Evolutionary design of photometric systems and its application to Gaia

How do I find the optimal photometric system for a survey? Designing a photometric system to best fulfil a set of scientific goals is a complex task, demanding a compromise between often conflicting scientific requirements, and being subject to various instrumental constraints. A specific example is the determination of stellar astrophysical parameters (APs) – effective temperature, surface gravity, metallicity etc. – across a wide range of stellar types. I present a novel approach to this problem which makes minimal assumptions about the required filter system. By considering a filter system as a set of free parameters (central wavelengths, profile widths etc.), it may be designed by optimizing some figure-of-merit (FoM) with respect to these parameters. In the example considered, the FoM is a measure of how well the filter system can “separate” stars with different APs. This separation is vectorial in nature, in the sense that the local directions of AP variance are preferably mutually orthogonal to avoid AP degeneracy. The optimization is carried out with an evolutionary algorithm, a population-based approach which uses principles of evolutionary biology to efficiently search the parameter space. This model, HFD (Heuristic Filter Design), is applied to the design of photometric systems for the Gaia space astrometry mission. The optimized systems show a number of interesting features, not least the persistence of broad, overlapping filters. These HFD systems perform as least as well as other proposed systems for Gaia – as measured by this FoM – although inadequacies in all of these systems at removing degeneracies remain. Ideas for improving the model are discussed. The principles underlying HFD are quite generic and may be applied to filter design for numerous other projects, such as the search for specific types of objects or photometric redshift determination.