⚛️ phenomenology

No evidence for p- or d-wave dark matter annihilation from local large-scale structure

By analyzing full-sky gamma-ray predictions from local large-scale structure using constrained N-body simulations and comparing them with Fermi-LAT observations, this study establishes the tightest constraints to date on velocity-dependent p- and d-wave dark matter annihilation, finding no evidence for such signals and deriving limits significantly stronger than those from dwarf spheroidal galaxies.

Original authors: Andrija Kostić, Deaglan J. Bartlett, Harry Desmond

Published 2026-02-16

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CC BY 4.0

Original authors: Andrija Kostić, Deaglan J. Bartlett, Harry Desmond

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 Idea: Hunting for Dark Matter in the "Wrong" Places

Imagine you are trying to hear a whisper in a crowded room. Usually, you'd stand right next to the person whispering to hear them best. In the world of astronomy, scientists have been doing exactly this: they've been looking for signals from Dark Matter (the invisible stuff that holds galaxies together) in dwarf galaxies right next to our own Milky Way. These small galaxies are like the "whispering neighbors"—they are close, but they are also very quiet and slow.

For a long time, scientists assumed Dark Matter particles annihilate (smash into each other and disappear) at a constant rate, regardless of how fast they are moving. But what if that's wrong?

What if Dark Matter is like a speed demon? What if it only "annihilates" (creates a detectable signal) when it's moving very fast?

This paper asks: "If Dark Matter is a speed demon, where should we look for it?"

The Analogy: The Slow Turtle vs. The Fast Car

The Old Way (Dwarf Galaxies): Think of dwarf galaxies as a slow-moving turtle. Even if there are lots of turtles, they are moving so slowly that if Dark Matter needs speed to create a signal, the turtles are too sluggish to make any noise.
The New Way (Massive Clusters): Think of massive galaxy clusters as Formula 1 race cars. They are far away, but they are huge and moving incredibly fast. If Dark Matter needs speed to annihilate, these "race cars" are the perfect place to find the signal.

The authors of this paper realized that if Dark Matter relies on speed (specifically "p-wave" or "d-wave" annihilation), looking at the slow dwarf galaxies is a waste of time. We need to look at the fast, massive clusters of galaxies.

How They Did It: The "Cosmic Crystal Ball"

To test this, the scientists didn't just guess; they built a 3D digital twin of our local universe.

The Simulation (CSiBORG): They used a supercomputer to run a simulation called CSiBORG. Imagine this as a massive, virtual video game of the universe. They didn't just make random galaxies; they used a special algorithm (BORG) to reconstruct the actual positions of galaxies we see in the sky, creating a realistic map of where the invisible Dark Matter is hiding.
The Speed Check: They calculated how fast Dark Matter particles are moving in different parts of this map. They found that in the massive clusters (the "race cars"), the particles are zooming around much faster than in the dwarf galaxies (the "turtles").
The Telescope Check: They took their digital predictions and compared them to real data from the Fermi Space Telescope, which scans the entire sky for gamma rays (high-energy light).

The Results: Silence is Golden

The team looked for a specific type of gamma-ray signal that would appear if Dark Matter was annihilating at high speeds.

The Verdict: They found nothing. No signal.
The Implication: This doesn't mean Dark Matter doesn't exist. It means that if Dark Matter does annihilate based on speed, it's doing so at a rate much, much lower than we hoped.

The "Tighter Net" Analogy:
Imagine trying to catch a fish with a net.

Previous studies used a net with holes the size of a basketball (looking at dwarf galaxies).
This study used a net with holes the size of a grain of rice (looking at massive clusters).
Because they used a much finer net, they could rule out a much wider range of possibilities. Their new limits on how fast Dark Matter can annihilate are 100 times tighter for "p-wave" and 10 million times tighter for "d-wave" than previous studies.

