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BASIC EXTRAGALACTIC ASTRONOMY - Part 5: Black Holes and Quasars

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Rudy E. Kokich, Alexandra J. Kokich, Andrea I. Hudson

22 Feb, 2020



Part 5:                                                Black Holes and Quasars





Black holes are regions of space of such extreme gravitational field intensity (space-time curvature) that no particle of matter or electromagnetic radiation can escape their gravitational influence. In 1784 John Michell, an English clergyman and natural philosopher, was the first to propose the existence of massive "dark stars" with such intense gravitational pull that their escape velocity would exceed the speed of light. In 1796 the idea was given credence by French mathematician Pierre-Simon Laplace. In 1915 Einstein's theory of general relativity offered a theoretical framework for explaining how a sufficiently compressed mass might curve spacetime to create a black hole. Later the same year, Karl Schwarzschild, while in the trenches on the Russian front, derived the first precise solution to Einstein's field equations relating mass, energy, and gravitation in terms of local spacetime curvature.


Schwarzschild's equation for a non-rotating black hole, where G is the gravitational constant, defines the radius, Rs, of a sphere which must contain mass M in order for the escape velocity to be equal to the speed of light, C.


Rs = 2GM / (C^2)                                                                                                                             (36)


Rs, named the Schwarzschild radius, specifies the radius of a sphere, or the event horizon of a non-rotating black hole, within which all particles, photons included, must fall into the central body. In the middle of a black hole lies a point, a gravitational singularity, where spacetime curvature, gravitation, and density become undefinable, and physical laws cease to make mathematical sense. It can be calculated that at 1.5 times the Schwarzschild radius lies the photon sphere, where photons, if undisturbed by infalling matter, are contained in circular orbits around the black hole.


It is not surprising that initially most scientists, Einstein included, considered this black hole model to be a mathematical curiosity with no equivalent in physical reality. The attitude persisted for decades, especially with presumed impossibility of observational confirmation. Since the 1950's astronomy research gradually expanded from visible light to cover the full range of the electromagnetic spectrum, from radio waves to gamma rays. The discovery of new objects in the high-energy X-ray and gamma ray bands, like magnetars, active galactic nuclei (AGN), quasars, and blazars, suggested that nuclear reactions alone were not sufficient to generate the release of such enormous levels of energy. X-rays are a form of electromagnetic radiation of frequency and energy levels a thousand times higher than those of the visible light. Whereas visible light is emitted at temperatures on the order of 10,000 K, X-rays are produced when matter is heated to tens and hundreds of millions K. The existence of black holes, where such temperatures are brought about by gravitational compression of matter, became ever more plausible as a possible explanation.


The first suspected stellar mass black hole, discovered in 1971, was Cygnus X-1, an x-ray binary star system in which an invisible, compact object appears to be pulling mass from a large, visible companion. Stellar mass black holes are now thought to form by gravitational collapse of large stars at the end of their life cycles. In 1974, the detection of a strong x-ray source in the center of our galaxy, Sagittarius A, led to the discovery of a supermassive black hole (SMBH) weighing about four million Suns. Evidence now suggests that most, if not all, galaxies have a supermassive black hole in the center, some as massive as billions of Suns, which seems to play a crucial role in the formation of the galaxy. In 2000, in galaxy M82, NASA's Chandra X-ray Observatory space telescope discovered a new type of black hole of intermediate-mass between stellar mass black holes and supermassive black holes. In 2005, in spiral galaxy M74, a similar x-ray source was discovered around an intermediate-mass black hole estimated at 10,000 solar masses. Such objects which radiate 10 - 1,000 times more x-ray energy than neutron stars were named Ultra-Luminous X Ray Sources (ULX).


In addition to the originally described black hole components: (1) the gravitational singularity, (2) the event horizon, and (3) the photon sphere, all of which emit no detectable radiation, the current model for a visible black hole includes additional features.


