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BASIC EXTRAGALACTIC ASTRONOMY Part 8: Central Supermassive Black Holes - Discovery and Properties


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BASIC EXTRAGALACTIC ASTRONOMY

 

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

22 February, 2021

 

 

Part 8:                Central Supermassive Black Holes - Discovery and Properties

 

 

(34) THE DISCOVERY OF CENTRAL SUPERMASSIVE BLACK HOLES

 

Several lines of observational evidence have led to the conclusion that virtually all major galaxies contain a central supermassive black hole (SMBH) ranging from millions to tens of billions of solar masses.

 

In 1909, Edward Fath reported emission lines in the spectra of M 81 and NGC 1068 galactic nuclei, suggesting powerful sources of high energy ionizing radiation. Over the next several decades, Vesto Slipher, Milton Humason, Carl Seyfert, and others reported spectroscopic evidence of emission lines, some narrow and some broad, in the central regions of those nearby galaxies which had exceptionally bright nuclei.

 

With the advent of radio astronomy in the mid 1930s, some of these galaxies, including the center of the Milky Way, were also found to be sources of radio emissions. Further, numerous quasars were discovered which were strong radio wave emitters, but presented in the optical band as high redshift star-like objects of great luminosity. Early on it became evident that such extreme energy outputs could not be generated by starburst activity alone. No reasonable mechanism was proposed until 1958, when Soviet Armenian astrophysicist Viktor Ambartsumian, who had introduced the term Active Galactic Nucleus, suggested that these galactic nuclei must contain bodies of immense mass, small size, and unknown nature. Accretion, or gravitational compression and heating of infalling matter around such bodies would be able to account for extreme energy outputs. Although the idea was initially met with skepticism, a path was opened toward the possibility that black holes, hypothesized by Karl Schwarzschild in 1915 (see Part 5, Section 22), are not merely a mathematical curiosity, but actually exist in physical reality.

 

The advent of X-ray astronomy in the 1960s revealed that some active galactic nuclei and quasars are also strong X-ray sources. The discovery opened a new universe of energetic phenomena which presented persuasive evidence for the existence of black holes. Temperatures of tens and hundreds of millions K are necessary for the generation of X-rays, up to a thousand times higher than temperatures of even the hottest stars. In theory, the most efficient process for generating these temperatures would be the release of potential (gravitational) energy of infalling matter onto the accretion disk of a black hole. Resulting mass to energy conversion by nuclear fission could be orders of magnitude higher than the efficiency in stellar nuclear fusion. However, at the time, this compelling theory lacked proof.

 

The first stellar mass black hole, confidently identified in 1971, was Cygnus X-1, an X-ray binary star system in which an invisible, small object is pulling mass from a large, visible companion. In 1974, a much stronger X-ray source, Sagittarius A, was discovered in the center of the Milky Way galaxy, and was eventually attributed to the presence of a supermassive black hole (SMBH). The launch of fully imaging space X-ray observatories, starting with Einstein in 1978, and followed in 1999 by ROSAT, XMM-Newton, and Chandra, led to the detection of numerous Ultra-Luminous X-ray Sources, or ULX, associated with all types of galaxies. While the least luminous of these objects (10^32 to 10^33 watts) can be explained by beamed emissions from ordinary X-ray binary stars, energy levels released by most of these sources greatly exceed what is possible from stellar processes, including supernovae, neutron stars (pulsars), and stellar-mass black holes. It is presently thought that ULX emissions are caused by accretion around SMBH or intermediate-mass black holes, IMBH, with masses of hundreds to thousands solar.

 

Extreme energy levels and a wide range of emitted radiation, from radio waves to gamma rays, were one line of evidence for the existence of central SMBH.

