یکی از تفاوتهای اصلی این سیاهچاله چگالی کمتر آنهاست. چگالی سیاهچالهها جرم آن تقسیم بر حجم ناشی از شعاع شوارتزشیلد است. این مقدار میتواند کمتر از چگالی آب باشد. علت آن این است که شعاع شوارتزشیلد سیاهچاله بهطور خطی با جرم افزایش مییابد پس میتوان آن را به صورت زیر نوشت:
که در آن R، شعاع سیاهچاله، M، جرم آن و k ضریب تناسب است؛ و بنابرین داریم:
و به همین دلیل هرچه سیاهچاله پرجرمتر باشد چگالی آن کمتر است و همچنین به علت بزرگ بودن افق رویداد، نیروی تیدال سیاهچالههای کلانجرم به طرز قابل ملاحظهای کمتر است.
جرم این سیاهچالهها به خاطر بلعیدن اجرام دور خود همواره افزایش مییابد و این بلعیدن موجب فعال شدن ظاهر مرکز سیاهچاله در طیف الکترومغناطیسی و مخصوصاً انرژی بالا میشود به همین دلیل تصور میرود این سیاهچاله مسئول فعالیت قوی اختروشها باشند. درخشندگی سیاهچالههای کلانجرم در اختروشها بین ده تا صدبرابر درخشندگی بقیه اختروش است. همچنین تصور بر این است که هسته کهکشانی فعال (AGN) نیز سیاهچاله باشد.
از محاسبه روی مدار این ستاره جرم مرکز گردش ۴٫۱ میلیون جرم خورشید به دست میآید.
اندازه این جرم مرکزی وضوحاً باید کمتر از ۱۷ ساعت نوری باشد و گرنه ستاره اس۲ با آن برخورد میکند یا به خاطر نیروی تیدال تکهتکه میشد. در واقع در مشاهدات جدید نشان میدهد که این شعاع نباید بیشتر ۶٫۲۵ ساعت نوری یعنی به اندازه قطر مدار اورانوس باشد.
فقط یک سیاهچاله میتواند در چنین حجمی چنین جرمی را جا دهد.
↑ ۳٫۰۳٫۱۳٫۲Combes, Françoise (2010). "The origins of black holes". Mystries of Galaxy Formation [رازهای تشکیل کهکشان] (به English). Springer. p. ۶۹–۷۰. ISBN978-1-4419-0867-4. |access-date= requires |url= (help)نگهداری یادکرد:زبان ناشناخته (link)
↑«طبقهبندی سیاه چاله». وبگاه آکادمی علوم فضایی ایران. بایگانیشده از اصلی در ۴ دسامبر ۲۰۱۱. دریافتشده در ۳۰ ژوئیه ۲۰۱۱. بیش از یک پارامتر |پیوند بایگانی= و |archiveurl= دادهشده است (کمک); بیش از یک پارامتر |تاریخ بایگانی= و |archivedate= دادهشده است (کمک); بیش از یک پارامتر |بازبینی= و |accessdate= دادهشده است (کمک)
Largest type of black hole; usually found at the center of galaxies
This is the first direct image of a supermassive black hole, located at the galactic core of Messier 87. It shows radio-wave emission from a heated accretion ring orbiting the object at a mean separation of 350 AU, or ten times larger than the orbit of Neptune around the Sun. The dark center is the event horizon and its shadow. The image was released in 2019 by the Event Horizon Telescope Collaboration.
Supermassive black holes are classically defined as black holes with a mass above 0.1 million to 1 million M☉. Some astronomers have begun labeling black holes of at least 10 billion M☉ as ultramassive black holes. Most of these (such as TON 618) are associated with exceptionally energetic quasars. Even larger ones have been dubbed stupendously large black holes (SLAB) with masses greater than 100 billion M☉. Although they noted there is currently no evidence that stupendously large black holes are real, they noted that supermassive black holes almost that size do exist. Some studies have suggested that the maximum mass that a black hole can reach, while being luminous accretors, is of the order of ~50 billion M☉.
