Soltan argument
Encyclopedia
The Sołtan argument is an astrophysical
theory outlined in 1982 by Polish
astronomer
Andrzej Sołtan. It maintains that if quasar
s were powered by accretion
onto a supermassive black hole
, then such supermassive black holes must exist in our local universe as "dead" quasars.
wrote a paper suggesting that "dead quasars" were found at the center of the Milky Way
and nearby galaxies by arguing that given the quasar-number counts, luminosities, distances, and the efficiency of accretion into a "Schwarzschild throat" through the last stable circular orbit (note that at the time the term black hole
had not yet been coined), roughly 1010 quasars existed in the observable universe
. This number density of "dead quasars" was attributed by Lynden-Bell to high mass-to-light ratio objects found at the center of galaxies. This is essentially the Sołtan argument, though the direct connection between black hole masses and quasar luminosity function
s is missing. In the paper, Lynden-Bell also suggests some radical ideas that are now fully integrated into modern understanding of astrophysics including the model that accretion disks are supported by magnetic field
s, that extragalactic cosmic ray
s are accelerated in them, and he estimates to within an order of magnitude the masses of several of the closest supermassive black hole
s including the ones in the Milky Way
, M31
, M32
, M81
, M82
, M87
, and NGC 4151
.
Thirteen years later, Sołtan explicitly showed that the luminosity
(
) of quasars was due to the accretion rate of mass onto black holes given by:
where
Given the number of observed quasars at various redshift
s, he was able to derive an integrated
energy density
due to quasar output. Since observers on Earth are flux limited, there are always more quasars that exist than are observed and thus the energy density he derived is a lower bound. He obtained the value of approximately 10−10 erg
s per cubic meter.
Sołtan calculated the mass density of accreted material as it is directly related to the energy density of quasar light. He derived a value of approximately 1014 solar mass
es per cubic Gigaparsec. This mass would be discretely distributed (since quasars are single point sources); given an average mass of approximately ten million solar masses, it would be statistically likely for a "dead quasar" to be within a few megaparsecs of Earth.
At this time, evidence was already accumulating that supermassive black holes were found at the center of large galaxies, which are distributed approximately on the order of a megaparsec apart from each other. This argument therefore made a reasonable case that supermassive black holes were at one time ultraluminous quasars.
Astrophysics
Astrophysics is the branch of astronomy that deals with the physics of the universe, including the physical properties of celestial objects, as well as their interactions and behavior...
theory outlined in 1982 by Polish
Poland
Poland , officially the Republic of Poland , is a country in Central Europe bordered by Germany to the west; the Czech Republic and Slovakia to the south; Ukraine, Belarus and Lithuania to the east; and the Baltic Sea and Kaliningrad Oblast, a Russian exclave, to the north...
astronomer
Astronomer
An astronomer is a scientist who studies celestial bodies such as planets, stars and galaxies.Historically, astronomy was more concerned with the classification and description of phenomena in the sky, while astrophysics attempted to explain these phenomena and the differences between them using...
Andrzej Sołtan. It maintains that if quasar
Quasar
A quasi-stellar radio source is a very energetic and distant active galactic nucleus. Quasars are extremely luminous and were first identified as being high redshift sources of electromagnetic energy, including radio waves and visible light, that were point-like, similar to stars, rather than...
s were powered by accretion
Accretion (astrophysics)
In astrophysics, the term accretion is used for at least two distinct processes.The first and most common is the growth of a massive object by gravitationally attracting more matter, typically gaseous matter in an accretion disc. Accretion discs are common around smaller stars or stellar remnants...
onto a supermassive black hole
Supermassive black hole
A supermassive black hole is the largest type of black hole in a galaxy, in the order of hundreds of thousands to billions of solar masses. Most, and possibly all galaxies, including the Milky Way, are believed to contain supermassive black holes at their centers.Supermassive black holes have...
, then such supermassive black holes must exist in our local universe as "dead" quasars.
History
As early as 1969, Donald Lynden-BellDonald Lynden-Bell
Donald Lynden-Bell CBE FRS is an English astrophysicist, best known for his theories that galaxies contain massive black holes at their centre, and that such black holes are the principal source of energy in quasars. He was a co-recipient, with Maarten Schmidt, of the inaugural Kavli Prize for...
wrote a paper suggesting that "dead quasars" were found at the center of the Milky Way
Milky Way
The Milky Way is the galaxy that contains the Solar System. This name derives from its appearance as a dim un-resolved "milky" glowing band arching across the night sky...
and nearby galaxies by arguing that given the quasar-number counts, luminosities, distances, and the efficiency of accretion into a "Schwarzschild throat" through the last stable circular orbit (note that at the time the term black hole
Black hole
A black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that...
had not yet been coined), roughly 1010 quasars existed in the observable universe
Observable universe
In Big Bang cosmology, the observable universe consists of the galaxies and other matter that we can in principle observe from Earth in the present day, because light from those objects has had time to reach us since the beginning of the cosmological expansion...
