Magnetic fields are critical at many scales to galactic dynamics and structure, including multiphase pressure balance, dust processing, and star formation. Dynamo action determines their dynamical structure and strength. Simulations of combined large- and small-scale dynamos have successfully developed mean fields with strength and topology consistent with observations but with turbulent fields much weaker than observed, while simulations of small-scale dynamos with parameters relevant to the interstellar medium yield turbulent fields an order of magnitude below the values observed or expected theoretically. We use the Pencil Code accelerated on GPUs with Astaroth to perform high-resolution simulations of a supernova-driven galactic dynamo including heating and cooling in a periodic domain. Our models show that the strength of the turbulent field produced by the small-scale dynamo approaches an asymptote at only modest magnetic Prandtl numbers. This allows us to use these models to suggest the essential characteristics of this constituent of the magnetic field for inclusion in global galactic models. The asymptotic limit occurs already at magnetic Prandtl number of only a few hundred, many orders of magnitude below physical values in the the interstellar medium and consistent with previous findings for isothermal compressible flows.

翻译：磁场在星系动力学与结构的多尺度过程中具有关键作用，包括多相压力平衡、尘埃演化及恒星形成等过程。发电机机制决定了磁场的动力学结构与强度。现有的大尺度与小尺度耦合发电机模拟已成功生成平均磁场，其强度与拓扑结构与观测相符，但湍流磁场强度远低于观测值；而采用星际介质相关参数的小尺度发电机模拟所得湍流磁场强度，较理论预期或观测值低一个数量级。本研究利用GPU加速的Pencil Code结合Astaroth框架，在周期性边界条件下对超新星驱动的星系发电机进行高分辨率模拟，并包含加热与冷却过程。模型表明：小尺度发电机产生的湍流磁场强度在中等磁普朗特数条件下即趋近渐近值。这一发现使我们能够据此构建磁场关键特征参数，供全球星系模型集成使用。该渐近极限在磁普朗特数仅数百时即已出现——此数值较星际介质的实际物理值低多个数量级，与先前等温可压缩流体的研究结论一致。