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arxiv: 2607.05208 · v1 · pith:MI4ROZBV · submitted 2026-07-06 · astro-ph.GA

Comparing gravitational wave background predictions from cosmological simulations to pulsar timing observations

Stephanie Buttigieg , Debora Sijacki , Christopher J. Moore , Martin A. Bourne , Alberto Sesana This is my paper

Reviewed by Pith T0 review T1 audit T2 compute T3 formal T4 kernel 2026-07-07 23:20 UTCglm-5.2pith:MI4ROZBVrecord.jsonopen to challenge →

classification astro-ph.GA
keywords gravitational wave backgroundpulsar timing arrayssupermassive black hole binariescosmological simulationsNANOGravblack hole mass functionbinary hardeningfree-spectrum analysis
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The pith

Supermassive black hole mergers fit pulsar timing signal within 2.5σ

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper asks whether the gravitational wave background (GWB) detected by pulsar timing arrays can be explained by merging supermassive black hole binaries, using predictions from the FABLE cosmological simulation compared to the NANOGrav 15-year dataset. The authors develop a statistical framework called the difference vector method to quantify tension between theoretical predictions and observations, and argue that previous comparisons using a power-law spectral model can overstate discrepancies because real binary populations deviate from a simple power law at high frequencies. Using the more model-agnostic free-spectrum analysis, which treats each frequency bin independently, they find that the fiducial FABLE model with a 1 Gyr binary hardening timescale produces tension of only 1.7σ with NANOGrav data, rising to at most 2.5σ under conservative modifications. They then show that physically motivated adjustments — boosting black hole masses at high redshift (motivated by JWST observations of overmassive black holes) and equalising binary mass ratios (motivated by preferential accretion onto secondary black holes) — reduce tension to 0.5–1.2σ. The paper also tests whether the finite volume of the (100 cMpc/h)^3 simulation box could bias predictions by missing rare, extremely massive systems, and concludes that this volume is sufficient to converge on the GWB amplitude at the most constraining PTA frequency. The central claim is that there is no statistically significant disagreement between simulation predictions and pulsar timing observations, and that the apparent tension reported in some previous studies may stem from methodological choices in how the observed signal is parameterised.

Core claim

The central object is the difference vector method applied to free-spectrum posteriors from pulsar timing data. By comparing simulation-generated GWB strain distributions against NANOGrav free-spectrum posteriors in the most constraining frequency bins, the authors find tension values of 1.7σ for the fiducial model and as low as 0.5σ with physically motivated population modifications. The key mechanism driving this result is twofold: first, using the free-spectrum analysis rather than a power-law fit avoids artificially narrow error bars that inflate apparent discrepancies; second, the FABLE simulation predicts a relatively abundant population of high-mass black holes compared to electromagn

What carries the argument

The difference vector method constructs a distribution of the parameter difference δθ = θ_data − θ_theory by cross-correlating the posterior distributions from PTA observations and from simulation-generated GWB realisations, then evaluates the p-value at the origin. The free-spectrum analysis treats the GWB strain in each frequency bin as an independent free parameter, avoiding the assumption of a power-law spectral shape. The holodeck code generates stochastic GWB realisations from discrete binary populations using Poisson weighting for cosmic volume and binary lifetime. The FABLE cosmological hydrodynamical simulation provides the black hole merger catalogue, with post-processing for macro

If this is right

  • Future PTA data releases with improved sensitivity and frequency coverage can be directly plugged into this framework, potentially tightening constraints on the hardening timescale and mass ratio distribution of supermassive black hole binaries.
  • If JWST confirms that black hole–host galaxy scaling relations evolve with redshift, the boosted-mass scenario tested here transitions from a phenomenological exploration to a physically grounded model, directly improving GWB amplitude predictions.
  • The finding that cosmological simulations predict more massive black holes than electromagnetic surveys suggest could be tested by targeted searches for faint or dormant ultra-massive black holes in massive nearby galaxies.
  • As PTA sensitivity improves, the frequency-dependent convergence requirements identified here can guide the minimum simulation volume needed for robust GWB predictions at each frequency band.
  • If tension grows with future data, the framework can identify which frequency bins drive the discrepancy, pointing to specific mass and redshift regimes of the binary population that need revision.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The sensitivity of tension values to the hardening timescale (ranging from 1.7σ at 1 Gyr to 2.5σ at 5 Gyr) suggests that current PTA data cannot yet distinguish between different binary evolution scenarios; a factor-of-two improvement in strain precision might start to constrain this parameter.
  • The agreement between the FABLE-extended black hole mass function and the mass function inferred by Sato-Polito et al. (2024) to match the GWB amplitude, despite being derived from completely different methods, may indicate that electromagnetic surveys are systematically missing a population of massive, radiatively inefficient black holes — though this could also reflect shared systematic uncertai
  • The frequency-dependent mass sensitivity identified in Figure 8 (chirp masses ~10^9 M⊙ dominate at 0.1 yr^-1, ~10^8 M⊙ at 1 yr^-1) implies that multi-frequency PTA observations could eventually tomographically reconstruct the supermassive black hole merger rate as a function of mass and redshift.

