Relativistic corrections for measuring Hubble’s constant to 1% using stellar standard candles^⋆

Institute of Physics, Laboratory of Astrophysics, École Polytechnique Fédérale de Lausanne (EPFL), Observatoire de Sauverny, 1290 Versoix, Switzerland
e-mail: richard.anderson@epfl.ch

Received: 25 June 2021
Accepted: 8 November 2021

Abstract

We have estimated relativistic corrections for cosmic distance estimates based on stellar standard candles such as classical Cepheids and stars near the tip of the red giant branch (TRGB stars) with the goal of enabling a future unbiased 1% measurement of Hubble’s constant, H₀. We considered four effects: K corrections, time dilation, the apparent change of host dust extinction due to non-comoving reference frames, and the change of observed color due to redshift. Using stellar model atmospheres, we computed extinction-dependent K corrections for a wide range of effective temperatures, between 3500 and 6000 K, iron abundances between [Fe/H] = −2.0 and 0.5, surface gravity between log g = 2.0 and 0.0, and host reddening (up to E(B − V)^host = 0.5) for a range of redshifts corresponding to distances of ∼20−120 Mpc (z between 0.005 and 0.03) in several HST, JWST, and 2MASS filters. The optical-near-infrared (NIR) Wesenheit function applied by the Cepheid distance ladder is particularly useful for limiting the magnitude of K corrections and for mitigating complications arising from host dust extinction. Missing host extinction corrections related to the circumgalactic medium and circumstellar environments arising from stellar mass loss are discussed as potential systematics of TRGB distance measurements. However, their effect is estimated to be insufficient to explain differences in H₀ values based on Cepheids or TRGB supernova calibrations. All stellar standard candle observations require relativistic corrections in order to achieve an unbiased 1% H₀ measurement in the future. Applying the K correction, the redshift-Leavitt bias correction, and a correction for the Wesenheit slope redshift dependence, the Cepheid-based H₀ measurement increases by 0.45 ± 0.05 km s⁻¹ Mpc⁻¹ to H₀^SH0ES = 73.65 ± 1.30 km s⁻¹ Mpc⁻¹, raising the tension with the early-Universe value reported by the Planck Collaboration from 4.2σ to 4.4σ. For TRGB-based H₀ measurements, we estimate a ∼0.5% upward correction for the methodology employed by Freedman et al. (H₀^CCHP = 70.2 ± 1.7 km s⁻¹ Mpc⁻¹) and an even smaller −0.15% downward correction for the methodology employed by Anand et al. (H₀^EDD = 71.4 ± 1.8 km s⁻¹ Mpc⁻¹). The opposite sign of these corrections is related to different reddening systematics and reduces the difference between the studies by ∼0.46 km s⁻¹ Mpc⁻¹. The optical-NIR Wesenheit function is particularly attractive for accurate distance measurements because it advantageously combines measurements in filters where K corrections have opposite signs. The JWST/NIRCAM F277W filter is of particular interest for TRGB stars thanks to its insensitivity to (weak) host reddening and K corrections below the level of 1% at Coma cluster distances.