The self-* properties commonly associated with the concept of autonomic computing are capabilities desirable for avionics software platforms. They decrease the configuration effort and inherently provide new fault tolerance and resource savings possibilities. The rigid certification process and the requirements for a static and predetermined system behavior are, however, in contradiction with the adaptive and flexible nature of autonomic computing systems. We propose a partition-based architecture providing autonomic features for avionics software platforms while being compliant to regulations and accepted technologies, such as ARINC 653. The core is a platform consciousness based on a domain-specific model and a novel MAP-QE-K cycle. Moreover, we suggest a planning intelligence, a virtual qualification authority, and a minimized execution unit. For each component we define the required design assurance level and possible realization techniques. We discuss the overall feasibility and point out central challenges in the fields of runtime verification and models at runtime. These challenges need to be solved up to the realization of autonomic avionics, e.g. a virtual security assessment and a qualifiable domain-specific model database.