Why This Matters

We Know Where to Look: If Dark Matter is a speed demon, we now know we must look at the biggest, fastest galaxy clusters, not the small, slow dwarf galaxies.
Ruling Out Theories: They have proven that certain popular theories about how Dark Matter behaves are likely wrong. If Dark Matter were annihilating at the rates some theories predicted, they would have seen a bright flash in the massive clusters. They didn't.
The "Thermal Relic" Mystery: There is a theory that Dark Matter is a "thermal relic" (leftover from the Big Bang). The authors checked if their new, strict limits rule this out. They don't. Dark Matter can still be a thermal relic; it just has to be even more "shy" (annihilate even less often) than we thought.

The Bottom Line

This paper is like a detective saying, "We stopped looking for the thief in the quiet library (dwarf galaxies) and started looking in the busy train station (massive clusters). We didn't find the thief, but we now know exactly how quiet the thief must be to have escaped us."

They haven't found Dark Matter yet, but they have drawn a much tighter circle around where it can't be, bringing us one step closer to understanding what it actually is.

1. Problem Statement

The search for dark matter (DM) via indirect detection typically focuses on dwarf spheroidal galaxies (dSphs) due to their high mass-to-light ratios and proximity. However, this strategy relies on the assumption that the DM annihilation cross-section ( $\sigma$ ) is independent of velocity (s-wave).

Many theoretical models predict velocity-dependent annihilation, specifically:

p-wave: $\sigma v \propto v^2$ (dominant for fermionic DM annihilating to spin-0 particles).
d-wave: $\sigma v \propto v^4$ (dominant for real scalar DM).

In these scenarios, the annihilation rate is heavily suppressed in low-velocity dispersion environments like dSphs. Consequently, dSphs provide weak constraints on velocity-dependent models. Instead, massive extragalactic halos (galaxy clusters) with high velocity dispersions should produce significantly stronger gamma-ray signals. The authors aim to test these models by searching for gamma-ray emission from the local large-scale structure (LSS) rather than relying solely on dSphs.

2. Methodology

The authors employ a "forward modeling" approach combining constrained cosmological simulations with Fermi-LAT gamma-ray data.

A. Constrained Simulations (CSiBORG)

Data Source: They utilize the CSiBORG suite of 101 constrained N-body simulations. These simulations reconstruct the 3D dark matter density field of the local Universe (within $\sim 155 h^{-1}$ Mpc) by matching the observed positions of galaxies in the 2M++ catalogue.
Algorithm: The initial conditions are inferred using the BORG (Bayesian Origin Reconstruction from Galaxies) algorithm, which marginalizes over galaxy bias parameters.
Resolution: The simulations resolve halos down to $M_{200m} \approx 4.4 \times 10^{11} M_\odot$ . The analysis focuses on halos up to $\sim 200$ Mpc.

B. Velocity-Dependent J-Factor Calculation

The gamma-ray flux depends on the "J-factor," which integrates the DM density and velocity distribution along the line of sight.

Formalism: For velocity-dependent annihilation, the J-factor ( $J_\ell$ $J_{ℓ}$ ) involves higher-order moments of the velocity distribution.
- p-wave ( $\ell=1$ ): Requires the second moment of velocity ( $\langle v^2 \rangle$ ). The authors assume spherical symmetry and solve the Jeans equation with an NFW density profile. They test anisotropy parameters ( $\beta$ ) and find $\beta=0$ (isotropic) to be the most conservative choice.
- d-wave ( $\ell=2$ ): Requires the fourth moment of velocity ( $\langle v^4 \rangle$ ). Since the system of equations is not closed, they assume an ergodic distribution function to derive an analytical solution for $\langle v^4 \rangle$ based on the Jeans equation.
Output: They generate full-sky J-factor maps at HEALPix resolution ( $n_{side}=2048$ ), which are then degraded to $n_{side}=256$ for inference.

C. Gamma-Ray Data and Likelihood

Data: Fermi Large Area Telescope (LAT) data (Mission weeks 9–634) in the energy range 500 MeV – 50 GeV.
Masking: Regions with galactic latitude $|b| < 30^\circ$ are masked to reduce Galactic foregrounds and the Galactic Center Excess (GCE).
Model Components: The total flux model includes:
1. DM annihilation (template derived from CSiBORG J-factors).
2. Isotropic background.
3. Galactic diffuse emission (using Fermi templates).
4. Point sources (4FGL-DR3 catalog).
Inference: A Markov Chain Monte Carlo (MCMC) algorithm (No U-Turn Sampler) is used to jointly infer the amplitude of the DM signal and the normalization of astrophysical backgrounds. The analysis marginalizes over uncertainties in the density field reconstruction (by averaging over 101 simulation realizations) and astrophysical templates.