 

Another line of evidence comes from astrophysical jets, or relativistic jets, which are massive outflows of superheated plasma ejected at relativistic speeds from the cores of some active galaxies and quasars (See Part 5, Section 22). Such jets, thin, long, and often beaded, some stretching over three million light years, were first detected in 1918 by Heber Curtis, who reported an inexplicable jet radiating from the nucleus on optical images of the nearby galaxy Messier 87. Similar features have since been observed in many other objects, and in all bands, from radio waves to X-rays. Once again, temperatures and energy levels required for such phenomena are many orders of magnitude greater than the levels that can be produced by nuclear reactions in ordinary stars, and are only found within accretion disks of black holes.

 

Since the 1990s, a number of astronomers - among them recent Nobel Prize recipients Andrea Ghez and Reinhard Genzel - have been observing Sagittarius A, a strong radio and X-ray source in the center of our Galaxy. Observations were made in the infrared band because the region is obscured in the visible band by thick layers of gas and dust in the galactic plane. Following tight elliptical orbits of stars around the source, they identified the location of a dark "supermassive compact object" of approximately 4.1 million solar masses that is generally recognized to be consistent with a minimally accreting supermassive black hole.

 

Fig 8-1 MW SMBH orbits

Fig. 8-1: Plots of star orbits around a "supermassive compact object" in the center of our Galaxy

 

In 2019, the Event Horizon Telescope Collaboration team released the first ever image of the accretion disk around the central supermassive black hole in neighboring galaxy Messier 87. The image, created with long-base interferometry techniques using radio telescopes across the entire planet, bears a remarkable resemblance to theoretical predictions based on computer simulations.

[https://aasnova.org/2019/04/10/first-images-of-a-black-hole-from-the-event-horizon-telescope/]

 

While direct visualization is the most convincing evidence for the existence of central supermassive black holes, for technical and economic reasons the method is not applicable to large scale surveys of remote galaxies. Plotting star orbits around central SMBHs in other galaxies is also not practicable for the same reasons. Fortunately, spectroscopic analysis of the motions of stars and globular clusters (in the near-visible bands), and of interstellar gas clouds (in the radio bands) yields good results in detecting central SMBHs in remote galaxies, and in estimating their mass.

 

 

(35) SPECTROSCOPIC ANALYSIS, VELOCITY DISPERSION, AND DERIVED SYSTEM PROPERTIES

 

In gravitationally bound systems, the motion of particles is dependent to the total mass of the system. In general terms, higher mass leads to more rapid motion of particles around the center of gravity.This motion may be rotationally stabilized, as in the disks of spiral galaxies, or random, as in globular clusters, elliptical galaxies, some irregular galaxies, and central bulges of spiral galaxies. Higher total mass also leads to greater velocity dispersion, which is the variability, or spread of individual particle velocities around their mean velocity. In a random system near a galactic center, approximately half of the light sources (stars, clusters, and gas clouds) will be moving away from the observer, and will manifest a relative Doppler redshift, while the other half moving toward the observer manifest a blueshift relative to the mean. As a result, spectroscopic analysis of the system will show broadening of spectral lines. In reverse logic, wider spectral lines imply higher velocity dispersion, more rapid random motion of light sources, and higher total mass of a gravitationally bound system. The presence of a central supermassive black hole will significantly increase stellar velocity dispersion in the nucleus of a galaxy from what is anticipated based on the mass of luminous matter alone.

 

Fig. 8-2: The relation between velocity dispersion and spectral line width. Red and blue colors represent Doppler shifted regions of the central wavelength, not actual colors.

 

The spectral region most commonly used for estimating velocity dispersion is the infrared singly ionized Calcium (CaII) triplet at the wavelengths of 8498 A, 8542 A, and 8662 A

 

Velocity dispersion is a very useful measure which has been empirically related to a number of physical properties of gravitationally bound systems from star clusters, to galaxies, to entire galaxy clusters, and to the properties of galactic central SMBHs.

