Gravitational-wave background from supermassive black holes without merger trees: Tidally regulated mergers and direct inference from the NANOGrav 15 yr data

Shin'ichiro Ando

REVIEW

Gravitational-wave background from supermassive black holes without merger trees: Tidally regulated mergers and direct inference from the NANOGrav 15 yr data

Shin'ichiro Ando

Cosmology and Nongalactic Astrophysics · Submitted 5 Oct 2026 · 125 references

Pith's verdict: The real contributions are the tidal-stripping coupling and the parameter-free wandering-BH census; the Δ_KH = +0.31 headline rests on a disclosed but unsigned data edit.

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CitationShin'ichiro Ando. "Gravitational-wave background from supermassive black holes without merger trees: Tidally regulated mergers and direct inference from the NANOGrav 15 yr data." arXiv:2610.06220 (2026). https://pith.science/paper/3WDYHF6C

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Editor's note

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Colleague,

The genuinely new piece here is the continuous coupling of tidal stripping to Chandrasekhar dynamical friction inside a PTA population model. It yields a sharp, nearly redshift-independent stall at ξ ≈ 0.04 and, as a deterministic output with no fitted freedom, a wandering-black-hole census whose mass fraction cancels Δ_KH in the ratio and is therefore independent of the fit. That census is the most interesting thing in the paper. The tree-free triple integral over the Y11-calibrated kernel is also clean work: reproducing the N-body amplitude to 3.4% against 14% for the raw LC93 kernel is a real gain, and the systematics budget in Table III is unusually thorough, each entry backed by a direct numerical experiment.

The headline Δ_KH = +0.31 dex is a different matter. The paper is scrupulously honest that the central number rests on excluding the 15.8 nHz bin, that the exclusion is justified by an unreleased chromatic-noise product, and that the two corrections to the retained data run in opposite directions and cannot be netted (Sec. V A; b209, b216, b217, b339). Retaining the bin gives +0.42; the retained bins carry a −0.07 dex normalization bias. The net is ±0.1 dex, about half the 68% width, which means the 91% posterior-mass statement is not a quantified significance. That is a data-selection judgment, not a model property, and the paper owns it. The stress-test note holds up on reading the text.

Two other soft spots, in proportion. “Robust to local calibration” holds for the sign, not the magnitude: the three calibrations span +0.31 to +0.59 dex, a spread larger than the quoted posterior width. And the headline validation of the tidal physics—the 10% wandering mass budget matching Romulus—sits on two acknowledged, un-netted biases (no seed-mass BHs painted, wanderers assigned the same scaling relation as centrals, b308), while the number census fails outright for Milky-Way-mass halos (0.5 vs ~12, b314). The authors flag all of this themselves, which is to their credit.

Net: a serious, well-argued paper. It is for anyone working on the nHz tension, PTA population modeling, or wandering-BH demographics. It deserves a real referee. I would send it out, on the understanding that the headline number gets revisited once the corrected free-spectral densities are public—the framework stands on the stall physics and the census regardless of what happens to Δ_KH.

Referee report

Significance

If the results hold, the framework is a substantive advance: it eliminates tree shot noise, calibrates the kernel against N-body rates (amplitude agreement 3.4%, versus 14% for the raw LC93 kernel), and turns the delay stage into predictive physics rather than a fitted constant efficiency. The wandering-black-hole census is computed before any likelihood is formed and is invariant to a uniform Δ_KH shift, so it is circularity-free as a test of the delay physics; the care the paper takes on this point is exemplary. The systematics budget (Table III) is unusually thorough, with each entry quantified by a direct numerical experiment, and the positive sign of the black-hole mass offset is robust: it holds under all three local calibrations (+0.31, +0.51, +0.59 dex) and with or without the excluded bin. The remaining issues concern the magnitude and significance of the headline Δ_KH, not the framework's validity.

Major objections (3)

[Sec. V A; Sec. VI A] The headline value Δ_KH = +0.31^{+0.20}_{-0.23} dex with 91% posterior mass above zero is quoted against a data set the paper itself describes as 'neither the published analysis nor the chromatic one' (b209, b216, b217, b339). The two corrections separating the fiducial set from a true chromatic refit act in opposite directions and the net is unsigned: the retained 13 bins still carry the superseded amplitude normalization (biasing Δ_KH down by ~0.07 dex), while discarding the 15.8 nHz bin rather than re-measuring it removes more power than the reanalysis does (biasing it up); retaining the bin shifts the median to +0.42^{+0.23}_{-0.24} dex. Because the net effect is of order ±0.1 dex, comparable to half the quoted 68% width, the 91% significance as stated is not a fully quantified statement against the actual data; the robust content is a positive excess at roughly the 1–2σ level. I recommend either propagating the data-edit uncertainty into the likelihood explicitly (for example, reporting results for a range of 15.8 nHz bin amplitudes bracketed by the published and re-analyzed values), or reframing the headline as a sign/qualitative constraint and softening the significance language accordingly. The paper's disclosure of this issue is excellent; the abstract and conclusions, however, still present +0.31 dex as the primary quantitative result. The authors acknowledge this: “How this fiducial relates to a full chromatic-noise refit is bounded but not signed: the superseded amplitude normalization carried by the retained bins biases ∆KH up by∼0.07 dex, while discard- ing the eighth bin outright, rather than at its corrected value, biases it down (Sec. V A).”
[Sec. VII A; abstract] The claim of robustness of Δ_KH to local mass calibration is contradicted by the paper's own systematics test: the three calibrations give +0.31 (Kormendy–Ho), +0.51 (McConnell–Ma), and +0.59 (Marconi–Hunt) dex, a spread of ~0.28 dex that exceeds the quoted ±0.20/0.23 posterior width. The abstract's statement that the result is 'robust to the delay model, merger kernel, local mass calibration, and its redshift evolution' (b7) therefore holds only for the sign of the offset, not its magnitude. This spread should be either folded into the headline as a systematic or the robustness claim explicitly restricted to the sign. Relatedly, the redshift-evolution test returns Δ_KH,1 = -0.00^{+0.96}_{-0.94}, which is consistent with no evolution but far too broad to support a robustness claim; the text presenting that result should carry the same caveat as the calibration swaps.
[Sec. VI B] The 'matches without tuning' claim for the wandering-black-hole mass fraction (10% at galaxy scale versus Romulus's ~10%) rests on two biases the paper explicitly declines to net (b308): omitting seed-mass black holes underestimates the mass share, while assigning wanderers the same M_BH–M_bulge relation as central black holes (whose satellites are undermassive for their hosts) overestimates it. Without a quantitative estimate of the magnitudes of these two effects, the agreement could be partly coincidental, and the 'no tuning' reading is stronger than the evidence supports. I request at least a bracketing calculation (e.g., the mass-share range obtained by letting the wanderers' scaling-relation offset vary between zero and the full host-satellite offset). The acknowledged number discrepancy in Milky-Way-mass halos (0.5 versus ~12 wanderers, b314) further weakens the census-wide 'no tuning' reading and should be reiterated wherever the 10% match is cited. The authors acknowledge this: “Two biases act on the mass shares above in opposite directions, and we do not attempt to net them: not painting seed-mass black holes makes our share an underestimate, as noted above, while assigning wander- ers the same scaling relation as central black holes makes it an overestimate, since wanderers descend from stripped satellites and are undermassive for their hosts [86].”

