Freeze-in dark matter in neutron stars

This paper proposes that neutron stars, formed in core-collapse supernovae with early-Universe-like temperatures, can produce and retain freeze-in dark matter which subsequently annihilates to inject energy, thereby offering a unique method to constrain extremely weakly coupled dark matter models with scattering cross-sections as low as $O(10^{-70})\,\rm cm^2$ through observable late-time heating signatures.

The Gist

Here is an explanation of the paper "Freeze-in dark matter in neutron stars" using simple language, analogies, and metaphors.

The Big Picture: A Cosmic Trap

Imagine the universe is a giant, dark room filled with invisible dust (Dark Matter). Scientists know this dust is there because it has gravity, but they can't see it or touch it. The problem is that this dust is so "shy" (it interacts so weakly with normal matter) that our most sensitive detectors on Earth can't find it.

This paper proposes a clever new way to catch this shy dust: Neutron Stars.

Think of a Neutron Star as a cosmic "super-trap." It is the incredibly dense, dead core of a massive star that exploded. It has gravity so strong that it acts like a vacuum cleaner, sucking in anything that gets too close.

The Story: How the Trap Works

The authors suggest a three-step process involving a cosmic explosion and a slow-motion energy leak.

1. The Birth: The "Big Bang" in a Box

When a massive star dies, it explodes in a supernova. For a brief moment (about 20 seconds), the center of this explosion gets as hot as the entire universe did just after the Big Bang.

• The Analogy: Imagine a pressure cooker. When you turn it on high, the heat is so intense that it starts creating new, exotic ingredients (Dark Matter particles) out of the steam (normal particles like neutrinos).
• The "Freeze-in": Usually, scientists look for Dark Matter that was made in huge quantities in the early universe. But this paper looks at "Freeze-in" Dark Matter. This is like a leaky faucet that drips so slowly you barely notice it. The particles are made so rarely that they never reach a "full" state; they just slowly accumulate.

2. The Capture: The "Gravity Net"

When these new Dark Matter particles are born in the explosion, most of them are moving too fast and fly away into space. However, the Neutron Star has a gravity well so deep (like a bottomless pit) that it catches a small fraction of these particles.

• The Result: The Neutron Star becomes a prison cell filled with invisible Dark Matter. The paper calculates that for every billion atoms in the star, about a million of these invisible particles get trapped inside.

3. The Leak: The "Slow Energy Leak"

Here is the twist. Once the Neutron Star is born, it starts to cool down, like a hot cup of coffee left on a table.

• The Reverse Process: The trapped Dark Matter particles are now sitting in the deep gravity well. Eventually, two of them might bump into each other and annihilate (destroy each other), turning back into normal energy (neutrinos and heat).
• The Metaphor: Imagine the Dark Matter is a battery that was charged during the explosion. Now, billions of years later, the battery is slowly leaking its energy back into the star.
• The Signature: This energy leak heats the Neutron Star up. If we look at very old, cold Neutron Stars, they should be freezing. But if they are slightly warmer than physics says they should be, it's a sign that this "Dark Matter battery" is leaking energy inside them.

Why This Matters: Catching the "Uncatchable"

The authors built a specific model to test this idea. They found that:

1. Current detectors are blind: The "shyness" of these particles is so extreme that Earth-based experiments would need to be 25 orders of magnitude more sensitive to see them. That's like trying to hear a whisper from across the galaxy while standing next to a jet engine.
2. Neutron Stars are the only tool: Because the Neutron Star acts as a giant collector and a long-term storage battery, it amplifies this tiny signal.
3. The Constraints: By looking at the temperature of the coldest known Neutron Star (PSR J2144-3933), the authors can say, "If Dark Matter existed with these specific properties, this star would be hotter than it is." Since the star is cold, they can rule out certain types of Dark Matter models.

Summary Analogy: The Silent Alarm

Imagine you are trying to detect a ghost that is so quiet it makes no sound.

• Earth Detectors: You are standing in a quiet library, listening for a whisper. You can't hear the ghost.
• The Neutron Star Method: You build a giant, hollow bell (the Neutron Star). You wait for the ghost to fly inside and get trapped. Once inside, the ghost starts tapping on the glass very slowly. Even though the tap is tiny, the bell amplifies the sound.
• The Result: If the bell doesn't ring, you know the ghost isn't there (or at least, not the kind you were looking for).

The Takeaway

This paper suggests that the universe's most extreme objects—Neutron Stars—are actually our best laboratories for finding the most elusive type of Dark Matter. By watching how these stars cool down over billions of years, we can detect the faint, slow "heartbeat" of Dark Matter particles that have been trapped inside them since the star was born.

Technical Summary

Here is a detailed technical summary of the paper "Freeze-in dark matter in neutron stars" by Maxim Pospelov and Samya Roychowdhury.

1. Problem Statement

The Standard Model (SM) of particle physics cannot explain Dark Matter (DM). While many DM candidates exist, Freeze-In (FI) DM models are particularly difficult to probe. In these models, DM particles ($\chi$) are produced via extremely weak couplings ($\alpha_{FI} \sim 10^{-26}$) from SM particles in the early Universe. Because the interactions are so feeble:

• DM never reaches thermal equilibrium.
• Direct detection experiments (relying on scattering cross-sections) are ineffective because the cross-sections are often below $10^{-50} \text{ cm}^2$.
• Indirect detection via annihilation is suppressed due to low number densities.

The authors address the challenge of constraining stable FI DM in the MeV to 100 MeV mass range, a region where traditional direct detection and cosmological observations offer little to no sensitivity.