Matter captured by the black hole forms an equatorial (4) accretion disk of superheated plasma whirling at nearly light speed around the event horizon, perpendicularly to the black hole's axis of rotation. Extreme pressure and temperature conditions in the accretion disk make possible the mass to energy conversion reaction whereby matter is converted to radiation, a fraction of which escapes into space to render the black hole observable.


Surrounding the accretion disk there may be (5) an opaque torus of cooler matter in high orbit around the black hole, which gradually spirals into the accretion disk.


(6) Polar jets, also called astrophysical jets, relativistic jets, or x-ray jets, are formed as superheated plasma is ejected at relativistic speeds along the black hole's axis of rotation, and escapes in the form of collimated particle beams perpendicularly to the accretion disk. The process is not well understood, but is probably driven by extremely strong, twisting magnetic fields and kinetic energy transfer from other particles approaching the event horizon in the equatorial plane. Such jets, thin and long, some stretching over three million light years, were first detected in 1918 on optical images of M87's core, which was later found to contain a supermassive black hole. Smaller jets are found near neutron stars and stellar mass black holes, while far more modest versions appear near some protostars.


Fig. 21: HST image of the polar jet emitted by the supermassive black hole in the center of the M87 galaxy. The jet is composed of subatomic particles accelerated to nearly the speed of light


Surrounding a polar jet there may be present a wide cone of (7) ionized gas clouds radiating the classical emission line spectrum.


The only components of actively accreting black holes which are directly observable in the electromagnetic spectrum are accretion disks, polar jets, and surrounding ionized gas clouds. Polar jets may remain detectable for millions of years after a black hole consumes all surrounding matter and stops accreting.


Fig. 22: Model of an accreting black hole showing the accretion disk, polar jets, and the event horizon.


Non-accreting black holes have no accretion disks and no active polar jets. They release no presently detectable radiation. Their existence can only be inferred through gravitational lensing of background luminous objects, rapid orbital motion of nearby stars, and possibly gravitational wave analysis.


In the meter-kilogram-second (MKS) system of units, the gravitational constant G = 6.674×10^-11, and the speed of light C = 3x10^8. Using Schwarzschild's  equation (36) we can calculate the diameter of a non-rotating black hole which contains the mass of the Sun, Ms = 2x10^30 kg:


Rs = 2GM / (C^2)

Rs = [ 2 (6.674×10^-11) (2x10^30) ] / (3x10^8)^2

Rs = 2,966 meters


The diameter of a non-rotating black hole of one Solar mass would be about 6,000 meters.


Using the same method with the mass of the Earth, Me = 6x10^24 kg, we obtain the radius of 8.9x10^-3 m, which is approximately the diameter of 18 mm, or less than 3/4 of an inch.


Notice in equation (36) that the radius of a black hole, Rs, is linearly proportional to the mass, M. Meanwhile, in equation (37), the black hole's volume, V, is proportional to the third power of the radius, where Pi = 3.142:


V = (4/3) Pi Rs^3                                                                                                                              (37)


Since average density, D, is equal to mass divided by volume:


D = M / V                                                                                                                                           (38)


we can combine equations (37) and (38):


D = M / [(4/3) Pi Rs^3]                                                                                                                      (39)


As the mass doubles, the radius of a black hole doubles, but the mass is contained in a volume eight times larger. Therefore, small black holes have exponentially higher average densities and steeper gravitational gradients than the large ones. We can use equation (39) to calculate that the average density of a one Solar mass black hole is approximately 10^16 g/cm^3, or 40 times the density of nuclear matter, while a supermassive black hole (SMBH) of 10^8 Solar masses has the average density of water, or 1 g/cm^3. As shown below, an ultramassive black hole (UMBH) of 16 billion Solar masses has an average density 51 times lower than air. It is then implicit, although counterintuitive, that much more extreme local physical conditions are required for the formation of small black holes rather than large ones.


Low density requirements for the creation of massive black holes make it easier to model SMBH formation in galaxy centers and UMBH formation in the primordial universe. Essentially, any region of space will spontaneously collapse into a supermassive black hole if it contains a sufficient quantity of matter within a specified Schwarzschild radius, even if the average density of matter in the region seems very low. The process may involve gravitational collapse of vast gas clouds which were common in the primordial universe while it was still small and dense in the early stages of expansion.


