Magnetic field amplification and decay in cosmic string wakes

TL;DR

This work investigates how magnetic fields evolve in magnetized plasmas flowing around a moving cosmic string, combining analytical insights based on flux freezing and Zel'dovich-type deformation with 2D OpenMHD simulations. It identifies a clear lengthscale-dependent dichotomy: magnetic fields are amplified when perturbation scales exceed the charged-particle gyroradius, with $\frac{B^{fin}}{B^{ini}}$ related to the deformation tensor as $\frac{B^{fin}}{B^{ini}} = \frac{1}{(1 + D_{12})^{1/2}}$ and $B \propto \rho^{1/2}$, whereas perturbations at or below the gyroradius lead to breakdown of Alfven's theorem and field decay. The transition lengthscale is tied to the gyroradius $r_g = \frac{m u_0}{q B} = \frac{u_0}{\omega_B}$, signaling non-ideal effects and potential magnetic reconnection in the wake. These results have implications for electromagnetic signatures in cosmic string wakes (e.g., synchrotron radiation, GRBs) and highlight how microphysical plasma scales govern cosmological magnetic-field evolution.

Abstract

We do a detailed study on vortex formation in a magnetized plasma within the spacetime of a moving cosmic string using analytical and numerical methods. The conical spacetime around the cosmic string causes the frozen-in magnetic field to deform due to the fluid flow. We find that the overdensity in the wake region amplifies the magnetic field. This amplification depends on the direction and the lengthscale of the magnetic perturbations. Alfvens theorem of flux conservation explains this result. However, our study also shows that the magnetic field can decay depending on the perturbation lengthscale, due to the breakdown of Alfvens theorem at a certain lengthscale. This lengthscale is the gyroradius of the charged particles in the plasma. Our findings are significant for understanding magnetic reconnection in cosmic string wakes.

Figures (7)

• Figure 1: Evolution of the magnetic field energy in the cosmic string wake for a value $\alpha_1 = 0.01$. The magnetic field energy is given in scaled units and hence is dimensionless
• Figure 2: Evolution of the peak value of the magnetic field in the cosmic string wake. The value after a few time steps is five times the initial value of the magnetic field. The magnetic field is given in scaled units and hence is dimensionless.
• Figure 3: The figure representing the deformation of the magnetic field lines in a fluid flowing around a cosmic string. The point at which the axes $dq_1$ and $dq_2$ meet is the place at which the cosmic string is placed.
• Figure 4: Evolution of the magnetic field energy in the cosmic string wake for a value $\alpha_2 = 0.01$.
• Figure 5: Evolution of the peak value of the magnetic field in the cosmic string wake. The value saturates to about five times the initial value even in this case.