The origin of magnetic fields

Introduction

Magnetic fields are ubiquitous in astrophysics, and have been observed on almost every scale from stars and planets to the interstellar medium in galaxies up to even galaxy clusters. One can distinguish two main scenarios for their origin: the primordial scenario, where magnetic fields form even before the recombination epoch, as well as the astrophysical scenario, where magnetic fields build up during structure formation, as a result of astrophysical processes.

Our understanding of both scenarios has evolved considerably during the last decades, and, while primordial fields are certainly constrained from observations of the Planck satellite, there is a wealth of primordial formation mechanisms that are able to produce at least a weak field (see e.g. the still excellent review by Grasso & Rubinstein (2001)). It should thus be generally emphasized that both scenarios are not mutually exclusive, as the presence of a primordial field does not rule out subsequent amplification, and the presence of astrophysical generation mechanisms does not mean that there was no primordial field before.

In the following, we will predominantly focus on the origin of astrophysical magnetic fields and their efficient amplification. As it was shown over the last series of years, the latter can be highly efficient, leading to strong magnetic fields at early times, which helps us to understand the high radio fluxes observed at high redshift (e.g. Ivison et al. 2010). In the following, we will introduce the amplification mechanism, and subsequently discuss its relevance during the formation of the first stars, black holes, in high-redshift galaxies and during galaxy mergers. A nice example for an observed magnetic field structure in the M 51 galaxy is given below:

Fig. 1: Magnetic field structure in M 51, using data from the Very Large Array and the Effelsberg telescope (background: HST image). Credit: R. Beck & A. Fletcher.

The amplification of magnetic fields

A weak magnetic seed field can be generated through many different processes. In addition to the primordial formation mechanisms mentioned above, the Biermann battery effect can produce weak seed fields due to the relative motion between ions and electrons. Also plasma instabilities can strongly contribute to the generation of magnetic fields, and particularly good candidates are currently the spontaneously emitted collective aperiodic field fluctuations described by Schlickeiser & Felten (2013). For a review on the astrophysical generation mechanisms, we refer here to the review by Ryu et al. (2012).

Assuming such a weak field is in place, a very efficient mechanism to amplify the magnetic field is the small-scale dynamo. This mechanism was initially described by Kazantsev (1968), originally under the assumption of an incompressible gas, assuming spatially homogeneous Kolmogorov turbulence. A sketch of the so-called twist-stretch-fold mechanism due to the turbulent motions is given below:

Fig. 2: A sketch of the small-scale turbulent dynamo for magnetic field amplification (courtesy: Jennifer Schober).

In the kinematic regime, this dynamo leads to an exponential growth of the magnetic field, on timescales corresponding to the eddy-turnover time on the resistive scale. When saturation occurs on that scale, amplification continues on the next-higher scales with their respective eddy-turnover times. As a result, one finds a power-law type amplification in the non-linear regime (e.g. Schekochihin et al. 2002).

While the original investigations assumed incompressible Kolmogorov-type turbulence, it has subsequently been shown that the small-scale dynamo can operate also under highly compressible conditions with supersonic turbulence, implying a steeper turbulent spectrum. The latter is indeed essential, as astrophysical turbulence for instance in the interstellar medium of galaxies is highly supersonic. Using numerical simulations, we have confirmed the efficient, exponential growth of magnetic fields for a large range of different Mach numbers:

Fig. 3: Exponential growth of magnetic fields for a large range of turbulent Mach numbers (Federrath et al. 2011).

The corresponding density structure is given below for a case with a particularly high turbulent Mach number, comparing both compressive and solenoidal driving. The solenoidal driving generally leads to a more volume filling field, while in case of compressive driving, both the gas and the magnetic field is concentrated into filaments.

Fig. 4: Density structure at Mach 10 for both compressible and solenoidal driving (Federrath et al. 2011).

The applicability of the small-scale dynamo in compressible situations has not only been confirmed via numerical simulations, but also via analytic theory. Particularly relevant are the investigations by Schober et al. (2012) and Bovino et al. (2013) in the kinematic regime, and the extension by Schleicher et al. (2013) to the non-linear regime.

