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The spectrum of magnetized turbulence in the interstellar medium

Nature Astronomy volume 9, pages 1195–1205 (2025)Cite this article

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Abstract

The interstellar medium (ISM) of our Galaxy is magnetized, compressible and turbulent, influencing many key ISM properties, such as star formation, cosmic-ray transport, and metal and phase mixing. Yet, basic statistics describing compressible, magnetized turbulence remain uncertain. Utilizing grid resolutions up to 10,0803 cells, we simulated highly compressible, magnetized ISM-style turbulence with a magnetic field maintained by a small-scale dynamo. We measured two coexisting kinetic energy cascades, \({{\mathcal{E}}}_{{\rm{kin}}}(k)\propto {k}^{-n}\), in the turbulence, separating the plasma into scales that are non-locally interacting, supersonic and weakly magnetized (n = 2.01 ± 0.03 ≈ 2) and locally interacting, subsonic and highly magnetized (n = 1.465 ± 0.002 ≈ 3/2), where k is the wavenumber. We show that the 3/2 spectrum can be explained with scale-dependent kinetic energy fluxes and velocity–magnetic field alignment. On the highly magnetized modes, the magnetic energy spectrum forms a local cascade (n = 1.798 ± 0.001 ≈ 9/5), deviating from any known ab initio theory. With a new generation of radio telescopes coming online, these results provide a means to directly test if the ISM in our Galaxy is maintained by the compressible turbulent motions from within it.

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Fig. 1: The current density, magnetic field and mass density structure in what is presently the world’s largest supersonic MHD turbulence simulation.
Fig. 2: The energy spectra, fundamental turbulence scales and shell-to-shell energy flux transfer functions.
Fig. 3: The scale-dependent alignment of the velocity and magnetic field and energy flux.

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Data availability

All raw data for temporally averaged energy spectra, probability distribution functions and structure functions presented in the study are available via GitHub at https://github.com/AstroJames/10k_supersonicMHD. The raw simulation data (for example, three-dimensional fields, which are many hundreds of TBs in total) and the data shown in Supplementary Figs. 1–4 are available from the corresponding author upon reasonable request.

Code availability

Access to the basic simulation code (FLASH) used in this manuscript can be obtained via reasonable request at https://flash.rochester.edu/site/flashcode.

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Acknowledgements

We acknowledge the useful discussions with D. Fielding, A. Chernoglazov and A. Beresnyak on the local anisotropy and alignment structure functions, and the more general discussions about this work with R. Bandyopadhyay, P. K.-S. Kempski, E. Quataert, A. Philippov, P. Mocz, B. Ripperda and C. Thompson. Funding: J.R.B. acknowledges financial support from the Australian National University (ANU), via the Deakin PhD and Dean’s Higher Degree Research (theoretical physics) Scholarships and the Australian Government via the Australian Government Research Training Program Fee-Offset Scholarship and the Australian Capital Territory Government-funded Fulbright scholarship. J.R.B., C.F., R.S.K. and S.C. also acknowledge high-performance computing resources provided by the Leibniz Rechenzentrum and the Gauss Centre for Supercomputing (GCS) grants pr32lo, pr73fi and GCS large-scale project 10391. C.F. acknowledges funding by the Australian Research Council (Discovery Projects grants DP230102280 and DP250101526) and the Australia–Germany Joint Research Cooperation Scheme (UA-DAAD). C.F. also acknowledges high-performance computing resources provided by the Australian National Computational Infrastructure (grant ek9) and the Pawsey Supercomputing Centre (project pawsey0810) in the framework of the National Computational Merit Allocation Scheme and the ANU Merit Allocation Scheme. R.S.K. acknowledges support from the European Research Council (ERC) via the ERC Synergy Grant ‘ECOGAL’ (project ID 855130), from the German Excellence Strategy via the Heidelberg Cluster of Excellence (EXC 2181 - 390900948) ‘STRUCTURES’, and from the German Ministry for Economic Affairs and Climate Action in project ‘MAINN’ (funding ID 50OO2206). R.S.K. also expresses thanks for local computing resources provided by the Ministry of Science, Research and the Arts (MWK) of The Länd through bwHPC and the German Science Foundation (DFG) through grant INST 35/1134-1 FUGG and 35/1597-1 FUGG, and also for data storage at SDS@hd funded through grants INST 35/1314-1 FUGG and INST 35/1503-1 FUGG. J.R.B. and A.B. also acknowledge the support from NSF Award 2206756.

Author information

Authors and Affiliations

  1. Department of Astrophysical Sciences, Princeton University, Princeton, NJ, USA

    James R. Beattie & Amitava Bhattacharjee

  2. Canadian Institute for Theoretical Astrophysics, University of Toronto, Toronto, Ontario, Canada

    James R. Beattie

  3. Research School of Astronomy and Astrophysics, Australian National University, Canberra, Australian Capital Territory, Australia

    James R. Beattie & Christoph Federrath

  4. Australian Research Council Centre of Excellence for All-Sky Astrophysics in 3 Dimensions (ASTRO 3D), Canberra, Australian Capital Territory, Australia

    Christoph Federrath

  5. Zentrum für Astronomie, Institut für Theoretische Astrophysik, Universität Heidelberg, Heidelberg, Germany

    Ralf S. Klessen

  6. Interdisziplinäres Zentrum für Wissenschaftliches Rechnen, Universität Heidelberg, Heidelberg, Germany

    Ralf S. Klessen

  7. Center for Astrophysics, Harvard & Smithsonian, Cambridge, MA, USA

    Ralf S. Klessen

  8. Elizabeth S. and Richard M. Cashin Fellow, Radcliffe Institute for Advanced Studies at Harvard University, Cambridge, MA, USA

    Ralf S. Klessen

  9. Leibniz Supercomputing Centre of the Bavarian Academy of Sciences and Humanities, Garching, Germany

    Salvatore Cielo

Authors
  1. James R. Beattie
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  2. Christoph Federrath
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  3. Ralf S. Klessen
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  4. Salvatore Cielo
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  5. Amitava Bhattacharjee
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Contributions

J.R.B. led the entirety of the project, including the GCS large-scale project 10391, ran the simulations, co-developed the FLASH code and analysis programs used in this study and led the writing and ideas presented in the manuscript. C.F. co-led the GCS large-scale project 10391, is the lead developer of the FLASH code and the analysis pipelines used in the study and contributed to the ideas presented in this study and the drafting of the manuscript. R.S.K. co-led the GCS large-scale project 10391, and contributed to the ideas presented in this study and drafting of the manuscript. S.C. provided technical advice and assistance during the GCS large-scale project proposal and during the runtime of the simulations, provided support visualizing the large datasets and contributed to the ideas presented in this study and the drafting of the manuscript. A.B. contributed to the ideas presented in this study and the drafting of the manuscript.

Corresponding author

Correspondence to James R. Beattie.

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Supplementary Figs. 1–4.

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Beattie, J.R., Federrath, C., Klessen, R.S. et al. The spectrum of magnetized turbulence in the interstellar medium. Nat Astron 9, 1195–1205 (2025). https://doi.org/10.1038/s41550-025-02551-5

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