Dark, deep, deconfining: Phase transitions in neutron stars as powerful probes of hidden sectors

This paper proposes that interactions between hidden sector particles and neutron star nucleons can overcome energy barriers to trigger deconfinement phase transitions, potentially converting neutron stars into black holes or gamma-ray bursts, thereby allowing the observed existence of ancient neutron stars to set constraints on dark matter interactions and nucleon decay lifetimes that are orders of magnitude stricter than terrestrial limits.

The Gist

Imagine a neutron star as a cosmic pressure cooker. Inside, the matter is squeezed so tightly that it's like a giant ball of atomic nuclei (protons and neutrons) packed together. Scientists believe that if you squeeze this matter hard enough, it should "melt" into something even stranger: a soup of free-floating quarks (the tiny particles that make up protons and neutrons). This is called a "phase transition," similar to how ice melts into water.

However, there's a problem. Even though the pressure is high, there's a massive "energy wall" (a barrier) preventing this melting from happening spontaneously. It's like trying to push a boulder over a huge hill; the boulder (the star) is sitting in a valley, and it needs a massive shove to get over the hill and roll down into the "quark soup" valley.

The Mystery: Why hasn't the star melted yet?
For decades, scientists have wondered what could provide that massive shove. They've looked at things like the star spinning down, crashing into other stars, or absorbing gas from a neighbor. But the authors of this paper argue that none of these natural events are strong enough to break the barrier. The hill is just too high.

The New Idea: Dark Matter as the Shove
The paper proposes a new, invisible agent that could provide the necessary push: Dark Matter.

Think of Dark Matter as a ghostly wind blowing through the star. Usually, it passes right through without doing anything. But the authors suggest that if this "wind" hits the star's core with enough force (specifically, if the dark matter particles are heavy enough and interact strongly enough), it could deliver a single, massive punch.

If this punch is hard enough, it breaks the energy wall. Suddenly, the "ice" melts. A tiny bubble of quark soup forms. Because this new state is more stable, the bubble grows rapidly, eating up the rest of the star in a chain reaction.

The Aftermath: A Cosmic Explosion or a Black Hole
What happens next depends on the star's recipe (its "equation of state"):

1. The Explosion: The star might release a massive burst of energy, creating a Gamma-Ray Burst (GRB)—a blinding flash of light visible across the universe.
2. The Collapse: Alternatively, the star might lose its structural support and instantly collapse into a black hole.

The Detective Work: Using "Old" Stars as Clues
Here is the clever part of the paper. We have observed neutron stars that are billions of years old. They are still there, still spinning, and haven't exploded or turned into black holes.

The authors use this fact as a powerful detective tool. They say: "If dark matter were strong enough to break that energy wall and trigger these explosions, we would have seen these old stars disappear or explode by now. Since they are still here, dark matter cannot be that strong."

By calculating exactly how much "push" dark matter would need to cause a disaster, and then comparing that to the fact that the stars are still safe, the authors set incredibly strict limits on how dark matter behaves.

Why is this a big deal?
Usually, to find dark matter, we build giant detectors underground on Earth and wait for a particle to hit them. This paper shows that the entire universe is full of giant, ancient detectors (neutron stars) that have been watching for billions of years.

Because these stars have been "looking" for so long and are so dense, the authors' method is tens of orders of magnitude more sensitive than any experiment we can build on Earth. They can rule out dark matter theories that would otherwise seem possible.

In Summary:

• The Setup: Neutron stars are stuck in a "frozen" state because of a high energy barrier.
• The Trigger: Dark matter could theoretically provide the energy to break this barrier, causing the star to melt into quark matter.
• The Result: This would cause the star to explode or collapse into a black hole.
• The Evidence: Since ancient neutron stars are still alive and well, dark matter didn't trigger this.
• The Conclusion: This proves that dark matter interacts with normal matter much more weakly than we thought, setting the strictest limits on its behavior ever recorded.

The paper also notes that if the energy barrier were lower than expected, this same logic could be used to prove that protons (the building blocks of matter) are incredibly stable, lasting for trillions of times longer than the current age of the universe.

Technical Summary

Technical Summary: Dark, Deep, Deconfining: Phase Transitions in Neutron Stars as Powerful Probes of Hidden Sectors

Problem Statement
The interiors of neutron stars (NSs) provide a unique environment for the potential conversion of hadronic matter into a stable strange quark phase (uds matter), a process theorized to be the ground state of nuclear matter. This conversion requires a first-order Quantum Chromodynamics (QCD) deconfinement phase transition (PT). However, the transition is hindered by a significant energy barrier ($U_{max}$) arising from the surface tension of nascent quark matter droplets. While various astrophysical mechanisms (e.g., spin-down, accretion, mergers) have been proposed to overcome this barrier, the authors argue that the barrier height (ranging from $\mathcal{O}(10)$ to $\mathcal{O}(10^4)$ MeV) is likely too high for these standard mechanisms to trigger a transition within the age of the universe. Consequently, many NSs are presumed to remain purely hadronic. The paper posits that interactions with hidden sector particles (dark matter) could provide the requisite energy injection to surmount this barrier, potentially converting a hadron star (HS) into a strange star (QS) or a black hole (BH).

