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We establish an approximation of the activity current $T_c$ in the parameterspace of a holomorphic family $f$ of rational functions having a markedcritical point $c$ by parameters for which $c$ is periodic under $f$, i.e., isa superattracting periodic point. This partly generalizes a Dujardin--Favretheorem for rational functions having preperiodic points, and refines aBassanelli--Berteloot theorem on a similar approximation of the bifurcationcurrent $T_f$ of the holomorphic family $f$. The proof is based on a dynamicalcounterpart of this approximation.

Equidistribution of rational functions having a superattracting periodic point towards the activity current and the bifurcation current