Probing Primordial Black Hole Mergers in Clusters with Pulsar Timing Data

Introduction to the show: ident: Astrophysics Radio. Generated commentary on the latest astrophysics papers.

Vera: We're looking at the paper: "Probing Primordial Black Hole Mergers in Clusters with Pulsar Timing Data".

Jocelyn: Here's the gist of the paper. The gist: The analysis systematically addresses whether the stochastic gravitational wave background suggested by Pulsar Timing Array (PTA) datasets can be substantial enough to compete with that from scalar induced GWs, finding that scalar-induced GWs dominate in a broad PBH mass distribution, although specific PBH models with enhanced clustering could yield a background dominated by PBH mergers.

Vera: PBH Mass Function Derivation The paper derives the PBH mass function from a power law primordial spectrum of curvature perturbations using the Press-Schechter formalism.

Jocelyn: The mass is approximated by the horizon mass at re-entry, given by MH(k) = 4πM2p/H(1) ≃ 20 M⊙ k106 Mpc−1 g4∗,s(Tcr)g−3∗(Tcr) (2).

Vera: The PBH mass function fPBH(m) is then expressed in terms of the primordial power spectrum Pζ (k) and the critical threshold δc.

Paper summary: Vera: To recap, this paper looks at the possibility that the stochastic gravitational wave background suggested by pulsar timing array datasets is sourced by primordial black holes, specifically performing a Bayesian search in IPTA DR2 for a combined GW background arising from scalar perturbations and unresolved PBH mergers.

Jocelyn: They assumed a broad PBH mass distribution for this analysis, and they incorporated constraints on the curvature power spectrum from CMB mu-distortions and the overproduction of PBHs which significantly suppress the contribution of PBH mergers to the total GW background.

Subrahmanyan: The key finding they report is that scalar-induced GWs dominate in the nHz frequency range, while PBH mergers alone cannot account for the observed signal under the standard PBH formation scenario involving Gaussian perturbations and including only Poissonian PBH clustering.

Vera: They also found that specific PBH models, such as those with enhanced clustering, could yield a GW background dominated by PBH mergers.

Jocelyn: So they’re basically saying that scalar-induced GWs are the main driver for the observed signal in this analysis, but if you look at enhanced clustering, PBH mergers become more relevant again.

Subrahmanyan: That points toward the need to investigate how much clustering actually impacts merger rates for those specific models because they suggest a much more dense PBH cluster could lead to much enhanced merger rates with respect to their computations.

Vera: This whole investigation into whether PBHs can explain the PTA signal is important because it sets a benchmark against the astrophysical origin of this common-spectrum process.

Jocelyn: It’s a test of how robust these PBH models are when you introduce more complex physics like enhanced clustering, which is something we haven't fully constrained yet with our current pulsar observations.

Subrahmanyan: The paper uses a phenomenological approach to treat the parameter for clustering as a free parameter and additionally perform a Bayesian search with this nuisance parameter to account for that enhancement and various other uncertainties in the merger rates discussed in Section IV A.

Conclusion: Vera: So, wrapping up on "Probing Primordial Black Hole Mergers in Clusters with Pulsar Timing Data," the authors show that the contribution to the GWB from PBH binaries, both early and late channels, is largely subdominant with respect to the GWB from scalar induced perturbations for power law PBH mass distributions.

Jocelyn: They also state it’s not possible to explain the PTA signal with only PBH binaries in late-time PBH clusters under the assumption of standard PBH formation scenario involving Poissonian fluctuations.

Subrahmanyan: The paper strongly favors an astrophysical origin for the reported common-spectrum process over the specific PBH models considered in this analysis, which is a key conclusion they draw from their Bayesian inference.

Vera: What this means for us on the ground is that while we are looking at PBHs as a possibility, the current data points toward an explanation that comes from astrophysical processes.

Jocelyn: It’s also important to remember the caveat they mentioned, which is that for explaining the PTA signal with late PBH binaries, the required clustering factor R cl is about O(one hundred four) Gpc-three yr-one larger than what comes from Poissonian fluctuations.

Subrahmanyan: That difference in required clustering tells us a lot about what’s missing in our understanding of how these PBH clusters actually form and how they merge, which is where future observations or simulations could help clarify things.

Vera: And the analysis itself has some limitations, so we should be mindful that it only explores the possibility under a broad PBH mass distribution derived using Gaussian curvature perturbations.

Jocelyn: That’s right, so we’re not testing every possible PBH mass function, just this one specific one for this particular investigation into the IPTA DR2 data.

Subrahmanyan: And looking forward, the paper shows that PBH mass distributions with n s about one are statistically preferred because they naturally suppress low-mass PBHs from overclosing the Universe and don't require a small-scale cut-off k max.

Vera: It’s a nuanced result, showing how constraints from CMB mu-distortions and LVK bounds interact with the potential PBH scenarios.

Jocelyn: This paper serves as an important check on whether we should be looking for a simple PBH explanation or if the astrophysical background is indeed the right fit for this nHz signal.