Galactic Dynamos

Axel Brandenburg^{1 2 3 4}& Evangelia Ntormousi^{5 6}

1Nordita, KTH Royal Institute of Technology and Stockholm University, Hannes Alfvéns väg 12, SE-10691 Stockholm, Sweden 2The Oskar Klein Centre, Department of Astronomy, Stockholm University, AlbaNova, SE-10691 Stockholm, Sweden 3McWilliams Center for Cosmology & Department of Physics, Carnegie Mellon University, Pittsburgh, PA 15213, USA 4School of Natural Sciences and Medicine, Ilia State University, 3-5 Cholokashvili Avenue, 0194 Tbilisi, Georgia 5Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa, Italy 6Institute of Astrophysics, Foundation for Research and Technology-Hellas, Vasilika Vouton, GR-70013 Heraklion, Greece

November 28, 2022 YYYY. AA:1–47 https://doi.org/10.1146/((please add article doi)) Copyright © YYYY by Annual Reviews. All rights reserved

Keywords

Spiral galaxies, Milky Way, large-scale magnetic fields, circumgalactic medium, magnetic Reynolds number

Abstract

Spiral galaxies, including the Milky Way, have large-scale magnetic fields with significant energy densities. The dominant theory attributes these magnetic fields to a large-scale dynamo. We review the current status of dynamo theory and discuss various numerical simulations designed to explain either particular aspects of the problem or to reproduce galactic magnetic fields globally. Our main conclusions can be summarized as follows.

• Idealized direct numerical simulations produce mean magnetic fields, whose saturation energy density tends to decline with increasing magnetic Reynolds number. This is still an unsolved problem.

• Large-scale galactic magnetic fields of microgauss strengths can probably only be explained if helical magnetic fields of small or moderate length scales can rapidly be ejected or destroyed.

• Small-scale dynamos are important throughout a galaxy’s life, and probably provide strong seed fields at early stages.

• The circumgalactic medium (CGM) may play an important role in driving dynamo action at small and large length scales. These interactions between the galactic disk and the CGM may provide important insights in understanding galactic dynamos.

We expect future research in galactic dynamos to focus on the cosmological history of galaxies and the interaction with the CGM as means of replacing the idealized boundary conditions used in earlier work.

Contents

1. INTRODUCTION ................................................................................................ 2 2. DYNAMOS ....................................................................................................... 3

2.1. Historical remarks ........................................................................................... 4 2.2. The need for magnetic diffusivity: the example of steady flows ......................................... 6 2.3. Dynamos in turbulent and time-dependent flows ......................................................... 8 2.4. Early examples of dynamos................................................................................. 8 2.5. Large-scale dynamos and averaging ....................................................................... 11 2.6. Types of large-scale dynamos .............................................................................. 12 2.7. Small-scale dynamos ........................................................................................ 14

3. CATASTROPHIC QUENCHING AND MAGNETIC HELICITY FLUXES .................................... 15 3.1. Catastrophic quenching for uniform magnetic fields...................................................... 15 3.2. Catastrophically slow saturation in closed domains....................................................... 15 3.3. Alleviating catastrophic quenching by magnetic helicity fluxes .......................................... 17

4. TEST-FIELD METHOD AND NONLOCALITY IN SPACE AND TIME .................................... 18 4.1. Parameterization of the mean electromotive force........................................................ 18 4.2. Mean-field coefficients ...................................................................................... 18 4.3. Methods for measuring and other effects ............................................................... 19 4.4. Using test fields ............................................................................................. 19 4.5. Nonlocality .................................................................................................. 20

5. SETTING THE SCENE FOR DYNAMO ACTION IN REAL GALAXIES .................................... 21 5.1. Possibilities for seed magnetic fields ....................................................................... 21 5.2. Dynamos from gravitational collapse and other instabilities ............................................. 27

6. GALACTIC MEAN-FIELD DYNAMOS ......................................................................... 28 6.1. Global magnetic field structure ............................................................................ 28 6.2. Dynamo models for specific galaxies ...................................................................... 29 6.3. Galactic models with magnetic helicity flux ............................................................... 29 6.4. Galactic rotation measure signature ....................................................................... 30 6.5. Synchrotron emission from mean-field models ............................................................ 31 6.6. and polarizations....................................................................................... 32

7. TURBULENCE SIMULATIONS OF GALACTIC DYNAMOS................................................. 33 7.1. Physical parameters of the ISM............................................................................ 33 7.2. Numerical approaches ...................................................................................... 34 7.3. Local dynamo simulations of galaxy portions ............................................................. 35 7.4. Global isolated galaxy simulations ......................................................................... 36

8. INTERACTION WITH THE CGM.............................................................................. 38 8.1. Magnetization of the galaxy by inflows.................................................................... 38 8.2. Magnetization of the CGM by outflows ................................................................... 40 8.3. The impact of the environment on the galactic dynamo................................................. 40

9. CONCLUSIONS .................................................................................................. 40

1. INTRODUCTION

Many spiral galaxies have microgauss magnetic fields, so that their magnetic energy densities are comparable to the thermal, kinetic, and cosmic ray energy densities; see Ruzmaikin et al. (1988) for an early book on the subject, and Shukurov & Subramanian (2022) for a recent one; hereafter SS22. Similar magnetic field strengths have also been detected in galaxies at larger redshifts up to 1 (Bernet et al. 2008, Mao et al. 2017).