Minor objections (4)

[Sec. V A] The mapping from the 12% amplitude revision to -0.07 dex on Δ_KH is internally inconsistent: with A_yr ∝ 10^{5Δ/6}, a shift of -0.07 dex gives 10^{-0.0583} ≈ 0.87, i.e. a 13–14% reduction, whereas a 12% reduction corresponds to about -0.06 dex. The two numbers should be reconciled.
[Sec. II C; Fig. 1] The text states that the Y11 kernel tracks the N-body reference to within ±(20–50)% pointwise while agreeing to 3.4% in the amplitude; it would help to add one sentence noting explicitly that the amplitude-level agreement relies on sign cancellation of the pointwise residuals in the triple integral, since a reader could otherwise infer a pointwise accuracy that the paper does not claim.
[Sec. IV B] Eq. (9) defines the influence-radius density ρ_inf from σ via the M_BH–σ relation, so σ enters both the hardening rate and the density normalization; the statement that 'only the combination Hρ enters Eq. (9)' is correct at fixed scaled ρ× but would benefit from a clause noting that σ itself is shared between the two factors.
[Sec. VI A] The e_t posterior is prior-truncated at e_t ≤ 0.9 and correctly read as a lower bound, but the quoted 68% interval (0.67^{+0.16}_{-0.35}) sits near the boundary; stating the fraction of posterior mass at the prior edge would make the truncation's influence on the quoted median immediately legible.

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The paper

The paper claims

A merger-tree-free integral over an N-body-calibrated halo kernel computes the nHz background fast enough for direct PTA sampling; it stalls 38% of satellite black holes at $z=0$ and prefers a $+0.31$ dex black-hole mass excess.

The reading

This paper attempts to show that the nanohertz gravitational-wave background from supermassive-black-hole binaries can be computed without Monte Carlo merger trees: a deterministic triple integral over an N-body-calibrated halo accretion kernel, resolution-free by construction and cheap enough to be sampled directly inside a Markov chain against pulsar-timing data. Coupling the satellite's tidal mass loss continuously to dynamical friction supplies the distinctive physics, a sharp, nearly redshift-independent critical mass ratio at $\xi \simeq 0.04$ below which satellites are stripped faster than they sink, so that 38% of accreted satellites are unmerged by $z=0$ and the predicted background drops 11.2% relative to fixed-mass merger-time formulas. Fitting the resulting five-parameter model directly to the NANOGrav 15 yr Hellings–Downs-correlated free spectrum, with one noise-flagged bin excluded, yields a black-hole mass normalization $\Delta_{\rm KH} = +0.31^{+0.20}_{-0.23}$ dex above the local black-hole–bulge relation, a preference that is insensitive to the choice of delay model, merger kernel, and mass calibration (b54). The same calibrated dynamics, with no fitted freedom, predict a wandering-black-hole mass budget of about 10% in galaxy-scale halos, matching cosmological simulations without tuning (b41). This matters because it turns the loudness of the nanohertz sky into a specific statement about black-hole masses versus local calibrations, and because it offers an electromagnetically testable population—stalled satellites and wandering black holes—independent of the gravitational-wave fit.

What carries the argument

The argument is carried by two coupled elements. The first is the merger-rate engine: the Y11 subhalo accretion-rate distribution, an excursion-set branching statistic recalibrated against cosmological simulations and treated as a continuous kernel, which multiplied by the Sheth–Tormen mass function and integrated over host mass, accretion redshift, and satellite mass counts every branch–branch crossing of the ensemble of merger trees exactly once, reproducing the N-body reference amplitude to 3.4% against a 14% bias for the raw Lacey–Cole kernel (b27). The second is the delay physics: a simulation-calibrated tidal stripping law is integrated simultaneously and continuously with Chandrasekhar dynamical friction, in which the drag force is proportional to the satellite's surviving bound mass and never switches off, because the tightly bound stellar core acts as an unstrippable floor. The competition between the two clocks produces the sharp, nearly redshift-independent critical mass ratio $\xi \simeq 0.04$: below it the dark-matter envelope is stripped before the decay completes, the drag collapses onto the core, and the satellite stalls. Per-binary stellar-hardening turnovers and a rescaled eccentric-harmonic spectrum complete the emitted signal, and the whole chain is cached so that a likelihood evaluation costs milliseconds, enabling direct sampling with no emulator.

Extended reading notes

Core claim

The central claim is that the observed nanohertz background is best read as a population in which a substantial share of satellite black holes never reach their host's nucleus: the tidally regulated delay leaves 38% of accreted satellites unmerged by $z=0$, of which 21% are stalled in the strong sense of still owing more than a Hubble time of sinking, a parameter-free prediction of the calibrated stripping-and-sinking dynamics rather than an output of the fit (b3, b4). Against the NANOGrav 15 yr Hellings–Downs free spectrum, with the 15.8 nHz bin excluded because a subsequent chromatic-noise reanalysis attributes its excess to pulsar noise, the five-parameter posterior prefers a black-hole mass normalization $+0.31^{+0.20}_{-0.23}$ dex above the Kormendy–Ho relation, a preference held by 91% of the posterior mass that is deliberately kept conservative, while retaining the bin gives $+0.42^{+0.23}_{-0.24}$ dex (b7). Because the inferred quantity is degenerate with the occupation fraction and mass scatter, the data demand at least this much mass excess. The spectral shape is compatible with, but does not require, eccentric binaries or dense stellar environments (b8). The gravitational-wave fit alone barely distinguishes the delay models—the 11.2% amplitude difference is absorbed by the mass normalization—but the models diverge sharply in their electromagnetic predictions, and a wandering-black-hole census in galaxy-scale halos is proposed as the discriminating test.

Load-bearing premise

The inferred mass excess of $+0.31$ dex rests on excluding the 15.8 nHz bin on the authority of a chromatic-noise reanalysis whose corrected free-spectral densities have not been released (b209, b217); retaining that bin shifts the normalization to $+0.42$ dex, and the thirteen retained bins still carry a superseded amplitude normalization that biases the result down by about 0.07 dex (b339, Sec. V A).

