[Paper Review] Galactic dynamo seeds from non-superconducting spin-polarised strings

L. C. García de Andrade|arXiv (Cornell University)|Jan 12, 2014

Solar and Space Plasma Dynamics19 references3 citations

TL;DR

This paper proposes that non-superconducting, spin-polarized cosmic strings in Einstein-Cartan-Maxwell gravity generate primordial magnetic fields via torsion and vorticity, yielding cosmological seed fields of order $10^{-22}$ G, compatible with galactic dynamo requirements. The model uses torsion-induced magnetic fields and vorticity-driven fields to reproduce observed intergalactic magnetic fields ($\sim10^{-5}$ G) without superconductivity.

ABSTRACT

Earlier Enqvist and Olesen have shown that formation of ferromagnetic planar walls in vacuum at GUT scales in comoving plasmas may generate a large scale magnetic field of $B_{now}\simeq{10^{-14}G}$. In this paper we show that starting from classical Einstein-Cartan-Maxwell strong gravity, a spin-polarised ferromagnetic cylinder gives rise to a cosmological magnetic field of the order $B_{now}\simeq{10^{-22}G}$. Vorticity of cylinder is used to obtain galactic magnetic fields. Magnetic fields up to $B\sim{10^{9}G}$ can be obtained from the spin density of the cylinder. If matching conditions are used cosmological magnetic fields of the order of $B\sim{10^{-16}R\frac{Gauss}{cm}}$ where $R$ is the radius of the cosmic strings. For a cosmic string with the radius of an hydrogen atom the cosmic magnetic field is $B\sim{10^{-32}Gauss}$ which is enough to seed galactic dynamos.

Motivation & Objective

• To investigate whether non-superconducting, spin-polarized cosmic strings can generate primordial magnetic fields sufficient to seed galactic dynamos.
• To explore the role of spacetime torsion and vorticity in magnetogenesis within Einstein-Cartan-Maxwell gravity.
• To compute magnetic fields from spin-polarized cylinders using matching conditions and vorticity, comparing results with observed intergalactic magnetic fields.
• To demonstrate that electric currents in these strings are too weak to support superconductivity, distinguishing them from previous models.
• To validate the model against observational constraints, including $B \sim 10^{-5}$ G for the intergalactic medium and $B \sim 10^{-22}$ G for dynamo seeding.

Proposed method

• Derives exact solutions of Einstein-Cartan-Maxwell (ECM) field equations for a spin-polarized cylindrical cosmic string with non-zero torsion and vorticity.
• Applies matching conditions between interior and exterior spacetime metrics in Riemann-Cartan spacetime to relate magnetic fields to string radius and spin density.
• Uses Cartan’s structure equations to compute torsion $T^i = 2k\sigma \delta^i_0 \theta^1 \wedge \theta^2$ and curvature components $R^i_j$ from connection forms $\omega^i_j$.
• Computes magnetic field via $B_z \sim \sigma$ and relates it to torsion via $B_z \sim \frac{c^3}{4\pi G}T$, using $T \sim 10^{-17} \, \text{cm}^{-1}$ from laboratory experiments.
• Evaluates vorticity-driven fields using Harrison-Rees vorticity $\Omega \sim 10^{-9} \, \text{rad/s}$, yielding $B_z \sim 10^{-5}$ G.
• Compares results with Biot-Savart law for superconducting strings to show that current is too weak for superconductivity, confirming non-conducting nature.

Experimental results

Research questions

• RQ1 Can non-superconducting spin-polarized cosmic strings generate primordial magnetic fields strong enough to seed galactic dynamos?
• RQ2 How does spacetime torsion in Einstein-Cartan-Maxwell gravity contribute to magnetic field generation in cosmic strings?
• RQ3 What is the role of vorticity in producing large-scale magnetic fields consistent with the intergalactic medium?
• RQ4 How do matching conditions in Riemann-Cartan spacetime relate the magnetic field to the radius and spin density of cosmic strings?
• RQ5 Why are these cosmic strings non-conducting despite having magnetic fields?

Key findings

• Magnetic fields of order $B_{\text{now}} \sim 10^{-22}$ G are generated via torsion in spin-polarized cosmic strings, sufficient to seed galactic dynamos.
• Using Harrison-Rees vorticity $\Omega \sim 10^{-9}$ rad/s, the model produces a magnetic field of $B_z \sim 10^{-5}$ G, matching the observed intergalactic magnetic field.
• For a cosmic string with radius equal to that of a hydrogen atom ($R \sim 10^{-8}$ cm), the magnetic field is $B \sim 10^{-32}$ G, still viable as a seed field.
• The electric current in these strings is too weak to support superconductivity, confirming they are non-conducting, unlike previous models.
• The relation $B_z \sim \frac{c^3}{4\pi G}T$ links magnetic field directly to torsion, with $T \sim 10^{-17}$ cm⁻¹ yielding $B \sim 10^{-22}$ G.
• The model reproduces observed magnetic fields using only torsion and vorticity, without requiring superconductivity or strong currents.