A direct proof of the existence of a black hole would be if one actually observes the orbit of a particle (or a cloud of gas) that falls into the black hole. Note that this proof of the existence of stellar black holes is not entirely observational but relies on theory: we can think of no other object for these massive compact systems in stellar binaries besides a black hole. The combination of these facts makes it more and more likely that the class of compact stars with a mass above 3.0 solar masses are in fact black holes. All identified neutron stars have a mass below 3.0 solar masses none of the compact systems with a mass above 3.0 solar masses display the properties of a neutron star. The derived masses come from observations of compact X-ray sources (combining X-ray and optical data). Whenever such properties are observed, the compact object in the binary system is revealed as a neutron star. They show differential rotation, and can have a magnetic field and exhibit localized explosions (thermonuclear bursts). However, neutron stars may have additional properties. Black holes and neutron stars are therefore often difficult to distinguish. The energy release for black holes and neutron stars are of the same order of magnitude. The black hole, therefore, is observable in X-rays, whereas the companion star can be observed with optical telescopes. Stellar black holes in close binary systems are observable when the matter is transferred from a companion star to the black hole the energy released in the fall toward the compact star is so large that the matter heats up to temperatures of several hundred million degrees and radiates in X-rays. They are intermediate-mass black holes (in the center of globular clusters) and supermassive black holes in the center of the Milky Way and other galaxies. There is observational evidence for two other types of black holes, which are much more massive than stellar black holes. As of June 2020, the binary system 2MASS J05215658+4359220 was reported to host the smallest-mass black hole currently known to science, with a mass 3.3 solar masses and a diameter of only 19.5 kilometers. In September 2015, a rotating black hole of 62±4 solar masses was discovered by gravitational waves as it formed in a merger event of two smaller black holes. Until 2016, the largest known stellar black hole was 15.65☑.45 solar masses. If black holes that small exist, they are most likely primordial black holes. (See, for example, the discussion in Schwarzschild radius, the radius of a black hole.) There are no known processes that can produce black holes with mass less than a few times the mass of the Sun. The lower the mass, the higher the density of matter has to be in order to form a black hole. In the theory of general relativity, a black hole could exist of any mass. The maximum observed mass of neutron stars is about 2.14 M ☉ for PSR J0740+6620 discovered in September, 2019. In 1996, a different estimate put this upper mass in a range from 1.5 to 3 solar masses. In 1939, it was estimated at 0.7 solar masses, called the TOV limit. The maximum mass that a neutron star can possess (without becoming a black hole) is not fully understood. If the collapsing star has a mass exceeding the TOV limit, the crush will continue until zero volume is achieved and a black hole is formed around that point in space. If the mass of the collapsing part of the star is below the Tolman–Oppenheimer–Volkoff (TOV) limit for neutron-degenerate matter, the end product is a compact star - either a white dwarf (for masses below the Chandrasekhar limit) or a neutron star or a (hypothetical) quark star. It is inevitable at the end of the life of a large star when all stellar energy sources are exhausted. The gravitational collapse of a star is a natural process that can produce a black hole. The angular momentum of a stellar black hole is due to the conservation of angular momentum of the star or objects that produced it. By the no-hair theorem, a black hole can only have three fundamental properties: mass, electric charge, and angular momentum.
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