Insensitivity of The Distance Ladder Hubble Constant Determination to Cepheid Calibration Modeling Choices

TL;DR

Problem: The Hubble constant measured via Cepheid-calibrated supernovae shows a tension with Planck-derived predictions under $\Lambda$CDM. Approach: relax Cepheid modeling assumptions to test for biases, including intrinsic color, line-of-sight extinction, and nonlinearity, using Gaussian-mixture clustering and model-free interpolation within a joint distance-ladder fit. Findings: the inferred $H_0$ remains robust, $H_0 = 73.3 \pm 1.7$ km s$^{-1}$ Mpc$^{-1}$, across extended Cepheid models, indicating Cepheid systematics in the modeled space cannot resolve the discrepancy. Significance: supports the credibility of local distance-ladder $H_0$ measurements and motivates pursuing other systematics or new physics; independent cross-checks (e.g., Gaia anchors, H0LiCOW) remain crucial to fully resolve the Planck–Cepheid tension.

Abstract

Recent determination of the Hubble constant via Cepheid-calibrated supernovae by \citet{riess_2.4_2016} (R16) find $\sim 3σ$ tension with inferences based on cosmic microwave background temperature and polarization measurements from $Planck$. This tension could be an indication of inadequacies in the concordance $Λ$CDM model. Here we investigate the possibility that the discrepancy could instead be due to systematic bias or uncertainty in the Cepheid calibration step of the distance ladder measurement by R16. We consider variations in total-to-selective extinction of Cepheid flux as a function of line-of-sight, hidden structure in the period-luminosity relationship, and potentially different intrinsic color distributions of Cepheids as a function of host galaxy. Considering all potential sources of error, our final determination of $H_0 = 73.3 \pm 1.7~{\rm km/s/Mpc}$ (not including systematic errors from the treatment of geometric distances or Type Ia Supernovae) shows remarkable robustness and agreement with R16. We conclude systematics from the modeling of Cepheid photometry, including Cepheid selection criteria, cannot explain the observed tension between Cepheid-variable and CMB-based inferences of the Hubble constant. Considering a `model-independent' approach to relating Cepheids in galaxies with known distances to Cepheids in galaxies hosting a Type Ia supernova and finding agreement with the R16 result, we conclude no generalization of the model relating anchor and host Cepheid magnitude measurements can introduce significant bias in the $H_0$ inference.

Figures (7)

• Figure 1: The constraints on the intrinsic color parameters $C_0$, $C_p$, and $C_\gamma$ of equation \ref{['eq: color model']} assuming the Cepheid period-magnitude relationship of equation \ref{['eq: ceph period magnitude']} used in [][]riess_2.4_2016, but with intrinsic color $(V-I)^0$ instead of the total color $(V-I)$. The posterior is jointly constrained by the Cepheid sample and our intrinsic color and period likelihood as described in the text. The degeneracy between $C_0$ and $C_\gamma$ is due to the limited metallicity information from the external color data of sandage_new_2004tammann_new_2003, which only contains information from LMC and Milky Way Cepheids.
• Figure 2: The $68\%$ confidence regions for the six clusters that maximize the BIC criterion in period-color space. The significant overlap in cluster support leads us to adopt a weighted mixed-cluster treatment of individual Cepheids, where each Cepheid is assigned a weight in each cluster proportional to the mixture model probability of residing in that cluster.
• Figure 3: The posterior distribution of $M_{\rm Ceph}$ for each of the $6$ Cepheid clusters depicted in figure \ref{['fig: clusters']}. The constraints on $M_{\rm Ceph}$ in each cluster are consistent at the level of about $1 \sigma$ or less, as are the constraints when the results are propagated to inferences on $H_0$. The weight of the global $H_0$ constraint comes from the intermediate-period Cepheids represented by clusters $5$ and $6$ which share significant support. These clusters contain a large overlap of both host and anchor Cepheids, which reduces uncertainties from extrapolation.
• Figure 4: The contraint on the value of $R_H$ for each galaxy in the sample, under a wide prior of $R_H = 0.39 \pm 0.1$ to regularize hosts with insufficient information for a strong determination. Overlaid is the value of the correlation of $H_0$ with the value of $R_H$ in each galaxy; a measurement of $R_H$ in fields with significant correlation will have the most effect on $H_0$.
• Figure 5: The contraints on $H_0$ under the various extended models of section \ref{['sec: new analysis']} compared to the baseline model of [][]riess_2.4_2016. The value of $H_0$ shows remarkable consistency across all models, and the constraint (both in expectation and variance) shows tremendous robustness to particular assumptions in the Cepheid magnitude model of equation \ref{['eq: general Cepheid magnitude']}.