Kurzgesagt – In a Nutshell
Sources – Largest Black Hole
We would like to thank the following experts for their support:
Prof. Matthew Caplan
Illinois State University
Sources:
– The largest things in the universe are black holes. In contrast to things like planets or stars they have no physical size limit, and can literally grow endlessly.
A planet can only grow to about 10 times the mass of Jupiter before it is considered a small star.
#Evidence of an Upper Bound on the Masses of Planets and Its Implications for Giant Planet Formation, Kevin C. Schlaufman, 2018
A star can only grow to be a few hundred times the mass of our Sun due to the Eddington limit.
#Eddington mass limit, Encyclopaedia Britannica, retrieved 2021
https://www.britannica.com/science/Eddington-mass-limit
Quote: “Eddington mass limit, also called Eddington limit, theoretical upper limit to the mass of a star or an accretion disk. The limit is named for English astrophysicist Sir Arthur Eddington. At the Eddington mass limit, the outward pressure of the star’s radiation balances the inward gravitational force. If a star exceeds this limit, its luminosity would be so high that it would blow off the outer layers of the star. The limit depends upon the specific internal conditions of the star and is around several hundred solar masses.”
There are discussions on what the biggest black holes could be. Currently it is believed that the size of a black hole is only limited by time itself. Since the universe is believed to have existed for roughly 13.8 billion years, supermassive black holes can't have grown to more than 100 billion solar masses, as this paper below suggests.
#Is there a maximum size for black holes in galactic nuclei?, Kohei Inayoshi and Zoltán Haiman, 2016
https://iopscience.iop.org/article/10.3847/0004-637X/828/2/110
Quote: “This prevents SMBHs from growing above ~10^11 M☉ in the age of the universe.”
– The smallest kind of black holes may or may not exist. If they do, they are probably the oldest objects in the universe, older even than atoms. They would have formed just after the big bang, when the universe was so dense with violent energy, that any tiny pocket that was just slightly more dense than its neighbours could produce a black hole.
These very early or ‘primordial’ black holes could be some of the first cosmic objects to appear and they could inform us about the density fluctuations in the early Universe.
#Primordial Black Holes - Recent Developments, B.J.Carr, 2004
https://www.slac.stanford.edu/econf/C041213/papers/0204.PDF
Quote: “Black holes with a wide range of masses could have formed in the early Universe as a result of the great compression associated with the Big Bang.”
Quote: “One of the most important reasons for studying PBHs is that it enables one to place limits on the spectrum of density fluctuations in the early Universe. This is because, if the PBHs form directly from density perturbations”
#What are primordial black holes?, Astronomy.com, 2019
https://astronomy.com/news/2019/07/primordial-black-holes
Quote: “There was only a small period of time — about 1 second — following the Big Bang when primordial black holes could have formed. But in the extreme world of our expanding early universe, a lot can happen in just one second. And the later in this window of time that primordial black holes formed, the more massive they would be.”
For comparison, the first atoms appeared 240,000 to 340,000 years after the Big Bang.
#First Light & Reionization, NASA James Webb Space Telescope, retrieved 2021
https://www.slac.stanford.edu/econf/C041213/papers/0204.PDF
Quote: “After the Big Bang, the universe was like a hot soup of particles (i.e. protons, neutrons, and electrons). When the universe started cooling, the protons and neutrons began combining into ionized atoms of hydrogen and deuterium. Deuterium further fused into helium-4. These ionized atoms of hydrogen and helium attracted electrons turning them into neutral atoms. Ultimately the composition of the universe at this point was 3 times more hydrogen than helium with just trace amounts of other light elements.
This process of particles pairing up is called "Recombination" and it occurred approximately 240,000 to 300,000 years after the Big Bang.”
– The smallest Primordial Black Hole that could still be around would be a trillion kilograms or so, the mass of a big mountain. And yet they would be no bigger than a proton.
Any black hole smaller than a trillion kilograms would have evaporated by now through Hawking radiation.
#Primordial Black Holes as Dark Matter: Recent Developments, B.J.Carr, 2004
https://www.slac.stanford.edu/econf/C041213/papers/0204.PDF
Quote: “PBHs smaller than about 10^15 g would have evaporated by now with many interesting cosmological consequences ”
If you compress an object with mass to a certain radius, it will create a gravitational field such that the escape velocity from that object is greater than the speed of light. We call this radius the Schwarzschild radius and generally, black holes are objects which have reached this size. There is a simple equation that ties this Schwarzchild radius to a black hole’s mass.
Schwarzschild radius = 2 x Gravitational Constant x Mass / C^2
The radius will be in metres.
The Gravitational constant is 6.67408 × 10^-11 m^3/kg/s^2.
