as it orbits, we can estimate the mass of the black hole.

Figure 2: Painting of GX 339-4 binary-system (2009/ On the left is the blackhole, surrounded by an accretion disk, and on the right is the companion star.

Figure 2, illustrates GX 339-4, a low-mass X-ray binary located about 26000 light-years away in the constellation Ara. In the system, an evolved star, no more massivethan the sun, orbits a black hole estimated at 10 solar masses, emitting X-ray photonsfrom disk regions close to the black hole.


2 Supermassive Black Holes

2.1 Definition and characteristics

Massive or supermassive black holes are the biggest type of black holes in our universe.These huge objects have a mass ranging from 106 to 109 solar masses and, so far, theyare detected only in the center of a galaxy. Observational evidence indicates that at leastone supermassive black hole lies at the center of almost every galaxy.In contrast to stellar black holes, which is expected to have a huge density, these oneshave a small density and sometimes close to the density of water. Considering a non-rotating black hole, we know that ρ = M

Vand V = 4


3. Also, the Schwarzschild radiusis proportional to the mass of the BH, according to (1.3). Therefore, we conclude thatthe density of a BH is

ρ ∝M−2 (2.1)

We see that, the bigger the mass, the lower the density is. This is expressed in lengthunits, where the mass is, also, expressed in length. To be more exact, in our usual,ordinary units

ρ =3c6

32πG3M2≈ 1.85 · 1019




kg/m3 (2.2)

Another characteristic is the tidal forces. In massive black holes these forces are muchweaker than in stellar black holes. In length units

Ftidal =M

R3∝M−2 (2.3)

which means, that a person who approaches a massive black hole will experience no bigdifference in the force between his head and his legs. Theoretically, this person could livefor a moment, but the radiation and energy, which are trapped into the inner horizon,would vaporize him.

2.2 Supermassive black holes in active galaxies

There are different observational ways to detect and determine the mass of a supermassiveblack hole. Of course, many of them have been made from the Hubble Telescope (HST),the Chandra X-Ray Observatory (CXO), or the ESO (European Southern Observatory),but here we will not proceed to the technical part.All galaxies, we have seen so far, are populated by a supermassive black hole. Some ofthem are active galaxies, such as Seyfert galaxies and quasars, and some of them areinactive. With the word ’active’, we mean that they contain an Active Galactic Nuclei(AGN). AGN is a region in the galaxy, orbiting around and outside the Event Horizon,where high intensity electromagnetic radiation is emitted, particularly X-rays. Therefore,we can take an X-ray picture of the AGN and through its analysis, using techniques, likereverberation mapping, we can estimate the central dark mass.Quasars are one type of AGN. They emit more energy than all the stars of our galaxy,giving us a spectacular show of radiation, because they ’feed’ supermassive black holes.Most of them have died out today, but they were populous at the early universe, in an


era called Era of Quasars. This epoch of maximal quasar activity in the universe, datingfrom 109 to 1010 years after the Big Bang, peaked at the same time, or slightly before,the epoch of maximal star formation. Moreover, they are highly redshifted, ranging fromz=3 to z=6, or even higher, depending on their position in the universe. Quasars are,also, surrounded by accretion luminous gas disks, consisting mostly of ionic and atomicform of Hydrogen, while relativistic Plasma Jets are created due to the magnetic fieldof the matter, before it enters the Horizon. These jets are emitted from the poles ofthe black hole and they travel long distances into space, with a speed close to the speedof light. The detection of the first Quasar occurred in 1950. That was, also, the firstevidence for these giant dark objects.

Figure 3: Quasar PKS 1127-145, taken by Chandra X-Ray Obrervatory in 2000. Theimage is 60 arcsec on a side.

The luminosity of a quasar corresponds to

L ' 1042 → 1047erg · s−1 (2.4)

Let us now examine the Eddington limit for such luminosities. Specifically, let us assumea quasar with L = LEdd = 1046erg · s−1 ' 1012L�. The Eddington limit is the highestlimit in the luminosity of any object and it is reached when the radiation force is equalto the gravitational force (hydrostatic equilibrium). Therefore, it should be

Frad ≤ Fgrav (2.5)

That implies a lower limit of the BH mass for a given luminosity

MBH > 0.8 · 108M�


1046erg · s−1


So, in order to power up a quasar which radiates close to the above Eddington limit, withsuch a huge luminosity, a deep relativistic gravitational potential of a supermassive blackhole is needed with a mass of at least MBH = 8 · 107M�. Such a mass would have a sizeslightly larger than 1AU.


