Cosmology with Contaminated Samples: Methods of Measuring Dark Energy with Photometrically Classified Pan-STARRS Supernovae

The Pan-STARRS (PS1) Medium Deep Survey discovered over 5,000 likely supernovae (SNe) but obtained spectral classifications for just 10% of its SN candidates. We measured spectroscopic host galaxy redshifts for 3,073 of these likely SNe and estimate that $\sim$1,000 are Type Ia SNe (SNe Ia) with light-curve quality sufficient for a cosmological analysis. We use these data with simulations to determine the impact of core-collapse SN (CC SN) contamination on measurements of the dark energy equation of state parameter, $w$. Using the method of Bayesian Estimation Applied to Multiple Species (BEAMS), distances to SNe Ia and the contaminating CC SN distribution are simultaneously determined as a function of redshift. We test light-curve based SN classification priors for BEAMS as well as a new classification method that relies upon host galaxy spectra and the association of SN type with host type. By testing several SN classification methods and CC SN parameterizations on 1,000-SN simulations, we conservatively estimate that CC SN contamination gives a systematic error on $w$ ($\sigma_w^{CC}$) of 0.014, 30% of the statistical uncertainty. Our best method gives $\sigma_w^{CC} = 0.005$, just 11% of the statistical uncertainty, but could be affected by incomplete knowledge of the CC SN distribution. Our method determines the SALT2 color and shape coefficients, $\alpha$ and $\beta$, with $\sim$3% bias. Real PS1 SNe without spectroscopic classifications give measurements of $w$ that are within 0.5$\sigma$ of measurements from PS1 spectroscopically confirmed SNe. Finally, the inferred abundance of bright CC SNe in our sample is greater than expected based on measured CC SN rates and luminosity functions.