Reanalyzing Megamasers: a low value of $H_0$ from a local probe changes our view of the Hubble Tension

Technical Summary: A Low Value of $H_0$ in Tension with the Distance Ladder from Megamasers Using Peculiar Velocity Reconstruction

Problem Statement
The "Hubble tension" represents a significant discrepancy between measurements of the Hubble constant ($H_0$) derived from the Cosmic Microwave Background (CMB) ($67.4 \pm 0.5$ km/s/Mpc) and those from the local distance ladder ($73.5 \pm 0.81$ km/s/Mpc). A critical piece of evidence in resolving whether this tension stems from new physics or systematic errors in the distance ladder is the independent measurement of $H_0$ using megamasers. Megamaser distances are geometric and do not rely on the traditional distance ladder. Previous work by Pesce et al. (2020) (P20) analyzed megamaser data and found an $H_0$ value consistent with the distance ladder and in tension with the CMB. However, P20 modeled peculiar velocities primarily as random Gaussian noise. This approach fails to account for coherent bulk flows and non-Gaussian tails in the velocity distribution caused by infall into nonlinear structures, potentially introducing a systematic bias in the redshift corrections.

Methodology
This study re-analyzes the six-galaxy megamaser sample from P20, focusing on correcting observed redshifts for peculiar velocities using a superior velocity field reconstruction.

1. Velocity Reconstruction: Instead of treating peculiar velocities as Gaussian noise, the authors utilize the M25 reconstruction (McAlpine et al. 2025). Unlike the previous C15 reconstruction (Carrick et al. 2015), M25 combines the 2M++ redshift survey with constrained cosmological simulations. This allows M25 to resolve the velocity field on smaller scales and capture non-linear galaxy motions more accurately.
2. Data Correction: The authors apply both C15 and M25 peculiar velocity corrections to the redshifts of the six megamaser galaxies. They note that in the M25 reconstruction, all six galaxies exhibit positive peculiar velocities, with the three most distant galaxies participating in a large, coherent outflow.
3. Likelihood Analysis: The authors fit a distance-redshift relation assuming a flat $\Lambda$CDM cosmology with fixed matter density ($\Omega_m = 0.3$). The likelihood function minimizes the difference between measured distances and model distances.
4. Uncertainty Modeling: A key methodological improvement is the treatment of the velocity reconstruction uncertainty ($\sigma_v$). The authors add $\sigma_v$ in quadrature to the distance measurement uncertainties. They explore two approaches:
   • Fixing $\sigma_v$ at various values (0 to 150 km/s).
   • Treating $\sigma_v$ as a free model parameter with a uniform prior, using Markov Chain Monte Carlo (MCMC) to marginalize over it.

Key Contributions

• Identification of Bias: The paper demonstrates that modeling peculiar velocities as Gaussian noise (as done by P20) fails to capture coherent flows and non-Gaussian outliers. In the specific case of the megamaser sample, the positive peculiar velocities systematically reduce the corrected redshifts, leading to an overestimation of $H_0$.
• Superior Reconstruction: The study establishes that the M25 reconstruction, by incorporating cosmological simulations, provides a more accurate correction for these velocities than the C15 method or simple Gaussian noise models.
• Re-evaluation of $H_0$: By applying the M25 reconstruction, the authors derive a new estimate for $H_0$ that shifts significantly away from the distance ladder value and toward the CMB value.

Results

• C15 vs. M25: Using the C15 reconstruction with $\sigma_v = 150$ km/s yields $H_0 = 71.5 \pm 2.6$ km/s/Mpc, consistent with P20's results. Using the M25 reconstruction with the same $\sigma_v$ yields a lower value of $H_0 = 69.7 \pm 2.6$ km/s/Mpc.
• Sensitivity to $\sigma_v$: The estimated $H_0$ is sensitive to the assumed velocity uncertainty. As $\sigma_v$ is reduced (placing more weight on galaxies with precise distance measurements like NGC 4258), the estimated $H_0$ decreases. For $\sigma_v = 0$, $H_0 = 68.4 \pm 0.9$ km/s/Mpc.
• Marginalized Result: When treating $\sigma_v$ as a free parameter and marginalizing over it (with a limit of 150 km/s), the M25-corrected data yields a maximum likelihood $H_0$ of $68.7$ km/s/Mpc.
• Statistical Tension: The probability that the M25-derived $H_0$ is as large as or larger than the distance ladder value ($73.5$ km/s/Mpc) is calculated to be $P(> H_{DL}) = 0.029$ (2.9%). This indicates a tension of greater than $2\sigma$ between the megamaser result (using M25) and the distance ladder, whereas the megamaser result is consistent with the CMB.

Significance and Claims
The authors argue that the Hubble tension is likely driven by a systematic error within the distance ladder rather than new physics. They contend that the previous agreement between megamaser data and the distance ladder was an artifact of biased peculiar velocity corrections. By using a high-resolution velocity reconstruction that accounts for coherent flows and non-Gaussian motions, the megamaser-derived $H_0$ aligns with the CMB and conflicts with the distance ladder.

The paper concludes that:

1. Megamasers remain a vital, independent check on the distance ladder, though more data and improved distance estimation methods are required for definitive conclusions.
2. Peculiar velocities are a significant source of bias in low-redshift $H_0$ determinations, necessitating accurate local velocity reconstructions.
3. The discrepancy suggests that the distance ladder requires further scrutiny regarding potential systematics in its calibration.