Optimal directed searches for continuous gravitational waves

Wide parameter space searches for long-lived continuous gravitational wave signals are computationally limited. It is therefore critically important that the available computational resources are used rationally. In this paper we consider directed searches, i.e., targets for which the sky position is known accurately but the frequency and spin-down parameters are completely unknown. Given a list of such potential astrophysical targets, we therefore need to prioritize. On which target(s) should we spend scarce computing resources? What parameter space region in frequency and spin-down should we search through? Finally, what is the optimal search setup that we should use? In this paper we present a general framework that allows us to solve all three of these problems. This framework is based on maximizing the probability of making a detection subject to a constraint on the maximum available computational cost. We illustrate the method for a simplified problem.