Mass is in kg.
C is the speed of light, equal to 299,792,458 m/s.
#The Schwarzschild Radius, Hyperphysics, retrieved 2021
http://hyperphysics.phy-astr.gsu.edu/hbase/Astro/blkhol.html
You can perform these calculations easily (as well as work out plenty of other parameters) using an online calculator such as this one:
#Black Hole Parameters, Ian Mallett, 2020
https://space.geometrian.com/calcs/black-hole-params.php
A proton has a radius of about 0.84 * 10^-15 m. According to our calculator, a trillion kg black hole has a radius of 1.48 * 10^-15 m which is slightly bigger than a proton.
#The next phase of the proton radius puzzle, MPG, 2020
https://www.mpq.mpg.de/6365594/11-next-phase-of-the-proton-radius-puzzle
And how heavy is a big mountain? Here is a way to calculate it:
Volume = Mass/Density
#UBC Earth and Ocean Sciences, F. Jones.2007
https://www.eoas.ubc.ca/ubcgif/iag/foundations/properties/density.htm
Assuming a rock density of 2500 kg/m^3, a trillion kg makes a volume of 400 million m^3 of rocks.
If we take a mountain to be a cone with a slope of 40 degrees, then it has a radius of X and a height of 1.19 X.
We solve this equation to find the height:
Volume = 3.142 * Height * Radius^2/3
Volume = 3.142 * 1.19X * X^2/3
400,000,000 = 3.142 * 1.19 X^3 /3
X=689.69
The mountain would be 689m in radius and 814m in height.
– A Primordial Black hole with the mass of earth would barely larger than a coin. This makes them very hard to find, so we haven’t actually observed any yet – if they exist they may even be the mysterious dark matter that holds galaxies together.
If we use the black hole calculator and input the mass of the Earth, at 5.972 × 10^24 kg, we get a Schwarzschild radius of 8.87 mm. If we compress the Earth to this size, it is considered a black hole. For comparison, a Euro coin has a radius of 11.6 mm and a dollar one has a radius of 13.25
#Black Hole Parameters, Ian Mallett, 2020
https://space.geometrian.com/calcs/black-hole-params.php
#Common sides of euro coins, European Commission
Quote: “€1
Diameter: 23.25mm.
Thickness: 2.33mm.
Weight: 7.50g.”
#Coin Specifications, US Mint
https://www.usmint.gov/learn/coin-and-medal-programs/coin-specifications
#Sun Fact Sheet, NASA, retrieved 2021
https://nssdc.gsfc.nasa.gov/planetary/factsheet/sunfact.html
– To make a black hole we need to compress enough matter so that it collapses into itself. After that, the more mass we throw at it, the larger it becomes. In today's universe, only the most violent cosmic events can create the necessary conditions, such as the merger of neutron stars or when the core of a very massive star collapses in a supernova.
#What Is a Black Hole?, NASA, 2014
https://www.nasa.gov/audience/forstudents/5-8/features/nasa-knows/what-is-a-black-hole-58.html
Quote: “Stellar black holes form when the center of a very massive star collapses in upon itself. This collapse also causes a supernova, or an exploding star, that blasts part of the star into space.”
#NASA missions catch first light from a gravitational-wave event, NASA Hubble Space Telescope, 2017
https://www.nasa.gov/audience/forstudents/5-8/features/nasa-knows/what-is-a-black-hole-58.html
Quote: “In NGC 4993, two neutron stars once spiraled around each other at blinding speed. As they drew closer together, they whirled even faster, spinning as fast as a blender near the end. Powerful tidal forces ripped off huge chunks while the remainder collided and merged, forming a larger neutron star or perhaps a black hole.”
– To have a unit to work with here, we’ll use the mass of our sun, about 2 million trillion trillion kilograms.
More exactly, the Sun’s mass is 1.9885 x 10^30 kg which is rounded to 2 million trillion trillion kilograms.
#Sun Fact Sheet, NASA, retrieved 2021
https://nssdc.gsfc.nasa.gov/planetary/factsheet/sunfact.html
– The smallest black holes we have solid evidence for likely came from neutron stars that got too massive and collapsed. The smallest known has 2.7 times the mass of the sun which works out to a sphere around 16 km in diameter, large enough to cover Paris.
A gravitational wave detection by the Laser Interferometer Gravitational-Wave Observatory (LIGO) revealed a neutron star merger that created a new compact object of 2.7 solar masses. Observing the X-rays released by that event suggest that it is a new black hole and not another neutron star.
We can calculate its size using the previous Schwarzschild radius equation.
