⚛️ phenomenology

Mass-Dependent Dark Matter Deficit from Inelastic Scattering

This paper proposes that exothermic inelastic dark matter with strongly velocity-dependent scattering, mediated by vector and scalar fields with opposite-sign contributions, explains the observed mass-dependent deficit of dark matter in the central regions of nearby galaxies by suppressing $s$ -wave conversion at low velocities while enabling $p$ -wave down-scattering at higher velocities to lower central densities.

Original authors: Daneng Yang, Yi-Zhong Fan

Published 2026-09-25

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CC BY 4.0

Original authors: Daneng Yang, Yi-Zhong Fan

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

Dark matter is the invisible scaffolding of the universe, a substance that does not emit light but exerts a powerful gravitational pull, holding galaxies together and shaping their evolution. For decades, astronomers have relied on computer simulations to predict how this hidden mass should be distributed within galaxies. These models suggest that as galaxies grow larger and more massive, their central regions should become increasingly dense with dark matter. However, a new wave of observations has begun to challenge this picture. By measuring the motion of stars and the distribution of gas in nearby galaxies, researchers have found that the most massive galaxies actually contain less dark matter in their centers than the simulations predict. This missing mass is not a small error; it is a systematic deficit that grows larger as the galaxy itself becomes more massive, a trend that standard physics cannot easily explain.

A team of researchers has proposed a new explanation for this discrepancy, suggesting that dark matter particles might be more complex than previously thought. Instead of being simple, static clumps, these particles could exist in two slightly different states, like two versions of the same coin. In this scenario, when two dark matter particles collide, they can switch from one state to the other. Crucially, this switch releases a small amount of energy, much like a spring uncoiling. The researchers found that this energy release depends heavily on how fast the particles are moving when they collide. At the slow speeds found in small, dwarf galaxies, this switching process is effectively shut down, leaving the dark matter distribution undisturbed. However, at the higher speeds typical of massive galaxies, the process becomes highly efficient.

The team developed a model where these particles interact through forces that change their behavior based on velocity. They simulated how this interaction would play out over billions of years in galaxies of different sizes. In the massive galaxies, the frequent, high-speed collisions cause the dark matter particles to switch states and release energy. This extra energy acts like a gentle push, heating up the dark matter and causing it to spread out, or "evaporate," from the dense center of the galaxy. This spreading creates the observed deficit of dark matter in the cores of large galaxies. In contrast, in smaller galaxies where the particles move more slowly, the switching mechanism remains dormant, and the dark matter stays concentrated, matching observations of those smaller systems.

To test this idea, the researchers ran detailed computer simulations of four different types of galaxies, ranging from small dwarfs to massive systems. They used the same set of rules for the dark matter particles in every simulation. The results showed that their model successfully reproduced the missing dark matter in all four types of galaxies. It explained why the deficit is small in dwarf galaxies, grows significantly in intermediate-sized galaxies, and becomes most pronounced in the largest systems. The model also accounted for the fact that in the most massive galaxy clusters, where particles move at extremely high speeds, the effect weakens again, keeping the theory consistent with observations of those distant, giant structures.

The researchers also considered whether standard processes, such as the explosion of stars or the activity of supermassive black holes, could be responsible for pushing the dark matter away. While these forces certainly play a role in galaxy formation, the team's work suggests they cannot fully explain the specific pattern of missing mass that increases steadily with galaxy size. Instead, the data points toward a fundamental property of the dark matter particles themselves. The proposed mechanism relies on a specific type of particle interaction that is sensitive to speed, a feature that standard models of dark matter do not include. By introducing this velocity-dependent behavior, the study offers a unified explanation for a puzzling trend that has emerged from recent, high-precision observations.

The study does not claim to have solved the mystery of dark matter entirely, but it provides a compelling new direction for understanding its nature. The model suggests that the dark matter in our universe is not a uniform, passive substance but one that can change its internal state and release energy under the right conditions. This behavior would leave a distinct fingerprint on the structure of galaxies, one that matches the growing gap between what we see and what we expected to see. If future observations of galaxy clusters and dwarf galaxies continue to align with these predictions, it could mean that the invisible mass shaping our universe is far more dynamic and interactive than we ever imagined.

Technical Summary: Mass-Dependent Dark Matter Deficit from Inelastic Scattering

Problem Statement
Recent observations combining spatially resolved stellar kinematics and neutral hydrogen data for 136 nearby galaxies reveal a systematic discrepancy with standard hydrodynamical simulations (TNG100, EAGLE, SIMBA, AIDA-TNG). Specifically, central dark matter densities in galaxies are increasingly lower than predicted as stellar mass increases, with the deficit extending from ~10 kpc to >50 kpc in massive systems. While baryonic feedback (e.g., AGN, mergers) can explain halo expansion in massive systems, the persistence of this deficit across a broad mass range, alongside constraints at cluster scales, suggests the possibility of velocity-dependent dark matter physics. Standard self-interacting dark matter (SIDM) models often struggle to simultaneously satisfy the core-cusp requirements of dwarf galaxies and the constraints of massive clusters.

