Asymmetric Cannibal Dark Matter: Constraints from Neutron Star

This paper proposes a novel asymmetric dark matter framework featuring $\mathbb{Z}_3$-mediated $3 \to 2$ cannibalistic self-interactions that deplete dark matter cores in neutron stars, generating significant thermal heating in old, isolated stars that could be detectable by future infrared telescopes and thereby expanding the viable parameter space for dark matter models.

The Gist

The Big Picture: A Cosmic Mystery

Imagine the universe is filled with invisible "ghosts" called Dark Matter. We know they are there because they have gravity (they hold galaxies together), but we can't see them, and we don't know what they are made of.

Scientists have a theory called Asymmetric Dark Matter (ADM). Think of this like the matter we see around us (stars, planets, you, me). We have more "stuff" than "anti-stuff." If we had equal amounts, they would destroy each other instantly. The theory suggests Dark Matter is the same: it's mostly made of "particles" with very few "anti-particles."

Usually, scientists think these dark particles just pile up inside heavy objects like Neutron Stars (the super-dense, dead cores of exploded stars) and sit there quietly. But this paper proposes a wild new idea: What if these dark particles are cannibals?

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The Main Character: The "Cannibal" Dark Matter

The authors propose a specific type of dark matter that has a special rule: Three particles can turn into two.

The Analogy: The Three-Headed Hydra

Imagine a group of three dark matter particles hanging out in the center of a neutron star.

• Normal Dark Matter: They just sit there.
• Cannibal Dark Matter: They get hungry. Three of them collide and merge into two larger, faster, and more energetic particles.
  • One particle disappears (it's "eaten").
  • The remaining two particles get a massive energy boost (like a sugar rush).

This is called a 3 → 2 reaction. It's like a game of musical chairs where every time the music stops, three people sit down, but only two chairs remain. The person who doesn't get a chair gets kicked out of the game, but the two who stay get a huge boost of energy.

The Neutron Star: The Cosmic Pressure Cooker

Neutron stars are incredibly dense. They are like the size of a city but have the mass of a sun. Because they are so heavy, they act like giant vacuum cleaners, sucking in dark matter from space.

1. The Trap: Dark matter falls into the star and gets trapped in the core.
2. The Feast: As the dark matter gets crowded, the "cannibal" reactions (3 → 2) happen more often.
3. The Result:
   • Fewer Particles: The total number of dark matter particles drops because three are turning into two.
   • More Heat: The energy released from "eating" the third particle heats up the remaining dark matter. This heat is then transferred to the neutron star itself.

Why This Matters: The "Old" Neutron Star

Neutron stars are born hot (millions of degrees) but they cool down over billions of years.

• Standard Theory: An old, isolated neutron star should be very cold (around 100–500 Kelvin). It should be invisible to our eyes.
• This Paper's Theory: If the dark matter inside is "cannibalistic," it keeps the star warm. The constant "eating" and energy release acts like a tiny internal heater.

The Prediction: Instead of being cold, an old neutron star might stay warm at about 2,000 Kelvin (roughly 3,000°F). That's hot enough to glow faintly in the infrared (like a warm ember), but not hot enough to glow in visible light.

The Detective Work: Hunting with Telescopes

The authors calculated that if we look at very old, lonely neutron stars with powerful new telescopes, we might see this faint infrared glow.

• The Tools: They mention the James Webb Space Telescope (JWST), the Extremely Large Telescope (ELT), and the Thirty Meter Telescope (TMT). These are like super-powered night-vision goggles for the universe.
• The Challenge: The stars are far away, and the signal is faint. It's like trying to see a single candle flame from 50 miles away in a foggy night. But, if the math is right, these telescopes might just catch that glow.

The "Asymmetry" Twist

The paper also deals with a tricky detail: Antimatter.
Usually, if you have dark matter and anti-dark matter, they annihilate (explode) and disappear.

