A black hole forms in two main scenarios: either too much material reaches the core of a star during its collapse, or a neutron star accumulates more material until it exceeds 2.1 to 3 solar masses.
Formation of Black Hole From Death Star.
The most direct method of forming a black hole comes during the death of very massive stars. As stars burn, the denser products from their fusion collect at the core. If the stars are massive enough, those products will eventually become further fuel, which then deposits even denser products onto the core. In the final days of a massive star's life, the silicon at the core will fuse, producing iron at astonishing rates. This sphere of iron will continue growing in mass until the pressure within it passes the Chandrasekhar limit or high-energy photons break apart the iron nuclei, at which point it will collapse.
During the collapse, a shock wave is formed as the core rebounds from its extreme densities. As the shock wave travels out, it stalls for a few hundredths of a second. During this period, neutrinos produced from the core accumulate behind the shock wave until the accumulated energy restarts it and fuels the forthcoming supernova. At the same time, as this accumulation, material that has already passed through the shock wave continues accreting or building up on the proto-neutron star core. If enough material reaches the core, gravitational instability will occur, causing a collapse into a black hole. If this happens before the shock wave is restarted, then the core will immediately cease to create more neutrinos, and those already formed will disappear within the event horizon. This drop in pressure behind the shock wave causes the whole star to collapse within, producing no explosion.
For certain large-mass stars between 25 and 40 solar masses, the shock wave is restarted before the core is pushed beyond gravitational stability. This results in a supernova that leaves behind a black hole. However, this explosion would be weaker in comparison as the core can no longer produce more neutrinos to further fuel the supernova.
The next question to ask is why would some stars' shock waves fail where others succeed. Truly massive stars, we are talking masses more significant than 40 solar masses, accrete so much material on their collapsed core that a black hole forms before the shock wave can restart. As the star collapses, its innards continue being absorbed into the event horizon, and thus, after a couple of hours, the star will be completely enveloped within the boundaries of the black hole.
Not every mass of stars will experience this fate. Two stars with the same mass can leave behind two different remnants. The driving factor for this is what is known as metallicity.
Formation Of Black Hole at High Metallicity
Metallicity, with regard to stars, refers to the composition of elements larger than hydrogen or helium in a star's mass. For reference, our sun has a metallicity of about 1.5 percent, meaning that 1.5 percent of the Sun's mass consists of elements heavier than helium. When astrophysicists talk about the masses of stars, they are referring to their initial mass. This initial mass is the mass of the star once the fusion of hydrogen begins in its cores. When we refer to metallicity, we are also talking about the initial composition.
As we look at this diagram showing that higher metallicities produce fewer black holes, this value is referring to the metallicity when the star was born, not when it collapses. Thus, the next question to ask is:
Why Does Increased Metallicity Reduce Black Hole Formation?
The high energy from fusion and thermal collisions within a star releases an immense amount of photons. These photons are absorbed or scattered around within the star for hundreds of thousands of years. Each one of these collisions exerts a minuscule amount of radiative pressure or force. That means, on average, the photons produced within the star are ever so slightly pushing the matter of the star outwards towards the surface.Larger atom nuclei or metallics have more protons and thus a greater positive charge. This means they can attract more electrons around them, creating a larger pool of electron energy states. This, in turn, means these electrons can absorb a larger sample of photon energy levels. All of this fancy talk is to say that gases containing metals are more opaque or harder for light to pass through than gases of just hydrogen and helium. That means more photons collide with this matter, causing more of that radiative force, pushing outwards.
This trapping of heat causes more intense convection currents within the star, which, coupled with heightened solar winds, cause matter to be blown away from the star over time. Here we can see how much mass a 90 solar mass star will lose in its lifetime depending on its metallicity. Thus, a higher metallicity will actually cause a star to lose more mass during its lifetime, particularly in the final stages. This makes it less likely to form a black hole when its life cycle ends.
If a star's death leaves behind a neutron star, there is still a possibility to form a black hole. Generally, neutron stars have a mass of about 1.4 solar masses, which is quite far from the more than 2.1 solar mass value mentioned at the start of the article. Thus, the most viable method for a neutron star to accumulate enough mass to reach this value is to interact with another stellar object. The most likely scenario for this event happening is in binary systems.
How are Binary Black Holes Formed?