 

For example, equation (43) approximates the total mass of a galaxy, M, based on its stellar velocity dispersion, S, where R is its radius, and G is the gravitational constant:

 

M = 5 R S^2 / G                                                                                                                                 (43)

 

The M - sigma relation empirically correlates the mass of a central supermassive black hole, Mbh, in solar masses, Ms, to the stellar velocity dispersion, S, measured from the spectrum of the galactic nucleus. The relation was originally presented in 1999 as the Faber-Jackson Law for Black Holes, but has since undergone a number of revisions based on a growing number of published central SMBH masses in nearby galaxies. According to McConnell et al. (2011) the relation is:

 

Log( Mbh / Ms ) = 8.29 + 5.12 Log( S / 200km/s )                                                                           (44a)

[https://arxiv.org/abs/1112.1078]

 

The most recent study by Marsden et al. (2020) suggests that the best statistical fit is given by:

 

Log( Mbh / Ms ) = 8.21 + 3.83 Log( S / 200km/s )                                                                           (44b)

[https://www.frontiersin.org/articles/10.3389/fphy.2020.00061/full]

 

An earlier work by American astronomers Sandra Faber and Robert Jackson in 1976 established the Faber-Jackson Relation which empirically correlated stellar velocity dispersion to the absolute magnitude for a sample of elliptical galaxies. They concluded that galactic luminosity is proportional to its stellar velocity dispersion raised to the 4th power. Based on much subsequent data, this relation has also undergone significant revisions, with the exponent now dependent on the size and type of the host galaxy. The relation essentially suggests that larger galaxies with higher absolute magnitude statistically have larger central SMBHs.

 

 

(36) PHOTOMETRIC ANALYSIS AND DERIVED CENTRAL SMBH PROPERTIES

 

Another method for detecting and estimating central SMBH properties is based on photometric measurements. The subject is treated at some length in Part 5 of this article series which discusses black holes and quasars. A revised and abbreviated section is given here for the sake of convenience.

 

Numerous galaxies manifest variability in their central regions throughout the electromagnetic spectrum. As previously mentioned, energy requirements (temperatures) for producing such high levels of radiation, from radio waves to gamma rays, exceed by many orders of magnitude anything which is possible in stellar nuclear fusion reactions. This implies the presence of supermassive gravitational whirlpools which generate energy by the accretion of matter. At present, black holes are the only known objects of such small size and extreme mass.

 

Black hole emissions can be highly variable. Generally speaking, variability is caused by changes in the availability of matter flowing into its accretion disk. Numerous black holes manifest optical long period variability of several magnitudes over an observation period of years.

 

Fig. 8-3: 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, the SMBH in the center of the Milky Way, was measured to change by a factor of 4 in one week, and by a factor of 2 in merely 40 minutes.

[https://arxiv.org/abs/astro-ph/0309076]

 

Short period fluctuations are particularly useful in estimating black hole properties.

 

On large scales, the shortest possible period of variability is determined by the diameter of the emitting object. To demonstrate, refer to Fig. 8-4, and consider an object 1,000 light seconds in diameter which emits aninstantaneous 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. 8-4: The diameter of a light source in light seconds can not be larger than the width of the light curve in seconds.During their long journey, travelling wavefronts are subject to cosmological magnification.

 

In reality, large 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 Article 4, 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)                                                                                                                    (45a)

 

Although redshift can be measured very precisely, the duration of the light-generating event is in practice virtually never accurately known, The only possible interpretation of equation (45a) then becomes:

 

D < C x Tp / (Z+1)                                                                                                                              (45b)

 

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                                                                                                                                          (45c)

 

As previously mentioned, 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 (45c) to estimate the mass and the size of 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

[https://arxiv.org/pdf/1002.4160.pdf]

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)                     (46a)

 

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 (46a) 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 ]                                                                            (46b)

 

Entering the black hole mass, M, into the Schwarzschild's equation (43) (see Part 5, section 22) will then give the radius of the event horizon, Rs, for a non-rotating black hole.