Quasar APM 8279 has a central ultramassive black hole estimated to contain 16 +/- 6 billion Solar masses. Since the mass of the Sun Ms = 2x10^30 kg, the mass of the black hole, M, is given by:


M = Ms x 16x10^9 = 16x10^9 x 2x10^30 = 3.2x10^40 = 3.2E40 kg


To calculate the size of the black hole, or its Schwarzschild radius, we use equation (36) and the MKS unit system, where G = 6.674×10^-11 = 6.674E-11, and C = 3x10^8 = 3E8


Rs = 2GM / (C^2)

Rs = 2 x 6.674E-11 x 3.2E40 / (3E8)^2 = 4.27E30 / 9E16

Rs = 4.75E13 meters = 4.75E13 / 1.496E11 astronomical units = 317.5 AU


The radius of APM 8279's black hole is 8 times greater than the mean distance between Pluto and the Sun. Its diameter is 0.01 light years.


We use equation (39) to calculate the average density of the quasar's black hole:


D = M / ((4/3) pi Rs^3)

D = 3.2E40 / (4x3.142x4.75E13^3 / 3) = 3.2E40 / 1.35E42

D = 2.38E-2 kg/m^3 = 23.8 g/m^3 = 0.0000238 g/cm^3


The average density of the black hole is about 42,000 times lower than the density of water, and about 51 times lower than the density of air at sea level.


The black hole's immense size and low density imply that in the vicinity of the event horizon the gravitational field gradient is very low, although the gravitational field intensity is extreme.





The presence of an accreting black hole is revealed by emitted electromagnetic radiation ranging from low energy radio waves to highly energetic X-rays and gamma rays. Differences in the broad spectrum between different black holes, and variability in broad spectrum properties of an individual black hole suggest that black holes generate energy by several different mechanisms. These can be generally divided into thermal processes and, relatively speaking, non-thermal processes.


Virtually all (but not all) energy generated by a black hole is derived from surrounding matter in the form of gas, dust, and stars attracted by its gravity vortex and captured into the accretion disk. Matter is there superheated to billions and even trillions of degrees by gravitational compression, friction, and fission reactions whereby atoms and molecules are torn apart into subatomic particles. Conditions in accretion disks are much more extreme than in the interior of the largest stars. Consequently the efficiency of mass to energy conversion is approximately 10 times higher. In a non-rotating black hole about 6 - 7% of incoming matter is converted to energy and radiated into surrounding space. In a rapidly rotating black hole of the same mass, the diameter of the event horizon is smaller, gravitational gradients higher, and up to 42% of incoming matter can be converted to radiation. The accretion disk emits radiation at all wavelengths, including X-rays, but most intensely in the ionizing UV range around the hydrogen Lyman series.


Not all matter which approaches the accretion disk is captured. Computer simulations show that in star-disk collisions, when a star is attracted toward a black hole, only about half of its mass is captured. The other half is gravitationally dispersed into a cloud of hot plasma, and catapulted out into space resulting in a luminous plume lasting hundreds of days.


Fig. 23: Accretion disk enrichment and formation of a luminous plume when a star is consimed by a black hole


Polar jets emit radiation from the superheated plasma within the jet itself where temperatures may reach billions and trillions of degrees. This results in strong radiation at all wavelengths, including the optical, but most intense in the high energy end of the spectrum. In optical and X-ray images, polar jets display shock waves of bead-like zones of plasma congestion receding from the black hole at relativistic speeds (see Fig. 21). Large polar jets can remain detectable for millions of years after the black hole itself consumed all available matter, and lost its accretion disk. Radiation from the polar jets may also energize any surrounding gas clouds and cause them to fluoresce in the form of a typical emission line spectrum.