Supermassive black holes have physical properties that clearly distinguish them from lower-mass classifications. First, the tidal forces in the vicinity of the event horizon are significantly weaker for supermassive black holes. The tidal force on a body at the event horizon is inversely proportional to the square of the mass: a person on the surface of the Earth and one at the event horizon of a 10 million M☉ black hole experience about the same tidal force between their head and feet. Unlike with stellar mass black holes, one would not experience significant tidal force until very deep into the black hole. In addition, it is somewhat counterintuitive to note that the average density of a SMBH within its event horizon (defined as the mass of the black hole divided by the volume of space within its Schwarzschild radius) can be less than the density of water. This is because the Schwarzschild radius is directly proportional to its mass. Since the volume of a spherical object (such as the event horizon of a non-rotating black hole) is directly proportional to the cube of the radius, the density of a black hole is inversely proportional to the square of the mass, and thus higher mass black holes have lower average density.
The Schwarzschild radius of the event horizon of a (nonrotating) supermassive black hole of ~1 billion M☉ is comparable to the semi-major axis of the orbit of planetUranus, which is 19
History of research
The story of how supermassive black holes were found began with the investigation by Maarten Schmidt of the radio source 3C 273 in 1963. Initially this was thought to be a star, but the spectrum proved puzzling. It was determined to be hydrogen emission lines that had been red shifted, indicating the object was moving away from the Earth.Hubble's law showed that the object was located several billion light-years away, and thus must be emitting the energy equivalent of hundreds of galaxies. The rate of light variations of the source dubbed a quasi-stellar object, or quasar, suggested the emitting region had a diameter of one parsec or less. Four such sources had been identified by 1964.
In 1963, Fred Hoyle and W. A. Fowler proposed the existence of hydrogen burning supermassive stars (SMS) as an explanation for the compact dimensions and high energy output of quasars. These would have a mass of about 105 – 109M☉. However, Richard Feynman noted stars above a certain critical mass are dynamically unstable and would collapse into a black hole, at least if they were non-rotating. Fowler then proposed that these supermassive stars would undergo a series of collapse and explosion oscillations, thereby explaining the energy output pattern. Appenzeller and Fricke (1972) built models of this behavior, but found that the resulting star would still undergo collapse, concluding that a non-rotating 0.75×106M☉ SMS "cannot escape collapse to a black hole by burning its hydrogen through the CNO cycle".
Edwin E. Salpeter and Yakov Zeldovich made the proposal in 1964 that matter falling onto a massive compact object would explain the properties of quasars. It would require a mass of around 108M☉ to match the output of these objects. Donald Lynden-Bell noted in 1969 that the infalling gas would form a flat disk that spirals into the central "Schwarzschild throat". He noted that the relatively low output of nearby galactic cores implied these were old, inactive quasars. Meanwhile, in 1967, Martin Ryle and Malcolm Longair suggested that nearly all sources of extra-galactic radio emission could be explained by a model in which particles are ejected from galaxies at relativistic velocities; meaning they are moving near the speed of light. Martin Ryle, Malcolm Longair, and Peter Scheuer then proposed in 1973 that the compact central nucleus could be the original energy source for these relativistic jets.
Arthur M. Wolfe and Geoffrey Burbidge noted in 1970 that the large velocity dispersion of the stars in the nuclear region of elliptical galaxies could only be explained by a large mass concentration at the nucleus; larger than could be explained by ordinary stars. They showed that the behavior could be explained by a massive black hole with up to 1010M☉, or a large number of smaller black holes with masses below 103M☉. Dynamical evidence for a massive dark object was found at the core of the active elliptical galaxy Messier 87 in 1978, initially estimated at 5×109M☉. Discovery of similar behavior in other galaxies soon followed, including the Andromeda Galaxy in 1984 and the Sombrero Galaxy in 1988.
Donald Lynden-Bell and Martin Rees hypothesized in 1971 that the center of the Milky Way galaxy would contain a massive black hole. Sagittarius A* was discovered and named on February 13 and 15, 1974, by astronomers Bruce Balick and Robert Brown using the Green Bank Interferometer of the National Radio Astronomy Observatory. They discovered a radio source that emits synchrotron radiation; it was found to be dense and immobile because of its gravitation. This was, therefore, the first indication that a supermassive black hole exists in the center of the Milky Way.
