Constraints on primordial black holes from the first part of LIGO-Virgo-KAGRA fourth observing run

Using LIGO-Virgo-KAGRA O4a data, this study establishes the strongest constraints to date on the abundance of primordial black holes in the $0.6-100 M_\odot$ mass range, finding no compelling evidence for their contribution to observed gravitational wave events despite allowing for a subset of cataloged mergers to be primordial in origin.

The Gist

The Big Picture: Hunting for "Ghost" Black Holes

Imagine the universe is a giant, dark ocean. Most of the black holes we know about are like ships made by human hands (astrophysical black holes). They are born when massive stars die and collapse. But there is a theory that some black holes are "ghost ships" (primordial black holes, or PBHs). These weren't made by dying stars; they were formed instantly by the sheer pressure of the Big Bang itself, right at the beginning of time.

The authors of this paper are like detectives listening to the ocean with incredibly sensitive hydrophones (the LIGO-Virgo-KAGRA detectors). They are trying to answer one question: Are any of the black hole collisions we hear coming from these ancient "ghost ships," or are they all just the usual "human-made" ones?

The Detective Work: Listening to the Waves

When two black holes crash into each other, they send ripples through space-time called gravitational waves. The detectors pick up these ripples. The team analyzed data from the first part of the fourth major listening session (called O4a), which caught 85 new signals.

They used three different strategies to figure out if any of these signals were "ghosts":

1. The "All Stars" Approach: They assumed every signal came from normal, star-born black holes. If they see more collisions than this model predicts, the extra ones might be ghosts.
2. The "Guess and Check" Approach: They didn't assume anything. They randomly picked groups of signals and asked, "What if these specific ones were ghosts?" They did this millions of times to see if any group fit the "ghost" profile better than the "star" profile.
3. The "Mixed Bag" Approach: They tried to fit a model where some signals are ghosts and some are stars, seeing if the data prefers a mix.

The Findings: The Ocean is Quiet

Here is what they found:

• The "Ghost" Limit: They set a very strict speed limit for how many ghost black holes can exist. If there were too many, the detectors would have heard a constant, loud roar of collisions. Since they didn't hear that roar, they can say with high confidence that ghost black holes make up less than a tiny fraction of the universe's dark matter.
  • Analogy: Imagine walking through a forest. If there were thousands of hidden birds singing, you'd hear a constant chorus. Since you only hear a few birds here and there, you know the forest isn't teeming with hidden singers.
• The "Heavy" vs. "Light" Range: They checked black holes ranging from very light (smaller than our Sun) to very heavy (100 times the Sun's mass).
  • For the "heavy" range (0.6 to 100 solar masses), they found the strongest limits yet.
  • For the "light" range, they checked if there were any ghost black holes orbiting inside our own galaxy. They found that current technology isn't sensitive enough to hear them yet, but they mapped out exactly how sensitive the detectors would need to be to catch them.
• The "Background Noise" Check: Even if individual collisions are too faint to hear, a sea of tiny, unresolvable collisions should create a background hum (like static on a radio). The team checked for this hum and found nothing. This confirmed their limits on the ghost black holes.

The Twist: When the Data Gets Confusing

The paper highlights a tricky part of detective work. When they tried to mix the "ghost" and "star" models together, the math sometimes liked the idea that a few specific, low-mass signals were ghosts.

• Analogy: Imagine you hear a noise in your house. It could be the wind (stars) or a ghost. If you have a very flexible explanation for the wind (e.g., "the wind can sound like anything"), the math might say, "Well, maybe this specific creak is a ghost."
• However, the authors realized this was a trick of the math. When they fixed the rules to be more realistic (e.g., "stars can't be lighter than 5 Suns"), the evidence for ghosts disappeared. The data showed no compelling evidence that ghost black holes are actually there. The "ghosts" were just the math trying to fit a square peg into a round hole.

The Conclusion

The paper concludes that while we can't prove ghost black holes don't exist, we can prove they aren't very common.

• The Verdict: The universe is mostly filled with the "normal" black holes made from dying stars.
• The Limit: If ghost black holes exist in the mass range the detectors can hear, they can only make up a very small percentage of the universe's dark matter (less than 0.1% to 1% depending on their size).
• The Future: The detectors are getting better. They are now sensitive enough to rule out huge numbers of ghost black holes, and in the future, they might finally hear the faint whisper of the ones that are still hiding.

In short: The detectors listened hard, found no loud chorus of ancient black holes, and concluded that if they are there, they are very rare guests in the cosmic neighborhood.

Technical Summary

Technical Summary: Constraints on Primordial Black Holes from the First Part of LIGO-Virgo-KAGRA Fourth Observing Run

Problem Statement
The first part of the fourth LIGO-Virgo-KAGRA (LVK) observing run (O4a) has unveiled 85 new gravitational wave (GW) signals from compact binaries, bringing the total catalog of detected events to 161. Population studies of this catalog reveal features in the black hole (BH) mass distribution, such as multiple peaks above a power-law continuum, which challenge standard astrophysical formation scenarios (e.g., isolated binary evolution or dynamical assembly). While these features could be explained by complex astrophysical channels, they also raise the possibility of a population of Primordial Black Holes (PBHs). PBHs, hypothesized to form from the collapse of large density fluctuations in the early Universe, would constitute a fundamentally different BH population with distinct merger rates, mass spectra, and spin distributions. The primary objective of this work is to derive updated constraints on the abundance of PBHs ($f_{\text{PBH}} \equiv \Omega_{\text{PBH}}/\Omega_{\text{DM}}$) using the expanded O4a dataset, addressing limitations in previous analyses by incorporating new data, refined modeling of binary formation channels, and stochastic GW background (SGWB) constraints.

