Reassessing the Constraints from SH0ES Extragalactic Cepheid Amplitudes on Systematic Blending Bias

The SH0ES collaboration Hubble constant determination is in a ${\sim}5\sigma$ difference with the $Planck$ value, known as the Hubble tension. The accuracy of the Hubble constant measured with extragalactic Cepheids depends on robust stellar-crowding background estimation. Riess et al. (R20) compared the light curves amplitudes of extragalactic and MW Cepheids to constrain an unaccounted systematic blending bias, $\gamma=-0.029\pm0.037\,\rm{mag}$, which cannot explain the required, $\gamma=0.24\pm0.05\,\rm{mag}$, to resolve the Hubble tension. Further checks by Riess et al. demonstrate that a possible blending is not likely related to the size of the crowding correction. We repeat the R20 analysis, with the following main differences: (1) we limit the extragalactic and MW Cepheids comparison to periods $P\lesssim50\,\rm{d}$, since the number of MW Cepheids with longer periods is minimal; (2) we use publicly available data to recalibrate amplitude ratios of MW Cepheids in standard passbands; (3) we remeasure the amplitudes of Cepheids in NGC 5584 and NGC 4258 in two HST filters ($F555W$ and $F350LP$) to improve the empirical constraint on their amplitude ratio $A^{555}/A^{350}$. We show that the filter transformations introduce an ${\approx}0.04\,\rm{mag}$ uncertainty in determining $\gamma$, not included by R20. While our final estimate, $\gamma=0.013\pm0.057\,\rm{mag}$, is consistent with the value derived by R20 and is consistent with no bias, the error is somewhat larger, and the best fitting value is shifted by ${\approx}0.04\,\rm{mag}$ and closer to zero. Future observations, especially with JWST, would allow better calibration of $\gamma$.