"We think these clusters formed with hundreds to thousands of black holes that rapidly sank down in the center," Carl Rodriguez, a theoretical astrophysicist at the Massachusetts Institute of Technology, said in a statement. Working with an international team of scientists, Rodriguez modeled how black hole collisions should function according to Albert Einstein's theory of general relativity. The researchers found that black holes initially created by stars within globular clusters should grow more to be than 50 times as massive as Earth's sun if they collide with other black holes.

"These kinds of clusters are essentially factories for black hole binaries, where you've got so many black holes hanging out in a small region of space that two black holes could merge and produce a more massive black hole. Then, that new black hole can find another companion and merge again."

"Insanely fast"

In 2016, the Laser Interferometer Gravitational-Wave Observatory (LIGO)made the first detection of the signatures of gravitational waves. According to Einstein's theory of general relativity, gravitational waves are released as energy when two black holes merge. LIGO's observations not only provided proof of gravitational waves, but they also confirmed the existence of stellar-binary black holes.

At the end of its lifetime, a massive star can blow off its material in a spectacular supernova. This can leave behind a stellar black hole at the stellar heart. Weighing in at around 10 times the mass of the sun, a stellar black hole can stretch just a few tens of kilometers across. 

Rodriguez and his colleagues decided to investigate how black holes behave within globular clusters, compact collections of stars that can be found in most galaxies. The population of clusters is dependent on the galaxy's size; huge elliptical galaxies can boast tens of thousands of globular clusters, while our own Milky Way holds around 200 such clusters. Because these regions are so dense, the researchers wanted to know if black holes that formed within them might behave differently from black holes in less populated regions.

Using a supercomputer, the researchers simulated the complex, dynamical interactions within 24 stellar clusters ranging from 200,000 to 2 million stars and over a range of densities and compositions. The scientists modeled the evolution of these clusters over 12 billion years, about as long as stars have existed in the universe, and followed their interactions with other stars and how black holes within them formed and evolved.

In the past, scientists studying stellar black holes inside of clusters analyzed the phenomenon using Newtonian physics, which, Rodriguez said, "works in 99.9 percent of all cases." He was more interested in the times when the simpler physics failed, however, and Einstein's theory took over.

"The few cases in which [Isaac Newton's theory of gravity] doesn't work might be when you have two black holes whizzing by each other very closely, which normally doesn't happen in most galaxies," Rodriguez said.

Newton's theory assumes that if the black holes didn't start off connected to one another, they would pass each other without affecting one another. But Newton's theory doesn't recognize gravitational waves, which Einstein predicted would arise from two massive objects — such as black holes — orbiting one another. 

Under Einstein's theory of general relativity, the close-passing black holes can emit a tiny pulse of gravitational waves, Rodriguez said. The change in energy can be enough to bind the two black holes together, causing them to eventually merge. 

Newtonian physics predicts that most binary black holes should have been booted out of the cluster by other black holes before they could merge. By taking Einstein's relativity into account, however, Rodriguez and his colleagues found that nearly half of the black holes would merge inside their stellar clusters, building a new generation of black holes more massive than those formed by stars alone.

LIGO should be able to spot mergers between black holes that formed within globular clusters. Previous research has put the size of stellar mass black holes between 10 and 100 solar masses, similar to the mass of the largest stars. However, the new study suggests that a black hole whose mass is greater than around 50 solar masses most likely formed not from individual stars but from a dense stellar cluster.

"If we wait long enough, then eventually LIGO will see something that could only have come from these star clusters, because it would be bigger than anything you could get from a single star," Rodriguez said.

How quickly the black holes are spinning will also affect what LIGO observes. If two black holes are spinning when they merge, the newly created, larger black hole will emit a gravitational wave moving "insanely fast" — as fast as 3,100 miles (5,000 kilometers) per second — in a single direction, Rodriguez said. That's much faster than the tens to hundreds of kilometers per second required to escape from a globular cluster.

The prediction of such a massive emission led scientists in the past to determine that the product of a black hole merger would be kicked out of the cluster, as most black holes are assumed to be rapidly spinning. However, the handful of black hole detections made by LIGO so far have only slow spins, contradicting this assumption.

So, Rodriguez and his colleagues slowed down the spins of the black holes in their simulation. The researchers found that with slow spins, nearly 20 percent of binary black holes from clusters had at least one member that came from a previous merger. These second-generation black holes can weigh from 50 to 130 solar masses, too large to form from a single star. Rodriguez said that if LIGO or other gravitational-wave telescopes detect an object within this mass range, there is a good chance that it came from a dense stellar cluster rather than from a single collapsing star.

"My co-authors and I have a bet against a couple people studying binary star formation that within the first 100 LIGO detections, LIGO will detect something within this upper mass gap," Rodriguez said. 

"I get a nice bottle of wine if that happens to be true."

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