6 mins read 05 May 2021

Unravelling the turbulent, magnetised dynamics of the interstellar medium

Magnetised turbulence can be found on all scales across the Universe, however, understanding it is highly challenging, and requires the largest supercomputers in the world, coupled with advanced physics and mathematics. ANU PhD student, James Beattie, discusses his latest work on understanding how the gas density fluctuates in the chaotic, turbulent interstellar medium.

Credit: Modified (James R. Beattie) from ESA/Herschel/NASA/JPL-Caltech CC BY-SA 3.0 IGO; R. Hurt (JPL-Caltech).

Most of the baryonic Universe is in a state of turbulence. On Earth turbulence provides the atmospheric pressure fluctuations that make the stars twinkle, determines the chaotic motions of oceans and weather patterns, and is a formidable foe in many engineering challenges that aim to minimise the amount of energy dissipated from a system. 

In fact, turbulence is so pervasive on Earth that it may come as no surprise that it plays a fundamental role on almost all scales of the Universe. For example on the scale of tens of light-years, in the cool, highly supersonic molecular gas clouds — the birthplace of stars —  turbulence regulates the amount of gas that is viable to collapse under its own mass to eventually form stars, i.e. the star formation rate of a cloud. 

Take a moment now to realise something very beautiful that has just been touched upon. The motions that mix our milk and coffee, our weather, are similar to the motions that regulate the number of stars that form in the interstellar medium (ISM). Unravelling this kind of universality is why I do and love physics.

Gas density of the Orion molecular cloud derived from the submillimeter emission using Herschel Space Observatory and, milk mixing into a cup of coffee. In both images, it is similar turbulent motions that set the structure and star formation potential of Polaris flare, and which mix the milk into the coffee, showing the universality of turbulence on all scales. Credit: Modified from ESA/Herschel/PACS, SPIRE/N. Schneider, Ph. André, V. Könyves (CEA Saclay, France) for the 'Gould Belt survey Key Programme.

The word “regulation” captures the duality of the role of turbulence in these molecular clouds: (1) the supersonic turbulence creates large over-densities through populations of shocks interacting within one another. The over-densities, which can be orders of magnitudes denser than the mean cloud density, are sculpted into filamentary, dendritic structures that are able to collapse under their own self-gravity and form stars; and (2) the turbulence mixes the gas constantly, trickling kinetic energy through all length scales in the cloud and hence provides support against gravitational collapse. So just as a quantum object can be a wave and a particle at the same time, turbulence can both prevent and facilitate the star formation process.

Because supersonic turbulence is crucial to understanding the nature of star formation in the last few decades theoretical and numerical astrophysicists have been on the frontline of both pioneering supersonic turbulence theory (the theory of compressible turbulence) and constructing simulations that capture the chaotic motions of turbulence, gravity and star formation (see this example), utilising hundreds of thousands of computing cores, for many millions of compute-core hours, on some of the biggest supercomputers in the world. 

It really has been only with the advent of strong coupling between the high-performance supercomputing world and astrophysics that we have been able to answer the most exciting questions about the dynamics of ISM.

Column density derived from submillimeter emission observed for a region in the Orion A molecular cloud using the Herschel Space Observatory overlaid with plane-of-sky magnetic field topology using the Planck 353 GHz polarization observations. We see a beautifully rich structure with over-dense regions in the cloud forming perpendicular to the magnetic field, demonstrating how magnetic fields shape molecular clouds in the ISM. Credit: Soler 2019.

One such question, which has been motivated by beautiful observations of complex magnetic field structure in the ISM, is how do magnetic fields influence the dynamical properties of the ISM? 

Astronomers either hate or love magnetic fields, but I bet if you are reading this article you love them, just like me. Regardless of our relationship with magnetic fields, more and more evidence is mounting that in particular regions of the ISM there are some very strong ones. Strong enough to have roughly the same amount of energy as the turbulent motions, which makes the gas density anisotropic (no longer does the flow look the same in all directions). This means we really cannot ignore them or the anisotropy when trying to understand the dynamics of these regions in the ISM, which is where our latest study comes in.

The density, ln(rho/rho_0), distribution (red) shown for a simulated molecular cloud. The right tail of the distribution describes the highest density filaments and regions in the molecular cloud, which, above some critical value, indicated with s_crit, will potentially collapse and form stars with some efficiency. This shows how the density distribution is vital for calculating the star formation potential that a molecular cloud has. Credit: illustration by James R. Beattie.

But how do we even start modelling these kinds of dynamical processes? Well, we have to now quickly put on our mathematical hats and think of the ISM as a set of coupled, stochastic (randomly fluctuating) fields, i.e. density field, velocity field, magnetic field, etc. 

They are coupled through the equations of magnetohydrodynamics and because each field is stochastic, we treat it like a random variable (like the height of a population, for example) and try to model the probability distribution of the field based on the physics of the fluid. 

For the gas density field, which is accessible via, for example, carbon monoxide (CO) line observations, there have been roughly three decades of work modelling how the variance of the distribution, which is visualised above, is a function of the gas kinematics.

Numerical simulations of magnetohydrodynamic turbulence when the magnetic field (blue) is weak (left) and strong (right). Yellow pathlines show the trajectories of parcels of gas in the simulations. When the magnetic field is weak the magnetic field and gas parcels are mixed isotropically through the fluid, but when the magnetic field is strong, the fluid becomes strongly anisotropic with the dynamics along and across the field becoming dissimilar. Credit: Beattie et al. 2020.

In our latest work, we extend the variance - gas kinematics relation into the strong magnetic field regime, where the variance no longer looks the same in all directions because of the magnetic field. 

The analytical theory relies upon the over-densities caused by two different types of shocks in the turbulence. The model has some very nice properties, like in the weak magnetic field limit previously developed models pop out. 

Our model also predicts an upper limit for the density variance, which is a very interesting result, because it means, in the presence of a strong magnetic field, the supersonic turbulence can no longer produce the larger and larger over-densities, which, as I wrote previously, feeds back into the star formation potential in these regions. 

To test our model we ran an ensemble of strong magnetic field, supersonically turbulent magnetohydrodynamic simulations and the match between our theoretical model and the simulation data looks very good, with just a single free parameter that captures how the over-densities fill the volume of the region.

With a density variance model in this regime we are taking the first steps towards constructing an analytical star formation model for the highly-magnetised ISM, and, just as cool, we are learning a little bit more about this thing that seems to be every we look — turbulence. 

We have a number of studies planned on both of these aspects for the near future, so keep a lookout for more breakthroughs in magnetised turbulence and molecular cloud-scale star formation coming from the Australian Space community!

James R. Beattie

James Beattie is a PhD student at the Mt Stromlo Observatory / Australian National University. James specialises in compressible fluids, turbulence, molecular cloud scale star formation, magnetic fields and high-performance computing. He also has contributed to ecological monitoring, computer vision and automation, and statistical models for biological system projects. He loves exploring the overlap between science and art and helping run outreach events for the Young Stars program, an outreach program for 6-12-year-olds based in Canberra.

Twitter: @AstroJamesBe

The paper is available on the pre-print server,