The gravitational fields around stars are expressed by Einstein’s equation of gravity. When the equation is solved, black holes emerge. Black holes are mysterious celestial bodies where self-gravity is intensified without limit since objects are excessively crammed into a small space. The marginal radius (the radius of shrinkage which if exceeded will create a black hole) is called the “Schwarzschild radius,” after Dr. Schwarzschild who first discovered it.
The Schwarzschild radius of the Sun is about 3km and the Earth’s about 1cm. If you were to compress the Earth to 1cm radius, it would become a black hole. The mechanism that forms such a tiny black hole is unknown, however. There are two types of black holes in the universe: relatively small black holes with a mass about three to 10 times that of the Sun; and huge black holes with a mass exceeding millions of times that of the Sun. Are there any medium-sized black holes with a mass hundreds to thousands of times that of the Sun in the universe? This question is the theme of this article.
Star-sized black holes and huge black holes
The Schwarzschild radius of a body with mass “M” is expressed as “2GM/c2.” “G” is the universal gravitational constant and “c” is the velocity of light. Both are fundamental natural constants that determine the structure of the universe. This shows that the Schwarzschild radius is simply proportional to mass. This fact is very important to investigate the nature of black holes. We can consider that, when we look at black holes from far away, their “volume” (sort of) is proportional to the cube of the Schwarzschild radius. Since density is given by mass/volume and a black hole’s mass is proportional to the Schwarzschild radius, the density of black holes is inversely proportional to the square of the Schwarzschild radius. This means that the heavier and larger the black hole is, the smaller its density. For example, the density of a black hole with a mass over one billion times the Sun is less than that of water.
It is believed that there are stars in the universe weighing up to 50 times the weight of the Sun. Stars whose original weight is over 10 times the Sun undergo supernova explosions in the final process of their evolution. After the explosions, the cores of burnt-out stars remain as either neutron stars or black holes. As the stars’ cores are extremely compressed, the protons and electrons all stick together to become neutrons. Ordinary stars burn with nuclear fusion reaction. The pressure of combustion and their own gravity are balanced to keep them stable. In contrast, neutron stars maintain their structure by a strong repulsive force between neutrons, although they no longer burn and, accordingly, cannot sustain their structure by pressure of combustion. The size of a typical neutron star is about the size of the JR Yamanote-loop line in Tokyo (about 10km radius) with a mass almost the same as the Sun. There is a limit even for neutron stars, however. If they are about three times heavier than the Sun, the repulsive force between neutrons is no longer able to sustain their structure. In the natural world, there is no force capable of competing against such strong gravity. These heavier bodies undergo gravitational collapse and become black holes.
Thus, some compact star cannot be anything but a black hole after finishing its activity, if it has a mass more than three times that of the Sun. In this way, more than 10 black holes have been indeed discovered in our galactic system. A black hole usually pairs with an ordinary star. By measuring the companion star’s movement by the Doppler shift of its spectrum lines, we can identify the black hole’s mass and gravity. These measurements are precise, so today there are no astronomers who doubt the existence of black holes. In this article, we call black holes that were formed after supernova explosions and have a mass about three to 10 times that of the Sun, “star-sized black holes.” The heaviest star-sized black hole ever measured has a mass 14 times that of the Sun.
Meanwhile, in the galaxies’ centers there are black holes that are much heavier than star-sized black holes. Most galaxies rotate and have strong gravity sources in their centers. Pulled by gravity, objects rush into the galaxy’s center and black holes are naturally formed, though we will not discuss their formation processes here. Let us call the black holes in the center of galaxies “huge black holes.” It is known that some kinds of black holes radiate a wide range of electromagnetic waves from radio to gamma rays (known as the Active Galactic Nucleus), resulting from the release of gravity energy produced when things fall into the center. Lately, as with star-sized black holes, it has become possible to directly measure the mass of huge black holes in the galaxy center using the movement of stars or other objects around them. For example, the mass of the black hole in the center of our galactic system is three million times the mass of the Sun and one in the galaxy called M87 has a mass about three billion times.