  Numerical dynamo models always employ parameter values that differ by orders
of magnitude from the values expected in natural objects. However, such models
have been successful in qualitatively reproducing properties of planetary and
stellar dynamos. This qualitative agreement fuels the idea that both numerical
models and astrophysical objects may operate in the same asymptotic regime of
dynamics. This can be tested by exploring the scaling behavior of the models.
For convection-driven incompressible spherical shell dynamos with constant
material properties, scaling laws had been established previously that relate
flow velocity and magnetic field strength to the available power. Here we
analyze 273 direct numerical simulations using the anelastic approximation,
involving also cases with radius-dependent magnetic, thermal and viscous
diffusivities. These better represent conditions in gas giant planets and
low-mass stars compared to Boussinesq models. Our study provides strong support
for the hypothesis that both mean velocity and mean magnetic field strength
scale as a function of power generated by buoyancy forces in the same way for a
wide range of conditions.