#GW170817 Most Likely Made a Black Hole, David Pooley et al., 2018
https://iopscience.iop.org/article/10.3847/2041-8213/aac3d6
Quote: “The merger of two neutron stars with mass 1.48 ± 0.12 M⊙ and 1.26 ± 0.1 M⊙—where the merged object has a mass of 2.74 M⊙ (Abbott et al. 2017a)—could result in either a massive neutron star or a black hole.”
Quote: “The X-ray data at 107–111 days suggest that the remnant is not a neutron star with magnetic field 10^12 G. This, in turn, suggests that the merged object is most likely a black hole.”
2.7 solar masses is 5.4 * 10^30 kg. According to our calculator, this black hole would have a radius of 7.97 km. The historical center of Paris fits inside a circle about 6 km in radius.
– Another lightweight black hole is the companion to the V723 Mon red giant star. This star is 24 times larger than our sun, 30 million kilometer in diameter. And yet, it is thrown around by a tiny black hole just 17.2 km wide. This tiny thing bullying the star is so much smaller that we can barely even show them in comparison.
The black hole companion to V723 Mon has a mass 2.91 times that of our Sun, giving it a radius of 8.596 km (diameter of 17.19 km) according to our calculator.
#A Unicorn in Monoceros: the 3M⊙ dark companion to the bright, nearby red giant V723 Mon is a non-interacting, mass-gap black hole candidate, T. Jayasinghe et al., 2020
https://iopscience.iop.org/article/10.3847/2041-8213/ab960f
Quote: “Detailed models of the light curves constrained by the period, radial velocities and stellar temperature give [...] a companion mass of Mcomp = 2.91 ± 0.08 M⊙, a stellar radius of Rgiant = 23.6 ± 1.0 R⊙, and a giant mass of Mgiant 0.87 ± 0.08 M⊙, consistent with our other estimates.”
The Sun's diameter is 1.4 million km.
#Our Sun, NASA
https://solarsystem.nasa.gov/solar-system/sun/by-the-numbers/
Quote: “Sun:EQUATORIAL RADIUS= 695,508km”
According to the source above, the red giant star at V723 Mon has a radius 23.6 times the Sun which makes it around 30 million km in diameter.
– One of the largest known stellar black holes is M33 X-7. It currently spends its time eating a 70 solar mass blue giant, bit by bit. As all that stolen matter circles towards the black hole, like water going down a drain, friction heats it up to temperatures high enough to shine 500,000 times brighter than our Sun! And yet, X-7 is ‘only’ 15.65 solar masses and 92 km wide, just big enough to cast a shadow on Corsica.
#Formation of the black-hole binary M33 X-7 via mass-exchange in a tight massive system, Francesca Valsecchi et al., 2010
https://arxiv.org/abs/1010.4809
Quote: “M33 X-7 is among the most massive X-Ray binary stellar systems known, hosting a rapidly spinning 15.65 M black hole orbiting an underluminous 70 M Main Sequence companion in a slightly eccentric 3.45 day orbit”
The logarithmic ratio between the brightness of the giant companion star at M33 X-7 and the Sun is 5.72 according to the table below.
This makes the giant star 10^5.72 = 524,807 times or about 500,000 times brighter than our Sun.
#The Eclipsing Black Hole X-ray Binary M33 X-7: Understanding the Current Properties, Francesca Valsecchi, 2009
According to the source one above, the black hole at M33 X-7 has a mass of 15.56 solar masses. If we plug that into our calculator, it has a radius of 45.95 km. That is a diameter of 91.9 km.
#Sun Fact Sheet, NASA, 2018
https://nssdc.gsfc.nasa.gov/planetary/factsheet/sunfact.html
Quote: “Luminosity (10^24 J/s) 382.8”
– To grow much larger, black holes have to either devour a lot of stars or better, merge with one another. The instruments that make it possible to detect these mergers are very new so we are currently discovering a lot of exciting things.
Gravitational wave detection is the new method we rely upon to observe bodies and events that do not emit light. LIGO or the Laser Interferometer Gravitational-wave Observatory is the foremost of the new tools we have to perform these observations.
#What is LIGO?, LIGO Caltech, retrieved 2021
https://www.ligo.caltech.edu/page/what-is-ligo
Quote: “LIGO stands for "Laser Interferometer Gravitational-wave Observatory". It is the world's largest gravitational wave observatory and a marvel of precision engineering. Comprising two enormous laser interferometers located 3000 kilometers apart, LIGO exploits the physical properties of light and of space itself to detect and understand the origins of gravitational waves (GW).”
Quote: “LIGO is blind. Unlike optical or radio telescopes, LIGO does not see electromagnetic radiation (e.g., visible light, radio waves, microwaves). It doesn't have to because gravitational waves are not part of the electromagnetic spectrum. ”
– Like two massive black holes that we detected in a galaxy 17 billion lightyears away. As they spun around each other violently, they released more energy in the form of gravitational waves than the combined light from all the stars in the milky way in 4400 years. The new black hole they formed is about the size of Germany and is 142 solar masses.