2.3 Observational evidence

A stronger observational evidence, for the existence of massive black holes, rises fromthe study of stellar dynamics near the center of inactive galaxies. These galaxies are con-sidered to be weakly active, or, others do not contain any AGN at all. As a result, it ispossible to observe more clearly the orbits of the stars close to the center. Thus, we mea-sure their rotational velocities V and the velocity dispersion σr. Velocity dispersion refersto the statistical dispersion of velocities about the mean velocity of the stars. It can, also,

be seen as the average velocity of the combined stellar motions, σr = 〈(υr − 〈υr〉)2〉1/2 .First of all, we need the line spectrum of the orbiting stars. Radial velocities, υr, are mea-sured from the Doppler shift of the lines, while the velocity dispersion, σr, is measuredfrom the line width. We know that redshift, z, which is interpreted here as relativisticDoppler shift, is connected to the radial velocity by

z =λobs − λemission


(1 + υr


1− υrc


− 1 (2.7)

For the non-relativistic case (z << 1) we get z ≈ υr/c. After some approximations, wecan connect the radial velocity υr to the rotational velocity V.Below are illustrated observational data from the galaxy of Andromeda, M31. This galaxycontains a nuclear star cluster embedded in a normal bulge. Its nucleus appears to bedouble, in HST, as shown in Figure 4. The blue nucleus (left) is the region of the centralblack hole and the yellow nucleus (right) is the star cluster orbiting around with theblue nucleus at a separate distance of almost 1.7pc. They cannot be both star clusters,because if they were, the dynamical friction would make them to merge in few orbitaltimes and that doesn’t happen.

Figure 4: HST WFPC2 color image of M31, obtained by Lauer et al (1998 Astron. J.116 2263).

Below in Figure 5, we see that the relative rotational velocity of the system increasesup to 200km/s before it drops to 0 in the center, while the velocity dispersion increases upto almost 250km/s towards the center. That implies a circular orbit period of 50000 years.


We, also, know that in the blue region lies the black hole, because the dispersion-peak isalmost centered on the blue nucleus.

Figure 5: Rotational velocity V(r) (bottom) and velocity dispersion σ(r) (top) of thenucleus major axis of M31. (Taken from Kormendy and Richstone in 1995).

In 1988, Kormendy derived for M31 a central dark object mass of M ' 3·107M�. Theformula he used, in order to calculate the enclosed mass, is derived by the combinationof the Collisionless Boltzmann Equation and the Poisson Equation :

M(r) =rV 2




The inner mass depends not only on the rotational velocity, but also on the radial velocitydispersion, due to the fact that in stellar systems, some dynamical supports come fromrandom motions of the stars. On the RHS of (2.8), it should, also, be a factor multiplyingwith the second term, which would contain the azimuthal dispersion velocities, σθ andσφ, but this factor is considered to be 1 for many galaxies. From the above, we derivethe central mass distribution M(r) and we compare it to the light distribution L(r). IfM(r)/L(r) rises rapidly as r → 0, then we have found a central dark object.

Gas dynamics is another useful technique for determining the inner mass, and it isbased on the observation of nebular emission lines from the central gas/dust disk in thegalaxies. Some active giant elliptical galaxies, such as M87, contain nuclear disks ofdust and ionized gas and they emit, also, in optical wavelengths. High resolution imageshave been taken from M87, and its optical spectrum shows the characteristic kinematicsignature of the rotating disk. The total velocity range is up to 1445 km/s.


Figure 6: High resolution image of the central region of the giant elliptical galaxy M87(1998).

In Figure 6, we see that the optical spectrum of M87 is highly Doppler shifted. Thatindicates a Keplerian rotation of the disk around a supermassive black hole of estimatedmass M ' 3 · 109M�. If there were no mass at the center, the optical spectrum would bestraight line.

Figure 7: Observational data (black stars) from M84 with four different Keplerian fitshave been over plotted to the data (2010).


In Figure 7, gas dynamics in M84, indicates an inner mass between 4.2 · 108M� and4.7 · 108M�. ’Black stars’ correspond to observational data, while blue, green, red, andorange lines show Keplerian fits, corresponding to a central dark mass of 4.3, 4.5, 4.7 and4.2 in units of 108M� respectively. A best fit for this model can not be extracted withcertainty, but the range where the mass lies can be deduced.Maser dynamics is, also, another powerful tool in estimating black hole masses and itis based on radio interferometry of water maser emission from circular molecular disksaround massive black holes. Analogously to the gas dynamics method, maser dynamicsdepends on measuring velocities from water megamasers, orbiting in a torus surroundingthe central black hole. Maser dynamics follows two independent ways of measuringvelocities. On the one hand, it uses observations of nonsystemic-velocity componentsorbiting the black hole in a Keplerian motion. On the other hand, the near-systemiccomponents allow us to measure the drift and the centripetal acceleration, in order tocalculate the central mass.

