Comparison of the newly derived approximate formula for dynamical friction F_DF with data from various numerical experiments . The corresponding ratio is given as function of the non-linearity parameter η. The top panel shows results from a variety of simulations with adiabatic index γ = 5/3, varying the Mach number, soundspeed, and object mass. The bottom panel shows results from a variety of simulations with varying Mach number for different adiabatic indices as labelled.