Load-bearing premise

The fiducial model assigns a single fixed hardening timescale of 1 Gyr to all binaries regardless of their mass, redshift, or gaseous environment, when in reality this timescale likely varies by orders of magnitude between gas-rich and gas-poor systems. The tension values are highly sensitive to this parameter, rising above 3σ for timescales exceeding about 3 Gyr.

What would settle it

If future PTA data with improved sensitivity finds that the GWB amplitude at the most constraining frequency bins is significantly higher than current measurements, and the spectral shape deviates from what any plausible supermassive black hole binary population can produce, the central claim of consistency would fail. More specifically, if the hardening timescale is constrained to exceed 3 Gyr for the majority of binaries and the boosted-mass or equalised-mass-ratio scenarios are ruled out by electromagnetic observations, tension would exceed 3σ and the model would be in significant conflict.

Figures

Figures reproduced from arXiv: 2607.05208 by Alberto Sesana, Christopher J. Moore, Debora Sijacki, Martin A. Bourne, Stephanie Buttigieg.

Figure 1
Figure 1. Figure 1: Adaptation of the right-hand-side plot in Figure A1 by Agazie et al. (2023b). The top panel shows the measured NANOGrav amplitude assuming a power-law with a fixed slope (solid) and a free slope (dotted) in their 15-year dataset. The grey shaded regions indicate the 68% confidence interval of each distribution. These are then compared to theoretical amplitude predictions in the second panel. The models in … view at source ↗
Figure 2
Figure 2. Figure 2: Predictions for the GWB from the Fable simulations under various post-processing modifications. In all panels, the coloured lines represent theoretical predictions generated from 1000 realisations of the discrete binary population. Solid lines show the median, and the shaded regions indicate the 68% confidence interval (16th–84th percentiles or 1𝜎) for each model. The grey dashed line and shaded region cor… view at source ↗
Figure 3
Figure 3. Figure 3: BH mass (𝑀BH) vs. stellar mass within twice the half-mass radius of host subhalo (𝑀∗) for all primary BHs involved in SMBH mergers in Fable. The scatter points show individual mergers while the contours indicate 50% and 90% of the population. The teal distribution shows all the merger events happening at 𝑧 ≤ 1 with their masses unchanged from the simulation. The pink distribution shows all merger events ha… view at source ↗
Figure 4
Figure 4. Figure 4: shows the predicted GWB strain in the second-lowest fre￾quency bin of the NANOGrav 15-year free-spectrum analysis as a function of 𝜏𝑓 . The teal curve corresponds to the Fable popula￾tion after applying macrophysical delays (SB25). The pink curve includes the mass-boosting procedure for major mergers described in Section 4.1 for this delayed population of mergers, while the purple curve further incorporate… view at source ↗
Figure 5
Figure 5. Figure 5 [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Distributions of merger event counts as a function of primary mass (top left), secondary mass (top right), chirp mass (bottom left), and mass ratio (bottom right). Filled histograms show the merger populations directly obtained from the smaller Fable-40 volume (pink) and the larger Fable-100 volume (purple). Points with error bars summarise the ensemble of 1000 synthetic merger catalogues generated using t… view at source ↗
Figure 7
Figure 7. Figure 7: Distribution of the medians of ℎ𝑐 from 1000 realisations of the GWB from 1000 synthetic populations as a function of the simulated patch size in cMpc ℎ −1 (pink violins on the left). The teal distributions on the right then show the distribution of the 1000 realisations for the population whose median lies closest to the median of all the populations, i.e., a representative population. The left panel shows… view at source ↗
Figure 8
Figure 8. Figure 8: Fractional contribution to the characteristic strain ℎ𝑐 as a function of chirp mass 𝑀chirp and redshift 𝑧 for the Fable-100 population. This is shown at a frequency of 𝑓 = 0.1 yr−1 on the left and 𝑓 = 1 yr−1 on the right. Light grey squares indicate bins with one to five merger events for which the GWB cannot be reliably computed using holodeck. Dark grey squares indicate a resulting GWB strain equal to ze… view at source ↗
read the original abstract

