Critical magnetic Reynolds number of the weakly-collisional turbulent dynamo in supersonic plasmas

Weakly-collisional plasmas are found in several turbulent astrophysical environments, such as the Intra-galaxy-cluster medium (ICM) and the solar wind, where magnetic fields can be amplified by the turbulent dynamo. The onset of dynamo action is determined by the critical magnetic Reynolds number, Rm crit, above which turbulent motions amplify magnetic energy. Although Rm crit has been studied extensively in collisional magnetohydrodynamic (MHD) turbulence, its value in supersonic weakly-collisional plasmas remains unknown. Here we determine Rm crit using three-dimensional hybrid particle-in-cell (HPIC) simulations of solenoidally driven turbulence with a sonic Mach number about 2. We vary the magnetic Reynolds number over Rm about31 - 1000 and consider two initial plasma magnetisations, characterised by initial Larmor ratios r Larmor, 0/L box=1 and 100. We find that the magnetic energy grows exponentially at sufficiently large Rm and decays when magnetic diffusion dominates at low Rm. By fitting the magnetic-energy growth rate as a function of Rm, we measure Rm crit=190+21-17 and 198+16-18 for the initially magnetised and unmagnetised plasma, respectively. These values are the same within their uncertainties, indicating that the initial plasma magnetisation does not significantly affect Rm crit in the supersonic regime. The measured values are higher than those previously obtained for the subsonic weakly-collisional dynamo, showing that increasing compressibility makes weakly-collisional turbulent dynamo action more difficult to excite. The measured values are also approximately 1.5 times higher than the Rm crit value reported for supersonic MHD turbulence.