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Lensing the darkness: The matter density profile in cosmic voids from UNIONS

Using data from the UNIONS and BOSS surveys, this study presents a novel method to achieve the most significant detection to date of weak lensing in cosmic voids, revealing distinct matter density profiles for different void sizes and confirming a galaxy bias factor consistent with other works.

Original authors: Hunter L. Martin, Michael J. Hudson, Alex Woodfinden, Lucie Baumont, Thomas de Boer, Pierre A. Burger, Jack Elvin-Poole, Sébastien Fabbro, Samuel Farrens, Sacha Guerrini, Axel Guinot, Fabian Hervas-Pe

Published 2026-02-18

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Hunter L. Martin, Michael J. Hudson, Alex Woodfinden, Lucie Baumont, Thomas de Boer, Pierre A. Burger, Jack Elvin-Poole, Sébastien Fabbro, Samuel Farrens, Sacha Guerrini, Axel Guinot, Fabian Hervas-Peters, Hendrik Hildebrandt, Martin Kilbinger, Magdy Morshed, Ludovic van Waerbeke, Anna Wittje

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Picture: Mapping the "Empty" Spaces

Imagine the Universe isn't just a random sprinkling of stars. Instead, think of it like a giant, 3D spiderweb. The thick strands of the web are clusters of galaxies (overdensities), and the empty spaces between the strands are cosmic voids.

For a long time, astronomers focused on the "strands" because they are bright and easy to see. But this paper focuses on the "holes" in the web. These voids are the emptiest places in the Universe. The goal of this study was to weigh the emptiness. How much matter is actually missing from these holes? And does the "missing" matter behave differently in small holes versus giant holes?

The Main Characters

The Voids (The Holes): These are the targets. They are vast regions where there are very few galaxies.
The UNIONS Survey (The Flashlight): This is a massive telescope survey in the Northern Hemisphere. It acts like a high-powered flashlight, looking at the background of the Universe to see how light bends.
The BOSS Survey (The Map): This is a catalog of galaxies that helped the team identify exactly where the voids are located.
Weak Lensing (The Distortion): This is the tool used to "weigh" the voids.

The Analogy: The Trampoline and the Bowling Ball

To understand Weak Lensing, imagine a giant trampoline representing space.

Normal Gravity: If you put a heavy bowling ball (a galaxy cluster) on the trampoline, it creates a deep dip. If you roll a marble (light) past it, the marble's path curves toward the ball.
Cosmic Voids: A void is like the opposite of a bowling ball. It's a region where the trampoline is actually flatter or even slightly "bumped up" because there is less weight there.
The Effect: When light from distant galaxies passes through a void, it doesn't get pulled in; it gets pushed outward. It's like the light is being gently repelled by the emptiness. This causes the background galaxies to look slightly stretched or aligned in a specific pattern (radially) around the void.

What Did They Do?

The team combined data from two massive surveys (UNIONS and BOSS) to catch this subtle effect. It's like trying to hear a whisper in a noisy room. The "whisper" is the tiny distortion of light caused by the void.

The Challenge:
Detecting this is incredibly hard.

The Signal is Weak: Voids are empty, so they don't bend light as much as heavy galaxy clusters do.
The Noise: There is a lot of "static" (random shapes of galaxies) that can hide the signal.
The Definition Problem: How do you define the edge of a hole? Is it a perfect circle? The paper had to invent a new way to calculate the "noise" (covariance) to make sure their detection was real and not just a fluke.

The Big Discoveries

After crunching the numbers, they found some exciting things:

1. They Found the Signal!
They detected the "whisper" of the voids with a statistical certainty of 6.2 sigma.

Analogy: In science, "5 sigma" is the gold standard for a discovery (like finding a new particle). Getting 6.2 is like hearing a whisper so clearly that you are 99.9999% sure it's not just the wind. This is the most significant detection of its kind using spectroscopic data (high-precision galaxy maps) to date.

2. Small Holes vs. Big Holes
They found that small voids and giant voids look different.

Small Voids: These tend to have a "thicker wall" of galaxies around them. Imagine a small bubble in a soap film; the rim is very distinct.
Large Voids: These are more like vast, flat deserts. The transition from "empty" to "full" is more gradual.
Why it matters: This difference helps scientists understand how the Universe grew. Small voids might be "voids inside clouds" (holes inside a bigger clump of matter), while big voids are the true giants of the cosmic web.