The Hubble Space Telescope, launched in 1990, provided the resolution needed to perform more refined observations of galactic nuclei. In 1994 the Faint Object Spectrograph on the Hubble was used to observe Messier 87, finding that ionized gas was orbiting the central part of the nucleus at a velocity of ±500 km/s. The data indicated a concentrated mass of (2.4±0.7)×109M☉ lay within a 0.25″ span, providing strong evidence of a supermassive black hole. Using the Very Long Baseline Array to observe Messier 106, Miyoshi et al. (1995) were able to demonstrate that the emission from an H2O maser in this galaxy came from a gaseous disk in the nucleus that orbited a concentrated mass of 3.6×107M☉, which was constrained to a radius of 0.13 parsecs. Their ground-breaking research noted that a swarm of solar mass black holes within a radius this small would not survive for long without undergoing collisions, making a supermassive black hole the sole viable candidate. Accompanying this observation which provided the first confirmation of supermassive black holes was the discovery of the highly broadened, ionised iron
Kα emission line (6.4 keV) from the galaxy MCG-6-30-15. The broadening was due to the gravitational redshift of the light as it escaped from just 3 to 10 Schwarzschild radii from the black hole.
On April 10, 2019, the Event Horizon Telescope collaboration released the first horizon-scale image of a black hole, in the center of the galaxy Messier 87.
The origin of supermassive black holes remains an open field of research. Astrophysicists agree that black holes can grow by accretion of matter and by merging with other black holes. There are several hypotheses for the formation mechanisms and initial masses of the progenitors, or "seeds", of supermassive black holes.
One hypothesis is that the seeds are black holes of tens or perhaps hundreds of solar masses that are left behind by the explosions of massive stars and grow by accretion of matter. Another model hypothesizes that before the first stars, large gas clouds could collapse into a "quasi-star", which would in turn collapse into a black hole of around 20 M☉. These stars may have also been formed by dark matter halos drawing in enormous amounts of gas by gravity, which would then produce supermassive stars with tens of thousands of solar masses. The "quasi-star" becomes unstable to radial perturbations because of electron-positron pair production in its core and could collapse directly into a black hole without a supernova explosion (which would eject most of its mass, preventing the black hole from growing as fast). An alternative scenario predicts that large high-redshift clouds of metal-free gas, when irradiated by a sufficiently intense flux of Lyman–Werner photons, can avoid cooling and fragmenting, thus collapsing as a single object due to self-gravitation. The core of the collapsing object reaches extremely large values of the matter density, of the order of about 107 g/cm3, and triggers a general relativistic instability. Thus, the object collapses directly into a black hole, without passing from the intermediate phase of a star, or of a quasi-star. These objects have a typical mass of about 100,000 M☉ and are named direct collapse black holes.
Artist's illustration of galaxy with jets from a supermassive black hole.
Another model involves a dense stellar cluster undergoing core collapse as the negative heat capacity of the system drives the velocity dispersion in the core to relativistic speeds. Finally, primordial black holes could have been produced directly from external pressure in the first moments after the Big Bang. These primordial black holes would then have more time than any of the above models to accrete, allowing them sufficient time to reach supermassive sizes. Formation of black holes from the deaths of the first stars has been extensively studied and corroborated by observations. The other models for black hole formation listed above are theoretical.
Independently of the specific formation channel for the black hole seed, given sufficient mass nearby, it could accrete to become an intermediate-mass black hole and possibly a SMBH if the accretion rate persists.
The formation of a supermassive black hole requires a relatively small volume of highly dense matter having small angular momentum. Normally, the process of accretion involves transporting a large initial endowment of angular momentum outwards, and this appears to be the limiting factor in black hole growth. This is a major component of the theory of accretion disks. Gas accretion is the most efficient and also the most conspicuous way in which black holes grow. The majority of the mass growth of supermassive black holes is thought to occur through episodes of rapid gas accretion, which are observable as active galactic nuclei or quasars. Observations reveal that quasars were much more frequent when the Universe was younger, indicating that supermassive black holes formed and grew early. A major constraining factor for theories of supermassive black hole formation is the observation of distant luminous quasars, which indicate that supermassive black holes of billions of solar masses had already formed when the Universe was less than one billion years old. This suggests that supermassive black holes arose very early in the Universe, inside the first massive galaxies.
Artist's impression of stars born in winds from supermassive black holes.
A vacancy exists in the observed mass distribution of black holes. Black holes that spawn from dying stars have masses 5–80 M☉. The minimal supermassive black hole is approximately a hundred thousand solar masses. Mass scales between these ranges are dubbed intermediate-mass black holes. Such a gap suggests a different formation process. However, some models suggest that ultraluminous X-ray sources (ULXs) may be black holes from this missing group.