Editorial extensions

If this is right

If the central claim holds, the nanohertz background is loud relative to local black-hole calibrations by at least $\Delta_{\rm KH} = +0.31$ dex (rising to $+0.42$ dex if the 15.8 nHz bin is kept), and no underestimated merger-rate normalization can explain the excess, because it emerges from an independently calibrated N-body-matched kernel.
The 38% non-merged fraction (46±6% when still-hardening nuclear binaries are counted) is a parameter-free prediction: a census of wandering black holes and off-nuclear nuclei in $M_{200c} \sim 10^{12}\,M_\odot$ hosts should find the wandering mass share near 10%, not the 5.6% of the fixed-mass delay.
Since the delay model barely changes the fitted spectrum, the PTA data alone stake no claim about which black holes are left behind; the electromagnetic census is where the two delay models separate.
The same integral extends unchanged to the LISA band, where the occupation physics that is invisible to pulsar timing becomes the leading observable, and joint PTA–LISA sampling over shared parameters becomes feasible.
The spectrum no longer demands eccentric binaries or dense stellar environments, because the revised spectral index $\gamma = 3.5^{+0.7}_{-0.6}$ accommodates the circular, gravitational-wave-driven $13/3$ slope inside its 95% region.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the corrected chromatic-noise free-spectral densities are eventually released, the fiducial $+0.31$ dex figure could move in either direction (the paper itself states it cannot sign the net effect of its bin exclusion), yet the framework's structural contribution—an excess that survives kernel and calibration swaps—would likely stand.
The wanderer census has a near-term observational handle: stacking off-nuclear tidal-disruption events and spatially offset AGN into a volumetric wandering density would directly test the 10% mass-fraction prediction without waiting for deeper black-hole catalogs.
Because amplitude-only PTA fits constrain the black-hole mass scale only up to the $\Delta_{\rm KH}$–$\sigma_{\rm dex}$ degeneracy, the sharpest route to separating astrophysics from noise modeling may be joint fits that fold in continuous-wave non-detections, which break the degeneracy from outside the background.
Translated to the millihertz band, the same machinery suggests PTA and LISA should be treated as complementary constraints on shared parameters rather than sequential steps, with the occupation fraction the PTA band cannot see becoming the dominant LISA-band observable.

Original abstract

We present a semi-analytic framework that computes the gravitational-wave background (GWB) from supermassive black hole (SMBH) binaries by direct integration of an $N$-body-recalibrated extended Press-Schechter accretion kernel, bypassing Monte Carlo merger trees entirely. The calculation is resolution-free and fast enough to be sampled directly against pulsar-timing data with no emulator or precomputed model bank. Between halo accretion and black-hole binary formation, we couple the satellite's simulation-calibrated tidal mass loss continuously to Chandrasekhar dynamical friction. Satellites below a sharp, nearly redshift-independent mass-ratio threshold, $\xi \simeq 0.04$, are stripped faster than they sink and stall: their drag collapses onto the stellar core, and 38% of accreted satellites are unmerged by $z=0$. Combining this population model with per-binary stellar-hardening turnovers and eccentric spectra, we sample the five-parameter posterior directly against the NANOGrav 15 yr Hellings-Downs-correlated free spectrum, excluding the $15.8$ nHz bin, whose excess power a subsequent chromatic-noise reanalysis attributes to pulsar noise. The data prefer a black-hole mass normalization $+0.31^{+0.20}_{-0.23}$ dex above the locally calibrated black-hole-bulge mass relation, consistent with earlier indications that the nanohertz background is loud relative to local SMBH calibrations and robust to the delay model, merger kernel, local mass calibration, and its redshift evolution. The spectrum is compatible with, but does not require, eccentric binaries or dense stellar environments.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-10-06: 1 request, 6,051 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.64 · human participants 0.02 · controlled comparison 0.11 · randomized assignment 0.01 · states quantitative result 0.99 · compares with prior results 0.88 · mentions code or data availability 0.03.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

We present a semi-analytic framework that computes the gravitational-wave background (GWB) from supermassive black hole (SMBH) binaries by direct integration of an $N$-body-recalibrated extended Press-Schechter accretion kernel, bypassing Monte Carlo merger trees entirely. The calculation is resolution-free and fast enough to be sampled directly against pulsar-timing data with no emulator or precomputed model bank. Between halo accretion and black-hole binary formation, we couple the satellite's simulation-calibrated tidal mass loss continuously to Chandrasekhar dynamical friction. Satellites below a sharp, nearly redshift-independent mass-ratio threshold, $\xi \simeq 0.04$, are stripped faster than they sink and stall: their drag collapses onto the stellar core, and 38% of accreted satellites are unmerged by $z=0$. Combining this population model with per-binary stellar-hardening turnovers and eccentric spectra, we sample the five-parameter posterior directly against the NANOGrav 15 yr Hellings-Downs-correlated free spectrum, excluding the $15.8$ nHz bin, whose excess power a subsequent chromatic-noise reanalysis attributes to pulsar noise. The data prefer a black-hole mass normalization $+0.31^{+0.20}_{-0.23}$ dex above the locally calibrated black-hole-bulge mass relation, consistent with earlier indications that the nanohertz background is loud relative to local SMBH calibrations and robust to the delay model, merger kernel, local mass calibration, and its redshift evolution. The spectrum is compatible with, but does not require, eccentric binaries or dense stellar environments.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We present a semi-analytic framework that computes the gravitational-wave background (GWB) from supermassive black hole (SMBH) binaries by direct integration of an $N$-body-recalibrated extended Press-Schechter accretion kernel, bypassing Monte Carlo merger trees entirely.	contribution 0.70	0.95	0.13	asserted 1.00
s1	The calculation is resolution-free and fast enough to be sampled directly against pulsar-timing data with no emulator or precomputed model bank.	method 0.84	0.92	0.05	asserted 1.00
s2	Between halo accretion and black-hole binary formation, we couple the satellite's simulation-calibrated tidal mass loss continuously to Chandrasekhar dynamical friction.	method 0.98	0.76	0.03	asserted 1.00
s3	Satellites below a sharp, nearly redshift-independent mass-ratio threshold, $\xi \simeq 0.04$, are stripped faster than they sink and stall: their drag collapses onto the stellar core, and 38% of accreted satellites are unmerged by $z=0$.	result 0.83	0.87	0.09	asserted 1.00
s4	Combining this population model with per-binary stellar-hardening turnovers and eccentric spectra, we sample the five-parameter posterior directly against the NANOGrav 15 yr Hellings-Downs-correlated free spectrum, excluding the $15.8$ nHz bin, whose excess power a subsequent chromatic-noise reanalysis attributes to pulsar noise.	method 0.90	0.94	0.15	asserted 0.98
s5	The data prefer a black-hole mass normalization $+0.31^{+0.20}_{-0.23}$ dex above the locally calibrated black-hole-bulge mass relation, consistent with earlier indications that the nanohertz background is loud relative to local SMBH calibrations and robust to the delay model, merger kernel, local mass calibration, and its redshift evolution.	result 0.96	0.91	0.58	asserted 0.65
s6	The spectrum is compatible with, but does not require, eccentric binaries or dense stellar environments.	interpretation 0.66	0.87	0.09	hedged possibility 0.86

What kind of paper the classifier reports this is: method or tool 0.90 · evidence from analysis of existing data 0.94.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** FIG. 1. (a) The three halo merger kernels

**Figure 2.** FIG. 2. Time from halo accretion to galaxy merger under

**Figure 3.** FIG. 3. Characteristic strain at fiducial parameters (∆

**Figure 4.** FIG. 4. Spectral shapes for the tidal-delay population at fidu

**Figure 5.** FIG. 5. Posteriors of the five population parameters from the NANOGrav 15 yr free spectrum, under the

**Figure 6.** FIG. 6. Posterior-predictive characteristic strain for the tidal

**Figure 7.** FIG. 7. Wandering-black-hole census (satellites that do not

Figures reproduced from arXiv:2610.06220 by the authors.