It should however be emphasized that, while these investigations have shown that efficient amplification is possible at early times, the magnetic field generated by this dynamo will be tangled on the driving scale of turbulence. To produce a large-scale magnetic field, an Alpha-Omega dynamo is needed, where rotation twists the field in the azimuthal direction, while turbulence produces a poloidal component. It is the interaction between these two processes which then regularly amplifies the magnetic field.
Fig. 5: Sketch of the Alpha-Omega dynamo for the generation of large-scale magnetic fields.

Magnetic field amplification during high-redshift star formation

The studies mentioned so far have still explored the dynamo under relatively idealized conditions, assuming homogeneous isotropic turbulence. In astrophysics, this will usually not be the case, and it is likely that the dynamo has to operate simultaneously with other processes. We consider here in particular the possibility to drive the dynamo in a situation of gravitational collapse, as it will for instance occur during primordial star formation.

For this purpose, we have investigated the collapse in a turbulent weakly magnetized cloud. A typical situation during the collapse therefore looks like the following:

Fig. 6: Density and magnetic field structure in a turbulent collapsing cloud (Sur et al. 2010). As turbulence is typically underresolved in astrophysical simulations, the turbulent dynamo only kicks in once a critical resolution is reached. We find this resolution to correspond to about 34-64 cells per Jeans length. We have therefore systematically varied the resolution per Jeans length to test the conditions for the dynamo to occur. Correcting for the expected amplification due to gravitational compression, our result is the following:

Fig. 7: Magnetic field amplification during collapse for different resolutions per Jeans length (Sur et al. 2010).

We note that a lot of additional analysis on this case has been done by Christoph Federrath, including movies, and we refer therefore to his website for more information.

The amplification mechanism envisioned here works not only during an idealized collapse, but also in real cosmological halos, including realistic prescriptions for the cooling. This is clearly shown for instance in the following cosmological magneto-hydrodynamics simulation, where we explore the formation of a dark matter halo with about 10.000.000 solar masses, with a gas cooling through atomic hydrogen lines. Also here, once the critical resolution is reached (here slightly higher due to a more dissipative numerical scheme), the magnetic field is amplified significantly and becomes volume filling.

Fig. 8: Magnetic field strength in the central 4000 AU of a recently formed dark matter halo, for different resolutions per Jeans length (Latif et al. 2013).

The need for a high resolution in these simulations stemps from the fact that turbulence is usually underresolved in numerical simulations, and especially the turbulent cascade and the resistive scales are not explicitly modeled. Convergence is expected to occur when including these scales in the simulations, for instance via an enhanced magnetic resistivity. We have checked that in this case the results are indeed converging.

Magnetic fields and the far-infrared - radio correlation

The turbulent amplification of magnetic fields is not only important at high redshift, but also in present-day galaxies, where the small-scale turbulent component is typically stronger by at least a factor of 3 compared to the large-scale component. The radio emission produced by the cosmic-radios is therefore predominantly created by the tangled component. Combining the Kennicutt-Schmidt relation for star formation in galaxies with a model for turbulent energy injection by supernovae as well as the saturation values of the small-scale dynamo, one can show that the magnetic field will approximately scale with the star formation surface density to the power 1/3 (Schleicher & Beck 2013). Such a relation naturally gives rise to the far-infrared - radio correlation, with the far-infrared emission being produced by the reprocessed light from recently formed massive stars, while the radio emission is synchrotron emission of cosmic rays in the galactic magnetic field.

A quantitative comparison has been pursued by Schober et al. (2016), developing a detailed modeled for the far-infrared - radio correlation and comparing this with detailed observations by Yun et al. (2001) of local galaxies:
Fig. 9: Comparison of the far-infrared - radio correlation observed by Yun et al. (2001) with detailed models (Schober et al. 2016).

Magnetic fields in galaxy mergers

As significant amounts of turbulence are produced during mergers of galaxies, this provides another interesting case to explore the evolution of magnetic fields. Using simplified toy models based on the merger of two gaseous magnetized rotating disks, it is straightforward to show that for many different configurations a peak in the spatially averaged magnetic field strength will naturally occur, as described in the observational sample by Drzazga et al. (2012):

Fig. 10: Occurence of a peak in the spatially averaged magnetic field strength during the merger (Rodenbeck & Schleicher 2016).