Thousands of planets around supermassive black holes?
Three Japanese scientists have published a study that analyzes the possibility that planets may form in the dust disk orbiting a few parsecs away from the central engine of a 10-million-solar-mass black hole. According to their calculations, planet formation in such conditions is not only possible but could give rise to tens of thousands of planets, each with a typical mass of about ten Earth masses
Hubble, ALMA and other telescopes have shown us in recent decades extraordinary images of protoplanetary disks around young stars. Astronomers are convinced that those disks of dust and gas are the incubators from which planets form. It is difficult to obtain direct evidence of planet formation because it is a process that lasts for millions of years. But many studies and hydrodynamic simulations have made rather clear, at least in their general aspects, the aggregation mechanisms that lead from small grains of dust to the formation of planetesimals, then of protoplanets and, finally, of real planets.
The common element of planet formation theories is that the protoplanetary disks that give rise to planets are formed by residual material — dust and gas — left by the formation of the stars around which the disks themselves orbit. Moreover, the fact that between planetary systems and stars there is a very close bond is demonstrated beyond doubt by the over 4,000 extrasolar planets discovered so far, almost all of which are part of systems formed by one or more stars .
And yet there are other disks
Nothing, however, excludes, at least theoretically, that planets can also form within other dust and gas disks, not necessarily connected to a star, as long as there are favorable conditions in those disks for the slow aggregation of particles, which, over millions of years, leads to the birth of planets. We must ask ourselves, then: are there disks of gas and dust that do not orbit around a star and are to some extent similar to common protoplanetary disks? The answer is yes: they are the accretion disks that orbit around black holes and provide those voracious celestial monsters with the material they feed on.
In particular, supermassive black holes, those that live at the center of most galaxies, including the Milky Way, are potential candidates to host entire populations of planets in their enormous accretion disks. At least this is the conclusion reached by the first study  dedicated to exploring the fascinating possibility that planet formation can take place even in an environment at first sight highly inhospitable, like the one that surrounds million-solar-mass black holes.
To understand the results achieved by the three Japanese authors of this paper, it is first necessary to understand how the accretion disk around a supermassive black hole (or SMBH for short) is made. The structure is schematically illustrated in the following graph.
Black holes are frighteningly massive and compact objects, sources of such an intense gravitational attraction that not even light, once captured, can escape to the outside. The immense gravity exerted by SBMHs located in the center of most galaxies speeds towards them large masses of interstellar gas, which only partially end up inside the black hole. A large part of the gas remains in orbit around the SMBH, rotating faster and faster as it approaches its boundary, the so-called event horizon.
In the immediate vicinity of an SMBH, particle collisions heat the gas to billions of degrees. It is a hellish environment, which produces an extraordinary brightness in the order of 10¹² solar luminosities (i.e. thousands of billions of times the energy emitted every second by the Sun).
In this area, which can extend over several astronomical units  depending on the black hole’s mass, planetary formation is impossible. The temperature is so high that the dust, which is a basic element in the making of planets, cannot form (the granules generally sublimate at temperatures around 1,500 K). This innermost region of the accretion disk is a kind of highly efficient natural engine, which emits radiation streams, mostly in the X-ray and ultraviolet bands. It is precisely that radiation, with its particular spectroscopic signatures, that identifies the so-called active galactic nuclei, or AGN, discovered at the center of many galaxies, including Type I and Type II Seyfert galaxies.
A four-step process
But, at a few parsecs  of distance from the SMBH, the temperature drops below the dust sublimation point, giving rise to a dynamic and turbulent environment, agitated by masses of gas present in both atomic and molecular form. As the distance from the central black hole increases, the temperature decreases, which favors the formation of a relatively cold, dusty, dense and compact molecular gas torus. Moving a few more parsecs away from the dust sublimation radius, we reach the so-called snow line, analogous to the one that exists in common protoplanetary disks that orbit around many stars: starting from the snow line, the dust becomes icy. This means that the aggregation of dust particles mixed with ice can produce bodies containing significant fractions of water, as are the trans-Neptunian objects in the Solar System.
The hypothetical, but plausible, planet formation process described by the three authors of the study takes place around a 10-million-solar-mass SBMH, in an active galactic nucleus not too bright. The luminosity affects, in fact, the turbulence of the gas that carries the dust: too much brightness, like that generated by a black hole too massive or too voracious, would not allow the dust grains to aggregate to form planets in a cosmic time comparable to the age of the Universe. Therefore the SMBH’s accretion disks at the center of very bright objects such as quasars are not suitable places to favor the planet formation process. Instead, less bright AGNs, such as those in the center of Seyfert galaxies, are more favorable places.
In the model proposed by the study, the planet formation process takes place in a region of the accretion disk with an average temperature of about 100 K (−280 F), which extends radially for over two parsecs starting from the snow line .
The process takes place in four phases. During the first phase, called “hit-and-stick”, microscopic grains of icy dust about 1 tenth of a micron occasionally collide and stick together thanks to electrostatic forces. In this way, they form larger aggregates, but very porous internally and therefore of extremely low density.
When the aggregates reach the approximate size of 0.1 centimeters, the second phase begins, dominated by the compression force exerted by collisions. During this phase, the dust aggregates are transported by the turbulence of the gas in which they are immersed. The speed of collisions increases compared to the previous phase, causing a progressive compression of the aggregates, which now increase not only in mass and size but also in density, becoming less “fluffy”.
At the end of the compression phase, the initial dust aggregation seeds have now grown to an approximate size of 1 km. The first two phases of the process require a total of 380 million years to be completed, with the conditions so far listed.
