The small-scale dynamo (SSD) amplifies weak magnetic fields exponentially
fast via kinetic motions. While there exist well-established theories for SSDs
in incompressible flows, many astrophysical SSDs operate in supersonic
turbulence. To understand the impact of compressibility on amplified magnetic
fields, we perform an extensive set of visco-resistive SSD simulations,
covering a wide range of sonic Mach number M, hydrodynamic Reynolds
number Re, and magnetic Prandtl number Pm. We develop robust methods for
measuring kinetic and magnetic energy dissipation scales βΞ½β and
βΞ·β, as well as the scale at which magnetic fields are strongest
βpβ during the kinematic phase of these simulations. We show that
βΞ½β/βΞ·ββΌ Pm1/2 is a universal feature in the kinematic
phase of Pm β₯1 SSDs, regardless of M or Re, and we confirm
earlier predictions that SSDs operating in incompressible plasmas (either
Mβ€1 or Re < Recritββ100) concentrate
magnetic energy at the smallest scales allowed by magnetic dissipation, βpββΌβΞ·β, and produce fields organised with field strength and
field-line curvature inversely correlated. However, we show that these
predictions fail for compressible SSDs (M>1 and Re > Recritβ), where shocks concentrate magnetic energy in large-scale, over-dense,
coherent structures, with size βpββΌ(βturbβ/βshockβ)1/3βΞ·ββ«βΞ·β, where βshockββΌM2/[Re (Mβ1)2] is shock width, and βturbβ is the turbulent outer scale; magnetic field-line curvature becomes
almost independent of the field strength. We discuss the implications for
galaxy mergers and for cosmic-ray transport models in the interstellar medium
that are sensitive to field-line curvature statistics.Comment: 25 pages, 15 figures, submitted to MNRAS, json-file w/ dat