Utilizing Type Ia supernovae in a large, fast, imaging survey to constrain dark energy

Abstract

We study the utility of a large sample of Type Ia supernovae (SNe Ia) that might be observed in an imaging survey that rapidly scans a large fraction of the sky for constraining dark energy. We consider both the information contained in the traditional luminosity distance test as well as the spread in Ia SN fluxes at fixed redshift induced by gravitational lensing. As would be required from an imaging survey, we include a treatment of photometric redshift uncertainties in our analysis. Our primary result is that the information contained in the mean distance moduli of SNe Ia and the dispersion of SN Ia distance moduli complement each other, breaking a degeneracy between the present dark energy equation of state and its time variation without the need for a high-redshift (z ≳ 0.8) SN sample. Including lensing information also allows for some internal calibration of photometric redshifts. To address photometric redshift uncertainties, we present dark energy constraints as a function of the size of an external set of spectroscopically observed SNe that may be used for redshift calibration, N spec. Depending upon the details of potentially available, external SN data sets, we find that an imaging survey can constrain the dark energy equation of state at the epoch where it is best constrained w p, with a 1σ error of σ(w p) ≈ 0.03-0.09. In addition, the marginal improvement in the error σ(w p) from an increase in the spectroscopic calibration sample drops once N spec ∼ a few × 103. This result is important because it is of the order of the size of calibration samples likely to be compiled in the coming decade and because, for samples of this size, the spectroscopic and imaging surveys individually place comparable constraints on the dark energy equation of state. In all cases, it is best to calibrate photometric redshifts with a set of spectroscopically observed SNe with relatively more objects at high redshift (z ≳ 0.5) than the parent sample of imaging SNe. © 2009. The American Astronomical Society. All rights reserved.