Origin of Cosmic Magnetic Fields: From Small Random Aperiodic to Ordered Large-Scale Structures
Institut für Theoretische Physik, Lehrstuhl IV: Weltraum- und Astrophysik, Ruhr-Universität Bochum, Germany
Research Department: Plasmas with Complex Interactions, Ruhr-Universität Bochum, Germany.
Magnets have practically become everyday objects. Permanent ferromagnetism is a property of only a few densely packed materials, such as iron, in which the spin exchange interactions of individual atoms naturally line up in the same direction and create a residual persistent magnetic field. In the early universe, before iron and other magnetic materials had been created inside stars, such permanent magnetism did not exist.
Scientists have long wondered[1,2] where the observed cosmic magnetization came from, given that the fully ionized gas of the early universe contained no ferromagnetic particles. Many astrophysicists believe that galactic magnetic fields are generated and maintained by dynamo action[3,4], whereby the energy associated with the differential rotation of spiral galaxies is converted into magnetic field energy. However, the dynamo mechanism is only a means of amplification and dynamos require seed magnetic fields. Neither the dynamo process nor plasma instabilities generate magnetic fields out of nothing: they need finite seed fields to start from.
Before the formation of the first stars, the luminous proto-interstellar matter consisted only of a fully ionised gas of protons, electrons, helium nuclei and lithium nuclei which were produced during the Big Bang. The physical parameters that describe the state of this gas are, however, not constant. Density and pressure fluctuate around certain mean values, and consequently electric and magnetic fields fluctuate around vanishing mean values. This small but finite dispersion in the form of random magnetic fields has now been calculated, specifically for the proto-interstellar gas densities and temperatures that occurred in the plasmas of the early universe at redshifts z=4-7 of the reionization epoch, when something, probably the light from the first stars, provided the energy needed to break up the previously neutral gas that existed in the universe. The protons and electrons inside the plasma would have moved around continuously, simply by virtue of existing at a finite temperature. It is the finite variance of the resulting magnetic fluctuations, that subsequently led to the creation of a stronger magnetism across the universe.
There have been alternative proposals for cosmic seed magnetic fields. Indeed, as far back as 1950 the German astronomer Ludwig Biermann proposed that the centrifugal force generated in a rotating plasma cloud will separate out heavier protons from lighter electrons, thereby creating a separation of charge that leads to tiny electric and magnetic fields. However, this scheme suffers from a lack of suitable rotating objects everywhere, meaning that it could only ever generate the magnetic fields in a small portion of the medium.
To work out the field-strength variance of the fluctuations, Schlickeiser used a theory developed together with Peter Yoon of the University of Maryland. The fluctuations are aperiodic, which means that, unlike the variations in magnetic and electric fields that give rise to electromagnetic radiation, they do not propagate as a wave. Indeed, their wavelength, the spatial distance over which the fluctuations occur, and their frequency, dictating how long these fluctuations last, are uncorrelated, in contrast to light, for which the values of wavelength and frequency are tied to one another via the wave's velocity. Summed over all possible wavelengths and frequencies for the magnetic fluctuations in a gas at 10,000 K, which would have been roughly the temperature of the proto-interstellar medium at the time of reionization. The calculation revealed magnetic fields variances of about 10-16 Tesla inside very early-stage galaxies and around about 10-25 Tesla in the voids between the protogalaxies. These values compare with the roughly 30 millionths of a Tesla of the Earth's magnetic field and 0.01 Tesla typical of a strong refrigerator magnet. The magnetic field in the plasma of the early universe was thus very weak, but it covered almost 100 percent of the plasma volume. Being so weak it could serve providing the seeds of primordial magnetic fields. The seed fields are tied passively to the highly conducting proto-interstellar plasma as frozen-in magnetic fluxes.
Figure 1: Illustration of the hydrodynamical stretching and ordering of cosmic magnetic fields. On the left figure a turbulent random magnetic field pervades the medium between five protostars. The right figure shows the ordering and stretching of the magnetic field as one of the stars explodes as a supernova. The outgoing shock wave compresses and orders the magnetic field in its vicinity [Image courtesy: Stefan Artmann].
Earlier analytical considerations and numerical simulations[9-12] showed that any shear and/or compression of the proto-interstellar medium not only amplifies these seed magnetic fields, but also make them anisotropic. Considering a cube containing an initially isotropic magnetic field, which is compressed to a factor η ≪ 1 times its original length along one axis, these authors showed that the perpendicular magnetic field components are enhanced by the factor &eta-1. Depending on the specific exerted compression and/or shear, even one-dimensional ordered magnetic field structures can be generated out of the original isotropically tangled field configuration.
Hydrodynamical compression or shearing of the IGM medium arises from the shock waves of the supernova explosions of the first stars at the end of their lifetime, or from supersonic stellar and galactic winds. Fig. 1 sketches the basic physical process. The seed magnetic field upstream of these shocks is random in direction, and by solving the hydrodynamical shock structure equations for oblique and conical shocks it has been demonstrated, that the shock compression enhances the downstream magnetic field component parallel to the shock, but leaving the magnetic field component normal to the shock unaltered.
Consequently, a more ordered downstream magnetic field structure results from the randomly oriented upstream field. Such stretching and ordering of initially turbulent magnetic fields is also seen in the numerical hydrodynamical simulations of supersonic jets in radio galaxies and quasars. Obviously, this magnetic field stretching and ordering occurs only in gas regions overrun frequently by shocks and winds. Each individual shock or wind (with speed Vs compression orders the field on spatial scales R on time scales given by the short shock crossing time R/Vs, but signifant amplification requires multiple compressions. The ordered magnetic field filling factor is determined by the shock's and wind's filling factors which are large (80 percent) in the coronal phase of interstellar media and near shock waves in large-scale cosmic structures.
In cosmic regions with high shock/wind activity, this passive hydrodynamical amplification and stretching of magnetic fields continues until the magnetic restoring forces affect the gas dynamics, i.e. at ordered plasma betas near unity. As a consequence, magnetic fields with equipartition strength are not generated uniformly over the whole universe by this process, but only in localized cosmic regions with high shock/wind activity.
In protogalaxies significant and rapid amplification of the spontaneously emitted aperiodic turbulent magnetic fields results from the small-scale kinetic dynamo process[16,17] generated by the gravitational infall motions during the formation of the first stars[18-20]. Additional gaseous spiral motion may stretch and order the magnetic field on large protogalactic spatial scales.
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