Abstract
The SH0ES collaboration Hubble constant determination is in a
$\sim5\sigma$ 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.
2020 (R20) compared the light curves amplitudes of extragalactic and MW
Cepheids to constrain an unaccounted systematic blending bias,
$\gamma=-0.029\pm0.037\,mag$, which cannot explain the required,
$\gamma=0.24\pm0.05\,mag$, to resolve the Hubble tension. Further checks
by Riess et al. 2022 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 $Płesssim50\,d$, 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 $\approx0.04\,mag$ uncertainty in determining
$\gamma$, not included by R20. While our final estimate,
$\gamma=0.013\pm0.057\,mag$, is consistent with the value derived by R20,
the error is somewhat larger, and the best-fit value is shifted by
$\approx0.04\,mag$. Although the obtained $\gamma$ for this
crowding test is consistent with zero, folding (in quadratures) it is
$\approx3.0\sigma$ away from aligning with Planck. Future
observations, especially with JWST, would allow better calibration of $\gamma$.
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