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KiDS-Legacy: WIMP dark matter constraints from the cross-correlation of weak lensing and Fermi-LAT gamma rays

This paper presents constraints on WIMP dark matter decay and annihilation by analyzing the cross-correlation between 15 years of Fermi-LAT gamma-ray data and KiDS-Legacy weak lensing shear, finding no significant signal and establishing 95% upper bounds that complement other cosmological and local probes while forecasting improved limits with future Euclid-like surveys.

Original authors: Shiyang Zhang, Hendrik Hildebrandt, Ziang Yan, Tilman Tröster, Athithya Aravinthan, Marika Asgari, Deaglan J. Bartlett, Maciej Bilicki, Dominik Elsässer, Catherine Heymans, Benjamin Joachimi, Lauro Mo

Published 2026-06-03

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Shiyang Zhang, Hendrik Hildebrandt, Ziang Yan, Tilman Tröster, Athithya Aravinthan, Marika Asgari, Deaglan J. Bartlett, Maciej Bilicki, Dominik Elsässer, Catherine Heymans, Benjamin Joachimi, Lauro Moscardini, Dennis Neumann, Anya Paopiamsap, Robert Reischke, Benjamin Stölzner

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: Hunting for the Invisible Ghost

Imagine the universe is a giant, dark room filled with furniture. We can see the furniture (stars, galaxies, gas), but we know there is a massive amount of invisible "ghost" stuff (Dark Matter) holding the room together. We can't see the ghosts, but we know they are there because they have gravity—they pull on the visible furniture.

Scientists have a big question: What are these ghosts made of? One popular theory is that they are "WIMPs" (Weakly Interacting Massive Particles). The paper asks: If these WIMPs exist, do they ever bump into each other and disappear (annihilate) or fall apart (decay)? If they do, they should leave behind a tiny, faint trail of energy, like a ghost leaving a footprint in the dust.

The Detective Work: Two Different Cameras

To find these footprints, the researchers acted like detectives using two different types of cameras to look at the same patch of the universe:

The "Gravity Camera" (KiDS-Legacy): This is a telescope that looks at the shapes of distant galaxies. Because invisible dark matter pulls on light, it slightly stretches the shapes of these galaxies. By measuring these tiny distortions, the team created a 3D map of where the invisible dark matter is hiding.
The "Energy Camera" (Fermi-LAT): This is a space telescope that looks for high-energy light (gamma rays). If dark matter particles are bumping into each other or decaying, they should release gamma rays. The team looked at 15 years of data from this telescope to create a map of the "background glow" of the universe.

The Strategy: Looking for a Match

The scientists didn't just look at one map; they tried to cross-correlate them.

The Analogy: Imagine you have a map of where the wind is blowing (Dark Matter) and a map of where the leaves are swirling (Gamma Rays). If the wind is actually causing the leaves to swirl, the two maps should match perfectly. Where the wind is strongest, the leaves should be swirling the most.
The Goal: They wanted to see if the "gravity distortions" (where dark matter is) lined up with the "gamma-ray glow" (where dark matter might be exploding).

The Process: Cleaning the Noise

The universe is messy. The gamma-ray map isn't just dark matter; it's also filled with "noise" from real, visible things like black holes (blazars) and star-forming galaxies.

The researchers had to act like a sound engineer using a noise-canceling filter. They mathematically subtracted the known "loud" sources (like blazars) to see if a faint "whisper" of dark matter remained underneath.
They also had to deal with the "fuzziness" of the gamma-ray camera (the Point Spread Function), which blurs the image, making it hard to see small details.

The Results: The Silence

After crunching the numbers and comparing the two maps across 10 different energy levels and 6 different distances (redshifts), the result was... silence.

No Match Found: The map of where dark matter is did not line up with the map of where gamma rays are coming from in a way that suggests dark matter is exploding.
The Conclusion: They found no significant evidence that dark matter is annihilating or decaying in the way they looked for.

What This Means: Setting the "Speed Limit"

Even though they didn't find the ghosts, they learned something very important. Because they didn't see the "footprints," they can now set a strict speed limit on how fast the ghosts can be disappearing.

The Analogy: Imagine you are looking for a leak in a roof. You don't see any water dripping. You can't say "there is no leak," but you can say, "If there is a leak, it must be smaller than a pinprick."
The Paper's Claim: The authors calculated the maximum possible rate at which dark matter could be decaying or annihilating without them having seen it. They found that if dark matter is doing this, it must be doing it very, very slowly.

The Future: Sharper Eyes

The paper also looked ahead to future telescopes (like the Euclid mission).

The Analogy: They compared their current "blurry" camera to a future "4K Ultra-HD" camera.
The Forecast: They predict that with the new, wider, and deeper data from future surveys, they will be able to tighten these "speed limits" by about two times. This means future data will be twice as good at ruling out theories about how dark matter behaves.

Summary

In short, this paper is a report from a cosmic detective team. They used two powerful tools to look for signs of dark matter exploding. They didn't find the explosion, but they successfully proved that if it is happening, it is happening much more quietly than previously thought. They also showed that future telescopes will give us an even sharper look to solve the mystery.

