The German-French Cooperation Programme GENESIS describes the complex structure of the interstellar medium using a new mathematical method / The dispersion of interstellar turbulence in gas clouds before star formation unfolds in a cosmically small space
In interstellar dust clouds, turbulence must first dissipate before a star can form through gravity. A German-French research team has now discovered that the kinetic energy of the turbulence comes to rest in a space that is very small on cosmic scales, ranging from one to several light-years in extent. The group also arrived at new results in the mathematical method: Previously, the turbulent structure of the interstellar medium was described as self-similar – or fractal. The researchers found that it is not enough to describe the structure mathematically as a single fractal, a self-similar structure as known from the Mandelbrot set. Instead, they added several different fractals, so-called multifractals. The new methods can thus be used to resolve and represent structural changes in astronomical images in detail. Applications in other scientific fields such as atmospheric research is also possible.
The German-French programme GENESIS (Generation of Structures in the Interstellar Medium) is a cooperation between the University of Cologne’s Institute for Astrophysics, LAB at the University of Bordeaux and Geostat/INRIA Institute Bordeaux. In a highlight publication of the journal Astronomy & Astrophysics, the research team presents the new mathematical methods to characterize turbulence using the example of the Musca molecular cloud in the constellation of Musca.
Stars form in huge interstellar clouds composed mainly of molecular hydrogen – the energy reservoir of all stars. This material has a low density, only a few thousand to several tens of thousands of particles per cubic centimetre, but a very complex structure with condensations in the form of ‘clumps’ and ‘filaments’, and eventually ‘cores’ from which stars form by gravitational collapse of the matter.
The spatial structure of the gas in and around clouds is determined by many physical processes, one of the most important of which is interstellar turbulence. This arises when energy is transferred from large scales, such as galactic density waves or supernova explosions, to smaller scales. Turbulence is known from flows in which a liquid or gas is ‘stirred’, but can also form vortices and exhibit brief periods of chaotic behaviour, called intermittency. However, for a star to form, the gas must come to rest, i.e., the kinetic energy must dissipate. After that, gravity can exert enough force to pull the hydrogen clouds together and form a star. Thus, it is important to understand and mathematically describe the energy cascade and the associated structural change.
A team from the Geophysical and Plasma Physics Astrophysics group of the University of Calabria has developed a numerical model that helps to understand in detail the interaction between shock waves and turbulence. The result, published in the latest issue of PNAS (which dedicated the cover to it), has several applications in the field of astrophysics
It all began in the spring of last year, when a young Calabrian physicist, Domenico Trotta , after a period spent in London – at Queen Mary University – for his doctorate, returned to Italy. And it goes straight to the University of Calabria, in Cosenza. The university where he graduated, and where there is one of the largest research groups for the study of plasma in Europe. A worse time could not have chosen. «I started service on March 1st 2020. Just long enough to say good morning, sign the contract, and the lockdown has started . Suddenly I found myself alone, isolated at home, like everyone else », Trotta now recalls to Media Inaf. A shocking return. But he who has made shocks his object of study does not lose heart, on the contrary. His specialty is in fact the numerical simulation of shock waves – shock waves – which occur everywhere in nature. “Here at the University of Calabria there are many experts in turbulence, in solar wind. I had just finished my doctorate, in fact, on numerical shock simulations . So it was natural to try to reunite the two worlds a little. “
And this is how a research – funded through the H2020 Aida project – started, aimed at understanding what happens when a shock wave crashes against a turbulent environment. An encounter similar to that simulated in wind tunnels, for example, between cars and moving air. Except that air is a viscous material, and the effect it has on a car launched at high speed is to slow it down. The shocks and turbulences studied by Trotta and his colleagues – University of Calabria professors Francesco Valentini and Sergio Servidio , and David Burgess of Queen Mary University of London – are instead plasma- based.: a mixture of mostly free protons and electrons, not bound together. And the effects can be far more surprising.
What effects, then? To reconstruct them, the four physicists simulated a plasma made up of billions of particles on the supercomputer – plasma, in fact. And like in a video game they shot it at supersonic speeds like a shock wave – what astronomers call collisionless shoc k – until it collides with billions of other particles – always a plasma, but this time in a state of turbulence. In practice, they have reproduced in detail what happens all the time almost everywhere in the universe: every time the turbulent solar wind collides with the earth’s magnetosphere, for example, or the shock wave of a supernova when s ‘breaks with the surrounding interstellar medium.
