Ideal bandpasses for Type Ia supernova cosmology

To use Type la supernovae as standard candles for cosmology, we need accurate broadband magnitudes. In practice the observed magnitude may differ from the ideal magnitude-redshift relationship either through intrinsic inhomogeneities in the Type la supernova population, or through observational error. Here we investigate how we can choose filter bandpasses to reduce the error caused by both these effects. We find that bandpasses with large integral fluxes and sloping wings are best able to minimize several sources of observational error, and are also least sensitive to intrinsic differences in Type la supernovae. The most important feature of a complete filter set for Type la supernova cosmology is that each bandpass be a redshifted copy of the first. We design practical sets of redshifted bandpasses that are matched to typical high-resistivity CCD and HgCdTe infrared detector sensitivities. These are designed to minimize systematic error in well-observed supernovae; final designs for specific missions should also consider signal-to-noise ratio requirements and observing strategy. In addition, we calculate how accurately filters need to be calibrated in order to achieve the required photometric accuracy of future supernova cosmology experiments, such as the Supernova/Acceleration Probe (SNAP), which is one possible realization of the Joint Dark Energy Mission (JDEM). We consider the effect of possible periodic miscalibrations that may arise from the construction of an interference filter.