3. Key Contributions

First Full-Sky Field-Level Inference: This is the first study to perform a full-sky, field-level inference for velocity-dependent DM annihilation using constrained simulations, moving beyond the "stacking" of individual objects.
Analytical d-wave J-Factor: The paper provides a novel analytical derivation for the d-wave J-factor under the assumption of an ergodic distribution function, solving the fourth moment of the velocity distribution.
Systematic Uncertainty Quantification: The authors rigorously test systematic uncertainties, including:
- The choice of anisotropy parameter ( $\beta$ ).
- The impact of baryonic physics (noting that baryons could increase J-factors, making their limits conservative).
- The completeness of the simulation volume vs. external cluster catalogs (MCXC).
- The influence of point sources.

4. Results

A. Detection Status

No Evidence Found: The analysis finds no evidence for p-wave or d-wave DM annihilation across the mass range $m_\chi = 2 - 500$ GeV/ $c^2$ for various annihilation channels (quarks, leptons, gauge bosons).
Flux Consistency: The inferred flux amplitudes for the DM component are consistent with zero at $1\sigma$ confidence for all energy bins.

B. Constraints on Cross-Sections

The authors place 95% confidence upper limits on the annihilation coefficients $a_\ell$ (where $\sigma v = a_\ell (v/c)^{2\ell}$ ).

Example (b $\bar{b}$ channel, $m_\chi = 10$ GeV/ $c^2$ ):
- p-wave: $a_1 < 2.4 \times 10^{-21}$ cm $^3$ s $^{-1}$ .
- d-wave: $a_2 < 3.0 \times 10^{-18}$ cm $^3$ s $^{-1}$ .
Comparison to dSphs:
- The constraints are $\sim 2$ orders of magnitude tighter than those from dSphs for p-wave.
- The constraints are $\sim 7$ orders of magnitude tighter than those from dSphs for d-wave.
- Reasoning: Massive halos have velocity dispersions ( $\sim 1000$ km/s) orders of magnitude higher than dSphs ( $\sim 10$ km/s). Since p-wave scales as $v^2$ and d-wave as $v^4$ , the signal in clusters is vastly enhanced relative to dSphs.

C. Thermal Relic Viability

The authors calculate the required cross-section for DM to be a thermal relic with velocity-dependent annihilation.
The required values ( $a_1 \sim 10^{-25}$ , $a_2 \sim 10^{-25}$ ) are several orders of magnitude below the observational upper limits derived in this work.
Conclusion: The study cannot rule out DM being a thermal relic with velocity-dependent annihilation, but it provides the tightest constraints to date.

5. Significance

Paradigm Shift: The paper demonstrates that for velocity-dependent DM models, massive extragalactic halos are superior targets to dwarf galaxies. This reverses the standard hierarchy used in s-wave searches.
Methodological Benchmark: It establishes a robust framework for using constrained simulations (CSiBORG) and Bayesian inference to model the full-sky DM signal, accounting for reconstruction uncertainties.
Future Directions: The authors note that the dominant systematic uncertainty is the accuracy of the reconstructed halo masses (specifically the high-mass end). Future work should focus on higher-resolution simulations and improved reconstruction algorithms (e.g., Manticore) to further tighten these bounds.
Implications for GCE: The results suggest that velocity-dependent annihilation is unlikely to explain the Galactic Center Excess (GCE) if the required cross-sections are consistent with the thermal relic abundance, as the constraints from LSS are increasingly stringent.

In summary, this work significantly advances the indirect detection of dark matter by proving that the local large-scale structure provides the most powerful current constraints on p- and d-wave annihilation, surpassing traditional dwarf galaxy searches by orders of magnitude.