The mechanisms of black hole energy generation and emission mentioned so far are thermal processes, depending on particles of matter at extreme densities heated to extreme temperatures. Black holes also radiate energy by a non-thermal process whereby charged particles entangled in strong and rapidly twisting magnetic fields become accelerated (diverted) into helical paths along magnetic field lines. Polarized radiation emitted by particles changing direction at relativistic speeds is called synchrotron radiation, or cyclotron radiation for slower particles. In the process of emitting radiation the particles lose energy, and undergo magnetic braking. The vast majority of particles involved are electrons, but protons, heavier ions, and positrons (if any) may also be involved. The process generates a wide range of wavelength signals, from radio waves to optical to x-rays, where the signals do not precisely coincide in location or in timing.





Following a 1973 visit to Moscow where astrophysicists Zeldovich and Starobinsky persuaded him that rotating black holes should emit radiation, British theoretical physicist Stephen Hawking published an article in 1974 predicting that black holes emit blackbody radiation at temperature, T, when quantum effects near the event horizon are taken into account:


Tkelvin = 6E-8 / (black hole mass)                                                                                                (40)


This Hawking radiation, in the form of photons, neutrinos, and a variety of subatomic particles would have the effect of depleting black hole's rotational energy and mass, causing gradual black hole evaporation in non-accreting black holes. Since the temperature in equation (40) is inversely proportional to the black hole mass, microscopic black holes (with steep gravitational gradients) should have higher temperatures and dissipation rates than the large ones. As the mass of a black hole is reduced, the process is predicted to accelerate to the end-point where the black hole vanishes in a brief but powerful  pulse of gamma rays, releasing 10^33 erg of energy in the last 0.1 seconds. The energy of a terminal gamma ray flash is equivalent to about one million one megaton hydrogen bombs - extreme by human standards, but very minor in astronomical terms, and inconsistent with extragalactic and galactic gamma ray bursts.



Mathematical treatment of Hawking radiation is quite complex, but can be visualized in terms of quantum or vacuum fluctuations. In quantum field theory, Heisenberg uncertainty principle allows a temporary energy deficit at any point in space, so long as the energy is returned within a very short time interval. Throughout the universe, particle pairs of matter and antimatter come into transitory existence, acquiring energy from empty space, only to collide, self-annihilate, and promptly return the "borrowed" energy. When these vacuum fluctuations occur near the event horizon of a black hole, it is possible for one of the particles to fall into the black hole before annihilation, while the other one escapes as Hawking radiation. The energy deficit is made up by the black hole's gravitational field, which has the effect of lowering its mass.


Although well founded and accepted in theory, to date Hawking radiation has not been directly experimentally confirmed. In accreting black holes, the only ones we can currently identify, its presence would be overwhelmed by the far more energetic processes discussed in section 23). Gamma ray observations have so far found no evidence compatible with terminal gamma ray flashes.


But, indirect experimental evidence for Hawking radiation does exist.






Black hole emissions can be highly variable. Numerous black holes manifest optical long period variability of several magnitudes over an observation period of years. It is thought that long period variability is due to thermal processes resulting from changes in the total quantity of matter flowing into the accretion disk. This is primarily determined by the availability of gas, dust, and star material in the black hole's neighborhood. However, the Eddington effect plays an additional role in variability, whereby a burst of energy from inflowing matter generates radiation pressure, temporarily resisting inflow of additional matter. Luminous plumes of superheated plasma ejected from a black hole, either at the periphery of the accretion disk of within a polar jet, also contribute to long period variability. The slow process of heating and cooling large quantities of matter may last from hundreds of days to decades.

Fig. 24: Long period variability in accreting super-massive black holes of quasars


Black holes also manifest short period variability on the level of minutes to weeks. For example, in 2002 infrared flux density of Sagittarius A super-massive black hole (SMBH) was measured to change by a factor of 4 in one week, and by a factor of 2 in merely 40 minutes.



