O-operators and Nijenhuis operators of associative conformal algebras

We study O-operators of associative conformal algebras with respect to conformal bimodules. As natural generalizations of O-operators and dendriform conformal algebras, we introduce the notions of twisted Rota-Baxter operators and conformal NS-algebras. We show that twisted Rota-Baxter operators give rise to conformal NS-algebras, the same as O-operators induce dendriform conformal algebras. And we introduce a conformal analog of associative Nijenhuis operators and enumerate main properties. By using derived bracket construction of Kosmann-Schwarzbach and a method of Uchino, we obtain a graded Lie algebra whose Maurer-Cartan elements are given by O-operators. This allows us to construct cohomology of O-operators. This cohomology can be seen as the Hochschild cohomology of an associative conformal algebra with coefficients in a suitable conformal bimodule.