This refers to the gravitational wave event GW190521. LIGO detected the merger between a black hole of 65 solar masses and another of 85 solar masses. During this event, the mass of 8 Suns was converted into energy.
#GW190521: The most massive black hole collision observed to date, LIGO, 2020
https://www.britannica.com/science/E-mc2-equation
Quote: “For GW190521, the post-merger remnant black hole “weighs in” at around 142 M⊙ , putting it well out in front on LIGO-Virgo’s list of biggest black holes. This remnant mass is about 8M⊙ less than the combined masses of the two black holes that merged; this mass difference was converted into the energy of the gravitational-wave signal.”
Einstein’s mass-energy equivalence (E=mC^2) states that converting 1 kg of matter into pure energy releases 9 x 10^16 Joules. 8 Solar masses is 1.6 x 10^31 kg, which would become 1.44 x 10^48 Joules.
#E = mC^2, Encyclopædia Britannica, retrieved 2021
https://www.britannica.com/science/E-mc2-equation
Quote: “E = mC^2, equation in German-born physicist Albert Einstein’s theory of special relativity that expresses the fact that mass and energy are the same physical entity and can be changed into each other.”
#Supermassive Black Holes, David Weinberg, 2012
http://www.astronomy.ohio-state.edu/~dhw/A142/notes10.pdf
Quote: “Total luminosity of all stars in Milky Way is ∼ 3 × 10^10L⊙.”
One solar luminosity is 3.8 * 10^26 Watts. The Milky Way's luminosity is about 30 billion times that figure, at 1.14 * 10^37 Watts. We compare this value in Watts to the energy released in the GW190521 merger.
Time = Energy / Power
Time = 1.44 * 10^48 Joules / 1.14*10^37 Watts which is about 4400 years to within the precision available from our sources.
#Resolution B1, IAU, 2015
https://www.iau.org/static/resolutions/IAU2015_English.pdf
Quote: “The zero point was selected so that the nominal solar luminosity (LN = 3.828 × 10^26 W)”
#Supermassive Black Holes, David Weinberg, 2012
http://www.astronomy.ohio-state.edu/~dhw/A142/notes10.pdf
Quote: “Total luminosity of all stars in Milky Way is ∼ 3 × 10^10L⊙.”
According to our calculator, a black hole of 142 solar masses has a diameter of 840 km. This is similar to the 853 km North-South span of Germany.
#German Geography, German Culture, 2021
https://germanculture.com.ua/germany-facts/german-geography/
Quote: “Extending 853 kilometers from its northern border with Denmark to the Alps in the south, it is the sixth largest country in Europe. At its widest, Germany measures approximately 650 kilometers from the Belgian-German border in the west to the Polish frontier in the east.”
– And here we hit a curious gap in scale. There are lots of black holes up to 150 solar masses. And then there is nothing for a long time. Until we suddenly hit black holes, that are millions of times more massive.
The chart below highlights some of the black hole discoveries we’ve made. Highlighted at the top of the largest stellar black hole discovered with gravitational wave event GW190521. We find very few black holes of ‘intermediate’ mass and none bigger than 150 solar masses so far.
#Stellar Graveyard, with GW190521 Highlighted, LIGO, 2020
– Which is a bit confusing, because we had this idea of black holes consistently growing and growing. But for the most massive black holes this process is not fast enough to explain their existence today. The universe is simply not old enough for these supermassive black holes to have formed from eating stars and merging with each other. Something else must have happened.
Our understanding of the maximum size of a star that can create a black hole, and how fast that black hole can grow by absorbing matter through accretion, suggests that it is impossible for supermassive black holes to appear 13 billion years ago.
#Supermassive Black Holes, David Weinberg, 2012
https://arxiv.org/pdf/1811.04953.pdf
Quote: “The discovery of super-massive black holes (SMBHs) with masses in excess of 10^9 M⊙ at redshifts greater than z = 6 presents a significant difficulty for theories of black hole formation and growth. Black holes are expected to form as the end point of massive stars.”
Quote: “Even if PopIII remnant stars can remain in a region of high density, where local star formation is suppressed, a PopIII remnant would need to accrete at the Eddington limit for several hundred megayears in order to reach a mass of close to a billion solar masses by a redshift of 6.”
– To explain how we got the largest black holes in the universe, we might have needed the largest stars that ever existed: Quasi Stars. To get a sense for the scale, we can compare them to the largest stars that exist today. Our Sun is like a grain of sand next to them.