2. Methodology

The authors propose a novel astrophysical probe utilizing Neutron Stars (NS) formed in core-collapse supernovae (SN). The methodology involves three main stages:

A. Production Phase (Supernova Explosion)

• Context: During a core-collapse SN, the proto-neutron star reaches temperatures $T \sim 30\text{--}40$ MeV, mimicking early Universe conditions.
• Mechanism: SM particles (specifically neutrinos $\nu_\mu, \nu_\tau$) fuse to produce a vector mediator $V$, which subsequently decays into DM pairs ($\nu\bar{\nu} \to V \to \chi\bar{\chi}$).
• Retention: Unlike the early Universe where DM expands freely, the intense gravitational potential of the newborn NS traps a fraction of the produced $\chi$ particles. The authors calculate the retention probability based on the kinetic energy of the DM relative to the escape velocity of the NS.

B. Evolution Phase (Cooling and Thermalization)

• Once trapped, the DM population cools.
• Scenario A: DM self-interacts to thermalize to a "dark temperature" ($T_d$) below the escape energy.
• Scenario B: DM interacts weakly with SM particles (muons) inside the NS to thermalize.
• Crucially, the retained DM particles lack sufficient kinetic energy to re-produce the on-shell mediator $V$, suppressing the reverse production channel.

C. Annihilation Phase (Late-Time Heating)

• Over astronomical timescales ($t \sim 10^{16}$ s), the trapped DM undergoes the reverse process: annihilation ($\chi\bar{\chi} \to \text{SM}$).
• Because the DM is dilute and the coupling is tiny, this annihilation is extremely slow, occurring long after the SN event.
• The annihilation products (neutrinos) scatter off nucleons and electrons within the dense NS interior, depositing their energy as heat.
• Constraint: The authors compare the predicted heating rate ($dQ/dt$) against observational limits on the temperature of the coldest known neutron star, PSR J2144-3933 ($kT \lesssim 3$ eV).

D. Model Construction

To demonstrate feasibility, the authors construct a specific Leptonic Force Mediation model:

• Gauge Group: $L_\mu - L_\tau$ symmetry coupled to a dark sector.
• Particles: Stable DM $\chi$, vector mediators $X_\mu$ (light) and $V_\mu$ (heavy, $m_V \approx 3m_\chi$).
• Couplings: Defined by $\alpha_{FI}$ (production) and $\alpha_d$ (self-interaction/annihilation). Two regimes are analyzed:
  • Scenario A: Production via $2 \to 1$fusion ($\nu\bar{\nu} \to V$).
  • Scenario B: Production via $1 \to 2$decay of a thermalized$V$.

3. Key Contributions

1. New Probe for Freeze-In DM: The paper establishes that NSs act as "cosmic traps" for FI DM, offering a unique window to probe couplings ($\alpha_{FI} \sim 10^{-26}$) that are inaccessible to terrestrial direct detection experiments.
2. Quantification of Retention: The authors derive the fraction of DM retained by the NS, showing that while the total production is small ($\sim 10^{-6}$ DM per nucleon), the gravitational retention is sufficient to store significant energy.
3. Hierarchy of Rates: They demonstrate a critical hierarchy where the production rate ($R_{in}$) is fast during the SN, but the annihilation rate ($R_{out}$) is suppressed by off-shell mediators and low density, allowing the DM to survive until late times.
4. Scattering Cross-Section Estimates: They calculate that the scattering cross-section of this DM on electrons is $\sigma_{\chi e} \sim 10^{-70} \text{ cm}^2$, confirming that direct detection is impossible for these models.

4. Results

• Production Yield: For a cosmologically viable $\alpha_{FI}$, the SN produces approximately $O(10^{-6})$ DM particles per nucleon.
• Retention: For the specific mass ratio $m_V = 3m_\chi$, roughly a few percent of the produced DM is retained by the NS.
• Constraints on Parameter Space:
  • Mass Range: The method effectively constrains DM masses between 10 MeV and 100 MeV.
  • Coupling Limits:
    • If the self-coupling $\alpha_d$ is too large ($>10^{-6}$), DM annihilates too early, preventing late-time heating.
    • If $\alpha_d$ is too small, the heating rate is negligible.
    • The optimal constraint window is found for $\alpha_d \sim 10^{-10}$.
  • Exclusion Plot: The authors present exclusion contours in the $\{m_\chi, \alpha_{FI}\}$ and $\{m_\chi, \alpha_d\}$ planes. They show that NS heating excludes a region of parameter space that is completely unconstrained by any other method (direct detection, collider, or cosmology).
• Cross-Section Benchmark: The study confirms that the effective scattering cross-section probed by this method is in the ballpark of $\sigma_{\chi SM} \propto 10^{-70} \text{ cm}^2$.

5. Significance

• Overcoming the "Dark Sector" Blind Spot: This work provides the first robust method to constrain stable, weakly coupled DM in the MeV scale where standard WIMP searches fail.
• Astrophysical Laboratory: It re-frames neutron stars not just as gravitational objects, but as sensitive calorimeters for particle physics, capable of detecting energy injection from processes occurring over billions of years.
• Model Independence: While demonstrated with a specific $L_\mu - L_\tau$ model, the authors argue the mechanism applies to other FI scenarios, including dark photons and scalar Higgs portals.
• Future Directions: The paper motivates further study into NS collapse into black holes due to DM accumulation and electromagnetic signatures from DM annihilation outside the NS radius.

In summary, the paper demonstrates that late-time heating of neutron stars is a powerful, unique, and necessary tool for testing the "freeze-in" mechanism of Dark Matter production, filling a critical gap in the experimental landscape of particle physics.