Physics and Astronomy

Simulating gas dynamics and binary black holes on a computer

Supermassive black holes are the universe’s most immense single objects. These monsters can weigh more than a billion suns, and are the subjects of intense interest in the astronomical community. They are the engines powering the spectacular jets of material (so-called AGN jets) that emanate from the cores of some galaxies, and they offer precious clues about the growth of cosmic structure. One very famous supermassive black hole — lurking at the center of the galaxy M87, more than 50 million light years from Earth — made headlines last year when the Event Horizon Telescope (the name given to a global network of radio telescopes) made it the first black hole to be imaged directly.

These black holes were probably born in the early universe, left behind following the explosive deaths of first-generation stars. But how did they grow from seedlings (only 10 – 100 times the mass of the sun) into the giants they are today? This question is something astronomers have been trying to answer for decades. Most will agree that some of their growth is due to consuming the gas and debris from their host galaxies, but will concede this cannot be the entire story — there is a well-known maximum rate (called the Eddington limit) at which a black hole can accrete gas, and many black holes are simply too massive to have grown by accretion alone since the beginning of the universe. These black holes have likely grown faster by merging with partners: falling into orbit around one another, and eventually coalescing after after a long, inward spiraling dance. The details of this process are still murky — why, and how often do supermassive black hole mergers take place? And crucially, where are the supermassive black hole binaries, dancing toward coalescence?

Currently the best supermassive black hole binary candidate is a system known as OJ-287. This system exhibits regular outbursts (twice every 12 years), which can be explained if the smaller of the two black holes has a highly inclined and eccentric orbit, punching through and lighting up the larger one’s accretion disk (its meal of swirling debris) twice each orbit. These two objects are fatefully bound. On each orbit they get closer together, converting their orbital kinetic energy into gravitational wave radiation. In roughly 10,000 years from now, they will collide and merge together, producing a powerful burst of gravitational wave (GW) emission. Merger events like this would be detected by a space-based interferometric GW detector, such as the proposed LISA mission.

If OJ-287 is indeed a binary black hole, it would be proof that supermassive black holes do merge. But it raises a new question: how did these objects become bound to one another in first place? Such pairs might have been introduced when their respective host galaxies merged together. They could then have “sunk” to the center and become gravitationally bound when separated by 100’s to 1000’s of light-years. This is where things get tricky: when they are so widely separated, the orbit is barely affected by GW radiation. But the binary in OJ-287 has somehow shrunk to less than 0.1 light-year separation, close enough for GW’s to drive it to coalesce. The question of how a binary black hole’s separation can shrink to sub-light-year scales is so critical that it’s acquired a special name: “the final parsec problem.”

The solution to the final parsec problem is likely connected to a critical fact — black holes do not exist in a vacuum. The density of interstellar gas is small, on average one proton per cubic centimeter, but its effect on binary black holes over the course of billions of years can be critical. The black holes’ gravity pulls gas into a disk that swirls around the binary — a so-called circumbinary disk, or CBD. The dynamics of the binary and its CBD are complex, and beautiful: the circling black holes induce tidal interactions that push and pull gas in the CBD, causing some of it to fall inwards along narrow streams, and gather into smaller so-called minidisks which then accrete onto their respective black holes. The gas, in turn, exerts a gravitational pull on the binary, which might ultimately drive the black holes to spiral inwards… but it also might drive them apart!

To determine the effect of gas on the evolution of binary black holes, we need to unravel the complex dynamics of gas orbiting two black holes. This type of nonlinear physics problem can only be tackled with the aid of large-scale computer simulations, which solve the equations of gas dynamics and gravitation together, and at a very high level of detail.

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