There is an upper limit to how large supermassive black holes can grow. So-called ultramassive black holes (UMBHs), which are at least ten times the size of most supermassive black holes, at 10 billion solar masses or more, appear to have a theoretical upper limit of around 50 billion solar masses, as anything above this slows growth down to a crawl (the slowdown tends to start around 10 billion solar masses) and causes the unstable accretion disk surrounding the black hole to coalesce into stars that orbit it.
Distant supermassive black holes, such as J0313–1806, and ULAS J1342+0928, are hard to explain so soon after the Big Bang. Some postulate they might come from direct collapse of dark matter with self-interaction. A small minority of sources argue that they may be evidence that our universe is the result of a Big Bounce, instead of a Big Bang, with these supermassive black holes being formed before the Big Bounce.
Gravitation from supermassive black holes in the center of many galaxies is thought to power active objects such as Seyfert galaxies and quasars, and the relationship between the mass of the central black hole and the mass of the host galaxy depends upon the galaxy type.
An active galactic nucleus (AGN) is now considered to be a galactic core hosting a massive black hole that is accreting matter and displays a sufficiently strong luminosity. The nuclear region of the Milky Way, for example, lacks sufficient luminosity to satisfy this condition. The unified model of AGN is the concept that the large range of observed properties of the AGN taxonomy can be explained using just a small number of physical parameters. For the initial model, these values consisted of the angle of the accretion disk's torus to the line of sight and the luminosity of the source. AGN can be divided into two main groups: a radiative mode AGN in which most of the output is in the form of electromagnetic radiation through an optically thick accretion disk, and a jet mode in which relativistic jets emerge perpendicular to the disk.
Simulation of a side view of a black hole with transparent toroidal ring of ionized matter according to a proposed model for Sgr A*. This image shows the result of bending of light from behind the black hole, and it also shows the asymmetry arising by the Doppler effect from the extremely high orbital speed of the matter in the ring.
Some of the best evidence for the presence of black holes is provided by the Doppler effect whereby light from nearby orbiting matter is red-shifted when receding and blue-shifted when advancing. For matter very close to a black hole the orbital speed must be comparable with the speed of light, so receding matter will appear very faint compared with advancing matter, which means that systems with intrinsically symmetric discs and rings will acquire a highly asymmetric visual appearance. This effect has been allowed for in modern computer-generated images such as the example presented here, based on a plausible model for the supermassive black hole in Sgr A* at the centre of our own galaxy. However, the resolution provided by presently available telescope technology is still insufficient to confirm such predictions directly.
What already has been observed directly in many systems are the lower non-relativistic velocities of matter orbiting further out from what are presumed to be black holes. Direct Doppler measures of water masers surrounding the nuclei of nearby galaxies have revealed a very fast Keplerian motion, only possible with a high concentration of matter in the center. Currently, the only known objects that can pack enough matter in such a small space are black holes, or things that will evolve into black holes within astrophysically short timescales. For active galaxies farther away, the width of broad spectral lines can be used to probe the gas orbiting near the event horizon. The technique of reverberation mapping uses variability of these lines to measure the mass and perhaps the spin of the black hole that powers active galaxies.
In the Milky Way
Inferred orbits of 6 stars around supermassive black hole candidate Sagittarius A* at the Milky Way galactic center
From the motion of star S2, the object's mass can be estimated as 4.1 million M☉, or about 8.2×1036 kg.
The radius of the central object must be less than 17 light-hours, because otherwise S2 would collide with it. Observations of the star S14 indicate that the radius is no more than 6.25 light-hours, about the diameter of Uranus' orbit.
No known astronomical object other than a black hole can contain 4.1 million M☉ in this volume of space.
Infrared observations of bright flare activity near Sagittarius A* show orbital motion of plasma with a period of 45±15 min at a separation of six to ten times the gravitational radius of the candidate SMBH. This emission is consistent with a circularized orbit of a polarized "hot spot" on an accretion disk in a strong magnetic field. The radiating matter is orbiting at 30% of the speed of light just outside the innermost stable circular orbit.
On January 5, 2015, NASA reported observing an X-ray flare 400 times brighter than usual, a record-breaker, from Sagittarius A*. The unusual event may have been caused by the breaking apart of an asteroid falling into the black hole or by the entanglement of magnetic field lines within gas flowing into Sagittarius A*, according to astronomers.