Figure 8: Example of maser dynamics for estimating black hole masses in the galaxyNGC 4258. Adapted from Kormendy and Ho (2013).

The spectrum of the water maser emission, in the Seyfert galaxy NGC 4258, consistsof maser components at the systematic velocity of the galaxy, as well as high-velocitymasers, which are Doppler shifted. On the left of Figure 8, there is a diagram showingthe torus surrounding the central object and the position of non-systemic (red and blue)and near-systemic (green) masers. On the right, the same points are plotted in a velocityversus radius diagram. It is clearly seen that blue and red dots follow a Keplerian rotationcurve. The green filled circle is the corresponding mean velocity point. Keplerian rotationindicates that the motion is dominated by the black hole and, hence, we can estimateits mass from M = V 2R/G. Although this method seems promising, it still has somedisadvantages. That can happen when the mass of the disk enclosed by the masers iscomparable to the mass of the central object, or in the presence of a massive nuclear star


cluster. In those cases masers do not follow a Keplerian motion and, thus, we are notable to give an accurate estimation of the mass.Finally, another method detecting supermassive black holes could be gravitational lensing.Although this method works excellent to simulations, it is a far less common, since it hasnot been used in any real data. That is, because we need a pair of central images. Onebefore the formation of the hole (original image) and one after (bending image), in orderto determine the degree that the original image was bend and then connecting it to thecentral mass.

2.4 Sagittarius A*

The best place to search for a massive black hole is our own galaxy. In 1974, Balickand Brown found a compact radio source, 26000lyr far from our solar system. In 1982,the object was named Sagittarius A* (SgrA*) by Brown, to distinguish it from the moreextended emission of the Sagittarius complex, and to emphasize its uniqueness. Recentobservations from stellar dynamics of stars orbiting 0.2pc from its center, indicate a cen-tral mass of (4.3± 0.38) · 106M�. Many of the orbiting stars have radial velocities upto 1000km/s when they pass near the dark central of SgrA*, the velocity is increasingdramatically. Speeds such as this could only be explained, and achieved, with a darkmassive enclosed object as mention above.

Figure 9: Proper motion of stars in the center of the Milky Way (Kormendy and Ho,2013).


In the central region, apart from black hole, it could, also, be supposed that a clusterof smaller objects determines the stellar movement. But, the star S2, gave the answer tothis. S2 approached close enough to the central region and nothing was there, no activity.So, it had to be circling around a single massive dark object, rather than a cluster ofobjects.In Figure 9, panel (a) shows the orbit of almost 20 stars in the vicinity of the centralblack hole. Panel (b) shows the orbit of the star S2 as measured from 1992 to 2012.Blue and red dots are observations, while in green it is shown the pericenter of the orbit,which coincides with the location of SgrA*. Its period has been measured to be 15.8years and its orbit is almost closed, which tells us that almost all of the mass is locatedat its pericenter. Panel (c) shows the velocity curve for the same star.Measuring velocities, and assuming a Keplerian fit for the data we can easily estimatethe mass of the black hole at that location.

Figure 10: Enclosed mass as a function of radius from SgrA* in our galactic center (Takenfrom Schodel et al. in 2002).

In Figure 10, the data points are stars orbiting around SgrA* and, for each one, theenclosed mass for its Keplerian orbit has been determined. The enclosed mass for theseobservations corresponds to (2.6 ± 0.2) · 106M�. Recent observations indicate that theenclosed mass lies at (4.3± 0.38) × 106M�, as mentioned above. More analytically, thesolid curve is the best fit to all data points and represents the sum of a point mass2.6 · 106M� and a nearly isothermal stellar cluster with central density 3.9 · 106M� · pc−3,core radius 0.34pc and power-law index α = 1.8.


2.5 The M − σ relation

An important discovery is the relation only between the black hole mass and the velocitydispersion of the host galaxy bulge (M − σ), which is suggested in 2000. One usefulaspect of this relation is that it allows one to estimate a galaxy’s central black hole massonly from the velocity dispersion, which is more easily measured. Also, this relation givesa calibration to the mass estimation from the previous techniques mentioned above. Weare principally interested in predictions of the form




)= α + βlog



Figure 11: The M − σ relation for galaxies with dynamical measurements (2009).