• The Problem: If the star has too much anti-dark matter, it explodes and heats up the star too much via a different mechanism.
• The Solution: The authors show that even if the star starts with almost no anti-dark matter (a highly "asymmetric" state), the cannibal reactions (3 → 2) are so efficient that they actually create a tiny bit of anti-dark matter as a byproduct.
• The Balance: This creates a perfect balance where the "cannibal heating" is the dominant force, keeping the star warm without blowing it up.

Summary: The Takeaway

1. Dark Matter might be a cannibal: It eats itself (3 particles become 2) inside neutron stars.
2. This creates heat: The "eating" process releases energy that warms up the star.
3. Old stars shouldn't be cold: Instead of freezing, old neutron stars might glow faintly in infrared light because of this internal heating.
4. We can test it: New telescopes (like JWST and TMT) might be able to spot these warm, old stars, proving that dark matter isn't just a ghost, but a hungry, active participant in the universe.

In a nutshell: The authors suggest that if we look at old neutron stars with infrared telescopes, we might find them glowing warmer than expected. If we do, it's proof that dark matter particles are eating each other in the dark, keeping the stars cozy.

Technical Summary

1. Problem Statement

Neutron stars (NSs) serve as natural laboratories for probing Dark Matter (DM) interactions due to their extreme densities and gravitational fields. In the standard Asymmetric Dark Matter (ADM) scenario, DM particles are captured by NSs via elastic scattering with nucleons and accumulate in the core. Since ADM typically lacks efficient self-annihilation channels (due to a particle-antiparticle asymmetry), the accumulated DM can reach high densities, potentially leading to gravitational collapse into a black hole, which would destroy the NS. The survival of old NSs thus places stringent upper bounds on DM-nucleon cross-sections and DM masses.

However, standard ADM models often neglect number-changing self-interactions within the dark sector. If such interactions exist, they could deplete the DM population, preventing catastrophic collapse and altering the thermal evolution of the NS. The authors investigate a specific scenario where a $Z_3$ symmetry permits cannibalistic $3 \to 2$ self-interactions (three DM particles converting into two), which becomes efficient at high densities. The central problem is to determine how these interactions affect the DM population dynamics, the heating of the NS, and the resulting observational signatures in old, isolated neutron stars.

2. Methodology

The authors employ a coupled theoretical framework involving particle physics, astrophysics, and thermodynamics:

• Model Setup: They propose a complex scalar DM candidate ($\chi$) stabilized by a $Z_3$ symmetry. The Lagrangian includes trilinear ($\mu$) and quartic ($\lambda$) self-couplings, enabling $3 \to 2$ processes (e.g., $\chi\chi\chi \to \chi\chi^\dagger$) alongside standard $2 \to 2$ scattering and annihilation.
• Capture and Thermalization:
  • DM is captured via elastic scattering with neutrons ($\chi n \to \chi n$) and self-scattering ($\chi\chi \to \chi\chi$).
  • The authors calculate the thermalization time ($t_{th}$) and the radius of the thermalized DM core ($R_{th}$) inside the NS.
  • They assume the DM thermalizes efficiently with the NS interior before the NS cools significantly.
• Boltzmann Equations:
  • They derive coupled Boltzmann equations for the number densities of particles ($N_\chi$) and antiparticles ($N_{\chi^\dagger}$).
  • These equations account for capture rates ($C_B, C_{\chi\chi}$), annihilation to Standard Model (SM) particles, and the number-changing $3 \to 2$ reactions.
  • A key novelty is showing that even with a vanishing initial antiparticle abundance (purely asymmetric), the $3 \to 2$ process can regenerate a non-zero antiparticle population, enabling subsequent annihilation.
• Thermal Evolution:
  • The authors solve the differential equation for the NS interior temperature ($T_{int}$), balancing cooling (neutrino and photon emission) against heating.
  • Heating Mechanisms: They quantify three heating sources:
    1. Kinetic Heating: Energy deposition from DM-nucleon elastic scattering.
    2. Annihilation Heating: Energy from $\chi\chi^\dagger \to \text{SM}$.
    3. Cannibal Heating: Kinetic energy injection from $3 \to 2$ reactions, transferred to the NS via scattering.
  • They solve the coupled system of DM number evolution and NS temperature evolution self-consistently.