References

Works cited (125)

[8]

N. Agarwalet al., The NANOGrav 15 yr Data Set: Impacts of Customized Chromatic Noise Models on Gravitational Wave Analyses, (2026), arXiv:2606.28554 [astro-ph.CO]

View on Pith Pith review arXiv 2026
[1]

R. W. Hellings and G. S. Downs, Upper limits on the isotropic gravitational radiation background from pul- sar timing analysis, Astrophys. J. Lett.265, L39 (1983)

View on Pith 1983
[2]

G. Agazieet al.(NANOGrav), The NANOGrav 15 yr data set: Evidence for a gravitational-wave background, Astrophys. J. Lett.951, L8 (2023), arXiv:2306.16213

View on Pith Pith review arXiv 2023
[3]

J. Antoniadiset al.(EPTA, InPTA), The second data release from the European Pulsar Timing Array. III. Search for gravitational wave signals, Astron. Astro- phys.678, A50 (2023), arXiv:2306.16214

View on Pith Pith review arXiv 2023
[4]

D. J. Reardonet al., Search for an isotropic gravitational-wave background with the Parkes Pul- sar Timing Array, Astrophys. J. Lett.951, L6 (2023), arXiv:2306.16215

View on Pith Pith review arXiv 2023
[5]

H. Xuet al., Searching for the nano-hertz stochastic gravitational wave background with the Chinese Pulsar Timing Array Data Release I, Res. Astron. Astrophys. 23, 075024 (2023), arXiv:2306.16216

View on Pith Pith review arXiv 2023
[6]

M. T. Mileset al., The MeerKAT Pulsar Timing Ar- ray: the 4.5-yr data release and the noise and stochastic signals of the millisecond pulsar population, Mon. Not. Roy. Astron. Soc.536, 1467 (2025), arXiv:2412.01148 [astro-ph.HE]

View on Pith Pith review arXiv 2025
[7]

M. T. Mileset al., The MeerKAT Pulsar Timing Ar- ray: the first search for gravitational waves with the MeerKAT radio telescope, Mon. Not. Roy. Astron. Soc. 536, 1489 (2025), arXiv:2412.01153 [astro-ph.HE]

View on Pith Pith review arXiv 2025
[9]

B. Larsenet al., The NANOGrav 15 yr Data Set: Cus- tomized Chromatic Noise Models, Astrophys. J.1005, 29 (2026), arXiv:2606.28571 [astro-ph.HE]

View on Pith Pith review arXiv 2026
[10]

M. Rajagopal and R. W. Romani, Ultralow frequency gravitational radiation from massive black hole binaries, Astrophys. J.446, 543 (1995), arXiv:astro-ph/9412038

View on Pith Pith review arXiv 1995
[11]

A. H. Jaffe and D. C. Backer, Gravitational waves probe the coalescence rate of massive black hole binaries, As- trophys. J.583, 616 (2003), arXiv:astro-ph/0210148

View on Pith Pith review arXiv 2003
[12]

J. S. B. Wyithe and A. Loeb, Low - frequency gravita- tional waves from massive black hole binaries: Predic- tions for LISA and pulsar timing arrays, Astrophys. J. 590, 691 (2003), arXiv:astro-ph/0211556

View on Pith Pith review arXiv 2003
[13]

A. Sesana, A. Vecchio, and C. N. Colacino, The stochas- tic gravitational-wave background from massive black 17 hole binary systems: implications for observations with pulsar timing arrays, Mon. Not. R. Astron. Soc.390, 192 (2008), arXiv:0804.4476

View on Pith Pith review arXiv 2008
[14]

G. Agazieet al.(NANOGrav), The NANOGrav 15 yr data set: Constraints on supermassive black hole bina- ries from the gravitational-wave background, Astrophys. J. Lett.952, L37 (2023), arXiv:2306.16220

View on Pith Pith review arXiv 2023
[15]

A. Afzalet al.(NANOGrav), The NANOGrav 15 yr Data Set: Search for Signals from New Physics, As- trophys. J. Lett.951, L11 (2023), [Erratum: Astro- phys.J.Lett. 971, L27 (2024)], arXiv:2306.16219 [astro- ph.HE]

View on Pith Pith review arXiv 2023
[16]

W. H. Press and P. Schechter, Formation of galaxies and clusters of galaxies by self-similar gravitational conden- sation, Astrophys. J.187, 425 (1974)

View on Pith 1974
[17]

J. R. Bond, S. Cole, G. Efstathiou, and N. Kaiser, Ex- cursion set mass functions for hierarchical Gaussian fluc- tuations, Astrophys. J.379, 440 (1991)

View on Pith 1991
[18]

C. Lacey and S. Cole, Merger rates in hierarchical mod- els of galaxy formation, Mon. Not. R. Astron. Soc.262, 627 (1993)

View on Pith 1993
[19]

A. Sesana, Systematic investigation of the expected gravitational wave signal from supermassive black hole binaries in the pulsar timing band, Mon. Not. R. Astron. Soc.433, L1 (2013), arXiv:1211.5375

View on Pith Pith review arXiv 2013
[20]

D. Izquierdo-Villalba, A. Sesana, S. Bonoli, and M. Colpi, Massive black hole evolution models con- fronting the nHz amplitude of the stochastic gravita- tional wave background, Mon. Not. R. Astron. Soc.509, 3488 (2022), arXiv:2108.11671

View on Pith Pith review arXiv 2022
[21]

L. Z. Kelley, L. Blecha, L. Hernquist, A. Sesana, and S. R. Taylor, The gravitational wave background from massive black hole binaries in Illustris: spectral fea- tures and time to detection with pulsar timing ar- rays, Mon. Not. R. Astron. Soc.471, 4508 (2017), arXiv:1702.02180

View on Pith Pith review arXiv 2017
[22]

J. Ellis, M. Fairbairn, G. H¨ utsi, M. Raidal, J. Urru- tia, V. Vaskonen, and H. Veerm¨ ae, Prospects for fu- ture binary black hole gravitational wave studies in light of PTA measurements, Astron. Astrophys.676, A38 (2023), arXiv:2301.13854

View on Pith Pith review arXiv 2023
[23]