Another way to explain the existence of supermassive black holes is that they are not born from regular stars, but from gigantic quasi-stars that do not have the same limitations.
#The structure and evolution of quasi-stars, Warrick H. Ball et al., 2011
https://arxiv.org/pdf/1102.5098.pdf
Quote: “If the rate of mass infall is much higher then the envelope of the star does not reach thermal equilibrium during the lifetime of the star. In this case, the core collapses after hydrogen burning is complete. The structure that remains after core collapse is a stellar-mass BH embedded within a giant-like envelope, or a quasi-star. The attractive feature of a quasi-star is that the accretion rate on to the BH is limited by the Eddington rate of the entire object, which is initially much larger than that of the BH alone. The excess energy is carried away by convection.”
#Mitchell C. Begelman, Elena M. Rossi, Philip J. Armitage, Quasi-stars: accreting black holes inside massive envelopes, 2008.
https://academic.oup.com/mnras/article/387/4/1649/1091917
Quote: “Thus, quasi-stars should have radii of the order of 10^2–10^3 au and temperatures of a few thousand degrees.”
From this source we find that quasi stars would have a radius of 100 to 1000 AU, which is 15 billion to 150 billion km. The Sun has a radius of 0.7 million km.
The Quasi Stars would be 21.5 thousand to 215 thousand times larger.
This is similar to the difference between a house (10m scale) and a grain of sand (0.1 to 1 mm)
– We don’t know if Quasi Stars actually existed but they are an interesting concept how to supercharge black hole development. The idea is that the matter in the early universe was so dense that quasi stars could grow to thousands of times the mass of our sun. The cores of these stars might have been crushed by their own weight so much to actually collapse into black holes while the star was still forming. In contrast to stars today who would destroy themselves in the process, inside quasi stars, a deadly balance could emerge. Gravity pressed the supermassive star together, feeding the black hole and heating the material falling in to such degrees that the radiation pressure kept the star stable. And so these quickly growing black holes might have been able to consume the quasi star for millions of years and grow far bigger than any modern stellar black hole. Black holes several thousand times the mass of the Sun and wider than the entire earth. These black holes might have become the seeds for supermassive black holes.
The hypothetical origin of a quasi-star is a huge cloud of gas composed of nearly pure hydrogen, as existed in the early Universe. It collapses and forms a black hole at its center, which it then feeds at an accelerated rate. as described in the paper below:
#Quasi-stars: accreting black holes inside massive envelopes, Mitchell C. Begelman et al., 2008
https://arxiv.org/pdf/0711.4078.pdf
Quote: “In outline, the BVR model envisages a three-stage process for black hole formation. First, gas in metal-free haloes with a virial temperature above T ~ 10^4 K flows towards the centre of the potential as a result of gravitational instabilities, forming a massive, pressure-supported central object. [...] Eventually, when the core temperature attains T ∼ 5 × 10^8 K, neutrino losses result in a catastrophic collapse of the core to a black hole. We dub the resulting structure – comprising an initially low-mass black hole embedded within a massive, radiation-pressure-supported envelope – a quasi-star. Initially, the black hole is much less massive than the envelope. Over time, the black hole grows at the expense of the envelope, until finally the growing luminosity succeeds in unbinding the envelope and the seed black hole is unveiled. [...] Very rapid growth can then occur at early times, when the envelope mass greatly exceeds the black hole mass.”
As we can read from the chart below, these quasi-stars would have to be several thousand to many millions of times the mass of the Sun to create the black hole seeds that grow into the supermassive black holes we see today.
#Supermassive black hole seeds: updates on the“quasi-star model”, Elena Maria Rossi, 2017
A black hole would have to have a mass of 2157 solar masses so that it can have a radius larger than that of the Earth, which is 6371 km.
The black holes emerging from a Quasi-Star would have masses of up to 10,000 solar masses.
Their radius would be up to 29,533 km, which is 4.63 times larger than the radius of the Earth.
– In the Milky Way we have Sagittarius A*, a super massive black hole with about 4 million solar masses that is calm and collected and just does its thing. We know it sits there because we can see a number of stars being thrown around by a seemingly empty spot. And despite its incredible mass, it’s radius is still only 17 times our sun. Smaller than most giant stars, but millions of times more massive.
The Schwarzschild radius of this black hole with 4 million solar masses would be 11.8 million km according to the Schwarzschild radius calculation, which is 16.7 times the radius of our Sun.
#Supermassive Black Hole Sagittarius A*, NASA, 2013
https://www.nasa.gov/mission_pages/chandra/multimedia/black-hole-SagittariusA.html
Quote: “During 2012, Chandra collected about five weeks worth of observations to capture unprecedented X-ray images and energy signatures of multi-million degree gas swirling around Sgr A*, a black hole with about 4 million times the mass of the Sun.”