The result of these simulations can be found on the cover of the latest issue of PNAS , which you see on the side. And beyond the aesthetic appeal – with the magnetic field lines reminiscent of a Van Gogh painting – it is a result that shows what happens to the particles of the shock front when it collides with turbulence.
«The swirling structures that are observed, for example, in the Starry Nightby Van Gogh are frighteningly similar to everyday phenomena: turbulence in the sea, in rivers, in our coffee, and why not: in astrophysical shocks ”, explains Trotta. “In interplanetary space, however, history is more complicated than what we see here on Earth, in classical fluids, and perhaps even more convoluted than what happens in Van Gogh’s paintings. The astrophysical objects are immersed in a very complex fluid, the plasma precisely – a highly ionized state of matter and particularly sensitive to electric and magnetic fields. From the solar corona to the largest systems in the universe, such as galaxy clusters, the vast majority of observable matter is in the plasma state. When the plasma is very diluted (and this is the case with many astrophysical systems), collisions between particles are negligible and interactions between particles are mediated by electromagnetic forces. One of the fundamental characteristics of non-collisional plasmas is the possibility of accelerating particles at high energies ».
“Think of a surfer riding a wave,” adds Sergio Servidio. «For particles it is the same:“ riding ”the shock is accelerated. Now, however, these particles that surf on the shock receive an additional kick from the turbulence, from the swirling plasma areas with which they collide. And then they accelerate (or decelerate) again, gaining additional momentum. Similarly, astrophysical observations suggest that there are phenomena of extreme acceleration to shocks, where the particles also suffer the effect of turbulence and reach unthinkable energies. From this point of view, compared to a fluid, the so-called plasma turbulence is more complex, unpredictable and, despite the years of research, less understood ».
Examples of these interactions between shocks, plasmas and turbulence are numerous. “Think for example of our planet, which represents an obstacle for the plasma emitted by the sun”, observes Francesco Valentini. «The turbulent solar wind is forced by the presence of the terrestrial magnetosphere to stop its course in correspondence with the Earth. Since this flow is supersonic, a shock is created at the interface with the magnetosphere that marks the braking of the solar wind before the planet ( terrestrial bow shock). Other famous non-collisional shocks are those that result from the interaction between supernova explosions and the turbulent interstellar medium. Supernovae are believed to be the primary hotbed of very high energy cosmic rays. In all these cases, turbulence plays a fundamental role in the production of energetic particles, as already intuited in the first brilliant works of Enrico Fermi, in 1949 ».
Several results are presented obtained with the help of simulations, explain the researchers. Once the particles are accelerated by the shock and begin to propagate in the surrounding medium, the presence of turbulence plays a fundamental role in the evolution of the system. First of all, for higher turbulence levels, the particles are accelerated to higher and higher energies, extracting energy from the turbulent fluctuations. The turbulence is therefore able to “scramble” the particles produced by the shock. It has also been observed that turbulence changes some of the fundamental properties of the shock: for example, it induces strong distortions of the front.
«But turbulence is not a totally random state of matter, in turbulence there are structures, waves, fluctuations of different nature and magnetic reconnection. Therefore turbulence can not only accelerate but also decelerate, “trapping” the particles, which give energy to the surrounding environment. In this regard, we have developed a new diagnostics to quickly and accurately identify plasma areas where acceleration / deceleration or compression / expansion phenomena occur. Using this diagnostic, the plasma becomes a “mosaic” of interesting areas from the point of view of particle energetics. We have established that the turbulent electric field is an important ingredient in the acceleration process. For now, the new diagnostics has been applied to numerical simulations “, concludes Trotta,in-situ “.
Featured image: The three physicists of the University of Calabria, together with David Burgess of the Queen Mary University of London, of the article published in PNAS. From left: Sergio Servidio, Domenico Trotta and Francesco Valentini
Nobel laureate in physics Richard Feynman once described turbulence as “the most important unsolved problem of classical physics.”
Understanding turbulence in classical fluids like water and air is difficult partly because of the challenge in identifying the vortices swirling within those fluids. Locating vortex tubes and tracking their motion could greatly simplify the modeling of turbulence.