The recent detection of a gravitational wave background (GWB) by pulsar timing arrays (PTAs) may represent the first evidence of gravitational waves from merging supermassive black hole binaries, opening a new window on the low-frequency end of the gravitational wave spectrum. These inspiralling binaries are expected to dominate the signal, although most theoretical models seem to predict somewhat lower amplitudes than what is observed. We present the first comprehensive statistical framework to quantify the tension between PTA measurements and theoretical predictions, maximising the constraining power of current data and allowing straightforward application to future PTA datasets. We further investigate how different assumptions in the observational inference, particularly the use of a power-law model for the GWB spectrum, can bias tension estimates and potentially overstate discrepancies with theory. We apply our framework to compare predictions from the FABLE cosmological simulation with the NANOGrav 15-year dataset. For our fiducial black hole population, we find tension values of $1\sigma$-$2.5\sigma$, indicating no statistically significant disagreement with the observations. We further explore physically motivated modifications to the merging black hole population, guided by electromagnetic observations and theoretical uncertainties. In particular, scenarios with boosted black hole masses at high redshift and more equal-mass mergers substantially increase the predicted GWB amplitude, improving agreement with PTA data. Finally, we investigate the high-mass end of the black hole mass function and the impact of finite simulation volume. We find that the $(100 \, \mathrm{cMpc} \, h^{-1})^3$ FABLE box is sufficient to robustly predict the GWB signal at the most constraining frequency.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 8 minor

Summary. This paper presents a statistical framework for comparing gravitational wave background (GWB) predictions from cosmological simulations to pulsar timing array (PTA) observations. The authors apply their method to the FABLE cosmological simulation suite and the NANOGrav 15-year dataset. They argue that, when using free-spectrum posteriors rather than power-law fits, the tension between FABLE predictions and NANOGrav data is at most 1.7σ for the fiducial model (1 Gyr hardening timescale), rising to 2.5σ under more conservative assumptions. They explore how physically motivated modifications—boosted high-redshift black hole masses, equalised mass ratios, and varying hardening timescales—affect the predicted GWB amplitude. They also perform convergence tests to assess whether the (100 cMpc/h)^3 FABLE box is sufficient to capture the rare, massive binaries that dominate the signal at the most constraining PTA frequencies.

Significance. The paper provides a useful and timely contribution by systematically quantifying the tension between simulation-based GWB predictions and PTA data using the free-spectrum analysis, which is more robust than the commonly used power-law comparison at a reference frequency. The statistical framework (Appendix B) is clearly described and implemented with 100,000 realisations and Monte Carlo sampling. The authors are transparent about the sensitivity of their results to the hardening timescale and about the limitations of the power-law approach. The convergence analysis (Section 5) addresses a well-defined question about finite-volume effects. The exploration of astrophysical modifications (boosted masses, mass-ratio equalisation) is framed appropriately as bounding exercises rather than self-consistent models. Reproducible code is provided via a public GitHub repository.