 

Rs = 2GM / (C^2)                                                                                                                               (43)

 

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 m/s. For radius, Rs, in meters, and the black hole mass, M, in kilograms, Schwarzschild's  equation (43) becomes:

 

Rs = [ 2 (6.674×10^-11) M ] / (3x10^8)^2                                                                                         (43a)

 

 

(37) RELATIONSHIPS BETWEEN THE CENTRAL SMBH MASS AND THE HOST GALAXY

 

We have shown how stellar velocity dispersion and photometric studies of a galactic bulge are used to estimate the mass and the dimension of the central SMBH. These values have in turn been empirically related to the morphological properties of host galaxies.

 

In 2011, McConnell et al. related central SMBH mass in solar units, Mbh/Ms, and host galaxy luminosity in solar units, L/Ls, with the following empirical equation:

 

Mbh - L relationship:     Log( Mbh / Ms ) = 9.16 + 1.16 Log( L / Ls 10^11 )                                  (47)

[https://arxiv.org/abs/1112.1078]

 

Another study by Gutelkin et al. (2009) related central SMBH mass to the mass and the luminosity of the host galaxy. The following two diagrams are based on their data.

[https://arxiv.org/abs/0903.4897]

 

Fig. 8-5: The observed relationship between the central SMBH mass and host galaxy mass

 

Fig. 8-6: The observed relationship between the central SMBH mass and host galaxy luminosity

 

Substantial variance from the mean (on a logarithmic scale) indicates that the relationship between the central SMBH mass and host galaxy mass and luminosity is quite approximate. In general terms, larger galaxies contain larger central SMBHs, while most dwarf galaxies have no detectable ones. However, there are numerous inconsistencies and exceptions.

 

For example, the Milky Way SMBH has a mass of 4.1 million solar, while the Andromeda Galaxy SMBH has a much greater mass of 110-230 million solar, although the two galaxies are of approximately equal size. The moderately sized Triangulum Galaxy, M33, contains no SMBH at all. XMM-Newton studies of its central region detect an ULX compatible with an intermediate-mass black hole (IMBH) of only 1,500 solar. But the dwarf galaxy NGC 404 contains an IMBH nearly 35 times more massive. The supergiant elliptical galaxy M87, with baryonic mass about twice that of the Milky Way [https://arxiv.org/abs/astro-ph/0508463], has a central SMBH that is nearly 1,600 times greater, at 6.5 billion solar [https://arxiv.org/abs/1906.11243]. An even larger elliptical galaxy, A2261-BCG, 10 times the diameter, and 1,000 times the baryonic mass of the Milky Way, contains no detectable central black hole of any size. Yet, an elliptical radio galaxy 4C +37.11 was found to have two central SMBHs with a combined mass around 15 billion solar, orbiting each other at a distance of 24 light years with a period of 30,000 years [https://iopscience.iop.org/article/10.3847/1538-4357/aa74e1]. Another SMBH binary system (SMBHB), with masses of 18.35 billion and 150 million solar, was detected in the remote quasar OJ 287.

 

While a majority of dwarf galaxies does not have a central SMBH, there are exceptions in this area as well. A local early stage dwarf starburst galaxy without a central bulge, He 2-10, was discovered in 2011 to contain a 3 million solar mass SMBH. In 2014, a 20 million solar mass SMBH was detected in a dense ultracompact dwarf galaxy, M60-UCD1, constituting more than 10% of the total mass of the host galaxy. It was extraordinary to find a black hole five times larger than the Milky Way's in a galaxy which is more than 5,000 times smaller. In 2012, a 5 billion solar mass SMBH was reported in the compact lenticular galaxy NGC 1277, which constitutes about 5% of the total baryonic mass of the galaxy, or 20% of the stellar mass of the central bulge.

 

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See the following links for the previous parts of this article series:

 

Part 1 Redshift and Recession Velocity

Part 2 Distance, Luminosity, and the Hubble Parameter

Part 3 Luminosity corrections, Cosmological extinction, and Mass to luminosity conversion

Part 4 Luminosity distance, Cosmic dimensions, and Cosmic magnification

Part 5 Black holes and Quasars

Part 6 Galaxies - Discovery and Classification

Part 7 Galaxies - Morphological diversity

 

 


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