3. Testing the "Bias" (The Relationship between Light and Mass)
A major question in cosmology is: "Do galaxies trace the invisible dark matter perfectly?"

They compared the "shape" of the void (measured by light bending) with the "location" of the galaxies inside it.
They found that galaxies act as a slightly biased tracer. They are about 2.45 times more clustered in these empty regions than we might expect from a simple linear rule. It's like if you tried to map a crowd of people by only looking at the people wearing red hats; you'd get a good map, but you'd have to multiply your count by a specific factor to get the real number.

Why Does This Matter?

This paper is a stepping stone.

Proof of Concept: It proves that we can use "weak lensing" to weigh the emptiness of the Universe.
Future Tools: As we get better telescopes (like the upcoming Euclid and Roman space telescopes), we will be able to map these voids with even greater precision.
New Physics: By understanding these empty spaces, we can test theories about Dark Energy (what is pushing the universe apart) and Neutrinos (tiny, ghostly particles). Voids are so empty that they are very sensitive to these subtle forces.

The Bottom Line

The authors successfully turned the "darkness" of the Universe into a measurable signal. They proved that even the emptiest places in the cosmos have a shape, a weight, and a story to tell about how our Universe evolved. They didn't just find a hole; they weighed the hole and found it matches our best theories, opening the door for future discoveries.

1. Problem Statement

Cosmic voids are large underdense regions in the cosmic web that offer a unique environment for testing cosmological physics, particularly dark energy, neutrino mass, and modified gravity, due to their low density and relative insensitivity to baryonic effects. While void statistics (like size functions and cross-correlations) have been used to constrain cosmology, measuring the matter density profile of voids via weak gravitational lensing remains observationally challenging.

The primary challenges include:

Weak Signal: Voids have a maximum underdensity of $\delta = -1$ (a pure vacuum), resulting in a lensing signal significantly weaker than that of overdense clusters or galaxies.
Definition Ambiguity: Voids lack direct observational boundaries. Different void-finding algorithms (e.g., 2D projected vs. 3D ZOBOV) and center definitions (barycentre vs. circumcentre) yield different statistical properties and density profiles.
Systematics: Accurate measurement requires rigorous handling of shear systematics, covariance estimation (especially given the large scales involved), and the selection effects introduced by survey masks.
Lack of High-Significance Detection: Prior detections of void lensing from spectroscopic tracers were limited in significance (typically $<3\sigma$ ), often relying on photometric redshifts which introduce selection biases.

2. Methodology

The authors utilize the overlap between the Ultraviolet Near-Infrared Optical Northern Survey (UNIONS) for background source galaxies and the Baryon Oscillation Spectroscopic Survey (BOSS) LOWZ and CMASS catalogues for foreground voids.

Data Sets

Sources: UNIONS $r$ -band imaging (CFIS) provides $\approx 83.8$ million galaxy shapes. Redshift distributions are calibrated using a Self-Organizing Map (SOM) trained on overlapping spectroscopic surveys.
Lenses (Voids): 3D voids identified in the BOSS LOWZ ( $0.2 < z < 0.43$ $0.2 < z < 0.43$ ) and CMASS ( $0.43 < z < 0.75$ $0.43 < z < 0.75$ ) luminous red galaxy (LRG) catalogues using the Revolver code (based on the ZOBOV algorithm).
- Reconstruction: Redshift-space distortions (RSD) are corrected by reconstructing tracer positions to real space using the Zel'dovich approximation.
- Selection: Voids are filtered to ensure overlap with the UNIONS footprint. The final sample includes 2,975 voids (944 LOWZ, 2,031 CMASS).
- Sub-samples: The sample is split into "Small" and "Large" voids based on a weighted average radius ( $48.5 h^{-1}$ Mpc) to study size-dependent evolution.

Lensing Measurement

Stacking: Due to the weak signal, voids are stacked. Radial bins are scaled by the individual void radius ( $R/R_V$ ) to align features across the population.
Signal Extraction: The excess surface mass density ( $\Delta\Sigma$ ) is calculated as a weighted average of tangential shear ( $\gamma_t$ ) around the voids.
Systematic Removal: To remove shear systematics, the authors measure the $\Delta\Sigma$ signal around randomly distributed voids generated from 1,000 PATCHY mock catalogues. These mocks reproduce the survey geometry and selection effects. The random signal is subtracted from the data.