. This number density of "dead quasars" was attributed by Lynden-Bell to high mass-to-light ratio objects found at the center of galaxies. This is essentially the Sołtan argument, though the direct connection between black hole masses and quasar luminosity function
Luminosity function (astronomy)
In astronomy, the luminosity function gives the number of stars or galaxies per luminosity interval. Luminosity functions are used to study the properties of large groups or classes of objects, such as the stars in clusters or the galaxies in the Local Group....
s is missing. In the paper, Lynden-Bell also suggests some radical ideas that are now fully integrated into modern understanding of astrophysics including the model that accretion disks are supported by magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...
s, that extragalactic cosmic ray
Extragalactic cosmic ray
Extragalactic cosmic rays are very-high-energy particles that flow into our solar system from beyond our galaxy. The energies these particles possess are in excess of 1015 eV.- Origin :...
s are accelerated in them, and he estimates to within an order of magnitude the masses of several of the closest supermassive black hole
Supermassive black hole
A supermassive black hole is the largest type of black hole in a galaxy, in the order of hundreds of thousands to billions of solar masses. Most, and possibly all galaxies, including the Milky Way, are believed to contain supermassive black holes at their centers.Supermassive black holes have...
s including the ones in the Milky Way
Milky Way
The Milky Way is the galaxy that contains the Solar System. This name derives from its appearance as a dim un-resolved "milky" glowing band arching across the night sky...
, M31
Andromeda Galaxy
The Andromeda Galaxy is a spiral galaxy approximately 2.5 million light-years from Earth in the constellation Andromeda. It is also known as Messier 31, M31, or NGC 224, and is often referred to as the Great Andromeda Nebula in older texts. Andromeda is the nearest spiral galaxy to the...
, M32
Messier 32
Messier 32 is a dwarf elliptical galaxy about 2.65 million light-years away in the constellation Andromeda. M32 is a satellite galaxy of the famous Andromeda Galaxy and was discovered by Le Gentil in 1749. M32 measures only 6.5 ± 0.2 kly in diameter at the widest point...
, M81
Messier 81
Messier 81 is a spiral galaxy about 12 million light-years away in the constellation Ursa Major. Due to its proximity to Earth, large size and active galactic nucleus Messier 81 (also known as NGC 3031 or Bode's Galaxy) is a spiral galaxy about 12 million light-years away in the constellation Ursa...
, M82
Messier 82
Messier 82 is the prototype nearby starburst galaxy about 12 million light-years away in the constellation Ursa Major...
, M87
Messier 87
Messier 87 is a supergiant elliptical galaxy. It was discovered in 1781 by the French astronomer Charles Messier, who cataloged it as a nebulous feature. The second brightest galaxy within the northern Virgo Cluster, it is located about 16.4 million parsecs from Earth...
, and NGC 4151
NGC 4151
NGC 4151 is an intermediate spiral Seyfert galaxy located 43 million light years from Earth in the constellation Canes Venatici, discovered by Frederick William Herschel on March 17, 1787...
.
Thirteen years later, Sołtan explicitly showed that the luminosity
Luminosity
Luminosity is a measurement of brightness.-In photometry and color imaging:In photometry, luminosity is sometimes incorrectly used to refer to luminance, which is the density of luminous intensity in a given direction. The SI unit for luminance is candela per square metre.The luminosity function...
(
) of quasars was due to the accretion rate of mass onto black holes given by:where
is the efficiency factor
is the time rate of mass falling into the black hole
is the speed of lightSpeed of lightThe speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...
Given the number of observed quasars at various redshift
Redshift
In physics , redshift happens when light seen coming from an object is proportionally increased in wavelength, or shifted to the red end of the spectrum...
s, he was able to derive an integrated
Integral
Integration is an important concept in mathematics and, together with its inverse, differentiation, is one of the two main operations in calculus...
energy density
Energy density
Energy density is a term used for the amount of energy stored in a given system or region of space per unit volume. Often only the useful or extractable energy is quantified, which is to say that chemically inaccessible energy such as rest mass energy is ignored...
due to quasar output. Since observers on Earth are flux limited, there are always more quasars that exist than are observed and thus the energy density he derived is a lower bound. He obtained the value of approximately 10−10 erg
Erg
An erg is the unit of energy and mechanical work in the centimetre-gram-second system of units, symbol "erg". Its name is derived from the Greek ergon, meaning "work"....
s per cubic meter.
Sołtan calculated the mass density of accreted material as it is directly related to the energy density of quasar light. He derived a value of approximately 1014 solar mass
Solar mass
The solar mass , , is a standard unit of mass in astronomy, used to indicate the masses of other stars and galaxies...
es per cubic Gigaparsec. This mass would be discretely distributed (since quasars are single point sources); given an average mass of approximately ten million solar masses, it would be statistically likely for a "dead quasar" to be within a few megaparsecs of Earth.
At this time, evidence was already accumulating that supermassive black holes were found at the center of large galaxies, which are distributed approximately on the order of a megaparsec apart from each other. This argument therefore made a reasonable case that supermassive black holes were at one time ultraluminous quasars.