A new laboratory experiment uses a water vortex to investigate how planets form from material in protoplanetary gas and dust disks
This photo shows the upper part of the water tornado model. The acrylic glas tank has a diameter of 50 centimetres and is illuminated with LED strips. The water forms a vortex whose surface shape reproduces the profile of a gravitational field. The analysis showed that the motion of the water closely resembles the behaviour seen in protoplanetary discs.
© S. Schütt (University of Greifswald)
To the point
- Simple laboratory model for cosmic flows developed: A water tornado enables a realistic simulation of the dynamics of gas and dust in planet-forming discs.
- Kepler's laws confirmed in a water tank: The orbits of floating particles follow the same physical rules as celestial bodies in a gravitational field.
- Potential for experiments on planet formation: The cost-effective and versatile setup opens up new ways to study interactions between dust and gas under laboratory conditions.
Researchers from the University of Greifswald and the Max Planck Institute for Astronomy in Heidelberg (both in Germany) have developed a prototype experimental setup that simulates flow properties in accretion discs using a water tornado. The setup is inexpensive and easy to construct.
Planets form within discs of gas and dust
This artistic rendering of a planet-forming disc depicts a ring-like structure of gas and dust. This dust grows into planetesimals, which in turn become planets. The interaction between gas and dust is of particular interest to researchers, as it drives the process of planet formation.
© T. Müller (MPIA/HdA - CC BY-SA 4.0)
Accretion discs 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 discs 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 kilometres 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 artefacts may distort the outcome.
Analogue experiment complements simulation
This photo shows the setup of the water tornado model. The upper acrylic glass tank has a diameter of 50 centimetres and is illuminated with LED strips. Beneath it sits a narrower cylinder. Two black nozzles at the bottom feed water into the vessel through connected hoses. The resulting vortex replicates the surface shape of a gravitational potential. The analysis showed that the motion of the water is similar to that seen in protoplanetary discs.
© S. Schütt (University of Greifswald)
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 analogue experiments, the new approach offers two key advantages. Firstly, 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 discs 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 disc. Initial tests have shown that these laws largely hold in the water tornado model as well.
These findings 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 centre of a protoplanetary disc 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-centimetre-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-centimetre-wide cylinder. The usable experimental zone begins roughly 3 centimetres from the centre and extends almost to the tank's edge. The shape of the water tornado fulfils the required property of mimicking a gravitational field.
Water tornado mimics a protoplanetary disc
This diagram shows the angular velocities measured in the water tornado experiment, using plastic beads to visualise the water's motion. The blue data points represent angular velocity as a function of orbital radius. The dashed orange line indicates the theoretical relationship between angular velocity and orbital radius for circular orbits based on Kepler's third law. The smaller inset shows the same data in logarithmic form.
© S. Knauer et al. / MPIA (CC BY-SA 4.0)
To analyse the flow behaviour 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 behaviour, 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 discs. The researchers conclude that sufficiently small particles introduced into the laboratory vortex should behave in a similar manner to dust grains in real disc 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 analogue experiment are impressive," says Mario Flock, who leads computational studies of planet-forming discs at the Max Planck Institute for Astronomy. "I am confident that, with a few modifications, we can refine the water tornado model and bring it closer to scientific application."
The scientists hope that by optimising the container shape, they can reduce turbulence, leading to a calmer surface and more stable flows. This would allow for more precise characterisation of the experiment's desired properties.
Background information
In addition to MPIA researcher Mario Flock, contributors to the study include Stefan Knauer, Stefan Schütt, Floris Scharmer, Sebastian Haag, Nils Fahrenkamp, Andre Melzer, Daniel Siegel, and Peter Manz (all at the University of Greifswald).
Mario Flock heads a research group in the Planet and Star Formation (PSF) department at MPIA and was recently awarded a prestigious Consolidator Grant from the European Research Council (ERC), worth €2.13 million. The funded project, titled RAPTOR - Revealing Accreting Planets Through Observations and Refined Simulations, bridges theory and observation in the study of forming planetary systems.
The water tornado experiment is part of the SWADEX project, conducted at the Institute of Physics, University of Greifswald.
