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(abridged) Context: Rotation is thought to influence the size of convectiveeddies and the efficiency of convective energy transport in the deep convectionzones of stars. Rotationally constrained convection has been invoked to explainthe lack of large-scale power in observations of solar flows. Aims: The mainaims are to quantify the effects of rotation on the scale of convective eddiesand velocity, the depths of convective overshoot, and the subadiabaticDeardorff layers. Methods: Three-dimensional hydrodynamic simulations ofrotating convection in Cartesian domains were run. The results were comparedwith theoretical scaling results that assume a balance between Coriolis,inertial, and buoyancy (Archemedean) forces (CIA balance). Results: The scaleof convective eddies decreases as rotation increases, and ultimately reaches arotationally constrained regime consistent with the CIA balance. Using a newmeasure of the rotational influence on the system, it is shown that even thedeep parts of the solar convection zone are not in the rotationally constrainedregime. The simulations capture the slowly and rapidly rotating scaling lawspredicted by theory, and the Sun appears to be in between these two regimes.Both, the overshooting depth and the extent of the Deardorff layer, decrease asrotation becomes more rapid. For sufficiently rapid rotation the Deardorfflayer is absent. Conclusions: Relating the simulations with the Sun suggeststhat the convective scale even in the deep parts of the Sun is only mildlyaffected by rotation and that some other mechanism is needed to explain thelack of strong large-scale flows in the Sun. Taking the current results at facevalue, the overshoot and Deardorff layers are estimated to span roughly fiveper cent of the pressure scale height at the base of the convection zone in theSun.

Convective scale and subadiabatic layers in simulations of rotating compressible convection