Optimal planning of radial velocity observations for multi-planet extrasolar systems

¹ Sobolev Astronomical Institute, Saint Petersburg State University, Universitetskij pr. 28, Petrodvorets, Saint Petersburg 198504, Russia
² Pulkovo Astronomical Observatory, Pulkovskoje sh. 65/1, Saint Petersburg 196140, Russia

Abstract

Applications of the theory of the optimal design of radial-velocity planet-search surveys are discussed. Two important practical problems are considered. The first problem is finding the time for future observations to yield the maximum improvement of the accuracy of exoplanetary orbital parameters and masses. In this case, the optimal scheduling rules are designed to maximize the determinant of the Fisher information matrix (the so-called D-optimality criterion). This method is asymptotically equivalent to the maximization of the expected gain of the Shannon information provided by making extra observations. The second problem is finding the most favourable observing time for distinguishing alternative orbital fits (the design of discriminating experiments). In this case, the optimal scheduling rules are designed to maximize the Kullback-Leibler divergence information.
We also consider the potential efficiency of these methods of optimal planning of radial velocity observations for multi-planet systems.