But that challenge is easier in quantum fluids, which exist at low enough temperatures that quantum mechanics — which deals with physics on the scale of atoms or subatomic particles — govern their behavior.
In a new study published in Proceedings of the National Academy of Sciences, Florida State University researchers managed to visualize the vortex tubes in a quantum fluid, findings that could help researchers better understand turbulence in quantum fluids and beyond.
“Our study is important not only because it broadens our understanding of turbulence in general, but also because it could benefit the studies of various physical systems that also involve vortex tubes, such as superconductors and even neutron stars,” said Wei Guo, an associate professor of mechanical engineering at the FAMU-FSU College of Engineering and the study’s principal investigator.
The research team studied superfluid helium-4, a quantum fluid that exists at extremely low temperatures and can flow forever down a narrow space without apparent friction.
Guo’s team examined tracer particles trapped in the vortices and observed for the first time that as vortex tubes appeared, they moved in a random pattern and, on average, rapidly moved away from their starting point. The displacement of these trapped tracers appeared to increase with time much faster than that in regular molecular diffusion — a process known as superdiffusion.
Analyzing what happened led them to uncover how the vortex velocities changed over time, which is important information for statistical modeling of quantum-fluid turbulence.
“Superdiffusion has been observed in many systems such as the cellular transport in biological systems and the search patterns of human hunter-gatherers,” Guo said. “An established explanation of superdiffusion for things moving randomly is that they occasionally have exceptionally long displacements, which are known as Lévy flights.”
But after analyzing their data, Guo’s team concluded that the superdiffusion of the tracers in their experiment was not actually caused by Lévy flights. Something else was happening.
“We finally figured out that the superdiffusion we observed was caused by the relationship between the vortex velocities at different times,” said Yuan Tang, a postdoctoral researcher at the National High Magnetic Field Laboratory and a paper author. “The motion of every vortex segment initially appeared to be random, but actually, the velocity of a segment at one time was positively correlated to its velocity at the next time instance. This observation has allowed us to uncover some hidden generic statistical properties of a chaotic random vortex tangle, which could be useful in multiple branches of physics.”
Unlike in classical fluids, vortex tubes in superfluid helium-4 are stable and well-defined objects.
“They are essentially tiny tornadoes swirling in a chaotic storm but with extremely thin hollow cores,” Tang said. “You can’t see them with the naked eye, not even with the strongest microscope.”
“To solve this, we conducted our experiments in the cryogenics lab, where we added tracer particles in helium to visualize them,” added Shiran Bao, a postdoctoral researcher at the National High Magnetic Field Laboratory and a paper author.
The researchers injected a mixture of deuterium gas and helium gas into the cold superfluid helium. Upon injection, the deuterium gas solidified and formed tiny ice particles, which the researchers used as the tracers in the fluid.
“Just like tornadoes in air can suck in nearby leaves, our tracers can also get trapped on the vortex tubes in helium when they are close to the tubes,” Guo said.
This visualization technique is not new and has been used by scientists in research labs worldwide, but the breakthrough these researchers made was to develop a new algorithm that allowed them to distinguish the tracers trapped on vortices from those that were not trapped.
Their research was supported by the National Science Foundation and the U.S. Department of Energy. The experiment was conducted at the National High Magnetic Field Laboratory at Florida State University.
Featured image: An illustration showing quantum vortex tubes undergoing apparent superdiffusion. The white dots represent trapped particle that the researchers tracked to visualize and track the motion of the tubes, and the red lines represent the random patterns that the particles traveled. (Courtesy of Wei Guo)
Reference: Yuan Tang, Shiran Bao, Wei Guo, “Superdiffusion of quantized vortices uncovering scaling laws in quantum turbulence”, Proceedings of the National Academy of Sciences Feb 2021, 118 (6) e2021957118; DOI: 10.1073/pnas.2021957118
An international team of researchers from the University of Oxford, LMU Munich, ETH Zurich, BGI Bayreuth, and the University of Zurich discovered that a two-step formation process of the early Solar System can explain the chronology and split in volatile and isotope content of the inner and outer Solar System.
Their findings will be published in Science (Friday 22 January 2021; under embargo until 2pm US Eastern Time Thursday 21 January 2021).
