Investigating compressible and incompressible mode coupling in supersonic turbulent dynamos relevant to the interstellar medium

The turbulent magnetic field that is grown and maintained in our Galaxy is roughly an order of magnitude larger in strength than the ordered magnetic field. The only way to keep such a field energised is through a turbulent dynamo. Classical turbulent dynamo theory takes no account of compressibility of the plasma, however the plasma in the interstellar medium of our Galaxy is weakly-compressible and mildy-supersonic on large scales (~100pc), and highly-compressible and highly-supersonic on smaller scales (~10pc). Hence, for understanding the turbulent dynamo in our Galaxy, we must consider supersonic dynamos. Supersonic dynamos are less efficient both in growth rate and the final saturated magnetic to kinetic energy ratio compared to incompressible dynamos. A good explanation for why has not yet been made nor proven from first principles, and in fact there is reason to believe that compressible modes should enhance the dynamo through compression. To explore this question, we will utilise an advanced compressible transfer function framework outlined in Grete et al. (2017), tracking the energy fluxes in high resolution simulations, mode by mode, for all terms in the compressible / incompressible mode decomposed magnetohydrodynamic fluid equations. In particular, we will develop a better understanding for how compressible modes couple to incompressible modes (and vice versa) on various scales in the dynamo, in turn determining how compressible modes potentially inhibit dynamo action and solving this outstanding problem in compressible dynamo theory.