Galactic magnetic fields often also show large-scale coherence. The first evidence for a global Galactic magnetic field comes from optical polarization (Hiltner 1949, Hall 1949). The existence of magnetic fields was later confirmed for other galaxies using synchrotron emission (Segalovitz et al. 1976), which showed systematic large-scale magnetic fields roughly in the direction of the galactic spiral arms. There has long been a debate about the origin of such magnetic fields: are they primordial or dynamo-generated, or perhaps a combination of the two? Over the past few decades, there has been a shift in attention from a primordial to a dynamo-generated origin. In the meantime, however, there have also been significant developments in dynamo theory, and global numerical simulations are now becoming more realistic. They tend to show that large-scale magnetic fields can be generated by a dynamo, but the amplitudes may be insufficient or the time scales for their generation too long for the simulations presented so far.

In the present review, we focus on galactic dynamos and highlight some of the main developments since the time of the review of Beck et al. (1996). The broader problem of galactic magnetism that was addressed there will not be reviewed; we refer here to other excellent reviews by Beck (2001, 2015a), Beck & Wielebinski (2013), and Han (2017), and the book by SS22. A review of astrophysical dynamos covering the era before 2005 is given by Brandenburg & Subramanian (2005a). Regarding small-scale turbulent dynamos in partially ionized plasmas, we refer to the recent review by Xu & Lazarian (2021). We also recommend the reviews by Crutcher (2012), Hennebelle & Inutsuka (2019), and Pattle et al. (2022) on ISM magnetic fields.

Large magnetic Reynolds numbers Re_{M}: magnetic induction greatly exceeds diffusion

Catastrophic

quenching: limits the large-scale field at large Re_{M}

At the time of the review by Beck et al. (1996), there were results suggesting that the dynamo effect in mean-field theory is “catastrophically” quenched, i.e., it goes to zero as the magnetic Reynolds number (Re_{M}) becomes large (Vainshtein & Cattaneo 1992, Cattaneo & Hughes 1996). Specifically, the mean-field effect in question is what is referred to as the effect, which quantifies the component of the mean electromagnetic force in the direction of the mean magnetic field. “Catastrophic” can mean that the coefficient goes to zero as Re_{M} goes to infinity. More generally, however, it means that the resulting mean (or large-scale) magnetic field cannot be generated at the expected amplitudes or time scales. This led to a major crisis in dynamo theory, questioning the possibility of an effect dynamo in the nonlinear regime beyond just infinitesimally weak kinematic dynamo-generated magnetic fields.

Although there are still unresolved questions in nonlinear dynamo theory today, there have also been major developments in this field: the importance of magnetic helicity fluxes has been recognized, mean-field dynamo coefficients can now be determined from simulations without the restrictions imposed by analytic techniques, and new dynamo mechanisms beyond just the effect have been explored. At the same time, there has been significant progress in performing realistic

Magnetic helicity: Volume-integrated dot product of magnetic vector potential A and magnetic field B, A B

three-dimensional (3-D) magnetohydrodynamic (MHD) simulations of galaxy formation, allowing a new theoretical view of the problem, where the circumgalactic medium (CGM) plays an integral part. All these developments motivate a new review on galactic dynamos.

2. DYNAMOS

We begin by discussing historical and theoretical aspects of MHD and dynamos that are of particular importance in connection with the new developments in galactic dynamo research over the past few decades. The presence of a microphysical magnetic diffusivity plays here an important role. We begin with a historical perspective.

www.annualreviews.org ^{•} Galactic Dynamos 3

Observational tracers of galactic magnetic fields

Dust extinction / emission polarization. Elongated dust grains in the interstellar medium tend to align their minor axes with the mean magnetic field direction (Davis & Greenstein 1951). As a result, the light they emit in infrared wavelengths is polarized, with the polarization direction perpendicular to the mean direction of the magnetic field. Only recently has it been possible to trace extragalactic magnetic fields with this method (e.g.,the recent survey by Lopez-Rodriguez et al. 2022).

Since starlight emission is unpolarized, we can also measure dust polarization in absorption against stellar sources. If the distances to the stars are known, it is possible to map the magnetic field at different locations along the line-of-sight (e.g., the PASIPHAE survey, Tassis et al. 2018).

Synchrotron emission. Ultra-relativistic cosmic ray particles emit polarized synchrotron radiation in radio wavelengths as they gyrate around the galactic magnetic field. Synchrotron emission, which yields the plane-of-the-sky magnetic field component in the warm/hot ISM, has been the tracer of choice for studying extragalactic magnetic fields (see, e.g., Beck 2012, for a review).

In general, linear polarization is measured through the Stokes parameters , , and . Then the observed polarization angle is calculated from the expression

\frac{1}{2} arctan \frac{}{}1.

and the polarization fraction is \overline{^{2} ^{2}} / .

Faraday Rotation. When polarized radiation passes through an ionized magnetized medium, the plane of polarization is rotated by an angle ^{2}, where is the observed wavelength and

0 81 _{0}^{}_{}_{}2.

is in units of radians/ ^{2}. Here, is the distance to the source in pc, _{e} is the electron density in cm^{3} , and _{}is the line-of-sight magnetic field of the medium in microgauss (Burn 1966, Brentjens & de Bruyn 2005). If we have an estimate of the electron density, then Faraday rotation can yield the line-of-sight magnetic field.

2.1. Historical remarks

In Section 6 we will discuss the observational signatures of dynamo models in detail. Here, we will only briefly mention some observational results that were significant for the development of dynamo models. For later reference, we provide here a short overview of the existing galactic magnetic field tracers in the text box on “Observational tracers of galactic magnetic fields”.

In the late 1970s, synchrotron radiation from external spiral galaxies began to reveal the presence of large-scale ordered magnetic fields broadly aligned with the galactic spiral pattern. At the time, an obvious possibility was that these magnetic fields were the result of winding up a preexisting, large-scale field. This idea goes back to Piddington (1964) and Ôki et al. (1964), and is now commonly referred to as primordial origin of the magnetic field. The resulting magnetic field is then expected to have the form of a bisymmetric spiral (BSS). The BSS form has a characteristic