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Astrophysics in the bathtub

Experiment reproduces phenomena that could occur near black holes in a tank of water

Silke Weinfurtner / Nottingham University Vortex produced by the drain in the center of the tank, during the experiment that detected superradianceSilke Weinfurtner / Nottingham University

Waves that propagate on the surface of water become a little higher as they cross the region surrounding a whirlpool created by the open drain of a tank. Their size is amplified because they receive some of the rotational energy from the whirlpool, an effect called superradiance. The existence of this effect was first confirmed in an experiment conducted in 2016 by an international group of researchers led by German physicist Silke Weinfurtner of the University of Nottingham in the United Kingdom. In her laboratory, Silke and her colleagues—among them Brazilian physicist Maurício Richartz—produced this phenomenon using a glass tank and water containing a green fluorescent dye. The test was filmed with a 3D camera, which allowed the researchers to detect the increase in the height of the waves caused by superradiance. The effect is small, but it attracted the attention of the physicists because it simulates what is thought to occur with light near a rotating black hole. These results are described in an article published on June 12, 2017 in the journal Nature Physics.

“The theory behind superradiance is very well known, but no one had observed the phenomenon experimentally,” says Richartz, a professor at the Federal University of the ABC. He helped plan and carry out the experiment and says that, under the conditions in which the test was conducted, waves on the surface of the water can be described by equations of motion almost identical to those of light waves propagating near a black hole. As the equations are practically the same, the confirmation that superradiance occurs in waves formed in water represents the first concrete evidence that this phenomenon, although difficult to detect, must exist in the vicinity of black holes, as predicted by the theory. Until recently, theoretical studies have suggested that black-hole superradiance would cause a magnification of electromagnetic and gravitational waves too small to be observed by astronomers. In an article published this year in the journal Physical Review D, physicist João Rosa, of the University of Aveiro, Portugal, suggests that superradiance could be amplified in the vicinity of pairs of black holes and neutron stars. Signs of the phenomenon could then be detectable by the Square Kilometer Array (SKA) radio telescope, whose antennas will be installed in South Africa and Australia, and by the Interferometric Gravitational Wave Observatory (LIGO) in the United States.

Richartz met Silke Weinfurtner in 2009 in Canada. At the time, he was a PhD student and worked with Weinfurtner and Canadian physicist William Unruh of the University of British Columbia on one of the earliest experiments using water waves to investigate black hole physics. In that test, Weinfurtner, Unruh and their collaborators showed that waves flowing in water trapped in a channel had properties similar to what is known as Hawking radiation, a quantum effect that causes a black hole to gradually lose energy through the emission of subatomic particles.

The channel only allowed investigation of phenomena occurring in a single dimension, since its width and its depth were negligible in relation to its length, and Weinfurtner had the idea to design a two-dimensional device to investigate other phenomena related to black holes, such as superradiance. The group then planned the tank built in the Nottingham laboratory. At three meters (m) in length, 1.5 m in width, and with negligible depth, it is twice the size of a bathtub. A motorized paddle produces millimeter-high waves that propagate on the water’s surface and are amplified by superradiance from the whirlpool formed when the stopper is removed from the drain.

In water and in space
A black hole and the drain of a bathroom are more similar than you can imagine. The center of a black hole is always hidden by a sphere of complete darkness: the event horizon, a region from which nothing, not even light, escapes the intense gravitational pull. Similarly, there is a region in the whirlpool that pulls the water waves that come too close towards the center of the drain, acting as an event horizon for the waves. Whether in a bathtub or in space, the event horizon is enveloped by a layer called the ergosphere, which drags in everything that reaches it and rotates in the same direction as the black hole or the whirlpool.

Silke Weinfurtner / Nottingham University Graphic representation of amplification of waves on the surface of water as they cross the whirlpoolSilke Weinfurtner / Nottingham University

While the event horizon captures the waves that reach it, the ergosphere can amplify some of the waves that pass through it. In 1971, Belarusian physicist Yakov Zel’dovich, who had participated in the Soviet atomic bomb program, carried out initial calculations that suggested that a rotating black hole could amplify the electromagnetic and gravitational waves affected by its ergosphere. This amplification, however, would be so subtle that current astrophysical instruments would not yet have the precision needed to detect it.

In order to observe the superradiance of waves in water, Weinfurtner and a multidisciplinary team of researchers, some optics specialists and other fluid mechanics specialists, used a high-resolution 3D camera developed for the experiment together with the German company EnShape to record and measure the minute increase in the amplitude of the waves. The images allowed them to see that only surface waves with a specific frequency (3.7 oscillations per second) became 20% higher when crossing the whirlpool, a figure that coincides with that predicted by the theory.

Now, Weinfurtner and her team are working to increase the precision with which wave height and velocity are measured near the center of the whirlpool, where the event horizon for the waves in the water would be. “The detection of superradiance is not sufficient experimental proof of the existence of an event horizon for waves,” explains the physicist. “In addition to improving the precision of the equipment, we need to enhance our theoretical understanding of what happens in the whirlpool.”

1. Superradiance in dissipative systems (No. 15/14077-0); Grant Mechanism Scholarships abroad; Principal Investigator Maurício Richartz (UFABC); Investment R$ 30,029.80.
2. Analog models: Superradiance and stability (No. 13/15748-0); Grant Mechanism Scholarships abroad; Principal Investigator Maurício Richartz (UFABC); Investment R$ 19,515.98.

Scientific article
TORRES, T. et al. Observation of superradiance in a vortex flow. Nature Physics. June 12, 2017.