Technical Summary: KiDS-Legacy: WIMP dark matter constraints from the cross-correlation of weak lensing and Fermi-LAT gamma rays

Problem and Motivation
Dark matter (DM) constitutes approximately 27% of the Universe's mass-energy content, yet its microscopic properties remain unknown. Weakly Interacting Massive Particles (WIMPs) are a leading candidate, hypothesized to annihilate or decay into standard model particles, producing detectable gamma-rays. While indirect detection efforts have traditionally targeted high-density local regions (e.g., the Galactic Centre or dwarf spheroidal galaxies), the Unresolved Gamma-Ray Background (UGRB) offers a probe of DM across cosmological distances. The UGRB contains cumulative emissions from unresolved astrophysical sources (primarily blazars) and potentially a DM component. This paper investigates the nature of DM by cross-correlating the UGRB with weak gravitational lensing data. Unlike galaxy clustering, which traces biased tracers of matter, weak lensing provides an unbiased map of the total matter distribution, offering a complementary method to constrain DM annihilation and decay.

Methodology
The study performs a cross-correlation analysis between two distinct datasets:

Weak Lensing Data: The authors utilize the fifth data release of the Kilo-Degree Survey (KiDS-Legacy), covering 1347 deg². Galaxy shapes were measured using lensfit and calibrated with SKiLLS simulations. The sample was divided into six tomographic redshift bins ( $z \in [0.10, 2.00]$ ) based on Bayesian photometric redshifts.
Gamma-Ray Data: 15 years of Fermi-LAT observations (up to July 2023) were processed using Pass 8 event data. The analysis focused on the UGRB by masking the Galactic plane, point sources (using the 4FGL-DR3 catalogue), and regions with high diffuse emission. The data were binned into ten logarithmic energy intervals ranging from 0.5 to 1000 GeV.

Analysis Framework:

Power Spectrum Estimation: The cross-correlation angular power spectra ( $C_{g\kappa}^\ell$ ) between gamma-ray intensity ( $g$ ) and lensing convergence ( $\kappa$ ) were estimated using the pseudo- $C_\ell$ method (NaMaster/MASTER algorithm). The analysis utilized E-modes (cosmological signal) and B-modes (systematic null test) of the shear field.
Theoretical Modeling: The authors modeled the cross-power spectrum using the Limber approximation within a flat $\Lambda$ $Λ$ CDM cosmology. The model included:
- DM Annihilation and Decay: Window functions were constructed for WIMP annihilation and decay into three final states ( $b\bar{b}$ , $\mu^+\mu^-$ , $\tau^+\tau^-$ ). The annihilation signal incorporated a clumping factor ( $\Delta^2$ ) with three scenarios (low, mid, high) to account for subhalo concentration.
- Astrophysical Background: The UGRB was modeled assuming unresolved blazars are the dominant astrophysical source, utilizing a luminosity-dependent density evolution (LDDE) model.
Covariance and Likelihood: A hybrid covariance matrix was constructed, combining jackknife resampling (for diagonal variances) and Gaussian covariance from NaMaster (for off-diagonal correlations). A $\chi^2$ likelihood analysis was performed to derive 95% confidence upper limits on the thermally averaged annihilation cross-section ( $\langle \sigma_{ann}v \rangle$ ) and the decay rate ( $\Gamma_{dec}$ ).

Key Results

Non-Detection: The analysis found no statistically significant cross-correlation signal between the KiDS-Legacy weak lensing data and the Fermi-LAT UGRB. The global $\chi^2$ for the E-mode signal was 176.51 over 300 data points (consistent with a null hypothesis), and B-mode tests confirmed the absence of significant systematics.
Constraints: Based on the non-detection, the authors established 95% upper bounds on $\langle \sigma_{ann}v \rangle$ $⟨ σ_{ann} v ⟩$ and $\Gamma_{dec}$ $Γ_{d ec}$ for WIMP masses between 10 GeV and 1 TeV.
- The constraints are competitive with, and in some cases tighter than, previous cross-correlation studies using CFHTLenS, RCSLenS, and earlier KiDS data, particularly for low and mid clumping scenarios.
- When compared to local probes (e.g., IceCube, H.E.S.S., MAGIC), the cosmological cross-correlation approach provides complementary constraints, particularly effective at low masses (GeV/TeV range).
Discrepancy with Other Tracers: The paper notes a discrepancy with recent results from the Dark Energy Survey (DES), which reported significant ( $5.3\sigma$ to $8.9\sigma$ ) cross-correlation detections using galaxy shear. The authors attribute their null result to differences in effective sky coverage, the specific masking strategies employed (stricter LAT selections reducing photon counts and low- $\ell$ modes), and the fragmented geometry of the KiDS-Fermi overlap, which may reduce sensitivity to large-scale correlations.

Significance and Claims
The paper claims that while no DM signal was detected, the study successfully demonstrates the viability of using weak lensing cross-correlations to constrain DM properties on cosmological scales. The results highlight that weak lensing provides a robust, unbiased tracer of matter that is less dependent on galaxy bias assumptions than galaxy clustering.

The authors emphasize the complementary nature of their constraints relative to local searches and other cosmological tracers. Furthermore, they present forecasts for a future Euclid-like survey cross-correlated with Fermi-LAT. These forecasts suggest that such future data could tighten constraints on $\langle \sigma_{ann}v \rangle$ and $\Gamma_{dec}$ by a factor of approximately two. The authors caution that this improvement is limited not by the lensing data alone, but by the statistical uncertainties and Point Spread Function (PSF) limitations inherent in current and near-future gamma-ray maps.

The study concludes that while current data yields only upper limits, the methodology is sound and sets the stage for more sensitive constraints as future surveys (Euclid, LSST) and extended Fermi-LAT exposure reduce statistical noise and improve systematic control.