Binary systems, or binary stars, are two stellar objects that are gravitationally bound to each other, orbiting around their common center of mass. In the early Universe, neutron stars could often be found in binary systems since, if there is enough gas to form a star large enough to produce a neutron star, there's usually enough to form another within the same region.Anytime mass is accelerated, it produces gravitational waves. Therefore, objects orbiting each other are slowly losing minuscule amounts of energy as gravitational waves travel away. The strength of the energy lost from this is very strongly dependent on the distance between the orbiting bodies, as seen in this equation Professor Jeffries was kind enough to share and explain. This represents the approximate time scale to merge for a system in a circular orbit.
To get an idea of how weak and how long it takes for this decay to occur, let's imagine a pair of equal-mass neutron stars orbiting with a separation of 2 million kilometers. This is equivalent to a little over five times the moon's distance from Earth. At this distance, it will take roughly 2 billion years before they merge. It is initially a very weak and very gradual process, dealing with orbits far smaller than we are accustomed to. Nevertheless, 2 billion years is much less than the age of the universe. Many mergers have already occurred, and many more still have hundreds of millions of years to go. But the very last part of the orbital decay is where binary neutron star systems get very interesting.
Normal stars aren't able to orbit very close to each other; their surfaces will collide long before the loss of orbital energy to gravitational waves plays a significant factor. But neutron stars are so dense, with radii of just 10 kilometers, that they can achieve extremely close orbits. The Hulse-Taylor binary system is also separated by about 2 million kilometers, except this orbit is eccentric, so it transitions from roughly 3 million kilometers to just under 750,000. These are two objects with more mass than the Sun orbiting within a little over a Sun's radius of each other. If they were Suns, it would look like this. Even at these close proximities, it is calculated to take another 300 million years before they merge.
Now, let's fast forward to the final hour before the merger. One hour before two neutron stars merge, they are separated by a distance of about a thousand kilometers. They're completing three orbits every second, traveling at six percent the speed of light. Each revolution liberates 6 times 10^39 joules of energy into gravitational waves. This is equivalent to what the Sun produces over half a million years. One minute before the merger, they are still separated by roughly 360 kilometers, completing 14 orbits every second at 11 percent the speed of light. Over the last two billion years, around 7 times 10^44 joules, or five Sun lifetimes' worth of energy, have been radiated away to reach this point. This staggering amount is less than 10 percent of what's to come. Only during this final minute, the gravitational waves being produced are large enough to be detected here on Earth.
In the final second before the merger, they are still a hundred kilometers apart, traveling about 20 percent the speed of light. At this point, the tidal forces are so extreme the neutron stars begin to deform. At 30 to 40 kilometers, the neutron stars are ripped apart as their masses slam together, meeting at the center. This final collapse liberates roughly the same amount of gravitational energy as a core-collapse supernova, about 80 Sun lifetimes worth of energy. But instead of neutrinos, this energy is lost primarily to gravitational waves. This extreme event is known as a kilonova.
Can Kilonova Create a Black Hole?
The so-called kilonova is one to ten percent as bright as core-collapse supernovae. It is thought that these events are a potential source for the creation of the majority of the heaviest elements in the universe and so-called short-duration gamma-ray bursts that last a few seconds. Although the details are awesome, I won't go into them as this process deserves its own article someday. But the end result, after everything has settled, can be a rapidly spinning black hole.
The last, slightly less exciting method to form a black hole occurs when a neutron star is in a binary system with a regular star. As the star's volume increases in the later stages of its life, the outer layers of the star can become more strongly attracted to the neutron star's gravity than its host star. This matter is then passed over to it via a Roche lobe overflow. This accreting material can add to the neutron star's mass, but how efficiently is uncertain. X-ray bursts during accretion events such as these suggest that the material that reaches the extreme surface detonates and could be ejected away if enough manages to settle there. Eventually, gravitational instability will occur, causing a collapse into a black hole. Whether this actually happens is uncertain. The measured masses of black holes in binary systems seem to have a lower limit of about four to five solar masses. This suggests that accretion-born black holes are unlikely. However, it could simply be that these low-mass black holes would be very difficult to detect. The reality is still uncertain.
To summarize, black holes are remnants of massive stars, either birthed directly from the collapse and accretion of their iron cores or the merging of neutron stars left over from supernovae and some other stellar object. It is theorized that in the early Universe, gas was able to collapse directly into an intermediate-mass black hole of a thousand to ten thousand solar masses without the fusion of a star's core. But that's perhaps a topic for yet another day.