Imprints of primordial magnetic fields on the late-time Universe

Abstract

Primordial magnetic fields (PMFs) generated in the early Universe may leave observable imprints in the present-day large-scale structure. However, it remains unclear on which spatial scales primordial signatures can survive the nonlinear processes accompanying structure formation. The aim of this study is to investigate the evolution of PMFs during gravitational collapse and to determine the spatial scales on which primordial signatures can persist. We perform a suite of high-resolution direct numerical simulations of self-gravitating, magnetized halos. By varying the viscosity, we probe different Reynolds-number regimes and follow the coupled evolution of gravitational collapse and magnetohydrodynamic turbulence. At sufficiently high Reynolds numbers, turbulence generated during collapse triggers the onset of a small-scale dynamo, which amplifies magnetic energy below the Jeans scale and modifies the magnetic energy spectrum significantly. Whether dynamo amplification dominates the magnetic field evolution is determined by the competition between the dynamo growth time and the free-fall time. Our results highlight the importance of resolving the Jeans scale and the associated turbulent inertial range in cosmological MHD simulations to accurately capture the interplay between gravitational compression and dynamo amplification and to assess which structures retain memory of primordial fields.

Figures (14)

• Figure 1: Slices of the $x$--$z$ plane at $y=0$ of different quantities in Run H2b: On the top row the logarithm of the density is shown, on the middle row the rms velocity, and on the bottom row the rms magnetic field. Slices from left to right are taken at different times: from the initial setup ($t/t_\mathrm{ff,0}=0$) to later times ($t/t_\mathrm{ff,0}=0.86, 1.71, 2.57$).
• Figure 2: Analysis of the evolution of radial profiles in Run H2b. The panels show the radial profiles of the averaged density in a sphere within radius $r$ (top), the radial velocity $v_r$ and velocity dispersion $\sigma_v$ (middle), and the rms magnetic field strength (bottom). Thin vertical lines indicate the Jeans radius at different times. Time is encoded by line color, as indicated by the color bar at the top of the figure.
• Figure 3: Analysis of the time evolution of volume-averaged quantities in Run H2b. The top panel shows the mass density, averaged over the entire simulation domain $\langle \rho \rangle$ (dashed blue line) and the density averaged over the instantaneous Jeans volume $\langle \rho \rangle_\mathrm{J}$ (solid orange line). The middle panel shows quantities related to the velocity field. In particular, the rms velocity $U_\mathrm{rms}$ (solid blue line), the maximum value of the radial velocity $v_{r,\mathrm{max}}$ (dashed purple line), and the velocity dispersion averaged over the box $\langle\sigma_{v}\rangle$ (dashed-dotted magenta line). Also shown are the rms magnetic field $B_\mathrm{rms}$ (solid orange line) and the Reynolds number $\mathrm{Re}$ (dotted red line). In the bottom panel, the evolution of the resistive wavenumber $k_{\eta}$ (dashed blue line) and the Jeans wavenumber $k_{\mathrm{J}}$ are plotted. Gray-shaded regions mark wavenumbers that lie outside the range captured by the resolution of the simulation.
• Figure 4: Energy spectra for Run H2b. Top: Density spectra. Bottom: Kinetic energy spectra (blue). Magnetic energy spectra (red). Solid circles indicate the (time-dependent) position of the Jeans wavenumber $k_\mathrm{J}$ and open circles indicate the (time-dependent) position of the viscous wavenumber $k_\nu$, which is the same as the resistive wavenumber $k_\eta$. Both $k_\nu$ and $k_\eta$, are marginally resolved in this run.
• Figure 5: Analysis of quantities related to the dynamo instability for Run H2b. In the top panel, the evolution of the free-fall time is compared to the inverse of the measured growth rate of $B_\mathrm{rms}$ ($\gamma_\mathrm{DNS}$) and different theoretically predicted growth rates ($\gamma_{1/3}$, $\gamma_{0.43}$, and $\gamma_{1/2}$) in the red band. The middle panel shows the evolution of $B_\mathrm{rms}/\langle \rho \rangle^{2/3}$. The bottom panel shows various characteristic wavenumbers: the correlation wavenumbers of the magnetic ($k_\mathrm{M}$), the velocity ($k_\mathrm{K}$) and the density field ($k_\rho$), as well as the Jeans wavenumber ($k_\mathrm{J}$) and the resistive wavenumber ($k_\eta$),