Fluctuation dynamos in supersonic turbulence at ${\rm Pm} \gtrsim 1$

Abstract: Fluctuation dynamos provide a robust mechanism for amplifying weak seed magnetic fields in turbulent astrophysical plasmas. However, their behaviour in the highly compressible regimes characteristic of the interstellar medium (ISM) remains incompletely understood. Using high-resolution 3D magnetohydrodynamic simulations of supersonic turbulence with rms Mach number $\mathcal{M}_{\rm rms} \approx 11$, we explore fluctuation dynamos across magnetic Prandtl numbers ${\rm Pm} = 1-10$. At ${\rm Pm} = 1$, dynamo growth is slower and saturates at lower magnetic-to-kinetic energy ratios, with amplification in the kinematic phase dominated by compression rather than line stretching. In contrast, at ${\rm Pm} = 10$, vortical stretching emerges as the dominant mechanism, yielding faster growth, higher saturation levels, and stronger suppression of density-magnetic field correlations by magnetic pressure. This transition is reflected in the correlation coefficient between density and magnetic field strength, which is strongly positive at ${\rm Pm} = 1$ but decreases significantly at higher ${\rm Pm}$. Across all runs, the ratio of velocity-to-magnetic integral scales is $\sim 3.4$, independent of ${\rm Pm}$, while the ratio of viscous to resistive dissipation scales increase with the increase in ${\rm Pm}$. Synthetic Faraday rotation measures (RM) reveal coherence lengths of $\sim (1/4-1/3)$ of the forcing scale across the range of ${\rm Pm}$ explored. Using these coherence scales, we discuss the potential contribution of fluctuation dynamos to Faraday rotation expected from turbulent, gas rich young disk galaxies.