Detection of an unusually bright X-ray flare from Sagittarius A*, a supermassive black hole in the center of the Milky Way galaxy.
Artist's impression of a supermassive black hole tearing apart a star. Below: supermassive black hole devouring a star in galaxy RX J1242−11 – X-ray (left) and optical (right).
Unambiguous dynamical evidence for supermassive black holes exists only in a handful of galaxies; these include the Milky Way, the Local Group galaxies M31 and M32, and a few galaxies beyond the Local Group, e.g. NGC 4395. In these galaxies, the mean square (or rms) velocities of the stars or gas rises proportionally to 1/r near the center, indicating a central point mass. In all other galaxies observed to date, the rms velocities are flat, or even falling, toward the center, making it impossible to state with certainty that a supermassive black hole is present. Nevertheless, it is commonly accepted that the center of nearly every galaxy contains a supermassive black hole. The reason for this assumption is the M–sigma relation, a tight (low scatter) relation between the mass of the hole in the 10 or so galaxies with secure detections, and the velocity dispersion of the stars in the bulges of those galaxies. This correlation, although based on just a handful of galaxies, suggests to many astronomers a strong connection between the formation of the black hole and the galaxy itself.
Hubble Space Telescope photograph of the 4,400 light-year-long relativistic jet of Messier 87, which is matter being ejected by the 6.4×109M☉ supermassive black hole at the center of the galaxy
The nearby Andromeda Galaxy, 2.5 million light-years away, contains a (1.1–2.3)×108 (110–230 million) M☉ central black hole, significantly larger than the Milky Way's. The largest supermassive black hole in the Milky Way's vicinity appears to be that of Messier 87 (i.e. M87*), at a mass of (6.4±0.5)×109 (c. 6.4 billion) M☉ at a distance of 53.5 million light-years. The supergiant elliptical galaxy NGC 4889, at a distance of 336 million light-years away in the Coma Berenices constellation, contains a black hole measured to be 2.1×1010 (21 billion) M☉.
Masses of black holes in quasars can be estimated via indirect methods that are subject to substantial uncertainty. The quasar TON 618 is an example of an object with an extremely large black hole, estimated at 6.6×1010 (66 billion) M☉. Its redshift is 2.219. Other examples of quasars with large estimated black hole masses are the hyperluminous quasar APM 08279+5255, with an estimated mass of 2.3×1010 (23 billion) M☉, and the quasar S5 0014+81, with a mass of 4.0×1010 (40 billion) M☉, or 10,000 times the mass of the black hole at the Milky Way Galactic Center.
Some galaxies, such as the galaxy 4C +37.11, appear to have two supermassive black holes at their centers, forming a binary system. If they collided, the event would create strong gravitational waves. Binary supermassive black holes are believed to be a common consequence of galactic mergers. The binary pair in OJ 287, 3.5 billion light-years away, contains the most massive black hole in a pair, with a mass estimated at 18 billion M☉. In 2011, a super-massive black hole was discovered in the dwarf galaxy Henize 2-10, which has no bulge. The precise implications for this discovery on black hole formation are unknown, but may indicate that black holes formed before bulges.
On March 28, 2011, a supermassive black hole was seen tearing a mid-size star apart. That is the only likely explanation of the observations that day of sudden X-ray radiation and the follow-up broad-band observations. The source was previously an inactive galactic nucleus, and from study of the outburst the galactic nucleus is estimated to be a SMBH with mass of the order of a million solar masses. This rare event is assumed to be a relativistic outflow (material being emitted in a jet at a significant fraction of the speed of light) from a star tidally disrupted by the SMBH. A significant fraction of a solar mass of material is expected to have accreted onto the SMBH. Subsequent long-term observation will allow this assumption to be confirmed if the emission from the jet decays at the expected rate for mass accretion onto a SMBH.
A gas cloud with several times the mass of the Earth is accelerating towards a supermassive black hole at the centre of the Milky Way.
In 2012, astronomers reported an unusually large mass of approximately 17 billion M☉ for the black hole in the compact, lenticular galaxyNGC 1277, which lies 220 million light-years away in the constellation Perseus. The putative black hole has approximately 59 percent of the mass of the bulge of this lenticular galaxy (14 percent of the total stellar mass of the galaxy). Another study reached a very different conclusion: this black hole is not particularly overmassive, estimated at between 2 and 5 billion M☉ with 5 billion M☉ being the most likely value. On February 28, 2013 astronomers reported on the use of the NuSTAR satellite to accurately measure the spin of a supermassive black hole for the first time, in NGC 1365, reporting that the event horizon was spinning at almost the speed of light.
