The Pantheon+ Analysis: Improving the Redshifts and Peculiar Velocities of Type Ia Supernovae Used in Cosmological Analyses

We examine the redshifts of a comprehensive set of published Type Ia supernovae, and provide a combined, improved catalogue with updated redshifts. We improve on the original catalogues by using the most up-to-date heliocentric redshift data available; ensuring all redshifts have uncertainty estimates; using the exact formulae to convert heliocentric redshifts into the Cosmic Microwave Background (CMB) frame; and utilising an improved peculiar velocity model that calculates local motions in redshift-space and more realistically accounts for the external bulk flow at high-redshifts. In total we reviewed 2821 supernova redshifts; 534 are comprised of repeat-observations of the same supernovae and 1764 pass the cosmology sample quality cuts. We found 5 cases of missing or incorrect heliocentric corrections, 44 incorrect or missing supernova coordinates, 230 missing heliocentric or CMB frame redshifts, and 1200 missing redshift uncertainties. Of the 2287 unique Type Ia supernovae in our sample (1594 of which satisfy cosmology-sample cuts) we updated 990 heliocentric redshifts. The absolute corrections range between $10^{-8} \leq \Delta z \leq 0.038$, and RMS$(\Delta z) \sim 3\times 10^{-3}$. The sign of the correction was essentially random, so the mean and median corrections are small: $4\times 10^{-4}$ and $4\times 10^{-6}$ respectively. We examine the impact of these improvements for $H_0$ and the dark energy equation of state $w$ and find that the cosmological results change by $\Delta H_0 = -0.11$ km s$^{-1}$ Mpc$^{-1}$ and $\Delta w = -0.001$, both significantly smaller than previously reported uncertainties for $H_0$ of 1.4 km s$^{-1}$ Mpc$^{-1}$ and $w$ of 0.04 respectively.