Methodology
The authors employ state-of-the-art modeling of PBH binaries to analyze the LVK O4a data. The analysis considers three distinct approaches to modeling the astrophysical black hole (ABH) population to ensure robustness:

1. Astrophysics Only: Assumes all observed events are of astrophysical origin; constraints are derived from the non-observation of an excess of events.
2. Astrophysically Agnostic: Does not model the ABH population. Two methods are used: (i) random subset selection, where random subsets of the catalog are assumed to be PBHs, and (ii) a subset-marginalized likelihood (SML), which smoothly down-weights events inconsistent with the PBH population.
3. Astrophysically Informed: A joint fit modeling both ABH and PBH populations. The ABH population is modeled using a phenomenological power-law plus two peaks (PL+2P) parameterization, while the PBH population is modeled with a log-normal mass function.

The PBH merger rate is estimated analytically for early two- and three-body formation channels, assuming the PBHs are not initially formed in clusters. The mass function is modeled as log-normal, $\psi \propto \exp[-\ln^2(m/m_c)/2\sigma^2]$, where $m_c$ is the mode and $\sigma$ is the width. The analysis also incorporates:

• Resolvable Binaries: A hierarchical Bayesian approach is used to estimate the likelihood of observed events, calculating the expected number of events $N(\Lambda)$ based on the merger rate and detection probability.
• Galactic Sub-solar Binaries: The potential observability of Galactic PBH binaries in the sub-solar mass range ($10^{-4}–10^{-3} M_\odot$) is modeled using the Milky Way's dark matter halo density, though current sensitivity limits are assessed.
• Stochastic GW Background (SGWB): Constraints are derived from the non-detection of a SGWB generated by unresolvable PBH binaries, utilizing cross-correlation statistics between detector pairs.

Key Contributions

• Updated Constraints: The paper derives the strongest bounds to date on PBH abundance in the $0.6–100 M_\odot$ range using O4a data, extending sensitivity to the $10^{-4}–10^4 M_\odot$ range.
• Refined Modeling: The analysis introduces a new method for estimating model-agnostic constraints (SML) and incorporates contributions from galactic binaries and the SGWB, which were not fully integrated in previous LVK-based PBH studies.
• Comparison of Formation Channels: The study explicitly compares the impact of including the three-body formation channel versus only the two-body channel, demonstrating that the three-body channel is dominant for higher PBH abundances and significantly affects the derived constraints.
• Robustness Analysis: The authors perform joint fits to test the sensitivity of PBH inferences to analysis choices, specifically the lower mass cutoff ($m_{\text{min}}$) of the ABH population and the inclusion of low-mass outlier events.

Results

• Resolvable Binaries: The constraints from resolvable PBH binaries are the dominant limit, exceeding those from the SGWB by approximately three orders of magnitude. For monochromatic mass functions, the O4a data provides tight upper bounds on $f_{\text{PBH}}$ between $10^{-2}$ and $10^{-4}$ in the mass range $0.5–90 M_\odot$.
• Mass Function Width: For broader mass functions (larger $\sigma$), the constraints weaken slightly near $\langle m \rangle \sim 100 M_\odot$ but extend to higher masses. However, wider mass functions that allow for larger PBH fractions are generally ruled out by other independent constraints (e.g., CMB).
• Agnostic Limits: When allowing for a subset of events to be primordial, the constraints relax in the $2–20 M_\odot$ range. The agnostic methods (random subsets and SML) yield consistent results, providing robust, model-independent bounds.
• Joint Fits: In joint ABH+PBH fits, the Bayesian evidence initially favors a PBH contribution ($\ln B \approx 30.5$) when the ABH low-mass cutoff is free and low-mass events are included. However, this preference is driven by the flexibility of the phenomenological ABH model to accommodate low-mass events. When the analysis is restricted to $m_{\text{min}} = 5 M_\odot$ and the low-mass gap outlier (GW200210_092254) is excluded, the evidence for a PBH contribution vanishes ($\ln B \approx 1.7$).
• Galactic Binaries: No new constraints on PBH abundance are derived from galactic sub-solar binaries, as current LVK sensitivity is insufficient. However, a sensitivity floor is identified where $f_{\text{PBH}} \gtrsim 0.1$ would have been detectable in the $10^{-4}–10^{-3} M_\odot$ range.
• Comparison with Previous Works: The derived bounds are approximately an order of magnitude stronger than recent results in Ref. [54], primarily due to the inclusion of the three-body formation channel and improved suppression factors. Discrepancies with SGWB constraints in Ref. [73] are attributed to the omission of the three-body channel in that work.

Significance and Claims
The paper claims to provide the most stringent constraints to date on the abundance of primordial black holes in the solar-mass range, utilizing the full O4a dataset. The authors emphasize that their bounds are robust to assumptions about the astrophysical population. Crucially, the study concludes that while the data allows for a subdominant PBH population, there is no compelling evidence for such a contribution. The apparent preference for PBHs in certain joint fits is shown to be sensitive to analysis choices regarding the low-mass cutoff and the treatment of specific outlier events. Consequently, the LVK data currently supports the interpretation that the observed binary population is consistent with astrophysical origins, placing tight limits on the fraction of dark matter that could be composed of PBHs.