J. Ellis, M. Fairbairn, G. H¨ utsi, J. Raidal, J. Urru- tia, V. Vaskonen, and H. Veerm¨ ae, Gravitational waves from supermassive black hole binaries in light of the NANOGrav 15-year data, Phys. Rev. D109, L021302 (2024), arXiv:2306.17021

View on Pith Pith review arXiv 2024
[24]

O. Fakhouri, C.-P. Ma, and M. Boylan-Kolchin, The merger rates and mass assembly histories of dark matter haloes in the two millennium simulations, Mon. Not. R. Astron. Soc.406, 2267 (2010), arXiv:1001.2304

View on Pith Pith review arXiv 2010
[25]

X. Yang, H. J. Mo, Y. Zhang, and F. C. van den Bosch, An analytical model for the accretion of dark matter subhalos, Astrophys. J.741, 13 (2011), arXiv:1104.1757

View on Pith Pith review arXiv 2011
[26]

N. Hiroshima, S. Ando, and T. Ishiyama, Model- ing evolution of dark matter substructure and an- nihilation boost, Phys. Rev. D97, 123002 (2018), arXiv:1803.07691

View on Pith Pith review arXiv 2018
[27]

S. Ando, T. Ishiyama, and N. Hiroshima, Halo substruc- ture boosts to the signatures of dark matter annihila- tion, Galaxies7, 68 (2019), arXiv:1903.11427

View on Pith Pith review arXiv 2019
[28]

A. Dekker, S. Ando, C. A. Correa, and K. C. Y. Ng, Warm dark matter constraints using Milky Way satel- lite observations and subhalo evolution modeling, Phys. Rev. D106, 123026 (2022), arXiv:2111.13137

View on Pith Pith review arXiv 2022
[29]

S. Ando, S. Horigome, E. O. Nadler, D. Yang, and H.-B. Yu, SASHIMI-SIDM: semi-analytical subhalo modelling for self-interacting dark matter at sub-galactic scales, JCAP02, 053, arXiv:2403.16633 [astro-ph.CO]

View on Pith Pith review arXiv
[30]

R. K. Sheth and G. Tormen, Large scale bias and the peak background split, Mon. Not. R. Astron. Soc.308, 119 (1999), arXiv:astro-ph/9901122

View on Pith Pith review arXiv 1999
[31]

M. G. Kitzbichler and S. D. M. White, A calibration of galaxy merger timescales from the millennium sim- ulation, Mon. Not. R. Astron. Soc.391, 1489 (2008), arXiv:0804.1965

View on Pith Pith review arXiv 2008
[32]

M. Boylan-Kolchin, C.-P. Ma, and E. Quataert, Dynam- ical friction and galaxy merging timescales, Mon. Not. R. Astron. Soc.383, 93 (2008), arXiv:0707.2960

View on Pith Pith review arXiv 2008
[33]

S. Chen, A. Sesana, and C. J. Conselice, Constrain- ing astrophysical observables of galaxy and supermas- sive black hole binary mergers using pulsar timing arrays, Mon. Not. R. Astron. Soc.488, 401 (2019), arXiv:1810.04184

View on Pith Pith review arXiv 2019
[34]

J. Simon, Exploring proxies for the supermassive black hole mass function: Implications for pulsar timing arrays, Astrophys. J. Lett.949, L24 (2023), arXiv:2306.01832

View on Pith Pith review arXiv 2023
[35]

F. Jiang, A. Dekel, J. Freundlich, F. C. van den Bosch, S. B. Green, P. F. Hopkins, A. Benson, and X. Du, Satgen: a semi-analytical satellite galaxy generator – i. the model and its application to local-group satellite statistics, Mon. Not. R. Astron. Soc.502, 621 (2021), arXiv:2005.05974

View on Pith Pith review arXiv 2021
[36]

P. Boldrini, P. Di Matteo, D. Katz, L. Casamiquela, C. Laporte, M. Assuerus, M. Montuori, and G. van de Ven, CosmoDyn: a semi-analytic post-processing frame- work for the dynamical evolution of compact stellar systems and black holes in cosmological simulations, (2026), arXiv:2609.18821 [astro-ph.GA]

View on Pith Pith review arXiv 2026
[37]

S. Chandrasekhar, Dynamical friction. I. General con- siderations: the coefficient of dynamical friction, Astro- phys. J.97, 255 (1943)

View on Pith 1943
[38]

M. Tremmel, F. Governato, M. Volonteri, A. Pontzen, and T. R. Quinn, Wandering supermassive black holes in milky-way-mass halos, Astrophys. J. Lett.857, L22 (2018), [Erratum: Astrophys. J. Lett. 909, L31 (2021)], arXiv:1802.06783 [astro-ph.GA]

View on Pith Pith review arXiv 2018
[39]

A. Ricarte, M. Tremmel, P. Natarajan, C. Zimmer, and T. Quinn, Origins and demographics of wandering black holes, Mon. Not. R. Astron. Soc.503, 6098 (2021), arXiv:2103.12124

View on Pith Pith review arXiv 2021
[40]

D. Izquierdo-Villalba, S. Bonoli, M. Dotti, A. Sesana, Y. Rosas-Guevara, and D. Spinoso, From galactic nuclei to the halo outskirts: tracing supermassive black holes across cosmic history and environments, Mon. Not. R. Astron. Soc.495, 4681 (2020), arXiv:2001.10548

View on Pith Pith review arXiv 2020
[41]

J. Untzaga, S. Bonoli, D. Izquierdo-Villalba, M. Mezcua, and D. Spinoso, A link to the past: characterizing wandering black holes in milky way-type galaxies, Mon. Not. R. Astron. Soc.535, 3293 (2024), arXiv:2404.12354

View on Pith Pith review arXiv 2024
[42]

I. Dvorkin and E. Barausse, The nightmare scenario: measuring the stochastic gravitational-wave background from stalling massive black-hole binaries with pulsar- timing arrays, Mon. Not. Roy. Astron. Soc.470, 4547 (2017), arXiv:1702.06964 [astro-ph.GA]. 18

View on Pith Pith review arXiv 2017
[43]

W. G. Lamb, S. R. Taylor, and R. van Haasteren, Rapid refitting techniques for Bayesian spectral characteriza- tion of the gravitational wave background using pul- sar timing arrays, Phys. Rev. D108, 103019 (2023), arXiv:2303.15442

View on Pith Pith review arXiv 2023
[44]

H. Middleton, W. Del Pozzo, W. M. Farr, A. Sesana, and A. Vecchio, Astrophysical constraints on massive black hole binary evolution from Pulsar Timing Ar- rays, Mon. Not. Roy. Astron. Soc.455, L72 (2016), arXiv:1507.00992 [astro-ph.CO]

View on Pith Pith review arXiv 2016
[45]