In Figure 11, the color of the error ellipse indicates the Hubble type of the hostgalaxy: elliptical (red), S0 (green), and spiral (blue). Arrows indicate 3σ68 upper limitsto black hole mass. For reasons of clarity, we only plot error boxes for upper limitsthat are close to or below the best-fit relation. The saturation of the colors in the errorellipses, or boxes, is inversely proportional to the area of the ellipse or box. Squares aregalaxies that we do not include in our fit. The symbol indicates the method of the blackhole mass measurement: stellar dynamical (pentagrams), gas dynamical (circles), masers(asterisks). The line is the best fit relation and it is given by

MBH = 108.12 ·( σ

200 · km · s−1



2.6 Black hole ’feedback’

Every massive galaxy appears to have a massive black hole at its center whose mass isabout 0.2% of the mass of the galaxy’s bulge. A remarkable recent discovery, which ismotivated by M −σ relation, is that the central mass of the black hole is strongly corre-lated with the mass of the stellar bulge of its galaxy, rather than with the whole galaxy.According to this correlation, the growth of the massive black hole is proportional to thecentral galactic bulge. The relation, MBH ∝Mgb, is known as ’feedback’ and the precisenature of it, is still unknown.

Figure 12: Correlation between the mass of the massive black hole (central black point)and its host galactic central bulge (spherical central yellow region).


In Figure 12, we see that the bigger the supermassive black hole the bigger the centralbulge is, while other parts of the galaxy, such as the disk, remain almost unaffected.As mentioned above, why and how ’feedback’ occurs remains an open question. Theanswer should depend on how much of the releasing energy, from the accretion into thesupermassive black hole, interacts with the matter of the galaxy. As black hole growsto 0.2 of the bulge mass, through accreting matter, it releases nearly 100 times thegravitational binding energy of its host galaxy. So, feedback depends not only on thetype of the releasing energy, but also on the type of the galactic matter. For example, ifthe releasing energy is electromagnetic radiation and matter is just star, then very littleinteraction is expected.We can distinguish 2 forms of feedback, Radiative and Mechanical feedback. On the onehand, if the matter consists of gas, perhaps with embedded dust, the radiative output ofthe black hole can, both, heat the gas and accelerate it via radiation pressure. On theother hand, if significant AGN power emerges in winds or jets, mechanical heating andpressure accelerate the gas. The radiative form of feedback is most effective when theblack hole is accreting close to its Eddington limit, while the mechanical form operatesat rates below the Eddington limit and dominates in galaxies at late times, as shown byX-ray observations.

2.7 Possible theories of formation

Formation and evolution of supermassive black holes is an open field of research forscientists. Although, the accurate mechanism has not been found yet, many possibletheories have been proposed and here 3 of them are presented.Quasars are highly redshifted, due to the fact that they lie at long distances from us andthe universe is expanding. Therefore, by observing quasars, we take information of theearly universe. The shortest distant quasar is at about 1Gyr far away from us, whilethe longest is at 13Gyr, which is close to the age of the universe, which is measured tobe almost 13.7Gyr. Hence, supermassive black holes should have been created beforethe universe was 1 billion years old, in order to power up quasars. The first suggestedsolution to this problem is that the first massive black holes could have been created inthe early universe, as remnants of Population III stars. These stars represent the firstgeneration of stars formed out of zero metallicity gas, and numerical simulations suggestthat they were very massive, with M ≈ 100M�. According to specific calculations andmodels, these giant stars burned hot and fast and, hence, died young, creating manyintermediate-mass black holes and binary systems.

Below, in Figure 13, we see a region of a virtual early universe, which is set in motionby equations describing the properties of the primordial gas, which is gathered inside thewebs. Stars have been born in dense regions of the primordial gas, feeding with matterthese first intermediate-mass black holes. The blue points in the densest regions of theweb, is where the largest galaxies and black holes grew.


Figure 13: Computer simulation represents a region in the early universe.

A second suggestion is that supermassive black holes may have been formed fromgalactic mergers. Tow galaxies containing massive black holes in their center, may collideand create a new galaxy with a bigger supermassive black hole. The merging process isproposed by Einstein. According to his theory, when two massive bodies accelerate aroundeach other, they disturb spacetime, creating ripples, known as gravitational waves. Asthe waves propagate outwards, they carry some of the energy of the pair orbiting bodies,causing them to spiral closer and closer. Finally, the merging occurs after millions of years.CXO has taken images of NGC 6240, an active galaxy about 400 million light years fromthe Milky Way, as shown in Figure 14. According to X-ray images of the galactic nucleusof NGC 6240, this galaxy is the first identified to have two supermassive black holes inits center. These two black holes are 3000lyr apart and will eventually collide in a fewhundred million years, creating an even more massive object. This observation supportsthe idea that supermassive black holes can be formed from the collision of other galaxieswith massive black holes in their center. Actually, our galaxy is, also, thought to becreated through this process, and the ’terrifying’ part is that it may collide with theAndromeda galaxy in the future.


