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, ${\rm Rm}_{\rm crit}$, above which turbulent motions amplify magnetic energy. Although ${\rm Rm}_{\rm crit}$ has been studied extensively in collisional magnetohydrodynamic (MHD) turbulence, its value in supersonic weakly-collisional plasmas remains unknown. Here we determine ${\rm Rm}_{\rm crit}$ using three-dimensional hybrid particle-in-cell (HPIC) simulations of solenoidally driven turbulence with a sonic Mach number $\approx 2$. We vary the magnetic Reynolds number over ${\rm Rm}\approx31$-$1000$ and consider two initial plasma magnetisations, characterised by initial Larmor ratios $r_{\rm Larmor, 0}/L_{\rm box}=1$ and $100$. We find that the magnetic energy grows exponentially at sufficiently large ${\rm Rm}$ and decays when magnetic diffusion dominates at low ${\rm Rm}$. By fitting the magnetic-energy growth rate as a function of ${\rm Rm}$, we measure ${\rm Rm}_{\rm crit}=190^{+21}_{-17}$ 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 ${\rm Rm}_{\rm crit}$ 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 ${\rm Rm}_{\rm crit}$ value reported for supersonic MHD turbulence.