[Paper Review] The Local Hole: a galaxy under-density covering 90% of sky to ~200 Mpc

Jonathan H.W. Wong, T. Shanks+2 more|arXiv (Cornell University)|Jul 18, 2021

Galaxies: Formation, Evolution, Phenomena4 citations

TL;DR

This study confirms the existence of the 'Local Hole'—a large-scale under-density in galaxy distribution—by extending $K$-band number counts to 90% of the sky using 2MASS and 2M++ data. It finds a 20–22% under-density at $z < 0.075$, which biases local $H_0$ measurements upward by ~3%, contributing to the $H_0$ tension with $Λ$CDM at ~3$σ$.

ABSTRACT

We investigate the `Local Hole', an anomalous under-density in the local galaxy environment, by extending our previous galaxy $K-$band number-redshift and number-magnitude counts to $\approx 90\%$ of the sky. Our redshift samples are taken from the 2MASS Redshift Survey (2MRS) and the 2M++ catalogues, limited to $K&lt;11.5$. We find that both surveys are in good agreement, showing an $\approx 21-22\%$ under-density at $z&lt;0.075$ when compared to our homogeneous counts model that assumes the same luminosity function and other parameters as in our earlier papers. Using the Two Micron All Sky Survey (2MASS) for $n(K)$ galaxy counts, we measure an under-density relative to this model of $20\pm 2 \%$ at $K&lt;11.5$, which is consistent in both form and scale with the observed $n(z)$ under-density. To examine further the accuracy of the counts model, we compare its prediction for the fainter $n(K)$ counts of the Galaxy and Mass Assembly (GAMA) survey. We further compare these data with a model assuming the parameters of a previous study where little evidence for the Local Hole was found. At $13

Motivation & Objective

• To test whether the Local Hole—previously detected over a limited sky area—extends across a significantly larger fraction of the sky.
• To resolve the tension between local $H_0$ measurements and $Λ$CDM predictions by quantifying the impact of large-scale under-density on distance ladder results.
• To evaluate the validity of galaxy count models used in prior studies, particularly those assuming homogeneous luminosity functions.
• To reconcile conflicting results on the Local Hole, including those from Lavaux & Hudson (2011) and Jasche & Lavaux (2019), by comparing model predictions with data across multiple surveys.

Proposed method

• Extended $K$-band number-magnitude ($n(m)$) and number-redshift ($n(z)$) counts to ~90% of the sky, limited to $|b| \geq 5^\circ$ and $K < 11.5$, using 2MASS and 2M++ catalogues.
• Constructed a homogeneous galaxy counts model assuming a luminosity function and parameters consistent with prior work, used as a baseline for comparison.
• Compared model predictions with observed $n(K)$ counts from the GAMA survey at fainter magnitudes ($13 < K < 16$) to test model robustness.
• Evaluated the fit of the model against alternative models, including one with a lower luminosity function normalization from Lavaux & Hudson (2011), to assess sensitivity to LF assumptions.
• Quantified the under-density as a function of redshift and magnitude, and estimated its impact on local $H_0$ measurements via velocity bias from large-scale structure.
• Assessed significance of the under-density against $Λ$CDM expectations, finding tension at ~3$σ$ level due to scale and amplitude.

Experimental results

Research questions

• RQ1 Does the Local Hole under-density extend across a majority of the sky, beyond the ~20% coverage of previous studies?
• RQ2 To what extent does the observed under-density in $n(z)$ and $n(K)$ counts bias local measurements of the Hubble constant $H_0$?
• RQ3 Why do some studies (e.g., Lavaux & Hudson 2011) fail to detect the Local Hole, and is this due to incorrect assumptions about the luminosity function?
• RQ4 Can the observed under-density be reconciled with the $Λ$CDM model, or does it indicate a fundamental tension in cosmological structure formation?
• RQ5 How do the results from galaxy counts compare with dynamical evidence from supernovae and velocity flows?

Key findings

• The Local Hole extends to cover approximately 90% of the sky, with a significant under-density detected in both $n(z)$ and $n(K)$ counts at $z < 0.075$.
• A consistent under-density of $20 \pm 2\%$ is measured in $K$-band counts relative to the homogeneous model, confirming the result from redshift counts.
• The under-density leads to a ~3% overestimation of the local Hubble constant $H_0$, which helps alleviate but does not fully resolve the $H_0$ tension with early-Universe $Λ$CDM predictions.
• The model with a higher luminosity function normalization (used in this study) provides a significantly better fit to GAMA $n(K)$ counts at $13 < K < 16$ than the model with lower normalization from Lavaux & Hudson (2011).
• The observed under-density is inconsistent with $Λ$CDM cosmology at a ~3$σ$ significance level, indicating a potential large-scale inhomogeneity.
• The failure of some studies to detect the Local Hole is attributed to the use of luminosity function parameters derived from within the under-density itself, leading to a biased low normalization.