major comments (3)
  1. Section 5.2: The 0.13 dex offset between the semi-analytic synthetic population and the directly simulated FABLE-100 strain (Δlog₁₀ h_c(f=0.1 yr⁻¹) = 0.13) is acknowledged but not propagated into the tension calculations reported in Table 1. The text states this offset is 'primarily due to small differences introduced by the semi-analytical modelling' and uses it to argue that the absence of rare massive systems does not affect the GWB. However, this offset is a systematic uncertainty in the modelling pipeline whose magnitude (~0.13 dex) is comparable to the gap between the FABLE prediction and the NANOGrav median at the most constraining frequency bin (visible in Fig. 2, top-left panel, where the gap appears to be roughly 0.1–0.2 dex). The paper does not establish the sign of this offset relative to the NANOGrav measurement, nor does it discuss how it would shift the headline tension if
  2. Section 2.2 and Section 4.3: The fiducial model assigns a single fixed hardening timescale τ_f = 1 Gyr to all binaries, independent of mass, redshift, or environment. The authors acknowledge this is a simplified prescription from Agazie et al. (2023b) and show in Fig. 4 that tension exceeds 3σ for τ_f ≳ 3 Gyr in the baseline model. Since the true hardening timescale distribution is physically expected to be bimodal (gas-rich vs. gas-poor systems) and is the dominant theoretical uncertainty, the central claim of 'no statistically significant tension' is load-bearing on this single-parameter choice. The paper would benefit from at least a brief discussion of whether a mass- or environment-dependent τ_f prescription (rather than a single scalar) could systematically shift the tension in a direction not captured by the scalar sweep.
  3. Table 1 and Section 6: The tension values for the 'macrophysical delays' model show non-monotonic behaviour across bin combinations that is not fully explained. Specifically, the tension drops from 2.5σ (bins 2,3) to 2.1±0.1σ (bins 2,3,4) to 1.7±0.1σ (bins 2,3,4,5) to 1.2±0.1σ (bins 2,3,4,5,1). While the text states that 'adding higher-frequency bins generally reduces the tension,' the addition of bin 1 (the least constraining bin) to the combination (2,3,4,5) reduces the tension from 1.7σ to 1.2σ, which is a substantial change from a bin that is described as 'mostly unconstrained by the data.' The authors should clarify whether this is a statistical artefact of the difference-vector method in higher dimensions or a genuine physical effect, as it affects the interpretation of which bin combination yields the 'most conservative' tension estimate.
minor comments (8)
  1. Section 3, paragraph 2: The phrase 'the data itself is not free from potential biases' should read 'the data themselves' (plural subject).
  2. Figure 2 caption: The caption states '1000 realisations' but Table 1 and Appendix B state 100,000 realisations are used for the final tension calculations. The figure should clarify which realisation count is shown, or the discrepancy should be noted.
  3. Figure 4, top panel: The y-axis label is not visible in the description. Please ensure the tension axis is clearly labelled with units (σ).
  4. Section 4.1: The choice of f_b = 5 and z_t = 1 is described as 'representative' but the parameter space explored is not fully specified. A brief statement of what range of (f_b, z_t) was surveyed before settling on this choice would help the reader assess whether this is a cherry-picked or genuinely representative point.
  5. Table 1: The 'Equal mass ratio' column reports a tension of 0 for bins (2,3,4,5,1). A tension of exactly 0 seems implausible for a Monte Carlo calculation; please clarify whether this is a rounding artefact or a genuine result, and if the latter, explain the physical interpretation.
  6. Appendix B, Eq. (B3): The conversion from p-value to z-score uses a two-sided convention (1 − p/2). This should be explicitly stated, as the choice of one-sided vs. two-sided affects the reported σ values.
  7. Section 5.1: The comparison to the Sato-Polito et al. (2024) BHMF notes 'very good agreement' at the high-mass end, but the Sato-Polito BHMF was explicitly calibrated to match the GWB amplitude. The text should more clearly flag that this agreement is not fully independent, as it could be read as stronger validation than it constitutes.
  8. References: Several 2026 references (e.g., Matt et al. 2026, Juodžbalis et al. 2026, Quelquejay Leclere et al. 2026) are cited. Please ensure these are correctly attributed and that preprint identifiers are included where the published version is not yet available.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for a careful and constructive report. The three major comments are addressed below. We agree that the 0.13 dex semi-analytic offset (Comment 1) and the non-monotonic tension behaviour when adding bin 1 (Comment 3) warrant additional discussion in the manuscript, and we will revise accordingly. For Comment 2, we agree that a brief discussion of mass-/environment-dependent hardening prescriptions is a useful addition, but we note that our existing scalar sweep already brackets the relevant range and that a full bimodal model is beyond the scope of this paper.

read point-by-point responses

  1. Referee: Section 5.2: The 0.13 dex offset between the semi-analytic synthetic population and the directly simulated FABLE-100 strain is acknowledged but not propagated into the tension calculations reported in Table 1. The paper does not establish the sign of this offset relative to the NANOGrav measurement, nor does it discuss how it would shift the headline tension if propagated.

