Â鶹ÒùÔº

Water tornado in the laboratory: A simple experiment simulates planet formation

Researchers from the University of Greifswald and the Max Planck Institute for Astronomy (MPIA) in Heidelberg (both in Germany) have developed a prototype experimental setup that simulates flow properties using a water tornado to investigate key physical processes in protoplanetary disks. The setup is inexpensive and easy to construct.

Planets form within disks of gas and dust

Accretion disks exist throughout the universe in various sizes. A common feature is that gas orbits a central object whose gravity affects the surrounding matter. Some of the gas gradually spirals inward, increasing the mass of the central body.

Accretion disks also surround young stars. The gas is mixed with microscopic solid particles, which astronomers refer to as dust. These particles stick together and can gradually grow into objects thousands of kilometers in size—the precursors of planets. These complex processes, which include both orderly orbits and compact vortices, occur across a wide range of scales and are difficult to observe directly.

Researchers therefore often turn to simulations to reproduce the processes using mathematical formulations of physical laws. However, it is challenging for such simulations to capture all relevant scales over extended periods. Furthermore, simulation results must be compared with observations, since computational artifacts may distort the outcome.

Analog experiment complements simulation

The newly developed water tornado model may provide an elegant means of addressing some of these limitations. In contrast to previous attempts to create such analog experiments, the new approach offers two key advantages. First, it allows for a wide radial range to be simulated, whereas earlier models were limited to narrow, ring-shaped zones.

"Secondly, the motions and flows closely resemble those observed in planet-forming disks and planetary systems," explains Stefan Knauer from the University of Greifswald. Some of the fundamental physical principles governing planetary orbits were formulated in the early 17th century by Johannes Kepler and also apply to gas in a disk. Initial tests have shown that these laws largely hold in the water tornado model as well.

These findings, now in Monthly Notices of the Royal Astronomical Society: Letters, could enhance simulations by addressing aspects that remain hidden from direct observation and provide new understanding. One area of particular interest is how dust particles and gas interact with each other in ways that promote planet formation.

A water tank using aquarium components

When designing the experimental setup, it was crucial to replicate the gravitational potential of a star at the center of a protoplanetary disk as accurately as possible. An experiment with a simple design provided the solution to this task.

The water container consists of two transparent acrylic glass cylinders of different diameters, placed one on top of the other. At the base of the lower, 15-centimeter-wide cylinder is a central outlet. Two nozzles mounted farther out pump water in opposite directions, parallel to the tank floor. The pump is a commercially available aquarium device.

The water flow causes the fluid to rotate, forming a vortex whose surface extends from the bottom of the tank to the wall of the upper, 50-centimeter-wide cylinder. The usable experimental zone begins roughly 3 centimeters from the center and extends almost to the tank's edge. The shape of the water tornado fulfills the required property of mimicking a gravitational field.

Water tornado mimics a protoplanetary disk

To analyze the flow behavior at the water's surface, the research team introduced small polypropylene beads into the vortex. As this material has a density similar to water, the beads remained near the surface and were carried along by the swirling motion. Their positions were recorded using a high-speed camera, and a computer algorithm was used to calculate their trajectories.

As expected, many of the orbits did not conform to Kepler's first law, which states that celestial objects follow elliptical paths. Funnel-shaped experimental setups generally tend to produce spiral or non-closed trajectories. This limitation, however, can be mitigated by appropriately scaling the experimental design. The next version of the experiment will therefore be significantly larger.

On average, however, the other two of Kepler's laws appeared to describe the particles' motion well. The second law states that a line connecting a planet to the central body sweeps out equal areas in equal time intervals—implying that orbital speed is highest near the central object. The water tornado orbits exhibited similar behavior, though with minor temporal fluctuations.

Kepler's third law establishes a mathematical relationship between orbital period and orbital size. The beads in the water tornado conformed closely to this pattern as well.

A more detailed analysis also showed that the hydrodynamic parameters in the water tornado closely match those typically found in protoplanetary disks. The researchers conclude that sufficiently small particles introduced into the laboratory vortex should behave in a similar manner to dust grains in real disk environments.

From prototype to refined experiment

The setup described here is a prototype, intended to demonstrate the general feasibility and potential of this approach for astronomical research.

"The current results from this analog experiment are impressive," says Mario Flock, who leads computational studies of planet-forming disks at MPIA. "I am confident that, with a few modifications, we can refine the water tornado model and bring it closer to scientific application. We hope this new analog experiment will offer insights into how processes unfold across vast distances within planet-forming disks."

The scientists hope that by optimizing the container shape, they can reduce turbulence, leading to a calmer surface and more stable flows. This would allow for more precise characterization of the experiment's desired properties.