On 19 Dec 2017, around 03:00 UTC, the authors photographed an extragalactic transient optical event with an approximate apparent magnitude of 17.4 in the immediate proximity to the intermediate-mass black hole M74 X-1 ULX (also designated as CXOU J013651.1+15454) located in the spiral galaxy M74. The signal was subsequently undetectable on images with a limiting magnitude of 19.5 taken by P. Lewin on 24 Dec 2017 (18 inch CDK) and 25 Dec 2017 (14 inch SCT). The period could not be established based on a single observation, but rapid disappearance of the signal implies a brief event. M74 X-1 ULX, is known to exhibit pronounced short period variability on the order of several thousand seconds.



The find and the likely connection with M74 X-1 ULX  were reported on 24 Dec 2017. On April 2, 2018, Royal Astronomical Society announced the discovery of  72 extragalactic transient optical events during the Dark Energy Survey Supernova Programme (DES-SN) with the 4-meter telescope at the Cerro Tololo Inter-American Observatory (CTIO) in Chile. Unlike supernovas which last 4-6 months and have predictable maximum luminosity, these transient signals lasted only 2-3 weeks and had a very wide range of maximum luminosity. https://phys.org/new...explosions.html

Although the cause of these transients has not yet been established, non-thermal emissions by intermediate-mass black holes offer a reasonable possibility. Associated X-ray transients would strengthen the evidence.


Fig. 25: Extragalactic optical transient photograped by the authors in the immediate proximity to the intermediate-mass black hole M74 X-1 ULX on 19 Dec 2017.


Since time intervals in short period variability are insufficient for the process of heating up and cooling large quantities of matter, short period variability is probably caused by a non-thermal mechanism in which limited populations of charged subatomic particles are injected or drawn into the twisting magnetic fields, generating synchrotron radiation.





On very large scales, the shortest possible period of variability is determined by the diameter of the emitting object. To demonstrate, refer to Fig. 26, and consider an object 1,000 light seconds in diameter which emits an instantaneous flash of light from its entire volume. While travelling toward a distant observer, the leading edge wavefront, W1, will be separated from the trailing edge wavefront, W3, by 1,000 light seconds. The observed light curve will show an initial rise upon the arrival of W1, at time T1', a maximum on the arrival of W2 from the widest part of the emitting object, and a decline to baseline on the arrival of W3, at time T3'.


In theory, the shortest measured period of variability in seconds, Tp = T3' - T1', is equal to the time interval between travelling wavefronts, Tdw = Tw1 - Tw3, and indicates the largest possible diameter of the light-emitting object in light seconds, D = C x Tp = C x (T3' - T1' ), where C is the speed of light.


Fig. 26: The diameter of a light source in light seconds can not be larger than the width of the light curve in seconds.


In reality, objects do not emit truly instantaneous light flashes. The duration of a light-generating event, Te, including its gradual propagation throughout the volume of the source, is added to the time interval between travelling wavefronts, Tdw, to widen the light curve period: Tp = Tdw + Te.


Furthermore, in the case of distant, high redshift objects, the space between the first and the last travelling wavefront is subject to cosmological magnification caused by the expansion of the universe (see section 25). This has the effect of increasing the measured period, Tp, by one factor of (Z + 1).


A general relation between the light-emitting object's diameter (in light seconds), D, the measured period, Tp, the duration of the light-generating event (in seconds), Te, and redshift, Z, is then described by the following equation:


D = C x (Tp - Te) / (Z+1)                                                                                                                  (41)


Although redshift can be measured very precisely, the duration of the light-generating event is in practice virtually never accurately known, The best interpretation of equation (41) then becomes:


D < C x Tp / (Z+1)                                                                                                                           (41a)


In other words, the diameter of the object in light seconds must be smaller than the light curve period in seconds, corrected for cosmological magnification. Or, the variability period in seconds is always greater than the diameter of the source in light seconds due to the duration of light emission and the effect of cosmological magnification.