The paper presents a new theoretical framework for the formation and structure of the Solar System that can explain several key features of the terrestrial planets (like Earth, Venus, and Mars), outer Solar System (like Jupiter), and composition of asteroids and meteorite families. The team’s work draws on and connects recent advances in astronomy (namely observations of other solar systems during their formation) and meteoritics – laboratory experiments and analyses on the isotope, iron, and water content in meteorites.
The suggested combination of astrophysical and geophysical phenomena during the earliest formation phase of the Sun and the Solar System itself can explain why the inner Solar System planets are small and dry with little water by mass, while the outer Solar System planets are larger and wet with lots of water. It explains the meteorite record by forming planets in two distinct steps. The inner terrestrial protoplanets accreted early and were internally heated by strong radioactive decay; this dried them out and split the inner, dry from the outer, wet planetary population. This has several implications for the distribution and necessary formation conditions of planets like Earth in extrasolar planetary systems.
The numerical experiments performed by the interdisciplinary team showed that the relative chronologies of early onset and protracted finish of accretion in the inner Solar System, and a later onset and more rapid accretion of the outer Solar System planets can be explained by two distinct formation epochs of planetesimals, the building blocks of the planets. Recent observations of planet-forming disks showed that disk midplanes, where planets form, may have relatively low levels of turbulence. Under such conditions the interactions between the dust grains embedded in the disk gas and water around the orbital location where it transitions from gas to ice phase (the snow line) can trigger an early formation burst of planetesimals in the inner Solar System and another one later and further out.
The two distinct formation episodes of the planetesimal populations, which further accrete material from the surrounding disk and via mutual collisions, result in different geophysical modes of internal evolution for the forming protoplanets. Dr Tim Lichtenberg from the Department of Atmospheric, Oceanic and Planetary Physics at the University of Oxford and lead-author of the study notes: ‘The different formation time intervals of these planetesimal populations mean that their internal heat engine from radioactive decay differed substantially. Inner Solar System planetesimals became very hot, developed internal magma oceans, quickly formed iron cores, and degassed their initial volatile content, which eventually resulted in dry planet compositions. In comparison, outer Solar System planetesimals formed later and therefore experienced substantially less internal heating and therefore limited iron core formation, and volatile release.
‘The early-formed and dry inner Solar System and the later-formed and wet outer Solar System were therefore set on two different evolutionary paths very early on in their history. This opens new avenues to understand the origins of the earliest atmospheres of Earth-like planets and the place of the Solar System within the context of the exoplanetary census across the galaxy.’
This research was supported by funding from the Simons Collaboration on the Origins of Life, the Swiss National Science Foundation, and the European Research Council.
Heidelberg astrophysicists study interstellar gas clouds as part of an international cooperation.
Computer simulations of turbulence in interstellar gas and molecular clouds – simulations so complex they were inconceivable until now – have provided important new insights into the role turbulence plays in the formation of stars. For the first time, the results of the calculations suggest how these turbulent movements transition from the supersonic to the subsonic range. The work was conducted by an international research team led by scientists from the Centre for Astronomy of Heidelberg University and the Australian National University, Canberra. The simulations were carried out at the Leibniz Supercomputing Centre of the Bavarian Academy of Sciences and Humanities.
When and how interstellar gas clouds form stars are among astronomy’s key and most complex questions. “Interstellar gas, which makes up about ten to 15 percent of the visible matter in the Milky Way, does not uniformly penetrate the space between the stars, but in its distribution rather resembles rising and turbulent swirling smoke. And it is precisely this turbulent behaviour that is the key to understanding how interstellar gas clouds fragment and contract under their own gravitational weight to form stars and star clusters,” explains Prof. Dr Ralf Klessen of the Institute of Theoretical Astrophysics, which is part of the Centre for Astronomy of Heidelberg University.
These turbulent movements pose a particular challenge for research in that they tend to cascade from larger scales to smaller and smaller ones. They are similar to billows of smoke with their large, rapidly moving eddies and the smaller eddies that are carried along with them. This cascading process also takes place in the gas, dust and molecular clouds between the stars, known as the interstellar medium. According to Prof. Klessen, however, these clouds are many orders of magnitude “thinner” than a plume of smoke.