3. Key Contributions

• Novel Heating Mechanism: The paper identifies cannibal heating (driven by $3 \to 2$ self-interactions) as a dominant heating mechanism for old neutron stars in specific parameter spaces, surpassing both kinetic heating and annihilation heating.
• Regeneration of Antiparticles: They demonstrate that in a $Z_3$-symmetric complex scalar model, $3 \to 2$ processes can generate a non-zero antiparticle density even if the initial halo is purely asymmetric. This creates a feedback loop where annihilation becomes possible but is often sub-dominant to cannibal heating in high-asymmetry regimes.
• Suppression of Black Hole Formation: The number-depleting nature of $3 \to 2$ interactions prevents the uncontrolled accumulation of DM that would otherwise lead to black hole formation, thereby relaxing the constraints on DM-nucleon cross-sections derived from NS survival.
• Observational Predictions: The study predicts that cannibal heating can maintain old, isolated neutron stars at surface temperatures of $\mathcal{O}(1000)$ K, a regime significantly warmer than standard cooling predictions for such old objects.

4. Results

• Parameter Space: The authors map the viable parameter space in the plane of DM mass ($m_\chi$) and initial particle fraction ($f_\chi$).
  • For $m_\chi \sim 1$ GeV and high asymmetry ($f_\chi \gtrsim 0.85$), cannibal heating dominates.
  • The resulting equilibrium interior temperatures plateau at values between 1700 K and 2300 K, depending on the specific couplings ($\mu, \lambda$) and asymmetry.
• Dominance Regimes:
  • Low Asymmetry: Annihilation heating dominates.
  • Intermediate Asymmetry: Kinetic heating may dominate.
  • High Asymmetry ($f_\chi \gtrsim 0.85$): Cannibal heating dominates because the high capture rate increases the DM density, making $3 \to 2$ reactions highly efficient, while the scarcity of antiparticles suppresses annihilation.
• Observational Signatures:
  • The predicted surface temperatures ($T_{obs} \approx 1700\text{--}2300$ K) correspond to blackbody radiation in the near-infrared (NIR) band.
  • Detectability:
    • JWST: Potentially sensitive to these temperatures for very nearby sources ($\sim 10$ pc), though such targets are rare.
    • TMT (Thirty Meter Telescope) & ELT (Extremely Large Telescope): These future facilities, specifically instruments like IRIS (TMT) and MICADO (ELT), are highlighted as the most promising tools. They can detect the predicted thermal signatures (1200–3600 K) for sources at distances up to 50–100 pc with feasible exposure times ($10^7\text{--}10^8$ s).

5. Significance

This work significantly broadens the scope of Dark Matter constraints derived from neutron stars.

1. Relaxation of Constraints: By introducing a mechanism ($3 \to 2$) that naturally limits DM accumulation, the paper suggests that previous bounds on DM-nucleon cross-sections (based on the assumption of unlimited accumulation) may be too strict for models with number-changing self-interactions.
2. New Probe for ADM: It establishes old neutron stars as sensitive probes for the self-interaction structure of the dark sector, specifically testing for $Z_3$-symmetric number-changing processes.
3. Multi-Messenger Potential: The prediction of specific infrared thermal signatures provides a concrete target for upcoming infrared astronomy missions (JWST, TMT, ELT), offering a potential pathway to detect or constrain asymmetric cannibal dark matter through astrophysical observation rather than direct detection experiments.

In conclusion, the paper argues that "cannibal" dark matter does not just deplete the DM population to save the neutron star from collapse; it actively heats the star, creating a unique, observable thermal fingerprint that distinguishes it from standard cooling models and other DM heating scenarios.