For nearby objects with negligible redshifts, which are not subject to significant cosmological magnification, the equation is reduced to simply:


D < C x Tp                                                                                                                                       (41b)


In the previous section we mentioned that infrared flux density of Sagittarius A, the SMBH in the center of our galaxy, was measured to increase by a factor of 2 in merely 40 minutes. Since change in luminosity involves photons reaching the observer from the near to the far edge of the light source, the maximum occurs when photons from the widest, middle cross-section arrive to the observer. The time period, Tm = T2' - T1', between the minimum and the maximum on the light curve is an indicator of the radius, R, of the accretion disk. This can then be used in equation (41b) to estimate the mass and the size of the event horizon for an accreting, non-rotating black hole.


Tm = 40 min = 2400 sec.                                                                            Method (1)

R < C Tm = 300,000 Km/sec x 2,400 sec = 720x10^6 Km

1 Astronomical Unit = 149.6x10^6 Km

R < 720 / 149.6 = 4.8 AU


The radius of Sagittarius A accretion disk is smaller than 4.8 AU, or somewhat less than the orbit of Jupiter


The validity of this approach is shown by the following study by Morgan et al. based on the variability of eleven quasars


The study derives an empirical relationship between the accretion disk radius in cm, R, the black hole mass, M, and the solar mass, Ms:


log R = 15.8 + 0.8 log ( M / 10^9 Ms)                                                        Method (2)                   (42)


Solving this equation for Sagittarius A with 4 x 10^6 solar masses yields an estimated accretion disk radius of  5.1 AU, fairly consistent with Method (1).


If Method (1) is used to estimate the accretion disk radius, equation (42) in Method (2) can be solved for the black hole mass:


log ( M / 10^9 Ms ) = ( log R - 15.8 ) / 0.8

log M - log ( 10^9 Ms ) = ( log R - 15.8 ) / 0.8

log M = log ( 10^9 Ms ) + [ ( log R - 15.8 ) / 0.8 ]                                                                            (42a)


Entering the black hole mass, M, into the Schwarzschild's equation (36) will then give the radius of the event horizon, Rs, for a non-rotating black hole.





During the 1950's radio-astronomers discovered a large number of radio sources of small angular size which could not be associated with an optical image. After its radio signal position was accurately determined by lunar occultation, source 3c 273 became the first identified quasar (quasi-stellar radio source) when Maarten Schmidt associated it with a star-like optical image in 1963. Later the same year, Oke and Schmidt measured the quasar's redshift to be 0.15834, which places it at the light travel time distance of 1.976 billion light years, with the CZ recession velocity of 47,500 km/sec. From its redshift and apparent magnitude of 12.9 the quasar's absolute magnitude could be calculated as -26.71, or about 230 times brighter than the entire Milky Way galaxy. In subsequent years, more quasars were associated with optical sources with even higher redshifts and absolute magnitudes. The quasars were found to be powerful emitters at a wide range of frequencies, to have peculiar, sometimes unrecognizable spectra, and rapidly variable light curves indicating their sizes were smaller than the Solar system, At the time, physical nature of these objects remained controversial. The black hole concept was still regarded as a mathematical curiosity without manifestation in reality, and astronomers were at a loss to explain the mechanism of energy generation needed to produce measured luminosities..


Over the next quarter century, scientific instruments improved, theory evolved, and observations of the Cygnus X-1 system provided major evidence for the physical existence of black holes. Further evidence came from X-ray and large optical observatories. They revealed that many quasars are surrounded by faint galaxies with the same redshift as the central quasar, and that most, if not all, large galaxies contain a central super-massive black hole (SMBH) of millions and even billions of Solar masses.


By 1987 it became generally accepted that quasars are very remote objects powered by accretion disks and polar jets of super-massive black holes which occupy the nuclei of active galaxies. They are among the most luminous objects in the universe, some of which emit thousands of times more energy than a large galaxy across the entire electromagnetic spectrum, from radio waves to gamma rays. Unusual spectral features of quasars were attributed to very high redshifts due to extreme distances and recession velocities. Their peak energy wavelengths were found to lie around the hydrogen Lyman series in the ionizing ultraviolet band, indicating temperatures in the billions and trillions of degrees. Quasar 3C 273 was recently found to have color temperature in excess of 10 trillion K, which was previously thought to be physically impossible.



