Consistent extinction model for type Ia supernovae in Cepheid-based calibration galaxies and its impact on $H_{0}$

Technical Summary: Consistent Extinction Model for Type Ia Supernovae in Cepheid-based Calibration Galaxies and its Impact on $H_0$

Problem Statement
The current tension in cosmology arises from a significant discrepancy ($5.2\sigma$) between the Hubble constant ($H_0$) measured via the local distance ladder (using Cepheids and Type Ia supernovae in the SH0ES program) and the value inferred from the Cosmic Microwave Background (Planck) assuming a standard $\Lambda$CDM model. A critical component of the SH0ES measurement involves correcting Type Ia supernova magnitudes for host galaxy extinction. The standard approach (Popovic et al. 2023, hereafter P23) employs a probabilistic dust model trained on Hubble flow supernovae ($z > 0.03$) and extrapolates it to calibration galaxies (those with observed Cepheids).

The authors identify a systematic inconsistency in this extrapolation. The calibration sample is biased toward late-type, dust-rich galaxies, whereas the P23 model assigns different extinction properties based on host stellar mass ($M_\star$). Specifically, the P23 model assumes a low total-to-selective extinction coefficient ($R_B \approx 3.1$) for high-mass hosts ($M_\star > 10^{10} M_\odot$) and a standard value ($R_B \approx 4.0$) for low-mass hosts. The authors argue that this assumption leads to an underestimation of extinction for reddened supernovae in high-mass calibration galaxies, resulting in systematically fainter inferred absolute magnitudes and, consequently, an overestimated $H_0$. Furthermore, the P23 model's $R_B \approx 3.1$ for high-mass hosts conflicts with the Milky Way-like extinction curve ($R_B \approx 4.3$) used to correct Cepheid colors in the same galaxies.

Methodology
The authors re-analyze the Pantheon+ supernova compilation and SH0ES Cepheid distance moduli (Riess et al. 2022). Their methodology involves:

1. Consistency Testing: They perform likelihood analyses on the calibration sample, separating supernovae into high-mass ($M_\star > 10^{10} M_\odot$) and low-mass bins. They compare the best-fit absolute magnitude ($M_B$) and derived $H_0$ for these subsamples against random control samples. They find that high-mass hosts yield systematically fainter $M_B$ (higher $H_0$) compared to low-mass hosts and control samples, particularly for red supernovae ($c > 0$).
2. Model Modification: They propose a "minimalistic" modification to the extinction model applied solely to the calibration galaxies, while retaining the P23 model for the Hubble flow (where the model was trained). The new model involves two key changes:
   • Uniform $R_B$ Distribution: Instead of mass-dependent $R_B$, they assume a single, Milky Way-like Gaussian distribution for the total-to-selective extinction coefficient in both mass bins, with a mean $\langle R_B \rangle = 4.3$ and scatter $\sigma_{R_B} = 0.4$. This aligns the supernova extinction correction with the curve used for Cepheids.
   • Modified Reddening Distribution Shape: To preserve the effective slope ($\beta \approx 3.0$) of the supernova peak magnitude–colour relation and the mean reddening $\langle E(B-V) \rangle$ measured in the Hubble flow, they replace the exponential distribution of dust reddening $E(B-V)$ (used in P23) with a Gamma distribution. The shape parameter is tuned to $\gamma = 3.44$, which shifts the peak of the distribution to non-zero reddening while maintaining the correct mean.
3. Statistical Evaluation: They recompute the bias corrections ($\delta$) and floor uncertainties ($\sigma_{floor}$) for the calibration sample using the new model. They update the covariance matrix to reflect the reduced intrinsic scatter resulting from the lower $\sigma_{R_B}$. Finally, they perform joint fits of the calibration and Hubble flow data to derive a new $H_0$.

Key Contributions and Results

• Identification of Systematic Bias: The study demonstrates that the P23 model's assumption of $R_B \approx 3.1$ for high-mass calibration galaxies creates a $2.0\sigma$ to $2.3\sigma$ tension in the derived absolute magnitudes between high- and low-mass hosts. This bias is most pronounced for red supernovae.
• Improved Model Fit: The proposed new extinction model yields a significantly better fit to the calibration data, with a Bayesian Information Criterion improvement of $\Delta \text{BIC} = -11.0$ compared to the P23 model. This improvement is driven by both a reduction in $\chi^2_{min}$ (due to corrected biases) and a change in the likelihood normalization (due to reduced covariance uncertainties).
• Revised Hubble Constant: Applying the new model to the joint calibration and Hubble flow dataset results in a lower best-fit Hubble constant:
  $$H_0 = 70.5 \pm 1.0 \text{ km s}^{-1} \text{ Mpc}^{-1}$$
  This represents a reduction of approximately $2.9 \text{ km s}^{-1} \text{ Mpc}^{-1}$ compared to the standard SH0ES value ($73.4 \pm 1.0$).
• Reduction of Tension: The revised $H_0$ reduces the statistical tension with the Planck $\Lambda$CDM measurement from $5.2\sigma$ to $2.8\sigma$. The result is also consistent with independent measurements based on the Tip of the Red Giant Branch (TRGB).

Significance and Claims
The paper claims that the "Hubble tension" may be partially or largely driven by unaccounted-for systematic errors in the extinction modeling of calibration galaxies. The authors argue that the standard approach fails because it extrapolates a model trained on a mixed population of galaxies to a calibration sample that is exclusively composed of late-type, star-forming systems.

The significance of their work lies in demonstrating that:

1. Selection Bias Matters: The specific selection of calibration galaxies (requiring observable Cepheids) introduces a bias that is not captured by simply selecting "late-type" galaxies in the Hubble flow, as the latter selection may not precisely match the local dust environments of the calibration supernovae.
2. Extinction Physics: The assumption of a low $R_B$ ($\approx 3.1$) for high-mass hosts is physically inconsistent with the Milky Way-like extinction required for Cepheids in the same galaxies and with observational constraints on star-forming galaxies.
3. Second-Order Effects: The shape of the reddening distribution (specifically the second moment) is critical. The authors show that a Gamma distribution ($\gamma \approx 3.4$) better describes the data than the standard exponential model, implying a stronger correlation between dust and supernova positions in these specific galaxies.

The authors conclude that their revised extinction model provides a more consistent physical framework for the distance ladder, alleviating the apparent discrepancy between high- and low-mass hosts and significantly lowering the $H_0$ tension without invoking new physics. They note that while their model is strongly favored by the current data, further refinement using independent near-infrared observations and full forward modeling of dust properties is necessary to fully resolve the remaining residuals.