Covariance Modelling

A novel contribution is the derivation of an analytic Gaussian covariance adapted for void lensing:

The standard covariance formula (Krause et al. 2013) is simplified by neglecting sub-dominant terms ( $C_{VV}$ and $C_{V\kappa}$ ) and focusing on the shape noise and the large-scale structure (LSS) term ( $C_{\kappa\kappa}/n_V$ ).
Because voids have varying radii, the covariance is computed individually for each void and then summed/weighted, rather than using a fixed binning scheme.
This analytic model is validated against the empirical covariance derived from the 30 random mock catalogues.

Model Fitting

Two models are fitted to the data:

Analytic Profile: The five-parameter Hamaus-Sutter-Wandelt (HSW) model, modified by Barreira et al. (2015) to free the asymptotic scale parameter ( $r_{s2}$ ).
Void-Galaxy Cross-Correlation: Using the measurement from Woodfinden et al. (2022), the authors test the linear bias relation $\xi_{Vm} = \xi_{Vg} / b_{Vg}$ to constrain the galaxy bias in underdense environments ( $b_{Vg}$ ).

3. Key Contributions

Highest Significance Detection: Achieved a $6.2\sigma$ detection of the stacked weak lensing signal from spectroscopic voids, the most significant detection of its kind to date.
Novel Covariance Approach: Successfully adapted and validated an analytic Gaussian covariance model for void lensing, demonstrating its reliability against empirical mock-based estimates.
Size-Dependent Profiles: Provided evidence that small and large voids possess statistically distinct matter density profiles, with small voids showing more pronounced overdense walls.
Bias Constraint: Measured the void-galaxy bias factor ( $b_{Vg} = 2.45 \pm 0.36$ ), testing the linearity of the mass-light relation in voids.
Methodological Rigor: Demonstrated the necessity of using mock-based random catalogs to account for survey boundary selection effects in void lensing.

4. Key Results

Detection Significance: The full sample yields a $6.2\sigma$ detection. Sub-samples show $4.4\sigma$ (LOWZ), $3.4\sigma$ (CMASS), $4.5\sigma$ (Small), and $4.4\sigma$ (Large).
Matter Density Profiles:
- The profiles show clear underdensities with minima near the void radius.
- Small vs. Large: Small voids cross zero density just past $R_V$ , while Large voids cross zero at $\approx 2.5 R_V$ . Small voids exhibit a significant overdense wall (compensated/overcompensated), whereas large voids are undercompensated with less prominent walls.
- The difference between Small and Large profiles is significant at the $2.3\sigma$ level.
Integrated Density Contrast:
- At $0.5 R_V$ , all samples show consistent underdensities ( $\Delta \approx -0.25$ ).
- At $R_V$ , Small voids are compensated ( $\Delta \approx 0$ ), while Large voids remain undercompensated ( $\Delta \approx -0.07$ ).
- At $3 R_V$ , Small voids are slightly overcompensated, while Large voids remain undercompensated.
Galaxy Bias:
- The best-fit galaxy bias is $b_{Vg} = 2.45 \pm 0.36$ .
- This is consistent with the large-scale linear bias ( $b_g$ ) measured by Sugiyama et al. (2022) but slightly higher, consistent with predictions by Nadathur & Percival (2018) that $b_{Vg} > b_g$ due to stochastic selection effects.
- The data does not yet have sufficient precision to confirm the trend of $b_{Vg}$ increasing with decreasing void size predicted by Pollina et al. (2017).
Comparison with Simulations: The measured profiles are shallower than some simulated profiles (e.g., Nadathur & Hotchkiss 2015a), particularly for LOWZ voids, suggesting potential differences in void selection or unmodeled systematics.

5. Significance and Future Outlook

This work establishes that weak lensing around cosmic voids is a viable and high-significance cosmological probe using current ground-based survey data.

Cosmological Potential: The detection of the void lensing signal opens the door to using voids to constrain neutrino mass, modified gravity, and dark energy, as these theories predict specific deviations in void profiles.
Future Surveys: The authors project that next-generation surveys like Euclid and Roman, which will provide deeper, wider, and tomographic data (including photometric redshifts), will significantly improve signal-to-noise ratios.
Methodological Path: The paper highlights the need for emulators that can map specific void-finding algorithms to cosmological parameters to fully exploit the information content of void statistics in future large-scale structure analyses.

In conclusion, this paper represents a major step forward in "lensing the darkness," transforming cosmic voids from theoretical curiosities into robust observational tools for precision cosmology.