From this moment on, however, things are going much faster. During the third phase, the aggregates continue to grow in size and to compact, but the drive that increases their density no longer comes from collisions originating from the turbulence of the gas, but from self-gravity, due to their growing mass. The evolution of these objects is now determined by processes of heating and cooling, which depend on the specific characteristics of the environment in which they are immersed.
The fourth phase is dominated by gravitational instability. When the icy dust aggregates reach a sufficient mass, they become gravitationally unstable. The “protoplanets” are thus fragmented into spiral-shaped structures, from which the real “planets” emerge at the end, due to the collapse of the material they contain. The total duration of the last two phases is a few million years at most.
Planet formation on a colossal scale
What makes the model described in this study particularly fascinating is the scale, absolutely gigantic, of the planet formation phenomenon around an SMBH, compared to what happens in normal protoplanetary disks. According to the calculations presented by the three authors, up to 85,000 planets could form within a ring of the accretion disk that extends from the snow line up to 7 parsec away from the SMBH, each with an average mass of 10 Earth masses : a number of planets four orders of magnitude greater than that of any currently known planetary system!
There is a table in the study, shown below, which clearly shows these differences in scale, which are truly impressive.
Consider, for example, the mass of the central object. In
protoplanetary disks, this object is a star and its mass is in the order of a solar mass. In the case, instead, of SMBH’s accretion disks (called in the table circumnuclear disks), the mass of the central object, i.e. the black hole, is between millions and billions of solar masses. All the rest of the system, starting from the luminosity, scales following this huge initial mass difference.
In a protoplanetary disk, the dust disk has a typical size of 10–100 astronomical units: a tiny fraction of light year . In a circumnuclear disk, on the other hand, its size can reach 100 parsecs, i.e. over 300 light-years!
Finally, we come to the “building materials” of the planets. The mass of the gas in a protoplanetary disk is estimated at one-hundredth of the mass of the central star. In a circumnuclear disk, instead, the mass of the gas is approximately equal to one-tenth of the mass of the black hole: we are therefore in the order of millions of solar masses, in the case of an SMBH of 10⁷ solar masses.
As for the dust, in a protoplanetary disk its total quantity is equal to about 1 ten thousandths of a solar mass. Instead, in a circumnuclear disk we reach a value between 1,000 and 1,000,000 solar masses.
Given these numbers, it is not surprising that tens of thousands of planets more massive than Earth can form in the space of a few parsecs!
Unfortunately, the big limit of the theoretical model proposed by the three Japanese scientists is that it is not verifiable, at least not with the technological means we have today. Not even the most powerful telescopes and radio telescopes can solve details of the size of planets in the central parsecs of an active galaxy. For now, therefore, we can only limit ourselves to imagining what a great spectacle an immense array of planets could offer, hidden in the torus of gas and dust that slowly orbits  a few parsecs away from the blinding central engine of a ten-million-solar-mass black hole.
Could there be life on any of those planets? Who knows? What we do know is that, around stars like the Sun, the favorable conditions that have allowed life to colonize the Earth do not last forever. The sun, for example, will become hotter as it ages and in about a billion years from now it will invest our planet with such an intensity of radiation, to dry up the seas and probably make life impossible.
Similar risks would not exist for any planets formed in the outer regions of the circumnuclear disk of an SMBH. Black holes do not age and do not die , so that the planets that orbit around them, once formed, could enjoy an almost infinite time: a condition certainly favorable for life to take root and evolve. But this is, of course, pure speculation: we do not know, in the first place, whether planets can be formed in the dust disk of an SMBH; furthermore, we do not know the actual environmental conditions with which those hypothetical planets should confront. Many factors could make life impossible: for example, a very high frequency of collisions with bodies of various sizes (asteroids, comets, other planets); an excess of ionizing radiation during periods in which the black hole experiences peak activity; unknown chemical factors that prevent life from taking root, etc.
In any case, it is suggestive to think that an unfathomable variety of habitable worlds could exist in the heart of every galaxy, in what would seem to be the most inhospitable ecosystem, only a few parsecs away from the most powerful engines in the Universe.
 So far, astronomers have discovered only a very small group of bodies that appear to be rogue planets, i.e. unbound, orphan planets, far from any star. To be honest, it is not known whether they are real planets, thrown out of their native systems by unfortunate gravitational interactions, or they are brown dwarfs, that is failed stars, formed in the same way as real stars, i.e. from the gravitational collapse of a molecular cloud. As far as we know, rogue planets could be millions or even billions only in the Milky Way, but since it is very difficult to discover them, presently they represent only a negligible fraction of the planets belonging to star systems.
 The study, whose authors are three Japanese scientists, Keiichi Wada, Yusuke Tsukamoto, and Eiichiro Kokubo, was published on November 26, 2019, in The Astrophysical Journal.
 An astronomical unit is the average distance between the Earth and the Sun. It corresponds to about 93 million miles.
 One parsec equals 3.26 light-years or 19.17 trillion miles.
 The snow line is located at 4.7 parsecs away from the black hole in the case of a relatively low-light SBMH of 10⁷ solar masses.
 A light-year corresponds to 63,241 astronomical units.
 At 5.5 parsecs away from a 10⁷ solar mass black hole, a complete revolution requires something like 400,000 Earth years.
 At most, they evaporate, emitting the so-called Hawking radiation. But in the case of an SMBH, the process is so slow that it takes a time enormously longer than the current age of the Universe.