H. Middleton, A. Sesana, S. Chen, A. Vecchio, W. Del Pozzo, and P. A. Rosado, Massive black hole binary systems and the NANOGrav 12.5 yr re- sults, Mon. Not. Roy. Astron. Soc.502, L99 (2021), arXiv:2011.01246 [astro-ph.HE]

View on Pith Pith review arXiv 2021
[46]

J. Raidal, J. Urrutia, V. Vaskonen, and H. Veerm¨ ae, Ec- centricity effects on the supermassive black hole gravita- tional wave background, Astron. Astrophys.691, A212 (2024), arXiv:2406.05125

View on Pith Pith review arXiv 2024
[47]

A. Toubiana, L. Sberna, M. Volonteri, E. Barausse, S. Babak, R. Enficiaud, D. I. Villalba, J. R. Gair, J. E. Greene, and H. Quelquejay Leclere, Reconciling PTA and JWST, and preparing for LISA with POM- POCO: a Parametrisation Of the Massive black hole POpulation for Comparison to Observations, Astron. Astrophys.700, A135 (2025), arXiv:2410.17916 [astro- ph.GA]

View on Pith Pith review arXiv 2025
[48]

N. Aghanimet al.(Planck), Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys.641, A6 (2020), [Erratum: Astron.Astrophys. 652, C4 (2021)], arXiv:1807.06209 [astro-ph.CO]

View on Pith Pith review arXiv 2020
[49]

C. A. Correa, J. S. B. Wyithe, J. Schaye, and A. R. Duffy, The accretion history of dark matter haloes – I. The physical origin of the universal function, Mon. Not. R. Astron. Soc.450, 1514 (2015), arXiv:1409.5228

View on Pith Pith review arXiv 2015
[50]

A. D. Ludlow, S. Bose, R. E. Angulo, L. Wang, W. A. Hellwing, J. F. Navarro, S. Cole, and C. S. Frenk, The mass-concentration-redshift relation of cold and warm dark matter haloes, Mon. Not. R. Astron. Soc.460, 1214 (2016), arXiv:1601.02624

View on Pith Pith review arXiv 2016
[51]

B. P. Moster, T. Naab, and S. D. M. White, Galactic star formation and accretion histories from matching galaxies to dark matter haloes, Mon. Not. R. Astron. Soc.428, 3121 (2013), arXiv:1205.5807

View on Pith Pith review arXiv 2013
[52]

J. Kormendy and L. C. Ho, Coevolution (or not) of su- permassive black holes and host galaxies, Ann. Rev. As- tron. Astrophys.51, 511 (2013), arXiv:1304.7762

View on Pith Pith review arXiv 2013
[53]

W. Jianget al., The Sinking Statistics of Dark Mat- ter Subhalos Across Hierarchical Levels, Sci. China Phys. Mech. Astron. 10.1007/s11433-026-3090-0 (2026), arXiv:2604.05580 [astro-ph.GA]

View on Pith Pith review arXiv 2026
[54]

E. Leonova, M. Volonteri, C. Laigle, S. Nissanke, P. A. Oesch, and Y. Dubois, One Merge to Rule Them All: From Galaxy Interactions to Black Hole Mergers Using Horizon-AGN, (2026), arXiv:2605.12599 [astro-ph.GA]

View on Pith Pith review arXiv 2026
[55]

P. R. Capelo, C. Moreno Martinez, N. Koren, T. Zana, E. Bortolas, M. Bonetti, J. Fluri, T. Hofmann, and L. Mayer, Emulating the complex galactic-scale orbital dynamics of LISA massive black hole pairs with normal- izing flows, (2026), arXiv:2607.26125 [astro-ph.GA]

View on Pith Pith review arXiv 2026
[56]

J. Binney and S. Tremaine,Galactic Dynamics: Second Edition(Princeton University Press, 2008)

View on Pith 2008
[57]

A. R. Zentner, A. A. Berlind, J. S. Bullock, A. V. Kravtsov, and R. H. Wechsler, The physics of galaxy clustering. 1. A model for subhalo populations, Astro- phys. J.624, 505 (2005), arXiv:astro-ph/0411586

View on Pith Pith review arXiv 2005
[58]

F. Dosopoulou and F. Antonini, Dynamical friction and the evolution of supermassive black hole binaries: the final hundred-parsec problem, Astrophys. J.840, 31 (2017), arXiv:1611.06573

View on Pith Pith review arXiv 2017
[59]

M. C. Begelman, R. D. Blandford, and M. J. Rees, Mas- sive black hole binaries in active galactic nuclei, Nature 287, 307 (1980)

View on Pith 1980
[60]

M. Milosavljevi´ c and D. Merritt, The final parsec prob- lem, AIP Conf. Proc.686, 201 (2003), arXiv:astro- ph/0212270

View on Pith 2003
[61]

E. Barausse, I. Dvorkin, M. Tremmel, M. Volonteri, and M. Bonetti, Massive black hole merger rates: The effect of kiloparsec separation wandering and supernova feed- back, Astrophys. J.904, 16 (2020), arXiv:2006.03065

View on Pith Pith review arXiv 2020
[62]

E. S. Phinney, A practical theorem on gravitational wave backgrounds, (2001), arXiv:astro-ph/0108028

View on Pith Pith review arXiv 2001
[63]

G. D. Quinlan, The dynamical evolution of massive black hole binaries. 1. Hardening in a fixed stellar background, New Astron.1, 35 (1996), arXiv:astro- ph/9601092

View on Pith 1996
[64]

A. Sesana and F. M. Khan, Scattering experiments meet N-body – I. A practical recipe for the evolution of mas- sive black hole binaries in stellar environments, Mon. Not. R. Astron. Soc.454, L66 (2015), arXiv:1505.02062

View on Pith Pith review arXiv 2015
[65]

P. C. Peters, Gravitational radiation and the motion of two point masses, Phys. Rev.136, B1224 (1964)

View on Pith 1964
[66]

L. Sampson, N. J. Cornish, and S. T. McWilliams, Constraining the Solution to the Last Parsec Problem with Pulsar Timing, Phys. Rev. D91, 084055 (2015), arXiv:1503.02662 [gr-qc]

View on Pith Pith review arXiv 2015
[67]

S. R. Taylor, J. Simon, and L. Sampson, Constraints On The Dynamical Environments Of Supermassive Black-hole Binaries Using Pulsar-timing Arrays, Phys. Rev. Lett.118, 181102 (2017), arXiv:1612.02817 [astro- ph.GA]

View on Pith Pith review arXiv 2017
[68]

B. Kocsis and A. Sesana, Gas driven massive black hole binaries: signatures in the nHz gravitational wave back- ground, Mon. Not. Roy. Astron. Soc.411, 1467 (2011), arXiv:1002.0584 [astro-ph.CO]

View on Pith Pith review arXiv 2011
[69]

P. C. Peters and J. Mathews, Gravitational radiation from point masses in a keplerian orbit, Phys. Rev.131, 435 (1963)

View on Pith 1963
[70]

