Nearby spiral galaxies carry coherent (regular) magnetic fields of order a microgauss on kiloparsec scales, usually attributed to a mean-field dynamo acting on a much weaker seed. Sokoloff and Moss (2013) showed with thin-disc 'no-z' dynamo computations that a quasi-homogeneous cosmological seed field is a poor dynamo seed: such a seed contains only the slowly growing bisymmetric azimuthal mode, and with conventional estimates of the dynamo numbers the field decays for roughly the age of the Universe before any growth, unless the dynamo number is substantially larger (about Rω≃20R_{\omega}\simeq20 instead of ≃10\simeq10). The open problem is to decide, with physically grounded models and observations, whether the homogeneous cosmological-seed scenario can be rescued: whether very young galaxies plausibly have dynamo numbers large enough, whether turbulence or dynamical instabilities can distort a homogeneous field into a nonzero axisymmetric (m=0m=0) seed component fast enough for the dynamo to exploit, whether such a seed can form and survive from the early Universe until galaxy formation, and what quantitative radio diagnostics (LOFAR/SKA-class rotation measures) could distinguish this scenario from astrophysical seeding. Later reviews and simulations have largely bypassed rather than resolved these questions, favoring seeding by the small-scale dynamo, so the precise core remains open.

Background

Spiral galaxies are magnetized: the total interstellar magnetic field is of order 10 microgauss, and a coherent component of order a microgauss is ordered on scales of several kiloparsecs, as revealed by radio synchrotron emission and its polarization and by Faraday rotation of polarized background sources (rotation measure, RM, is the wavelength-squared-normalized rotation of the polarization plane, proportional to the line-of-sight integral of the electron density times the magnetic field). The standard explanation is a mean-field dynamo: interstellar turbulence, twisted by the galaxy's rotation (the alpha-effect, which converts toroidal into poloidal field via the helicity of Coriolis-forced turbulence) combined with differential rotation (the Omega-effect, which shears poloidal into toroidal field), amplifies the large-scale magnetic field against turbulent magnetic diffusion with diffusivity η\eta. In the thin-disc, alpha-Omega formulation the control parameters are the dynamo numbers Rα=α0R/ηR_{\alpha}=\alpha_{0}R/\eta and Rω=Ω0R2/ηR_{\omega}=\Omega_{0}R^{2}/\eta (with RR the disc radius, hh its semi-thickness, α0\alpha_{0} a typical alpha-coefficient and Ω0\Omega_{0} a typical angular velocity); their product D=RαRωD=R_{\alpha}R_{\omega} measures the strength of dynamo action, and contemporary spiral galaxies give Rα∼1R_{\alpha}\sim1, Rω∼10R_{\omega}\sim10 with large uncertainty. A widely used 'no-z' approximation replaces vertical derivatives by algebraic factors ∼1/h2\sim1/h^{2}, which is cheap but cannot represent field components parallel to the rotation axis of dipolar mid-plane parity, galactic winds, or turbulent diamagnetism, and it enforces even (quadrupolar) parity with respect to the galactic mid-plane. Decomposing the field in azimuthal Fourier modes, the axisymmetric mode m=0m=0 has the largest growth rate in a disc dynamo, while the bisymmetric mode m=1m=1 (one full magnetic reversal around the azimuth) grows more slowly because of its extra spatial structure. The dynamo only amplifies an existing field, so a seed is needed. One route is a weak battery-generated field amplified by the small-scale (fluctuation) dynamo — random, turbulence-driven stretching unrelated to the mean field — up to a fraction of equipartition with the turbulent energy, which then seeds the mean-field dynamo. The other route is a relic field created in the early Universe (a 'cosmological' or primordial seed) that survives until galaxy formation; gamma-ray observations even suggest weak intergalactic fields exist, and the source paper recalls the old idea of a strictly homogeneous field present from the Big Bang. That route requires the field to be strong enough, to have sufficient spatial coherence, and to survive damping between recombination and galaxy formation. Sokoloff and Moss (2013) tested the simplest version — a field homogeneous on the scale of the young galaxy — with a no-z thin-disc code. A uniform field lying in the disc plane is a pure m=1m=1 mode: differential rotation winds it up, but instead of growing it decays for about 14 dimensionless time units (the unit h2/ηh^{2}/\eta is about 0.78 Gyr, so this is roughly 11 Gyr, comparable to the age of the Universe), with the eventual growth coming only from numerical noise seeding the m=0m=0 mode. Growth from a homogeneous seed within a Hubble time requires substantially larger dynamo numbers, roughly Rω≃20R_{\omega}\simeq20 at Rα≃0.8R_{\alpha}\simeq0.8--11, well above conventional contemporary-galaxy estimates. The authors conclude that a quasi-uniform cosmological seed is a much worse dynamo seed than widely believed, but they explicitly do not exclude cosmological seeds: early galaxies might have larger dynamo numbers, and turbulence or dynamical instabilities might distort a homogeneous field, generating the m=0m=0 component that the dynamo can then amplify — the two rescue mechanisms their model cannot evaluate.

Problem Statement

Decide whether a large-scale quasi-homogeneous cosmological magnetic field can serve as the seed from which the galactic mean-field dynamo produces the observed microgauss coherent fields within the age of the Universe. The components of this single viability question are: (1) determine whether physically plausible conditions in very young galaxies yield dynamo numbers substantially larger than conventional contemporary-galaxy estimates (i.e., RωR_{\omega} of order 20 rather than of order 10), such that even a purely bisymmetric (m=1m=1) homogeneous seed is amplified to saturation within a Hubble time; (2) quantify the mechanisms and efficiency by which small-scale turbulence or dynamical instabilities distort a homogeneous cosmological field, establishing whether they generate a nonzero axisymmetric (m=0m=0) seed component rapidly and robustly enough during early galactic evolution for the faster-growing m=0m=0 dynamo mode to take over; (3) verify that the conclusions survive relaxing the no-z thin-disc model's acknowledged limitations — the untreated dipolar component parallel to the rotation axis, galactic winds, turbulent diamagnetism, and the enforced even mid-plane parity — with more general dynamo models; (4) establish whether a cosmological seed field of the required strength and coherence can be produced in the early Universe and can survive damping between recombination and galaxy formation; and (5) formulate quantitative observational discriminants (for facilities such as LOFAR, the Low-Frequency Array, and SKA, the Square Kilometre Array, principally via rotation-measure surveys) that can distinguish the homogeneous cosmological-seed scenario from astrophysical seeding by battery plus small-scale dynamo. The unresolved core posed by Sokoloff and Moss (2013) consists of the two rescue mechanisms their no-z model cannot evaluate, components (1) and (2), together with the observational tests of component (5) that they intended to formulate; component (3) is a robustness check on the no-z model's acknowledged caveats (the source paper cites existing results showing the preference for quadrupolar parity persists under galactic winds and turbulent diamagnetism, and argues that large-scale homogeneous seeds are inefficient whatever their orientation), and component (4) is a cosmological precondition of the scenario, whose origin the source paper explicitly does not itself consider. All five components are required for a complete answer: components (1), (2) and (3) jointly establish the physically grounded verdict — viable or not, under stated and justified early-galaxy conditions — component (4) settles the cosmological precondition that a seed of the required strength and coherence can be produced and survive to galaxy formation, and component (5) supplies the observable signatures that would confirm or exclude the scenario.

References

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