  Many astrophysical systems encompass very large dynamical ranges in space and
time, which are not accessible by direct numerical simulations. Thus, idealized
subvolumes are often used to study small-scale effects including the dynamics
of turbulence. These turbulent boxes require an artificial driving in order to
mimic energy injection from large-scale processes. In this Letter, we show and
quantify how the autocorrelation time of the driving and its normalization
systematically change properties of an isothermal compressible
magnetohydrodynamic flow in the sub- and supersonic regime and affect
astrophysical observations such as Faraday rotation. For example, we find that
$\delta$-in-time forcing with a constant energy injection leads to a steeper
slope in kinetic energy spectrum and less efficient small-scale dynamo action.
In general, we show that shorter autocorrelation times require more power in
the acceleration field, which results in more power in compressive modes that
weaken the anticorrelation between density and magnetic field strength. Thus,
derived observables, such as the line-of-sight magnetic field from rotation
measures, are systematically biased by the driving mechanism. We argue that
$\delta$-in-time forcing is unrealistic and numerically unresolved, and
conclude that special care needs to be taken in interpreting observational
results based on the use of idealized simulations.
