Simulations Reveal How Galaxies Grow Their Magnetic Fields

Galaxies are not merely vast collections of stars, gas, and dust; they are also threaded through with magnetic fields of remarkable strength and reach. Observations show that the total magnetic field in a typical galaxy amounts to around 15 microgauss, with a coherent large-scale component contributing up to a few microgauss while the remainder comes from turbulent fluctuations across a wide range of spatial scales. This magnetic energy is large enough to be dynamically significant, comparable in importance to the kinetic energy of the gas itself. Yet the question of how such fields arise, and how they shape the birth and evolution of galaxies, has long remained one of the most stubborn puzzles in astrophysics.

A major review published in Living Reviews in Computational Astrophysics by Maarit J. Korpi-Lagg, Mordecai-Mark Mac Low, and Frederick A. Gent surveys the state of the art in numerical modeling of galactic dynamos, the mechanisms by which conducting, turbulent plasma amplifies magnetic fields. The authors conclude that the evidence now strongly supports a two-stage picture. Small-scale dynamos, which amplify magnetic fluctuations on turbulent eddy timescales, operate during the formation of the first galaxies, growing fields faster than the galaxies accrete gas. Large-scale dynamos, driven by the differential rotation of galactic disks, subsequently build the organized fields observed in low-redshift spiral galaxies, bringing the field to equipartition with turbulence and giving it substantial power at the largest scales.

The theoretical framework rests on magnetohydrodynamics, which treats the magnetized interstellar plasma as a conducting continuum. The evolution of the magnetic field is governed by the induction equation, coupling the field to the velocity field, while the dynamics of the gas follow the Navier-Stokes equation including rotation, gravity, pressure, and Lorentz forces. In the interstellar medium, turbulence is driven by multiple sources: supernova explosions and their clustering into superbubbles, stellar winds and ionizing radiation, gravitational instability of the gas disk, and, especially in young galaxies, the turbulent accretion of fresh gas. Ionizing radiation delivers roughly an order of magnitude more energy than supernovae, though supernovae contribute more momentum, and the resulting multiphase structure of the gas strongly affects how dynamos operate.

Dynamo theory traditionally separates the magnetic field into mean and fluctuating components. In the kinematic regime, when the field is still too weak to influence the flow, turbulent motions correlated through rotation and shear generate a turbulent electromotive force whose leading terms are the alpha effect, describing the inductive twisting of field lines by helical turbulence, and turbulent diffusion. A long-standing concern was that this alpha effect could suffer catastrophic quenching as magnetic helicity conservation suppresses the inductive action. Modern mean-field models address this by including helicity fluxes, such as those carried by galactic fountains and winds, which allow the large-scale dynamo to saturate at the observed equipartition strengths rather than stalling far below them.

The small-scale, or fluctuation, dynamo operates differently. The interstellar medium is an extremely high magnetic Prandtl number fluid, with the ratio of magnetic to fluid resistivity estimated near ten billion billion, meaning magnetic fields dissipate on far smaller scales than the gas motions. Any flow whose magnetic Reynolds number exceeds a critical value of roughly 30 to 60 can exponentially amplify magnetic fluctuations on the turbulent eddy turnover time, far faster than the large-scale dynamo can act. Analytical theory predicts a characteristic Kazantsev spectrum for the growing field, and simulations confirm both this spectral shape and the rapid shift of magnetic power to larger scales as the dynamo saturates.

Perhaps the most striking recent result concerns seed fields. Kinetic simulations using hybrid and fully kinetic plasma models show that the Weibel instability can magnetize an initially unmagnetized turbulent plasma, and that small-scale dynamo action then amplifies those tiny fields to within a few percent of equipartition while increasing their characteristic length scale toward the turbulent driving scale. This process could operate behind the accretion shocks that form during the assembly of gas into galaxies, implying that galaxies may be born magnetized. The review’s authors argue that simulations of galaxy formation should therefore not begin with infinitesimal seed fields, since such a choice unphysically delays the onset of magnetohydrodynamic effects in galactic evolution.

At the kiloparsec scale, direct numerical experiments of supernova-driven, multiphase, rotating disks have now captured both dynamo modes simultaneously. In models resolved to parsec scales, the small-scale dynamo saturates within a few hundred megayears at only a few percent of equipartition with turbulence, a result that on its own conflicts with the observed strength of turbulent galactic fields. However, when differential rotation is included, the large-scale dynamo continues to grow after the small-scale dynamo saturates, and during the transition the turbulent field grows far more strongly than mean-field theory alone would predict, apparently through tangling of the emerging mean field. This tangling may explain why turbulent fields dominate the observed magnetic energy in real galaxies.

Global simulations of entire galaxies, including cosmological zoom-in models run with codes such as AREPO and RAMSES, reproduce the exponential growth of magnetic energy expected from the small-scale dynamo, confirmed both by growth rates and by the appearance of Kazantsev-like power spectra. In Milky Way-mass halos, magnetic pressure eventually rivals or exceeds the thermal pressure, while dwarf galaxies with shallower potentials saturate an order of magnitude lower. Synthetic observations of these models, including Faraday rotation maps and polarized synchrotron emission, now reproduce key features of the observed sky, particularly when sub-grid models of ionized regions around star clusters are included. The far-infrared radio correlation can likewise be reproduced by fully saturated small-scale dynamos coupled to cosmic ray transport.

Significant challenges remain. Numerical models still operate at magnetic Reynolds and Prandtl numbers many orders of magnitude below interstellar values, and only recently have local models reached resolutions where the small-scale dynamo growth rates converge. Measuring the turbulent transport coefficients that parameterize the large-scale dynamo, through methods such as the test-field technique, singular value decomposition, and the newer iterative removal of sources, reveals broadly consistent results but persistent discrepancies in turbulent resistivity. Whether helicity fluxes truly prevent catastrophic quenching awaits direct measurement in high Reynolds number experiments. Meanwhile, reconciling the ratio of mean to turbulent field strength between local models, which produce mean fields that are too strong, and global models, which often produce them too weak, will demand improved simulations, simulated observations, and ultimately global models that capture both dynamo modes in dwarf galaxies before scaling up to disks like our own.

Subject of Research: Numerical modeling of small-scale and large-scale dynamo mechanisms that generate and amplify magnetic fields in galaxies

Article Title: Computational approaches to modeling dynamos in galaxies

Article References: Korpi-Lagg, M. J., Mac Low, M.-M., & Gent, F. A. (2024). Computational approaches to modeling dynamos in galaxies. Living Reviews in Computational Astrophysics, 10(1), Article 3. https://doi.org/10.1007/s41115-024-00021-9

Image Credits: AI Generated

DOI: 10.1007/s41115-024-00021-9

Keywords: galactic dynamos, magnetic fields, magnetohydrodynamics, small-scale dynamo, large-scale dynamo, interstellar turbulence, supernova feedback, cosmic rays, Faraday rotation, numerical simulations, galaxy formation, magnetic helicity