Methodology
The authors propose a model of exothermic inelastic dark matter (IDM) featuring two nearly degenerate states, $\chi_1$ (ground) and $\chi_2$ (excited), with a mass splitting $\delta = m_2 - m_1 > 0$ . The model relies on the following mechanisms:

Interaction Potential: The dark sector couples via a vector mediator ( $V$ ) and a scalar mediator ( $S$ ) with opposite signs and unequal ranges. The resulting potential $W(r) = \frac{\alpha_V e^{-m_V r}}{r} - \frac{\alpha_S e^{-m_S r}}{r}$ changes sign at a specific radius $r_\star$ . This structure drives the $s$ -wave conversion amplitude through a zero at low velocities while retaining a $p$ -wave resonance at galaxy-scale velocities.
Scattering Dynamics:
- Exothermic Down-scattering ( $\chi_2\chi_2 \to \chi_1\chi_1$ ): Converts mass splitting into kinetic energy ("kick"), heating the dark matter and driving evaporation from halo centers. This process is enhanced at velocities of several hundred km/s (massive galaxies) but suppressed at dwarf velocities.
- Endothermic Up-scattering ( $\chi_1\chi_1 \to \chi_2\chi_2$ ): Forbidden below a threshold velocity $v_r < 2v_k$ (where $v_k = \sqrt{2\delta/m_\chi}$ ). This threshold naturally places the onset of inverse conversion at cluster velocities.
- Elastic Scattering: Remains active at low velocities, consistent with dwarf galaxy clustering patterns.
Cosmological Initial Conditions: A late dark-sector phase transition generates the mass splitting. The model assumes an asymmetric Dirac population to establish relic abundance. Crucially, the low-velocity suppression of down-scattering prevents the excited-state reservoir ( $\chi_2$ ) from being depleted before halo formation, ensuring a sufficient fraction ( $f_2 \approx 1/2$ ) is available to drive the exothermic process later.
Numerical Simulations: The authors employ a simplified $N$ -body framework reducing the phase space to radius and speed. They evolve isolated spherical halos with live dark matter and stellar particles initialized as Dehnen profiles fitted to TNG100 and observational data. The code implements coupled-channel scattering with tabulated rates for five channels ( $22\to11$ , $22\to22$ , $11\to11$ , $12\to12$ , $11\to22$ ), enforcing inelastic kinematics and allowing for halo expansion and evaporation.

Key Contributions and Results
Using a benchmark parameter set ( $m_\chi = 12.4$ GeV, $\delta = 18.1$ keV, $v_k = 513$ km/s), the study demonstrates:

Velocity-Dependent Suppression and Enhancement: The model successfully reproduces the observed mass dependence of the dark matter deficit.
- Dwarf Galaxies ( $v_r \sim 30$ km/s): Down-scattering is strongly suppressed ( $K_{22\to11}$ is negligible), and elastic scattering remains within the range favored by dwarf clustering observations. No significant deficit is generated, consistent with observations.
- Massive Galaxies ( $v_r \sim 300-500$ km/s): The $p$ -wave resonance enhances the exothermic down-scattering cross-section ( $\sigma/m_\chi \approx 0.95$ cm $^2$ /g at 300 km/s). This injects kinetic energy, lowering central dark matter densities and creating a deficit that grows with stellar mass.
- Clusters ( $v_r > 1000$ km/s): The inverse endothermic process opens, offsetting much of the exothermic heating. The net effect weakens, and the profile remains consistent with cluster-scale constraints (similar to an elastic model with $\sigma/m \approx 0.3$ cm $^2$ /g).
Quantitative Agreement: The model reproduces the inferred dark matter density profiles across four stellar-mass bins ( $\log_{10}(M_*/M_\odot) \approx 9.0$ to $11.5$). The simulated profiles match the observed median and population scatter, capturing both the magnitude and the systematic growth of the deficit with stellar mass.
Parameter Space Viability: The viable parameter region is organized around the zero of the $s$ -wave conversion amplitude. The model is not a finely tuned point but a finite band in the $(m_S, \alpha_S)$ plane where the $s$ -wave is suppressed at low velocities and the $p$ -wave is resonant at galaxy velocities.

Significance
The paper claims that the growing discrepancy between observations and hydrodynamical simulations in nearby galaxies may offer a glimpse of previously hidden dark matter microphysics. By attributing the mass-dependent deficit to velocity-dependent inelastic scattering, the model provides a unified explanation for:

The lack of a deficit in low-mass dwarfs.
The systematic increase of the deficit with stellar mass in intermediate-to-high mass galaxies.
The consistency with cluster-scale constraints where the effect diminishes.

The authors conclude that while baryonic processes may contribute, the specific systematic trend observed across the mass range follows directly from the velocity dependence of the scattering dynamics, offering a testable alternative to standard cold dark matter scenarios. The model predicts correlated signatures from dwarfs to clusters, suggesting that improved mass profile measurements in these regimes can distinguish between baryonic evolution and dark matter microphysics.

Technical Summary: Mass-Dependent Dark Matter Deficit from Inelastic Scattering

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