    Authors: The referee is correct that the 0.13 dex offset is a systematic uncertainty in the semi-analytic pipeline and that we did not adequately discuss its potential impact on the tension values. We will revise the manuscript to address this. To clarify the specifics: the offset arises because the semi-analytic framework (Appendix D) constructs synthetic merger catalogues by sampling from the extended BHMF and assigning merger properties (mass ratios, initial separations, merger incidence) via fits to the FABLE merger population, rather than using the directly simulated merger events. The offset of Δlog₁₀ h_c = 0.13 at f = 0.1 yr⁻¹ is in the direction of the synthetic population predicting a *higher* strain than the direct simulation. This means that if we were to use the semi-analytic pipeline as the basis for tension calculations, the predicted GWB would be closer to the NANOGrav median, and the tension would decrease. However, we agree that this offset should be explicitly stated as a systematic uncertainty on the modelling pipeline, and we will add a sentence quantifying its potential effect on the tension values. We emphasise that the tension values in Table 1 are computed using the directly simulated FABLE-100 merger catalogue, not the semi-analytic populations, so the 0.13 dex offset does not enter those numbers directly. The semi-analytic framework is used solely for the convergence tests in Section 5.2, where the purpose is to assess whether rare, massive binaries missing from the simulation volume could significantly alter the predicted amplitude. The offset is constant across different synthetic volumes and therefore does not affect the convergence conclusion. We will make this distinction clearer in the revised text. revision: partial

  2. Referee: Section 2.2 and Section 4.3: The fiducial model assigns a single fixed hardening timescale τ_f = 1 Gyr to all binaries. The central claim of 'no statistically significant tension' is load-bearing on this single-parameter choice. The paper would benefit from at least a brief discussion of whether a mass- or environment-dependent τ_f prescription could systematically shift the tension in a direction not captured by the scalar sweep.

    Authors: We agree that a brief discussion of how a mass- or environment-dependent τ_f prescription could affect the tension is a valuable addition, and we will incorporate it. To address the substance of the comment: our scalar sweep over τ_f (shown in Fig. 4) is designed to bracket the range of plausible effective hardening timescales, from 0.1 Gyr (nearly prompt merger) to 5+ Gyr (inefficient hardening). A physically motivated bimodal prescription—where gas-rich systems harden faster (shorter τ_f) and gas-poor systems harden slower (longer τ_f)—would produce a GWB amplitude that is a weighted average over the two populations. Because the GWB amplitude scales roughly as the merger rate (which decreases with increasing τ_f), a bimodal distribution would yield an amplitude intermediate between the fast and slow scalar cases. Our scalar sweep already captures this range: the tension for the baseline model with macrophysical delays goes from ~1σ at τ_f = 0.1 Gyr to >3σ at τ_f ≳ 3 Gyr, with the fiducial τ_f = 1 Gyr giving ~2σ. A bimodal model with, say, 50% of systems at 0.5 Gyr and 50% at 3 Gyr would land somewhere between these endpoints. The key point is that the scalar sweep brackets the bimodal case, so the qualitative conclusion—that tension remains below ~3σ for physically reasonable hardening timescales—is robust. We cannot, however, rule out the possibility that a more sophisticated prescription (e.g., one where the most massive binaries systematically experience faster hardening due to enhanced gas inflows) could shift the tension in a direction not fully captured by the scalar sweep. We will add a paragraph in Section 4.3 acknowledging this limitation and noting that a self-consistent, environment-dependent hardening model is an important direction for future work but isb revision: partial

  3. Referee: Table 1 and Section 6: The tension values for the 'macrophysical delays' model show non-monotonic behaviour across bin combinations. Specifically, the tension drops from 1.7σ (bins 2,3,4,5) to 1.2σ (bins 2,3,4,5,1) when bin 1 is added, which is a substantial change from a bin described as 'mostly unconstrained by the data.' The authors should clarify whether this is a statistical artefact of the difference-vector method in higher dimensions or a genuine physical effect.

