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Towards convergence of turbulent dynamo amplification in cosmological simulations of galaxies

Updated: Nov 14, 2023

Sergio Martin-Alvarez, Julien Devriendt, Adrianne Slyz, Debora Sijacki, Mark L. A. Richardson and Harley Katz


What is this about?

Our galaxy, like all others, harbours the secret answer to the fundamental question of how magnetic fields in galaxies, integral to the dynamics of the interstellar medium (ISM), attain their observed strengths. The leading theory? Dynamo amplification — a process believed to be a key player in amplifying weak magnetic seeds (billions of billions of times lower than microgauss) to the microgauss levels seen today. This dynamo action, driven by the turbulence within the galaxy, effectively transforms kinetic energy into magnetic energy. It's akin to a galactic engine of sorts, revving up the magnetism through the chaotic motions of gas and plasma.

Getting this 'turbulent engine' to turn on in simulations poses a formidable challenge: the process is intrinsically complex and highly dependent on the simulation's resolution. High resolutions are very expensive computationally: we want our simulations to model the entire galaxy as a whole, ideally submerged in a realistic (although 'fake') universe. Simultaneously, we want to also capture the small-scale turbulence: that means that the simulation is able to realistically 'see' blobs of gas travelling, colliding and fragmenting within the medium (the ISM) of the galaxy. Furthermore, ensuring that the simulated magnetic fields are divergence-free, a fundamental physical requirement from Maxwell's equations, adds an additional layer of computational complexity. This complexity is not just a technical hurdle but also a critical aspect in ensuring that our simulations mirror the real-world behaviour of galactic magnetic fields.

When studying turbulent dynamo amplification in galaxy simulations, a striking difference became apparent to me between their behaviour and that of 'turbulent boxes' — numerical experiments designed specifically for turbulent dynamo studies. Turbulent boxes are generally able to resolve the intricacies of gas motions and evolution even in diffuse regions, capturing the subtle interplay of forces at play in these less dense areas. In contrast, galaxy simulations, with their broader and more complex scope, traditionally concentrate on adding resolution to dense gas regions. As a result, their 'turbulence' has a less sharp appearance, looking more fluffy and blobby than the stringy and edgy gas in turbulence boxes.

The requirement for a more 'caring' treatment for non-dense gas is a well-known concept for those studying magnetism and turbulence. Therefore, to truly grasp the dynamo mechanism in galaxies, we needed an approach that married the detailed turbulence resolution of turbulent boxes with the comprehensive, large-scale modelling of galaxy simulations. And that was the genesis of this work here, aiming to bridge these two worlds and trying to pin down just how much of a difference would a better treatment of this non-dense gas would make.

Piqued your interest? This is how we can figure this out:

It all boils down to the nitty-gritty of our simulation techniques — specifically, how we discretise their domain (that means, how do we divide their volume into little pieces we can evolve and study). Let me break this down a bit:

First off, there's this thing called a 'quasi-Lagrangian refinement' strategy for refinement. It's a bit like trying to take a detailed picture with a camera that adjusts its focus based on where the heavier stuff is — in our case, stuff being gas, dark matter, and stars. In a simulated galaxy, this means different parts get snapped in varying resolutions, depending on how much 'stuff' is there. It's like having a detailed view of the crowded areas but a blurrier picture of the less crowded spots. Handy, but it has its problems, especially when we're trying to understand the whole galaxy in all its complex, turbulent glory.

Now, enter our new approach — this strategy that we dubbed 'quasi-Eulerian refinement'. Imagine this as setting the camera to a uniform high resolution, capturing every nook and cranny of the galaxy with equal clarity. We set a threshold and say, "Hey, if this area corresponds to the galaxy, you have to use the higher resolution available." This way, we're not just focusing on the dense, star-packed regions; we're also getting a clear picture of the warmer, sparser areas where hotter turbulence takes place. It's like having a finely-tuned lens that brings the entire galaxy into sharp focus.

You want to see how it looks? Here's a couple pictures:

Figure: the two rows show the same galaxy with our new quasi-Eulerian refinement (top row) and the standard quasi-Lagrangian refinement used by most simulations (bottom row). Left column: this one shows the gas density. The top row features extremely high resolutions in the diffuse gas, which leads to significantly more structure at intermediate densities (white). Central column: this one shows the magnetic energy. The bluer and greener the colours, the higher the energy. And again, we find much more magnetic energy in the top row, with our new refinement. Right column: this one shows a view of the galaxy from afar, submerged in its cosmological environment. The galaxy is situated at the centre, where three immense cosmological filaments meet. Colours indicate gas escaping the galaxy (red) and falling into it (blue). You can see how much substructure our new refinement generates, not only in the galaxy, but also in its surroundings, with much more gas escaping and expelled, and a lot of turbulence on large scales. Quite awesome, if I'm allowed to say so myself!

Looks quite amazing with the new refinement, doesn't it?

Guess What We Discovered?

Alright, get ready for some pretty cool stuff we found by tinkering with how we simulate galaxies, and did it pay off!

  • Much more turbulence: First up, our new quasi-Eulerian refinement strategy led to a significant boost of gas turbulence, especially true in the warm phase of the galaxy (the diffuse part where you can see a lot of structure appearing in the image above).

  • Much more magnetic energy: Switching from the standard quasi-Lagrangian approach to our new quasi-Eulerian method was a game changer for the galaxy’s magnetic energy, which increase much more rapidly, even with lower resolution (and this is somewhat counterintuitive, but is explained by the next point).

  • Much more agreement with theory: Indeed the quasi-Eulerian simulations consistently showed more magnetic energy growth than the quasi-Lagrangian ones. And guess what? Their amplification rates matches almost perfectly the theoretical predictions (and those from turbulent boxes), which is something that cosmological galaxy formation simulations never really managed to do before. It's a relief to see that when we model our galaxies in a manner analogous to these other type of studies, we actually get the same answer.

So, what’s the big picture here? While our current computer simulations are still playing catch-up with the real Universe, our new approach is a nice step forward. It makes a case for putting more 'love' into the modelling of turbulence and magnetism in galaxy formation simulations, and at the very least explains an important source of inconsistency when we find disparities with simplified theoretical models.

Dive Deeper: Where to read more:

For those interested in exploring our findings and methodologies further, I'd recommend reading the full paper. I look forward to your insights, questions, and discussions on this captivating exploration of galactic magnetism.

Here is a link to it:

Feel free to contact me with any questions you might have!

Un saludo!

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