– Because Supermassive black holes are so massive and located at the center of galaxies, many people imagine them a bit like the Sun in the solar system. An anchor that glues everything else together and forces it into an orbit. But this is a misconception. While the sun makes up 99.86% of all the mass in the solar system, SuperMassive Black Holes usually only have 0.001% of the mass of their galaxy. The billions of stars in galaxies are not gravitationally bound to them, instead it is the gravitational effect of dark matter which holds them together.
The Sun makes up 99.86% of the mass of the Solar System and holds everything together with its gravity.
#The Sun, Natural History Museum, 2021
https://www.nhm.ac.uk/discover/factfile-the-sun.html
Quote: ”The Sun is the biggest object in our solar system, with a distance of 695,508 kilometres from centre to surface. It contains 99.86% of the mass of the entire solar system and could contain roughly 1.3 million Earths.”
According to the paper below, most galaxies have a supermassive black hole at their center that has a mass about 100,000 times lower than the total mass of the galaxy. That is, 0.001%.
Smaller galaxies like our own Milky Way have a smaller ratio between the supermassive black hole mass and the total mass. Large galaxies have a bigger ratio.
#A relationship between supermassive black hole mass and the total gravitational mass of the host galaxy, Kaushala Bandara et al., 2009
https://iopscience.iop.org/article/10.1088/0004-637X/704/2/1135
#Dark Matter in Galaxies, Ken Freeman, 2001
https://sites.astro.caltech.edu/~george/ay20/eaa-darkmatter-obs.pdf
Quote: “All of these estimators together indicate that the enclosed mass of the Milky Way increases linearly with radius out to at least 150 kpc and that its total mass is about 15 × 10^11M⊙. The luminous mass is unlikely to exceed 1.2×10^11M⊙, so the mass of our Galaxy is probably more than 90% dark.”
– Many supermassive black holes aren’t gentle giants, especially when they are feeding on the clouds of mass in their galaxy. The one at the center of the BL Lacertae galaxy is devouring so much material that it produces jets of plasma accelerated to nearly the speed of light. If Earth was orbiting this huge body, it would seem 115 times larger than our Sun in the sky… and we’d be burnt to a crisp in seconds by its glowing hot accretion disk.
BL Lacertae has a black hole with an estimated 30 million solar masses. This would give it a radius of 88.6 million km (177.2 million km in diameter).
#BL Lacertae: X-ray spectral evolution and a black-hole mass estimate, Lev Titarchuk and Elena Seifina, 2017
https://arxiv.org/abs/1704.04552
Quote: “This Γ − Ṁ correlation allows us to estimate the black-hole (BH) mass in BL Lac to be MBH ~ 3 × 10^7M⊙ for a distance of 300 Mpc”
According to the triangle calculator below, an 88.6 million km wide object at a distance of 150 million km would appear to have a half-angle of 30.57 degrees in the sky. For comparison, the Sun with its 0.7 million km radius forms a disk with a half-angle 0.267 degrees. BL Lacertae would appear 115 times larger.
#The Right-angled Triangles Calculator
http://www.cleavebooks.co.uk/scol/calrtri.htm
– The galaxy Cygnus A has a super massive black hole with 2.5 billion solar masses and 14.7 billion km wide, which would mean that if it took the place of our Sun, it would swallow all the planets and stretch halfway to the edge of our Solar System. It is devouring so much mass and material that it churns its disk into a kind of magnetic funnel, spewing gas out making tremendous radio lobes, towering over the galaxy, half a million light years in diameter. That is 2.5 Milkyways wide.
The supermassive black hole Cygnus A has a mass 2.5 billion times that of our Sun, giving it a diameter of 49.35 au according to our calculator. We have chosen the radius of the Solar System to be 123 Astronomical Units.
Cygnus A would stretch 40% of the way across our Solar System, roughly halfway.
#Heliopause, Encyclopaedia Britannica, retrieved 2021
https://www.britannica.com/science/heliopause
Quote: “The heliopause is about 123 astronomical units (AU; 18 billion km [11 billion miles]) from the Sun.”
#Spectroscopy of the near-nuclear regions of Cygnus A: estimating the mass of the supermassive black hole, C. Tadhunter et al., 2003
https://arxiv.org/pdf/astro-ph/0302513.pdf
Quote: “Assuming that the ionized gas is circularly rotating in a thin disk and that the large line widths are due to activity-induced turbulence, the circular velocities measured from both the Keck and HST data lead to an estimate of the mass of the supermassive black hole of 2.5±0.7 x 10^9 M⊙.”