Figure 14: X-ray image of NGC 6240, containing two AGN at its center. Taken by CXO.

A third suggestion is that a supermassive black hole may be created from the mergingof many stellar black holes. Again, CXO has discovered an amazing number of ordinaryblack holes orbiting within 70lyr around the SgrA*, as shown in Figure 15.

Figure 15: X-ray image taken at Chandra X-ray Telescope, identifying a swarm of blackholes orbiting around SgrA* (Chandra Swarm).


As stellar black holes orbit around the galaxy, they are affected by lower-mass sur-rounding stars. Between them a gravitational net of action and reactions is created,which accelerates the stars and decelerates the black holes. As a result, black holes loserotational velocity and they should eventually merge with SgrA*, adding to its mass.

2.8 An interesting recent observation

So far, scientists have discovered almost 40 quasars with z > 6, containing supermassiveblack holes in their centers with masses of about 109M�. In 2015, astronomers detectedthe most luminous quasar in the sky at redshift z=6.3, which contains one of the biggestsupermassive black holes ever seen. Its code name is SDSS J010013.02+280225.8, or,J0100+2802 for short, and is located in 12,8 billion years far from Earth. The estimatedmass is 1.2 ·1010M�, which is consistent with the derived theoretical mass of 1.3 ·1010M�,assuming that this quasar accretes close to the Eddington limit. Although massive blackholes of similar size have been found in local giant elliptical galaxies and low-redshiftedquasars, this is the first, at z > 6, system known to have a black hole of such a size.

Figure 16: Known quasars at a diagram of their luminosity vs their central mass.

In Figure 16, we see that J0100+2802 is the brightest and the heaviest of all. Its


bolometric luminosity corresponds to

L = 1.6 · 1046erg · s−1 ' 4.2 · 1012L�, (2.11)

which makes it 4 times brighter than the so far brightest quasar SDSS J11481+5251(z=6.42) and 7 times brighter than the most distant known quasar ULAS J11201+0641(z=7.085). Bellow are given the optical spectrum and the rest-frame spectral energydistributions of these 3 quasars, by illustrating the difference in their luminosities, asmentioned above.

Figure 17: The optical spectra of J0100+2802 (z=6.3), taken in red, blue and blackcolours and the spectra of J11481+5251 (z=6.42), taken in green.

In Figure 17, the two spectra of J0100+2802 are offset upward by one and two verticalunits for reasons of clarity. Although the spectral resolution varies from very low tomedium, in all spectra the Lyα emission line, with a rest-frame wavelength of 1216


angstroms , is redshifted to around 8900 angstroms, giving a redshift of z=6.3. TheLyman-alpha line, or, Lyα is a spectra line of hydrogen, which is emitted when theelectron falls from quantum state with n=2 to the basic state with n=1. As we see,J0100+2802 is a weak-line quasar with continuum luminosity about four times higherthan that of J11481+5251 (in green on the same flux scale), which was previously themost luminous high-redshifted quasar known at z=6.42.

Figure 18: The rest-frame spectral energy distributions of J0100+2802 (red),J11481+5251 (black) and J11201+0641 (blue).

In Figure 18, are given the redshifts of these 3 quasars. Again, this figure showsthat the luminosity of J0100+2802 (z=6.3) in the ultraviolet/optical bands is about fourtimes higher than that of J11481+5251 (z=6.42), and seven times higher than that ofJ11201+0641 (z=7.085).


3 Conclusion

Supermassive black holes were introduced to astrophysics as purely theoretical concepts,which were needed to explain quasar luminosities, as well as, the high velocity dispersionthat matter appears at the center of the galaxies. Many possible theories, describing theirevolution and formation, have been proposed, but, without knowing the exact mechanism.Black holes are indeed the simplest objects in our universe and, at the same time, themost mysterious. However, as Steven Hawking said, General Relativity brings about itsown downfall by predicting singularities, because they indicate that spacetime will behighly distorted with a very small radius of curvature at the center of the black hole.Therefore, in order to discuss the center, we need to find a theory that combines GeneralRelativity and Quantum Mechanics. We need a Quantum Field Theory of Gravity.



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