Magnetic Fields in Cosmology

The existence of magnetic fields on cosmologically large scales is an unsolved problem in astrophysics. Theory favors a universe that did not begin with any magnetic fields present and classical magnetohydrodynamics restricts the spontaneous emergence of a magnetic state under the influence of ideal forces. In a paper entitled Twisting Space-Time: Relativistic Origin of Seed Magnetic Field and Vorticity appearing Physical Review letters Swadesh Mahajan and Zensho Yoshida propose a universal magnetic field generating effect using ideal special relativistic fluid dynamics. Mahajan and Yoshida's insight was that in describing magnetic fields, which are mathematically equivalent to a vorticity, a careful application of ideal dynamics in the framework of distortions caused by special relativity may result in the spontaneous emergence of a magnetic state in contrast to the previous theoretical result.

Magnetic fields are found to be important in every scale hierarchy of the universe. Most notably detailed images of galaxies paradoxically display regions of chaotic turbulence and beautiful grand coherent designs at once. Thus it is clear that turbulent motion on scales below hundreds of parsecs does not necessarily destroy coherent optical or magnetic features over scales of kiloparsecs. Indeed, magnetic fields are indirectly observed at optical and radio wavelengths by detecting the polarization of the electromagnetic field through the Faraday effect and also by the Zeeman splitting effect. The Faraday effect is the rotation of the linear polarization vector of light which occurs when polarized radiation passes through a magnetized and ionized medium. Radio observations are the most powerful technique and by measuring both the dispersion and polarization rotation the mean of the magnetic field along the line of sight can be measured. Such observations indicate a wide range of magnetic field are present in astrophysics. The image at right below shows the magnetic fields present in M51 which are likely similar in structure and strength to that of the Milky Way.

The total radio continuum emission from the "whirlpool" galaxy M51 (distance estimates range between 13 and 30 million light years) is strongest at the inner edges of the optical spiral arms, probably due to the compression of magnetic fields by density waves. The vectors give the orientations of the regular magnetic fields as derived from the polarized emission. The field lines follow nicely the optical spiral arms. Unexpectedly, strong polarized emission is observed also between the optical arms which indicates the action of a dynamo. This image was observed with the VLA in its most compact configuration at 6cm radio wavelength (broadband continuum). As the VLA cannot detect the diffuse, large-scale radio emission, data from the Effelsberg 100-m telescope in Germany at the same wavelength was added. Investigator(s):  Rainer Beck (MPIfR Bonn, Germany), Cathy Horellou (Onsala Space Observatory). Image courtesy of NRAO/AUI

Microguass fields are present in galaxies at scales of a few kiloparsecs and on the much larger scales of megaparsecs ordered fields of perhaps a few orders of magnitude less are present in galaxy clusters. Magnetic fields in astronomy are controlled by induction of partially ionized gas. A common model for creating these magnetic fields is the dynamo effect wherein an electrically conductive fluid accelerated by some kinetic force generates convective motions in the fluid; it is plausible that a turbulent hydromagnetic dynamo of some kind coupled to an inverse cascade of magnetic energy wold give rise to regular galactic magnetic fields. Following the basic dynamo theory magnetic field lines can be simulated for galaxies which are consistent with observations. The dynamo theory is actually a mechanism for maintaining or growing fields rather than creating them, but it is expected that minuscule primordial magnetic field seeds in the early universe of cosmological origin drive the magnetic fields observed today.

The magnetic dynamo and the primordial magnetic seed theories are both unsatisfactory. The model wherein the the large scale magnetic field in galaxies is the result of the twisting of a cosmological magnetic fields by galactic differential rotation is not satisfactory because a primordial field wound up by differential rotation ultimately decays in an effect known as flux expulsion. The primordial seed theory must explain the presence of large magnetic fields in higher redshift objects when the universe was much younger when the fields should not have had sufficient time to grow. Researchers disagree over what initial primordial field strength is necessary to create the magnetic fields seen today; estimates vary from as large as 10^-9 gauss [1] to 10^-30 gauss [2], but either way an alternative model would be welcome.

Mahajan and Yoshida's work was motivated by the search for a universal mechanism for magnetic field generation. They key to creating a magnetic field is the vorticity of an ionized material which is analyzed in this paper with topological constraints. In mathematical terms fundamental cosmology requires a topological constraint on the vorticity of the universe (consider that you wouldn't expect the universe to have a preferred rotation), however this constraint can be broken by the application of special relativity. The problem of magnetic fields lies in the fact that vorticity must vanish for every ideal force such as the entropy conserving thermodynamic forces (this can be proven though the governing Hamiltonian dynamics of an ideal fluid where ultimately Kelvin's circulation theorem shows that if the initial state has no circulation the later sate will also be vorticity-free). Introduction of the Lorentz factor γ=(1-(v/c)²)^-1/2 from special relativity destroys the exactness of the ideal thermodynamic force and allows spontaneous vorticity.

The authors find a new term that provides a magnetic field growing mechanism as long as the kinetic energy is inhomogeneous. The authors mechanism can provide a finite seed for even mildly relativistic flows. They provide an example for very standard parameters (electron density n=10¹⁰ cm³, temperature T= 20 eV and velocity, v, compared to c of v/c=10^-2) and find their relativistic drive mechanism remains dominate over other effects until magnetic fields of 1 gauss or so which is much larger than most magnetic fields ever observed, thus the relativistic drive is the only dominant effect. The relativistic drive mechanism will likely help us understand, among other things, the origin of magnetic fields in astrophysical and cosmic settings.

References:

[1] Beck, R., Brandenburg, A., Moss, D., Shukurov, A., & Sokoloff, D. (1996). GALACTIC MAGNETISM: Recent Developments and Perspectives Annual Review of Astronomy and Astrophysics, 34 (1), 155-206 DOI: 10.1146/annurev.astro.34.1.155

[2] Davis, A., Lilley, M., & Törnkvist, O. (1999). Relaxing the bounds on primordial magnetic seed fields Physical Review D, 60 (2) DOI: 10.1103/PhysRevD.60.021301

[3] Mahajan, S., & Yoshida, Z. (2010). Twisting Space-Time: Relativistic Origin of Seed Magnetic Field and Vorticity Physical Review Letters, 105 (9) DOI: 10.1103/PhysRevLett.105.095005