Cygnus A’s radio lobes extend 250,000 lightyears above and 250,000 lightyears below the Cygnus A galaxy. For comparison, the Milky Way is 200,000 lightyears in diameter.
#Cygnus A, Quasars, and Quandaries, Chandra Chronicles, 2001
https://chandra.harvard.edu/chronicle/0101/cyga2.html
Quote: “Still more problems for the collision theory became apparent when R.C. Jennison reported on new measurements of the structure of the Cygnus A radio source. It has the shape of a great cosmic dumbbell, with two huge lobes of high-energy particles located over half a million light years apart.”
– Another pretty large Super Massive Black hole sits in the galaxy Messier 87. It has 6.5 billion solar masses and was the first black hole we got an actual photo of. Or rather of the glowing gas around the edge of a menacing shadow. This sphere of darkness is so large that it covers our entire Solar System.
The mass of the black hole at the center of galaxy Messier 87 was refined to 6.5 billion solar masses in 2019. This would give it a radius of 19.2 billion km or about 128 AU.
#First M87 Event Horizon Telescope Results. VI. The Shadow and Mass of the Central Black Hole, The Event Horizon Telescope Collaboration, 2019
https://arxiv.org/ftp/arxiv/papers/1906/1906.11243.pdf
Quote: “Associating the crescent feature with the emission
surrounding the black hole shadow, we infer an angular gravitational radius of GM/Dc2 = 3.8 ± 0.4 μas. Folding in a distance measurement of 16.8 Mpc gives a black hole mass of M = 6.5 x 10^9 M⊙”
It is larger than the heliopause, commonly used ‘edge of the Solar System’, which sits at 123 AU.
#Heliopause, Encyclopaedia Britannica, retrieved 2021
https://www.britannica.com/science/heliopause
Quote: “The heliopause is about 123 astronomical units (AU; 18 billion km [11 billion miles]) from the Sun.”
– Now we reach the most massive black holes, perhaps the largest single bodies that will ever exist. These black holes have eaten so much that they've grown to tens of billions of solar masses, their gravity the engine for a ‘quasar’- an accretion disk shining brighter than thousands of galaxies full of stars. So massive that they deserve a title of their own - Ultramassive Black Holes.
Quasars are the result of extremely active giant black holes. The name comes from the early days of radio astronomy, where these bright sources of emissions were called ‘quasi-stellar radio sources’.
#X-Ray Astronomy Field Guide, Chandra X-Ray Observatory, retrieved 2021
https://chandra.harvard.edu/xray_sources/pdf/quasars.pdf
Quote: “Quasars are peculiar objects that radiate as much energy per second as a thousand or more galaxies, from a region that has a diameter about one millionth that of the host galaxy.”
Quote: “The power of a quasar depends on the mass of its central supermassive black hole and the rate at which it swallows matter. Almost all galaxies, including our own, are thought to contain supermassive black holes in their centers. Quasars represent extreme cases where large quantities of gas are pouring into the black hole so rapidly that the energy output is a thousand times greater than the galaxy itself.”
Ultramassive black holes are what astronomers categorize the handful of black holes that are far more massive than any other object detected in space.
#From Super to Ultra: Just How Big Can Black Holes Get?,NASA, 2012
https://www.nasa.gov/mission_pages/chandra/news/ultra_black_holes.html
Quote: “Astronomers have long known about the class of the largest black holes, which they call "supermassive" black holes. Typically, these black holes, located at the centers of galaxies, have masses ranging between a few million and a few billion times that of our sun.
This analysis has looked at the brightest galaxies in a sample of 18 galaxy clusters, to target the largest black holes. The work suggests that at least ten of the galaxies contain an ultramassive black hole, weighing between 10 and 40 billion times the mass of the sun. Astronomers refer to black holes of this size as "ultramassive" black holes and only know of a few confirmed examples.”
– The Ultra Massive Black Hole at the center of galaxy OJ 287 is 18 billion solar masses. It is so big that it has a Super Massive black hole, nearly forty times larger than sagittarius A star, orbiting it! This thing defies imagination and is really hard to compare to anything. It can fit three Solar Systems side by side comfortably inside of it.
Two black holes sit inside galaxy OJ 287. One is supermassive (150 million solar masses) and the other is ultramassive (18.35 billion solar masses).
A smaller black hole orbits OJ 287. It has 150 million solar masses. It has a radius of 443 million km.
Sagittarius A* has a radius of 11.8 million km.
That makes the smaller black hole orbiting OJ 287 37.5 times larger than Sagittarius A*.
We can calculate the radius of the latter to be 54 billion km or 355 AU. This is 2.88 times larger than the radius of the Solar System at 123 AU. This is enough to fit nearly three Solar Systems side-by-side.
