Accidental deep field bias in CMB T and SNe $z$ correlation

Abstract

Evidence presented by Yershov, Orlov and Raikov apparently showed that the WMAP/Planck cosmic microwave background (CMB) pixel-temperatures (T) at supernovae (SNe) locations tend to increase with increasing redshift ($z$). They suggest this correlation could be caused by the Integrated Sachs-Wolfe effect and/or by some unrelated foreground emission. Here, we assess this correlation independently using Planck 2015 SMICA R2.01 data and, following Yershov et al., a sample of 2783 SNe from the Sternberg Astronomical Institute. Our analysis supports the prima facie existence of the correlation but attributes it to a composite selection bias (high CMB T $\times$ high SNe $z$) caused by the accidental alignment of seven deep survey fields with CMB hotspots. These seven fields contain 9.2 per cent of the SNe sample (256 SNe). Spearman's rank-order correlation coefficient indicates the correlation present in the whole sample ($\rho_s = 0.5$, p-value $= 6.7 \times 10^{-9}$) is insignificant for a sub-sample of the seven fields together ($\rho_s = 0.2$, p-value $= 0.2$) and entirely absent for the remainder of the SNe ($\rho_s = 0.1$, p-value $= 0.6$). We demonstrate the temperature and redshift biases of these seven deep fields, and estimate the likelihood of their falling on CMB hotspots by chance is at least $\sim$ 6.8 per cent (approximately 1 in 15). We show that a sample of 7880 SNe from the Open Supernova Catalogue exhibits the same effect and we conclude that the correlation is an accidental but not unlikely selection bias.