M. Enoki and M. Nagashima, The effect of orbital eccen- tricity on gravitational wave background radiation from supermassive black hole binaries, Prog. Theor. Phys. 117, 241 (2007), arXiv:astro-ph/0609377

View on Pith Pith review arXiv 2007
[71]

S. Chen, A. Sesana, and W. Del Pozzo, Efficient com- putation of the gravitational wave spectrum emitted by eccentric massive black hole binaries in stellar environ- ments, Mon. Not. R. Astron. Soc.470, 1738 (2017), arXiv:1612.00455

View on Pith Pith review arXiv 2017
[72]

W. G. Lamb, S. R. Taylor, and R. van Haasteren, KDE representations of the gravitational wave background free spectra present in the NANOGrav 15-year dataset (v1.1.0), Zenodo (2023), doi:10.5281/zenodo.10344086

View on Pith doi:10.5281/zenodo.10344086 2023
[73]

A. Mitridate, D. Wright, R. von Eckardstein, T. Schr¨ oder, J. Nay, K. Olum, K. Schmitz, and T. Trickle, PTArcade, (2023), arXiv:2306.16377

View on Pith Pith review arXiv 2023
[74]

F. Elahi, D. Fortini, Y. Gouttenoire, N. Leister, and P. Schwaller, Big Bang Nucleosynthesis Con- fronts Domain Walls and First-Order Phase Transi- tions as the Pulsar Timing Array Explanations, (2026), 19 arXiv:2609.25950 [hep-ph]

View on Pith Pith review arXiv 2026
[75]

J. Goodman and J. Weare, Ensemble samplers with affine invariance, Comm. App. Math. Comp. Sci.5, 65 (2010)

View on Pith 2010
[76]

D. Foreman-Mackey, D. W. Hogg, D. Lang, and J. Goodman, emcee: The MCMC hammer, Publ. As- tron. Soc. Pac.125, 306 (2013), arXiv:1202.3665

View on Pith Pith review arXiv 2013
[77]

G. Sato-Polito, M. Zaldarriaga, and E. Quataert, Where are the supermassive black holes measured by PTAs?, Phys. Rev. D110, 063020 (2024), arXiv:2312.06756

View on Pith Pith review arXiv 2024
[78]

S. T. McWilliams, J. P. Ostriker, and F. Pretorius, Gravitational waves and stalled satellites from massive galaxy mergers atz≤1, Astrophys. J.789, 156 (2014), arXiv:1211.5377 [astro-ph.CO]

View on Pith Pith review arXiv 2014
[79]

S. Buttigieg, D. Sijacki, C. J. Moore, M. A. Bourne, and A. Sesana, Comparing gravitational wave back- ground predictions from cosmological simulations to pulsar timing observations, (2026), arXiv:2607.05208 [astro-ph.GA]

View on Pith Pith review arXiv 2026
[80]

C. M. F. Mingarelliet al., Pulsar timing arrays: the emerging gravitational-wave landscape, (2026), arXiv:2603.13643 [astro-ph.HE]

View on Pith arXiv 2026
[81]

C. Mattet al., Gravitational-wave Measurement of the MBH–Mbulge Intrinsic Scatter at High Redshift, As- trophys. J.1006, 63 (2026), arXiv:2603.11167 [astro- ph.HE]

View on Pith Pith review arXiv 2026
[82]

F. Shankar, M. Bernardi, R. K. Sheth, L. Ferrarese, A. W. Graham, G. Savorgnan, V. Allevato, A. Mar- coni, R. L¨ asker, and A. Lapi, Selection bias in dynam- ically measured supermassive black hole samples: its consequences and the quest for the most fundamental relation, Mon. Not. Roy. Astron. Soc.460, 3119 (2016), arXiv:1603.01276 [astro-ph.GA]

View on Pith Pith review arXiv 2016
[83]

C. J. Harris, K. Gultekin, and L. Blecha, Core Scour- ing Dynamics and Gravitational Wave Consequences: Constraints on Supermassive Black Hole Binary Hard- ening, Astrophys. J.1009, 131 (2026), arXiv:2601.07762 [astro-ph.GA]

View on Pith Pith review arXiv 2026
[84]

E. C. Gardineret al., Constraints on Supermassive Black Hole Binaries from the Lack of Resolvable Sources in the NANOGrav 15-yr Dataset, (2026), arXiv:2609.32306 [astro-ph.HE]

View on Pith Pith review arXiv 2026
[85]

T. L. Francoiset al., Scaling Relations for Binary Black Hole Merger Times from Cosmological Initial Condi- tions, (2026), arXiv:2607.07813 [astro-ph.GA]

View on Pith Pith review arXiv 2026
[86]

E. J. Welleret al., Tracing black hole and galaxy growth across environments since cosmic noon, Astrophys. J. 1008, 70 (2026), arXiv:2607.07793 [astro-ph.GA]

View on Pith Pith review arXiv 2026
[87]

S. Bonoli, D. Izquierdo-Villalba, D. Spinoso, M. Colpi, A. Sesana, M. Polkas, and V. Springel, Constraints on the early growth of massive black holes from PTA and JWST with L-GalaxiesBH, (2025), arXiv:2509.12325 [astro-ph.GA]

View on Pith arXiv 2025
[88]

E. J. Welleret al., The black hole occupation frac- tion as a fossil record of seeding, dynamics, and galaxy assembly, Astrophys. J. Lett.1008, L54 (2026), arXiv:2607.09853 [astro-ph.GA]

View on Pith Pith review arXiv 2026
[89]

A. K. Bhowmicket al., Supermassive Black Hole As- sembly from Heavy Seeds with Dynamical Friction in the BRAHMA Simulations: Implications for JWST, LISA, and the Local Universe, (2026), arXiv:2606.12851 [astro-ph.GA]

View on Pith Pith review arXiv 2026
[90]

M. Guolo, Demographics of Wandering Black Holes Powering Off-Nuclear Tidal Disruption Events, (2026), arXiv:2602.12970 [astro-ph.GA]

View on Pith arXiv 2026
[91]

I. Sfaradiet al., An Off-Nuclear Tidal Disruption Event Discovered At Late Times: The Case Of TDE 2023mfm, (2026), arXiv:2609.35998 [astro-ph.GA]

View on Pith Pith review arXiv 2026
[92]

X. Liet al., A Wandering 35,000-Solar-Mass Black Hole Fed by a Gravitational Wake, (2026), arXiv:2608.10719 [astro-ph.GA]

View on Pith Pith review arXiv 2026
[93]

U. Thakurdesaiet al., Hunting Wandering 3< z < 8 Black Holes: Spatial Offsets in Ionization Ratio and Continuum Emission, (2026), arXiv:2606.30715 [astro- ph.GA]

View on Pith Pith review arXiv 2026
[94]

N. J. McConnell and C.-P. Ma, Revisiting the Scaling Relations of Black Hole Masses and Host Galaxy Prop- erties, Astrophys. J.764, 184 (2013), arXiv:1211.2816 [astro-ph.CO]