#Spitzer Observations of the Predicted Eddington Flare from Blazar OJ 287, Seppo Laine et al., 2020
https://authors.library.caltech.edu/102834/1/Laine_2020_ApJL_894_L1.pdf
Quote: “The present BBH model, extracted from the accurate timing of 10 flares between 1913 and 2015 (D18), is specified by the following parameters: primary with mass 1.835 × 10^10 M⊙ and Kerr parameter a = 0.38, and a 1.5 × 10^8 M⊙ secondary in an eccentric (e ∼ 0.65) orbit with a redshifted orbital period of 12 yr.”
– TON 618, a black hole that we can observe consuming galaxies worth of matter is shining with the brightness of a hundred trillion stars, visible from 18 billion light years away. It has an incredible 66 billion solar masses. A black hole so large that it would take light a week to reach the singularity after crossing the event horizon. About 11 Solar Systems could sit inside of it side by side. It may very well be the largest single body in the universe. But in reality, it is probably even larger. Since TON 618 is so far away, we only see how it looked like 10 billion years ago.
The biggest black hole we have ever detected has a mass of nearly 70 billion solar masses. According to our calculator, it would have a radius of about 207 billion km or 1382 AU.
#Supermassive Black Hole Accretion and Growth, J. W. Moffat, 2020
https://arxiv.org/pdf/2011.13440.pdf
Quote: “The SMBH in active galactic nuclei and quasars span a mass range, extending up to nearly 10^11M⊙. The heaviest black hole is associated with the quasar TON 618 with a mass ∼ 7 × 10^10M⊙.”
Light travels at 299,792,458 m/s. So it would take light almost 8 days to traverse the radius of TON618. The Solar System has a radius of 123 AU, radius of TON 618 is 1382/123=11.2 times the solar system. .
The following database states that the light from TON 618 that reaches us today was released 2.962 billion years after the Big Bang, and that light took 10.337 billion years reach us.
#FBQS J122824.9+312837, NASA/IPAC Extragalactic database, retrieved 2021
Quote: “Light Travel-Time : 10.337 Gyr
Age at Redshift 2.202196 : 2.962 Gyr
Age of Universe : 13.299 Gyr”
EndCard Sources:
– We used Gaia’s sky map from:
#Gaia creates richest star map of our Galaxy – and beyond, 2018
Quote: “ESA’s Gaia mission has produced the richest star catalogue to date, including high-precision measurements of nearly 1.7 billion stars and revealing previously unseen details of our home Galaxy.”
– We used Schwarzschild equation and information as it is described in:
Schwarzschild radius:
#The Schwarzschild Radius, Perth Observatory, 2017
https://www.perthobservatory.com.au/news/the-schwarzschild-radius
– We used the screenshots from the following three publications:
Cygnus A paper:
#Tadhunter et al., Spectroscopy of the near-nuclear regions of Cygnus A: estimating the mass of the supermassive black hole, 2018.
https://arxiv.org/pdf/astro-ph/0302513.pdf
Messier 87 paper:
#The Event Horizon Telescope Collaboration, First M87 Event Horizon Telescope Results. VI. The Shadow and Mass of the Central Black Hole, 2019.
https://arxiv.org/ftp/arxiv/papers/1906/1906.11243.pdf
OJ 287 paper:
#Laine et al., Spitzer Observations of the Predicted Eddington Flare from Blazar OJ 287, 2020.
https://authors.library.caltech.edu/102834/1/Laine_2020_ApJL_894_L1.pdf
– Papers we show for the flip-through, we documented how we used each of them above along with citations:
https://arxiv.org/pdf/2011.13440.pdf
https://arxiv.org/pdf/1704.04552.pdf
https://arxiv.org/pdf/0711.4078.pdf
https://arxiv.org/pdf/1102.5098.pdf
https://iopscience.iop.org/article/10.1088/1742-6596/840/1/012027/pdf
https://arxiv.org/pdf/1811.04953.pdf
https://arxiv.org/pdf/1010.4809.pdf
https://iopscience.iop.org/article/10.3847/2041-8213/ab960f/pdf
https://iopscience.iop.org/article/10.3847/2041-8213/aac3d6/pdf
– We used the images of Penrose diagrams from the following two papers:
#Kodama, Hideo & Yoshino, Hirotaka. (2011). Axiverse and Black Hole
https://www.researchgate.net/figure/Penrose-diagram-of-the-Schwarzschild-black-hole_fig4_51951379
#Sabir, Mudassar. Black holes Information Paradox, 2015
https://www.researchgate.net/figure/Carter-Penrose-diagram-of-Kerr-black-hole_fig7_341509361
We took the image with orbits of stars within the central 1.0 X 1.0 arcseconds of Milky Way from:
#UCLA Galactic Center Group