The Black Hole Mass Gap as a New Probe of Millicharged Particles

This paper proposes that millicharged particles with masses between 35 keV and 200 keV could weaken pulsational pair-instability supernovae, thereby shifting the lower edge of the black hole mass gap to higher masses and providing a new method to constrain these particles using recent gravitational wave observations.

The Gist

Imagine the universe as a giant cosmic bakery. In this bakery, massive stars are like giant ovens baking cakes (black holes) of various sizes. For a long time, astronomers noticed something strange: there were no cakes in a specific size range. It was as if the bakery had a "forbidden zone" where cakes simply couldn't exist between 45 and 130 times the mass of our Sun. This is called the Black Hole Mass Gap.

Usually, when a star this massive runs out of fuel, it doesn't just quietly collapse. It goes through a violent, rhythmic shaking (like a giant heart beating too fast) that blows off huge chunks of its outer layers before it finally implodes. This process, called a "pulsational pair-instability supernova," acts like a cosmic trimmer, shaving the star down so small that the resulting black hole is too light to be in the "forbidden zone."

The New Suspect: The "Ghostly Leaky Faucet"

This paper introduces a new character into the story: Millicharged Particles (MCPs).

Think of these particles as tiny, invisible ghosts that can slip through walls. They have a tiny electric charge (much smaller than an electron) and are very light, but not too light.

Here is the problem they cause in our cosmic bakery:

1. The Leaky Faucet: Inside the core of a massive star, heat is generated by nuclear fusion. Normally, this heat is trapped, keeping the star stable. But if these ghostly MCPs exist, they act like a leaky faucet in the star's core. They carry energy away from the star much faster than usual, cooling the core down.
2. The Weakened Shaking: Because the core cools down faster, the star doesn't get as hot or as unstable as it should. The violent "heartbeats" (pulsations) that usually blow off the star's mass become weak and ineffective.
3. The Heavy Cake: Because the star can't shake off enough mass, it stays heavier than it should. Instead of being trimmed down to a small black hole, it collapses into a much heavier black hole.

The Detective Work

The authors of this paper are like detectives trying to solve a mystery using a scale.

• The Standard Model (No Ghosts): If we assume only known physics exists, the "trimming" process works perfectly. The heaviest black hole we should see before the "gap" starts is around 45 times the mass of the Sun.
• The Observation: Recent data from gravitational wave detectors (like LIGO) suggests that the "gap" might actually start higher up, near 45 solar masses (with some wiggle room).
• The Conclusion: If the gap is starting at that higher weight, it means the "trimming" process is failing. The only way the trimming fails is if the star is losing energy too fast. This points directly to our "ghostly faucet"—the Millicharged Particles.

The "Goldilocks" Zone

The paper finds that these particles would only be detectable if they are in a very specific "Goldilocks" zone:

• Not too light: If they are too light (like neutrinos), other telescopes have already seen them.
• Not too heavy: If they are too heavy, the star isn't hot enough to create them.
• Just right: They need to be between 35 and 200 keV (a specific weight range) and have a tiny electric charge.

If the recent gravitational wave data is correct, this specific zone of "ghostly particles" is now ruled out. It's like finding a fingerprint at a crime scene; if the crime (the heavy black hole) happened, the suspect (the particle) must have been there.

Why This Matters

This is a brilliant piece of detective work because it uses black holes to hunt for subatomic particles.

Usually, to find tiny particles, we build giant machines on Earth (like the Large Hadron Collider) and smash atoms together. But this paper shows that the universe itself is a giant particle accelerator. By looking at the "missing" black holes in the cosmic bakery, we can prove or disprove the existence of new, invisible particles that we can't make in our labs yet.

In short: If black holes are heavier than we thought they should be, it's because invisible "ghosts" are stealing the star's heat, preventing it from shedding its weight. By weighing the black holes, we can catch these ghosts.

Technical Summary

1. Problem Statement

The paper addresses the search for Feebly Interacting Particles (FIPs), specifically Millicharged Particles (MCPs), in a mass range ($35 \text{ keV} \lesssim m_\chi \lesssim 200 \text{ keV}$) and charge range ($10^{-10} \lesssim q \lesssim 10^{-9}$) that remains unconstrained by current astrophysical probes.

• The Black Hole Mass Gap (BHMG): Observations suggest a scarcity of black holes (BHs) in the mass range $45 - 130 M_\odot$. This gap arises from Pair-Instability Supernovae (PISN) and Pulsational Pair-Instability Supernovae (PPISN). In massive stars ($130-250 M_\odot$), the production of electron-positron pairs softens the equation of state, leading to collapse. Depending on the progenitor mass, this results in either total disruption (PISN, leaving no remnant) or pulsational mass ejection (PPISN, leaving a lighter BH).
• The Limitation of Current Probes: Existing constraints on MCPs come from:
  • Red Giant Branch (TRGB): Sensitive to very light MCPs ($m_\chi \lesssim 10 \text{ keV}$) but limited by lower core temperatures.
  • Supernova 1987A (SN 1987A): Sensitive to higher masses but only constrains larger couplings ($q \gtrsim 10^{-9}$) due to the extreme density and temperature conditions.
• The Gap: There is a "blind spot" in parameter space for MCPs with masses near the electron mass ($m_e \approx 511 \text{ keV}$) but slightly lighter. These particles are too heavy to be efficiently produced in cool stellar cores (TRGB) but their production rates in supernovae are suppressed by Boltzmann factors unless couplings are large. The authors propose that the BHMG offers a unique window to probe this specific region.