Methodology
The authors develop a framework to calculate the rate at which dark matter interactions could trigger this deconfinement phase transition in neutron stars. The methodology involves:

1. Barrier Analysis: The energy barrier for nucleation is modeled as $U(r, P) = -\frac{4\pi r^3}{3} n_{Q^*} |\Delta \mu| + 4\pi r^2 \sigma_{ST}$. The critical energy required to form a stable bubble is $U_{max}$. The authors adopt a conservative benchmark of $U_{max} = 10$ GeV, noting that lower barriers would require non-standard parameters (e.g., significantly reduced surface tension).
2. Energy Deposition Criteria: For a phase transition to occur, energy must be deposited within a critical radius ($r_{crit}$). The authors demonstrate that for dark matter masses $m_\chi \gtrsim 10$ GeV, deep inelastic scattering, self-annihilation, or decay can deposit sufficient energy within $r_{crit}$ to trigger a runaway chain reaction, converting the star.
3. Dark Matter Interaction Channels: The study considers three primary mechanisms for energy injection:
   • Scattering/Co-annihilation: Dark matter particles scattering inelastically with nucleons (depositing $> U_{max}$) or co-annihilating with nucleons (e.g., "dark anti-neutrons").
   • Self-Annihilation: Dark matter captured within the NS annihilating with itself.
   • Decay: Dark matter particles decaying into Standard Model final states (specifically $q\bar{q}$) within the NS.
4. Observational Constraints: The authors derive limits on dark matter parameters by imposing two "null hypothesis" criteria based on the non-observation of specific events:
   • GRB Rate Criterion: The rate of HS $\to$ QS transitions producing Gamma-Ray Bursts (GRBs) must not exceed the observed GRB rate ($\sim 1$ per galaxy per century).
   • Ancient NS Existence Criterion: The existence of old, massive neutron stars (specifically PSR J0952−0607, $M \approx 2.35 M_\odot$, age $\approx 4.9$ Gyr) implies they have not undergone a transition to a black hole (HS $\to$ BH).
5. Flux Calculations: The study calculates the dark matter flux through the NS, accounting for gravitational focusing and the "deconfinement radius" ($R_{dcf}$) where pressures exceed the transition threshold. Both captured (thermalized and unthermalized) and uncaptured dark matter populations are considered.

Key Contributions

• Novel Trigger Mechanism: The paper introduces dark matter scattering (in addition to annihilation and decay) as a viable trigger for deconfinement phase transitions, specifically highlighting deep inelastic scattering for high-mass dark matter.
• Unprecedented Sensitivity: By leveraging the enormous integrated flux of dark matter through neutron stars over Gyr timescales, the authors derive limits on dark matter interactions that are tens of orders of magnitude stronger than terrestrial direct detection experiments (e.g., LZ) and indirect searches for dark matter masses above $\sim 10$ GeV.
• Conditional Limits on Hidden Sectors: The study sets strict bounds on dark matter-nucleon scattering cross-sections, self-annihilation cross-sections, and decay lifetimes. For instance, it constrains nucleon decay lifetimes to $\sim 10^{64}$ years for barriers $\lesssim$ GeV, far exceeding laboratory limits.
• Differentiation of Scenarios: The analysis distinguishes between scenarios where dark matter is captured and thermalized versus unthermalized, showing how these affect the annihilation rates and resulting limits.

Results
The authors present exclusion plots (Fig. 1) for dark matter mass ($m_\chi$) versus interaction strength ($\sigma_{N\chi}$, $\sigma_{ann}$, or lifetime $\tau_\chi$):

• Scattering Limits: For $m_\chi > 10$ GeV, the limits on inelastic scattering cross-sections reach $\sim 10^{-85}$ cm$^2$, significantly surpassing the "neutrino floor" and direct detection limits.
• Annihilation Limits: Limits on self-annihilation cross-sections are derived for both captured and uncaptured scenarios. Captured, unthermalized dark matter yields limits $\sim 44$ orders of magnitude stronger than the uncaptured case due to the squared dependence of the annihilation rate on number density.
• Decay Limits: Limits on dark matter lifetimes reach $\sim 10^{58}$ s (for $m_\chi \approx 10$ GeV), improving upon previous studies that did not derive observational bounds.
• Proton Decay: In the regime of smaller energy barriers ($U_{max} \lesssim$ GeV), the framework yields lower limits on proton lifetimes of $\sim 10^{64}$ years.

Significance and Claims
The paper claims that neutron stars serve as "extraordinarily sensitive and unrivaled probes" of dark matter interactions with the visible sector. The significance lies in the ability to probe dark matter parameter spaces that are inaccessible to terrestrial experiments, specifically for masses above 10 GeV. The authors emphasize that these limits are conditional: they rely on the assumptions that (1) neutron stars are composed primarily of hadronic matter, and (2) the transition to quark matter is a first-order phase transition with a barrier height of $\sim 10$ GeV. If these assumptions hold, the non-observation of GRBs and the survival of ancient, massive neutron stars rule out a vast range of dark matter models. The work suggests that gains in certainty regarding QCD equation-of-state models are crucial to solidifying these fundamental physics constraints.