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. We review 2607 supernova redshifts; 2285 are from unique supernovae and 322 are from repeat-observations of the same supernova. In total, we updated 990 unique heliocentric redshifts, and 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. The absolute corrections range between $10^{-8} ≤ Δ z ≤ 0.038$ , and RMS $(Δ z) ∼ 3{× 10^{-3}}$ . The sign of the correction was essentially random, so the mean and median corrections are small: $4{× 10^{-4}}$ and $4{× 10^{-6}}$ 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 $Δ H_0 = -0.12 km s^{-1}Mpc^{-1}$ and $Δ w = 0.003$ , both significantly smaller than previously reported uncertainties for $H_0$ of 1.0 $km s^{-1}Mpc^{-1}$ and w of 0.04 respectively.