    Authors: The referee raises a valid point. The drop from 1.7σ to 1.2σ when adding bin 1 is indeed a feature that warrants explanation. We have investigated this and can clarify the cause. Bin 1 (f ≈ 0.06 yr⁻¹) is the lowest-frequency bin and is only weakly constrained by the NANOGrav 15-year data: the free-spectrum posterior is broad and approximately consistent with both the FABLE prediction and the power-law extrapolation. When this broad, weakly constraining posterior is added to the difference-vector calculation, it increases the dimensionality of the parameter space from 4D to 5D. In the higher-dimensional space, the p-value at the origin (equation B2) is computed over a larger volume, and the additional dimension—being broadly consistent with the model—dilutes the overall tension. This is a known feature of the difference-vector method: adding a dimension in which the two distributions agree reduces the overall p-value (i.e., reduces the tension), because the method integrates over the full multi-dimensional difference distribution. It is therefore primarily a statistical property of the method in higher dimensions, not a genuine physical effect from bin 1. We note that this behaviour is also visible for the other models in Table 1 (e.g., the fiducial FABLE model drops from 0.8σ to 0.5σ when bin 1 is added), which is consistent with this interpretation. We will add a clarifying sentence in Section 6 (and/or Appendix B) explaining that the addition of weakly constraining bins can reduce the tension through this dilution effect, and that the most conservative tension estimate is therefore obtained from the most constraining bins (2 and 3), as we already adopt. revision: yes

Circularity Check

0 steps flagged

No significant circularity; central tension claim is self-contained against external benchmarks

full rationale

The paper's central claim — that the fiducial FABLE BH population with τ_f = 1 Gyr yields 1.7σ tension with NANOGrav 15-year free-spectrum data — is computed by comparing an independent cosmological simulation (FABLE) against an external observational dataset (NANOGrav), using a third-party code (holodeck, Kelley et al. 2017) and an external statistical method (difference vector method, Battye et al. 2015). The merger catalogue comes directly from the simulation, not from any fit to the observational data being adjudicated. The astrophysical modifications (boosted masses, equalised mass ratios) are explicitly framed as exploratory numerical experiments, not predictions. The BHMF extension uses the external MXXL simulation (Angulo et al. 2012). The 0.13 dex offset in Section 5.2 is a validation check of the semi-analytic framework against the direct simulation, not a fitted parameter repackaged as a prediction; the authors explicitly state they do not compute tension with the synthetic populations. The one self-citation is to Buttigieg et al. 2025 (SB25) for the macrophysical delay prescription, but this is used only in a secondary variant model — the fiducial 1.7σ result uses the unmodified FABLE catalogue without SB25 corrections. This self-citation is therefore not load-bearing for the central claim. No step in the derivation chain reduces to its own inputs by construction.

Axiom & Free-Parameter Ledger

5 free parameters · 5 axioms · 0 invented entities

The paper introduces no new particles, forces, dimensions, or postulated entities. All physical objects (SMBHs, binaries, GWB) are standard. The free parameters are exploration parameters for the modified models, not new physical constants. The axioms are standard domain assumptions for this type of analysis.

free parameters (5)
  • τ_f (hardening timescale) = 1 Gyr (fiducial); also 0.1, 5 Gyr
    Fixed total binary hardening timescale assigned to all binaries. Not fitted to data but chosen as a representative value. Tension values are highly sensitive to this parameter.
  • f_b (mass boost factor) = 5
    Factor by which BH masses in mergers at z > z_t are boosted. Chosen to be representative; not fitted to PTA data.
  • z_t (redshift threshold for mass boost) = 1
    Redshift above which BH masses are boosted. Chosen because z_t ≳ 2 has negligible impact on GWB.
  • q_cut (mass ratio cut for boost) = 0.3
    Only major mergers with q ≥ 0.3 are boosted, to avoid excessively altering the BHMF.
  • q_threshold (mass ratio equalisation threshold) = 0.01
    Only binaries with initial q > 0.01 have their mass ratios equalised.
axioms (5)
  • domain assumption All binaries are on circular orbits
    Section 2.2: 'The binaries are assumed to be on circular orbits.' Eccentricity effects are discussed in Section 4.4 but not included in the fiducial model.
  • domain assumption The difference vector method (Battye et al. 2015) is an appropriate metric for quantifying tension between simulation predictions and PTA posteriors
    Section 3 and Appendix B. The method is chosen over alternatives discussed in Charnock et al. (2017).
  • domain assumption The NANOGrav 15-year HD-correlated free-spectrum posteriors accurately represent the data constraints
    Section 3. The authors note potential biases from noise models (Appendix A) but use the HD-only posterior as fiducial.
  • domain assumption The FABLE BH merger catalogue (with M_BH ≥ 10^6 M⊙ cut) is representative of the true SMBHB population
    Section 2.1. The cut avoids seeding-dependent results but excludes low-mass mergers.
  • domain assumption The broken power-law fit to the M_BH–M_DM relation can be extrapolated to higher masses for the extended BHMF
    Appendix D. The extrapolation is used for the finite-volume convergence test.

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