2. Methodology

The authors employed a multi-step approach combining stellar evolution simulations with gravitational wave data analysis:

• Stellar Evolution Simulations:

  • Used the MESA (Modules for Experiments in Stellar Astrophysics) code (version 12778) to simulate the evolution of non-rotating helium cores with metallicity $Z = 10^{-5}$.
  • Physics Implementation: The code was modified to include energy loss channels due to MCP emission. The dominant production mechanisms considered were Compton scattering ($e^- + \gamma \to e^- + \bar{\chi} + \chi$) and pair production ($e^- + e^+ \to \bar{\chi} + \chi$). Plasmon decay was neglected as it is kinematically suppressed for the target mass range.
  • Reaction Rates: Adopted the state-of-the-art $^{12}\text{C}(\alpha, \gamma)^{16}\text{O}$ reaction rate (from Ref. [44]) and used conservative resolution controls to accurately resolve the core collapse–PPISN transition.
  • Scenario: Simulated stars from the end of core helium burning through to their final fate (direct collapse, PPISN, or PISN).

• Physical Mechanism:

  • MCP emission acts as an additional cooling channel in the stellar core.
  • Enhanced cooling shortens the duration of core helium burning.
  • This reduces the time available for the $^{12}\text{C}(\alpha, \gamma)^{16}\text{O}$ reaction to convert Carbon to Oxygen, resulting in a lower $^{16}\text{O}/^{12}\text{C}$ ratio at the onset of pair instability.
  • A lower oxygen fraction and a larger convective carbon-burning shell resist collapse more effectively. Consequently, stars that would normally undergo PPISN (and lose mass) instead undergo direct collapse or experience weaker pulses, ejecting less mass.
  • Result: The transition from PPISN to PISN shifts to higher initial stellar masses, effectively shifting the lower edge of the BHMG to higher black hole masses.

• Data Comparison:

  • Compared simulation results against recent gravitational wave observations from the LVK (LIGO-Virgo-KAGRA) collaboration, specifically the analysis of the GWTC-4 catalog (Ref. [35]), which places the lower edge of the mass gap at $45^{+5}_{-4} M_\odot$ (90% credibility).

3. Key Contributions

• New Probe for MCPs: This is the first study to demonstrate that the Black Hole Mass Gap is sensitive to MCPs with masses in the O(10–100) keV range, a region previously unconstrained by TRGB or SN 1987A observations.
• Quantitative Bounds: The authors derive specific exclusion limits on the MCP parameter space ($m_\chi$ vs. fractional charge $q$) based on the location of the BHMG.
• Conservative Analysis: The study adopts conservative assumptions to ensure robustness:
  • Uses the $+3\sigma$ value for the $^{12}\text{C}(\alpha, \gamma)^{16}\text{O}$ rate (which pushes the SM prediction to higher masses, making it harder to exclude MCPs).
  • Excludes stellar rotation (which could also shift the gap to higher masses).
  • Interpolates discrete simulation scans to avoid overestimating bounds.

4. Results

• Shift in Mass Gap: The presence of MCPs shifts the lower edge of the BHMG to higher black hole masses.
  • For a fixed MCP mass, increasing the charge $q$ increases the cooling rate, shifting the gap edge further up.
  • For a fixed charge, increasing the mass $m_\chi$ suppresses production (Boltzmann suppression), reducing the effect.
• Exclusion Region: If the lower edge of the BHMG is confirmed to be at $45^{+5}_{-4} M_\odot$, the following region of MCP parameter space is excluded:
  • Mass: $35 \text{ keV} \lesssim m_\chi \lesssim 200 \text{ keV}$
  • Charge: $10^{-10} \lesssim q \lesssim 10^{-9}$
• Visual Confirmation: Figure 1 in the paper illustrates this new exclusion zone (hatched region), which sits between the constraints from SN 1987A (gray, upper bound on $q$) and TRGB (gray, lower mass bound).
• Sensitivity: The BHMG probe is competitive with or superior to SN 1987A constraints for MCP masses below $\sim 200 \text{ keV}$.

5. Significance

• Multimessenger Astrophysics: The paper highlights the power of using gravitational wave data (BH mass distributions) to constrain particle physics models, complementing traditional electromagnetic and neutrino-based probes.
• Filling the Parameter Gap: It identifies a specific, theoretically motivated region for MCPs (masses just below the electron mass) that has been difficult to test. If MCPs exist in this range, they could be detected via their impact on stellar evolution and the resulting BH mass distribution.
• Future Implications:
  • As more gravitational wave events are collected (e.g., in future observing runs), the precision of the BHMG location will improve, tightening these bounds.
  • The methodology can be extended to other FIPs (e.g., dark photons, axion-like particles) provided they are stable or have small branching ratios to Standard Model particles and are light enough to be produced in stellar cores.
  • The authors note that future work will investigate constraints from the R2-parameter in globular clusters to further test this region.

In summary, the paper establishes the Black Hole Mass Gap as a powerful, independent astrophysical laboratory for probing sub-MeV millicharged particles, offering the first constraints on a previously unconstrained region of the dark sector parameter space.