Although originally discovered at radio frequencies, about 90% of currently known quasars manifest little or no radio emission. A new term, quasi-stellar object, abbreviated as QSO, was developed to include the entire class. Since high resolution images show that QSOs are located in the centers of galaxies, QSOs are categorized as a major sub-class of active galaxies, or galaxies with active galactic nuclei (AGN). However, as Fig. 28 shows, a large population of high redshift QSOs, born in the early universe, are instead surrounded by extensive halos of irregularly organized matter which can not be classified as true galaxies. And, many types of active galaxies, although powered by accreting central black holes, are not sufficiently powerful to be regarded as QSOs.


All QSOs share the same general mechanism of energy production, however they present to the observer with a variety of observed characteristics. They differ in terms of absolute magnitudes, light variability, color temperature, optical spectral features, and energy distribution within different bands of electromagnetic radiation. Reasons for these differences lie in the mass of the black hole, the quantity and type of matter available for accretion, the presence of polar jets, the orientation of the accretion disk relative to the observer, and the degree of extinction by surrounding interstellar gas and dust.


Throughout the electromagnetic spectrum, the most luminous objects in the universe are blazars. These QSOs (AGNs) have accretion disks face-on to Earth, and polar jets pointed in the direction of Earth, radiating collimated beams of superheated plasma at relativistic speeds (see Fig.21). The luminosity observed on Earth can be up to 600 times higher than the luminosity emitted in the rest frame of the jet. This is due to the phenomenon of relativistic beaming, whereby observed radiation wavelength decreases, and energy increases by the Doppler effect of the light source moving toward the observer. While blazars emit most of their energy in the gamma ray band, their optical to infrared spectra manifest two broad humps. For high redshift objects, polarized synchrotron radiation emitted by the jet peaks in the infrared sub-mm band, and radiation generated by the accretion disk peaks in the optical band. From these data it is possible to determine the bolometric luminosity of the accretion disk, and to estimate the mass of the black hole.



Blazars manifest pronounced short period and large amplitude flux variability. BL Lacertae, which serves as a prototype for blazar sub-class BL Lac Object, was originally mistaken for a variable star. Another sub-class named Optically Violent Variable (OVV) Quasars is composed of rare, very luminous radio galaxies whose brightness in the optical band can change by 50% within one day.


In addition to QSOs, AGN galaxies include another large sub-class named Seyfert galaxies. These are characterized by a small central region of high luminosity which may appear as bright in the optical band as the rest of the galaxy. While only 5% emit radio frequencies, they are strong sources of high energy X-rays and moderate sources of gamma rays. They manifest variability ranging from several hours to years. Their spectra show bright emission lines of hydrogen and strongly ionized helium, nitrogen and oxygen, with Doppler broadening implying velocities up to 4,000 km/sec. It is believed such light is generated near accretion disks of supermassive black holes. Seyfert galaxies are powered by the same mechanism as QSOs. The main difference is that the nuclear source in QSOs is at least 100 times brighter, and renders the surrounding galaxy invisible in ordinary telescopes at great distances. 





The astrophysical technique called reverberation mapping uses the variability in the width of spectral lines of the light emanating from the accretion disk to estimate the total mass of a quasar. The following plot of 41,000 distant quasars is based on studies by Kurt et al. (2007) and Jiang et al. (2007, 2010), who analyzed data from the multiband Sloan Digital Sky Survey (SDSS).


Fig. 27: Masses of 41,000 distant quasars plotted against their redshifts


Due to high variance, the plot is not useful for estimating quasar mass based on its redshift. For example, at the redshift of 2, masses range between 100 million and above 10 billion Solar masses. However, the plot does reveal that super-massive black holes (SMBH) formed in the early universe were approximately 40 times more massive than those formed in more recent epochs. This is intuitive because the volume of the universe in the early stages of expansion was much smaller, and the average density of matter and radiation exponentially higher.