In this cascade, the turbulent energy decreases to a smaller and smaller scale, causing the large areas of turbulence, mostly moving at supersonic speed, to eventually move at subsonic speed. And it is precisely this transition – known as the sonic scale – that determines the properties of dense molecular cloud cores. This scale is believed to mark the transition zone from turbulence-dominated to gravity-dominated behavior. Once gravity dominates, star formation sets in.
“There are, of course, theoretical predictions as to where this transition zone should be. But its exact location, shape and width were previously unknown. The physical processes are so tremendously complex that they can only be studied with the help of computer simulations,” adds Prof. Klessen. As part of an international cooperation, the Heidelberg researcher and his colleague Prof. Dr Christoph Federrath from the Australian National University used resources from the Leibniz Supercomputing Centre to carry out the largest simulation of interstellar turbulence to date to study the transition from supersonic to subsonic turbulence.
Prof. Federrath describes the results as spectacular. The researchers not only confirmed the theoretically predicted position of the sonic scale but also determined the width and shape of the transition zone from the supersonic to the subsonic range. The transition is not sharp but occurs over a wide range of scale. “Theoretically, this transition zone defines the frequency with which new stars can be found in interstellar gas clouds,” explains Ralf Klessen. “We have therefore compared our prediction with observations of gas clouds in the Milky Way and obtained excellent agreement with their statistical properties,” continues the Heidelberg astrophysicist. From the point of view of the scientists, the simulations will be able to provide quantitative information for future turbulence-regulated models of star formation.
The research results were published in the journal Nature Astronomy.
The swirls, eddies, and wavy bands of Jupiter and Saturn may remind us of a soothing, starry, starry night—but they reveal these two gas giants to be stormy, turbulent places. The turbulence produces energy cascades, a non-linear transfer of energy between different scales of motion. These are as fundamental to understanding planetary dynamics as the cardiovascular system is to understanding the human body.
But scientists haven’t had a reliable way to quantify planetary turbulence—until now.
A global team led by scientists at the University of Rome, which included Boris Galperin, Ph.D., a professor at the USF College of Marine Science, described the advance in Geophysical Research Letters. The results show that the rate of the turbulence energy transfer—until now a black box of mystery—can be calculated relatively easily from a variable related to the planetary rotation and known as potential vorticity (PV).
The method was first developed by Galperin and his graduate student, Jesse Hoemann, and tested in the experiments conducted at the University of Rome during Jesse’s visit there. The method was confirmed using real velocity data extracted from images of Jupiter’s clouds movement captured by the 20-year-long Cassini mission, additional laboratory results performed in a rotating tank at the University of Rome in Italy, and computer simulations for Saturn.
Based on the calculations of PV, the team showed for the first time that the rate of the energy transfer in Jupiter’s atmosphere is four times greater than that in Saturn’s.
“Now you can see why I was really excited about this work,” said Galperin, who developed the original idea for the experiments several years ago.
Since the laws of turbulence, as any fundamental physical laws, are universal, the method can now be applied to other natural environments such as the ocean, Galperin said. Eddies in Earth’s ocean that look like the swirls on Jupiter, for example, come in different strengths, sizes, and lifetimes, and are critical to understanding Earth’s balances of energy, heat, salt, carbon dioxide, and more.
“This is the first estimate of Saturn’s turbulent power from observations, and this study paves the way for future data analysis in other planetary atmospheres,” said lead author Simon Cabanes, Ph.D., a post doc at the Department of Civil and Environmental Engineering (DICEA) of the University of Rome La Sapienza.
Deep learning, also called machine learning, reproduces data to model problem scenarios and offer solutions. However, some problems in physics are unknown or cannot be represented in detail mathematically on a computer. Researchers at the University of Illinois Urbana-Champaign developed a new method that brings physics into the machine learning process to make better predictions.
The researchers used turbulence to test their method.
“We don’t know how to mathematically write down all of turbulence in a useful way. There are unknowns that cannot be represented on the computer, so we used a machine learning model to figure out the unknowns. We trained it on both what it sees and the physical governing equations at the same time as a part of the learning process. That’s what makes it magic and it works,” said Willett Professor and Head of the Department of Aerospace Engineering Jonathan Freund.
Freund said the need for this method was pervasive.
