Growth or decay: universality of the turbulent dynamo saturation

The small-scale turbulent dynamo (SSD) is likely to be responsible for the magnetisation of the interstellar medium (ISM) that we observe in the Universe today. The SSD efficiently converts kinetic energy $E_{\rm kin}$ into magnetic energy $E_{\rm mag}$, and is often used to explain how an initially weak magnetic field with $E_{\rm mag} \ll E_{\rm kin}$ is amplified, and then maintained at a level $E_{\rm mag} \lesssim E_{\rm kin}$. Usually, this process is studied by initialising a weak seed magnetic field and letting the turbulence grow it to saturation. However, in this study, using three-dimensional, non-ideal magnetohydrodynamical turbulence simulations, we show that the same saturated state can also be achieved if initially $E_{\rm mag} \gg E_{\rm kin}$ or $E_{\rm mag} \sim E_{\rm kin}$. This is realised through a two-stage exponential decay (1. a slow backreaction that converts $E_{\rm mag}$ into $E_{\rm kin}$, and 2. Ohmic dissipation concentrated in anisotropic current sheets) into the saturated state, for which we provide an analytical model. This means that even if there are temporary local enhancements of $E_{\rm mag}$ in the ISM, such that $E_{\rm mag} > E_{\rm kin}$, e.g., through amplifications such as compressions, over a long enough time the field will decay into the saturated state set by the SSD, which is determined by the turbulence and magnetic dissipation. However, we also provide analytical models for the decay times and utilise wait-time statistics from compressive supernova events to show that if the magnetic field is enhanced above the saturated state, it will not have enough time to decay the field before the next supernova event. Hence, unless there exists a mechanism for destroying magnetic fields that is not in our non-ideal MHD models, the amplitudes of interstellar magnetic fields may also be a... (abridged).Comment: 18 pages. 14 figures. Submitted to MNRAS. Comments welcom