The plot also suggests that there is an upper limit to the size of ultra-massive black holes (UMBH), with masses exceeding 10 billion Suns. The limit seems to lie around 1E10.6, or 40 billion Solar masses. A possible explanation is that, due to enormous size and minimal density, these UMBH have extremely low gravitational gradients which are insufficient to generate stable accretion disks. Instead of falling into the black hole to feed its further growth, most of the intergalactic matter surrounding the black hole coalesces into giant nebulous regions and a myriad stars which continue to orbit the black hole for a number of generations. Simulations suggest that accretion disk instability and starburst activity begin well below the lower limit of UMBH mass of 10 billion Suns.


Working with the integral field spectrograph at the ESO’s VLT telescope, Borisova et al. (2016) documented a large nebulous halo around each one of the 19 quasars studied at redshifts between 3 and 4. In some cases, the halos extended more than a million light years from the central SMBH – about 20 times the radius of the Milky Way.

[ https://www.eso.org/public/archives/releases/sciencepapers/eso1638/eso1638a.pdf ]


Fig. 28: Nebulous halos around every SMBH studied which formed in the early universe


The starburst activity model was confirmed by Kurk et al. who studied five quasars with redshifts around 6, and masses ranging between 0.3 and 5.2 billion Suns. Using the infrared spectrograph at the VLT, they found spectroscopic evidence of Civ, Mgii, and Feii ions, suggesting previous generations of stellar nucleosynthesis. They measured Feii / Mgii line ratios of 2.75, which are similar to those in the younger, lower redshift quasars that formed  from matter of higher (albeit still relatively low) metallicity. They conclude that starburst activity and stellar nucleosynthesis around supermassive black holes commenced very early in the history of the universe.


Recent studies of quasar APM 8279 reveal that it is surrounded by very dense clouds of gas containing metals (in astrophysics, any element  heavier than helium), including iron, and molecules of water and carbon monoxide - all evidence of multiple generations of stellar nucleosynthesis as long as 12.1 billion years ago.


Chandra X-ray Observatory space telescope images of APM 8279 demonstrated another mechanism which limits UMBH growth. Chandra showed evidence of high speed winds blowing gas away from the black hole at speeds up to 0.4C, or 120,000 km/sec. The winds are caused by radiation pressure from intense X-rays generated at high temperatures in the inner parts of the black hole's accretion disk. Radiation pressure significantly limits the amount of matter which can be captured by a black hole. The process was mathematically described by Arthur Eddington in the early 20th century.





Most of the matter in the accretion disk of a black hole is consumed at the event horizon, while a fraction escapes in the form of radiation after mass to energy conversion. In small, dense, rapidly rotating black holes with extreme gravitational gradients near the event horizon, the radiated fraction can be up to 42%. In large, low density SMBH and UMBH found in the cores of quasars, gravitational gradients are much lower, and the radiated fraction is only about 6%.


In section 21) we estimated that, in order to maintain its luminosity, quasar APM 8279 converts 4.70 x 10^21 (about 4,700 billion billion) metric tons of matter into radiation every second. Since the mass of the Earth is about 6 x 10^21 metric tons, the quasar converts an "Earth" to radiation approximately every 1.3 seconds.


If 4.70 x 10^21 tons of matter per second lost to radiation constitutes 6% of the total mass consumption by the quasar, then the total rate of mass consumption (radiation plus accretion), Wt, is given by:


Wt = 4.70E21 x 100 / 6 = 4.70E23 / 6

Wt = 7.83 x 10^22 tons/sec = 2.47 x 10^30 tons/year


If 6% of this mass is lost to radiation, then the accretion rate, or the growth rate, Wg, of the quasar is 94% of Wt:


Wg = 0.94 x Wt = 0.94 x 7.83E22

Wg = 7.36 x 10^22 tons/sec = 2.32 x 10^30 tons/year


The quasar accretes approximately 12.3 "Earths" every second. Given the mass of the Sun of 2 x 10^27 tons, APM 8279 grows at an annual rate of about 1,160 Solar masses.



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