“It’s an old problem. People have been struggling to simulate turbulence and to model the unrepresented parts of it for a long time,” Freund said.
Then he and his colleague Justin Sirignano had an epiphany.
“We learned that if you try to do the machine learning without considering the known governing equations of the physics, it didn’t work. We combined them and it worked.”
When designing an air or spacecraft, Freund said this method will help engineers predict whether or not a design involving turbulent flow will work for their goals. They’ll be able to make a change, run it again to get a prediction of heat transfer or lift, and predict if their design is better or worse.
“Anyone who wants to do simulations of physical phenomena might use this new method. They would take our approach and load data into their own software. It’s a method that would admit other unknown physics. And the observed results of that unknown physics could be loaded in for training,” Freund said.
The work was done using the super-computing facility at the National Center for Supercomputing at UIUC known as Blue Waters, making the simulation faster and so more cost efficient.
The next step is to use the method on more realistic turbulence flows.
“The turbulent flow we used to demonstrate the method is a very simple configuration,” Freund said. “Real flows are more complex. I’d also like to use the method for turbulence with flames in it–a whole additional type of physics. It’s something we plan to continue to develop in the new Center for Exascale-enabled Scramjet Design, housed in NCSA.”
Freund said this work is at the research level but can potentially affect industry in the future.
“Universities were very active in the first turbulence simulations, then industry picked them up. The first university-based large-eddy simulations looked incredibly expensive in the 80s and 90s. But now companies do large-eddy simulations. We expect this prediction capability will follow a similar path. I can see a day in the future with better techniques and faster computers that companies will begin using it.”
A new method for verifying a widely held but unproven theoretical explanation of the formation of stars and planets has been proposed by researchers at the U.S. Department of Energy’s (DOE) Princeton Plasma Physics Laboratory (PPPL). The method grows from simulation of the Princeton Magnetorotational Instability (MRI) Experiment, a unique laboratory device that aims to demonstrate the MRI process that is believed to have filled the cosmos with celestial bodies.
The novel device, designed to duplicate the process that causes swirling clouds of cosmic dust and plasma to collapse into stars and planets, consists of two fluid-filled concentric cylinders that rotate at different speeds. The device seeks to replicate the instabilities that are thought to cause the swirling clouds to gradually shed what is called their angular momentum and collapse into the growing bodies that they orbit. Such momentum keeps the Earth and other planets firmly within their orbits.
“In our simulations we can actually see the MRI develop in experiments,” said Himawan Winarto, a graduate student in the Princeton Program in Plasma Physics at PPPL and lead author of a paper in Physical Review E interest in the subject began as an intern in the University of Tokyo-Princeton University Partnership on Plasma Physics while an undergraduate at Princeton University.
The suggested system would measure the strength of the radial, or circular, magnetic field that the rotating inner cylinder generates in experiments. Since the strength of the field correlates strongly with expected turbulent instabilities, the measurements could help pinpoint the source of the turbulence.
“Our overall objective is to show the world that we’ve unambiguously seen the MRI effect in the lab,” said physicist Erik Gilson, one of Himawan’s mentors on the project and a coauthor of the paper. “What Himawan is proposing is a new way to look at our measurements to get at the essence of MRI.”
The simulations have shown some surprising results. While MRI is normally observable only at a sufficiently high rate of cylinder rotation, the new findings indicate that instabilities can likely be seen well before the upper limit of the experimental rotation rate is reached. “That means speeds much closer to the rates we are running now,” Winarto said, “and projects to the rotational speed that we should aim for to see MRI.”
A key challenge to spotting the source of MRI is the existence of other effects that can act like MRI but are not in fact the process. Prominent among these deceptive effects are what are called Rayleigh instabilities that break up fluids into smaller packets, and Ekman circulation that alters the profile of fluid flow. The new simulations clearly indicate “that MRI, rather than Ekman circulation or Rayleigh instability, dominates the fluid behavior in the region where MRI is expected,” Winarto said.
The findings thus shed new light on the growth of stars and planets that populate the universe. “Simulations are very useful to point you in the right direction to help interpret some of the diagnostic results of experiments,” Gilson said. “What we see from these results is that the signals for MRI look like they should be able to be seen more easily in experiments than we had previously thought.”