In September 2014, data from different X-ray telescopes have shown that the extremely small, dense, ultracompact dwarf galaxyM60-UCD1 hosts a 20 million solar mass black hole at its center, accounting for more than 10% of the total mass of the galaxy. The discovery is quite surprising, since the black hole is five times more massive than the Milky Way's black hole despite the galaxy being less than five-thousandths the mass of the Milky Way.
Some galaxies lack any supermassive black holes in their centers. Although most galaxies with no supermassive black holes are very small, dwarf galaxies, one discovery remains mysterious: The supergiant elliptical cD galaxy A2261-BCG has not been found to contain an active supermassive black hole, despite the galaxy being one of the largest galaxies known; ten times the size and one thousand times the mass of the Milky Way. Since a supermassive black hole will only be visible while it is accreting, a supermassive black hole can be nearly invisible, except in its effects on stellar orbits.
In December 2017, astronomers reported the detection of the most distant quasar currently known, ULAS J1342+0928, containing the most distant supermassive black hole, at a reported redshift of z = 7.54, surpassing the redshift of 7 for the previously known most distant quasar ULAS J1120+0641.
Supermassive black hole and smaller black hole in galaxy OJ 287
Comparisons of large and small black holes in galaxy OJ 287 to the Solar System
In February 2020, astronomers reported the discovery of the Ophiuchus Supercluster eruption, the most energetic event in the Universe ever detected since the Big Bang. It occurred in the Ophiuchus Cluster in the galaxy NeVe 1, caused by the accretion of nearly 270 million solar masses of material by its central supermassive black hole. The eruption lasted for about 100 million years and released 5.7 million times more energy than the most powerful gamma-ray burst known. The eruption released shock waves and jets of high-energy particles that punched the intracluster medium, creating a cavity about 1.5 million light-years wide - ten times the Milky Way's diameter.
Hawking radiation is black-body radiation that is predicted to be released by black holes, due to quantum effects near the event horizon. This radiation reduces the mass and energy of black holes, causing them to shrink and ultimately vanish. If black holes evaporate via Hawking radiation, a supermassive black hole with a mass of 1011 (100 billion) M☉ will evaporate in around 2×10100 years. Some monster black holes in the universe are predicted to continue to grow up to perhaps 1014M☉ during the collapse of superclusters of galaxies. Even these would evaporate over a timescale of up to 10106 years.
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^Landau, Elizabeth; Bañados, Eduardo (December 6, 2017). "Found: Most Distant Black Hole". NASA. Retrieved December 6, 2017. 'This black hole grew far larger than we expected in only 690 million years after the Big Bang, which challenges our theories about how black holes form,' said study co-author Daniel Stern of NASA's Jet Propulsion Laboratory in Pasadena, California.
^Seidel, Jamie (December 7, 2017). "Black hole at the dawn of time challenges our understanding of how the universe was formed". News Corp Australia. Retrieved December 9, 2017. It had reached its size just 690 million years after the point beyond which there is nothing. The most dominant scientific theory of recent years describes that point as the Big Bang—a spontaneous eruption of reality as we know it out of a quantum singularity. But another idea has recently been gaining weight: that the universe goes through periodic expansions and contractions—resulting in a 'Big Bounce'. And the existence of early black holes has been predicted to be a key telltale as to whether or not the idea may be valid. This one is very big. To get to its size—800 million times more mass than our Sun—it must have swallowed a lot of stuff. ... As far as we understand it, the universe simply wasn't old enough at that time to generate such a monster.
^Frautschi, S (1982). "Entropy in an expanding universe". Science. 217 (4560): 593–599. Bibcode:1982Sci...217..593F. doi:10.1126/science.217.4560.593. PMID17817517. S2CID27717447. p. 596: table 1 and section "black hole decay" and previous sentence on that page: "Since we have assumed a maximum scale of gravitational binding – for instance, superclusters of galaxies – black hole formation eventually comes to an end in our model, with masses of up to 1014M☉ ... the timescale for black holes to radiate away all their energy ranges ... to 10106 years for black holes of up to 1014M☉