View on Pith Pith review arXiv 2013
[95]

A. Marconi and L. K. Hunt, The relation between black hole mass, bulge mass, and near-infrared lumi- nosity, Astrophys. J. Lett.589, L21 (2003), arXiv:astro- ph/0304274

View on Pith 2003
[96]

M. M. Kozhikkal, S. Chen, G. Theureau, M. Habouzit, and A. Sesana, Mass-redshift dependency of supermas- sive black hole binaries for the gravitational wave back- ground, Mon. Not. R. Astron. Soc.531, 1931 (2024), arXiv:2305.18293

View on Pith Pith review arXiv 2024
[97]

C. Mattet al., Inferring M BH–Mbulge Evolution from the Gravitational-wave Background, Astrophys. J.997, 188 (2026), arXiv:2508.18126 [astro-ph.HE]

View on Pith arXiv 2026
[98]

J. L. Tinker, A. V. Kravtsov, A. Klypin, K. Abazajian, M. S. Warren, G. Yepes, S. Gottl¨ ober, and D. E. Holz, Toward a halo mass function for precision cosmology: The limits of universality, Astrophys. J.688, 709 (2008), arXiv:0803.2706 [astro-ph]

View on Pith Pith review arXiv 2008
[99]

M. Shirasaki, T. Ishiyama, and S. Ando, Virial halo mass function in the Planck cosmology, Astrophys. J. 922, 89 (2021), arXiv:2108.11038 [astro-ph.CO]

View on Pith Pith review arXiv 2021
[100]

A. W. Graham, Galaxy morphology dependent (black hole mass)-(velocity dispersion) relations: implications for gravitational wave forecasts and cosmological simu- lations, (2026), arXiv:2606.05808 [astro-ph.GA]

View on Pith Pith review arXiv 2026
[101]

G. Sato-Polito and M. Zaldarriaga, Uncertainties in the supermassive black hole abundance and implications for the GW background, Phys. Rev. D114, 063052 (2026), arXiv:2509.08041 [astro-ph.GA]

View on Pith Pith review arXiv 2026
[102]

M. T. Tillman, B. Burkhart, C. M. F. Mingarelli, J. A. Casey-Clyde, L. Hernquist, S. Bose, E. Reg˝ os, and C. Hern´ andez-Aguayo, Implications of the Nanohertz Gravitational-wave Background for Galactic Feedback and Massive Black Hole Growth, Astrophys. J. Lett. 1003, L50 (2026), arXiv:2602.15938 [astro-ph.GA]

View on Pith Pith review arXiv 2026
[103]

S. Dattathriet al., Not all cores are equal: Phase- space origins of dynamical friction, stalling and buoy- ancy, Open J. Astrophys. 10.33232/001c.169864 (2025), arXiv:2511.11804 [astro-ph.GA]

View on Pith Pith review arXiv 2025
[104]

B. T. Chiang, F. C. van den Bosch, and M. A. Keim, Scatter, bias, and chaos of satellite orbits in triaxial dark matter haloes, (2026), arXiv:2608.26249 [astro-ph.GA]

View on Pith Pith review arXiv 2026
[105]

M. Bonetti, A. Sesana, E. Barausse, and F. Haardt, Post-Newtonian evolution of massive black hole triplets in galactic nuclei – III. A robust lower limit to the nhz stochastic background of gravitational waves, Mon. Not. R. Astron. Soc.477, 2599 (2018), arXiv:1709.06095

View on Pith Pith review arXiv 2018
[106]

K. Liet al., Set them free: extending RAMCOAL to model massive black hole triplets in hydrodynam- ical simulations of galaxies, (2026), arXiv:2607.04121 20 [astro-ph.GA]

View on Pith Pith review arXiv 2026
[107]

G. Sato-Polito and M. Zaldarriaga, Distribution of the gravitational-wave background from supermas- sive black holes, Phys. Rev. D111, 023043 (2025), arXiv:2406.17010 [astro-ph.CO]

View on Pith Pith review arXiv 2025
[108]

H. Hisamatsu and K. Kyutoku, Higher-order statistics of the stochastic gravitational wave background from supermassive black hole binaries, Phys. Rev. D114, 063041 (2026), arXiv:2605.17983 [astro-ph.HE]

View on Pith Pith review arXiv 2026
[109]

M. Zaldarriaga and G. Sato-Polito, Anisotropies in the PTA gravitational wave background: what can they teach us about supermassive black hole binaries?, (2026), arXiv:2608.22164 [astro-ph.CO]

View on Pith Pith review arXiv 2026
[110]

J. Raidal, J. Urrutia, V. Vaskonen, and H. Veerm¨ ae, Heavy tailed non-Gaussianity of the supermassive black hole gravitational wave background, Phys. Rev. D114, 043550 (2026), arXiv:2604.08506 [astro-ph.CO]

View on Pith Pith review arXiv 2026
[111]

M. Falxa, Approximating the statistics of a gravitational wave background, (2026), arXiv:2609.07686 [astro- ph.IM]

View on Pith Pith review arXiv 2026
[112]

W. G. Lamb, J. M. Wachter, A. Mitridate, S. C. Sarde- sai, B. B´ ecsy, E. L. Hagen, S. R. Taylor, and L. Z. Kelley, Finite populations and finite time: The non-Gaussianity of a gravitational wave background, Phys. Rev. D113, 123065 (2026), arXiv:2511.09659 [gr-qc]

View on Pith Pith review arXiv 2026
[113]

J. Yu, Z. Pan, X. Xue, and L. Dai, Population statis- tics of nanohertz gravitational wave sources, (2026), arXiv:2607.07477 [astro-ph.HE]

View on Pith Pith review arXiv 2026
[114]

M.-X. Lin, A. Lidz, and C.-P. Ma, Realization Vari- ance of Gravitational Wave Background Anisotropies from Shot Noise for Pulsar Timing Arrays, (2026), arXiv:2608.09929 [astro-ph.CO]

View on Pith Pith review arXiv 2026
[115]

J. Ellis, M. Fairbairn, J. Urrutia, and V. Vaskonen, Constraints on Dark Matter Models from Supermas- sive Black Hole Evolution, Phys. Rev. Lett.136, 131001 (2026), arXiv:2509.06955 [astro-ph.CO]

View on Pith arXiv 2026
[116]

J. Raidal, V. Vaskonen, J. Urrutia, and H. Veerm¨ ae, The Loud Tail of the Supermassive Black Hole Binary Population: Multimessenger Candidates and Prospects for SKAO, (2026), arXiv:2609.13363 [astro-ph.CO]

View on Pith Pith review arXiv 2026
[117]

B. Goncharov, G. Sato-Polito, X. Bi, and M. Zal- darriaga, A Joint Optimal Search for Gravitational Waves from Resolved and Unresolved Supermassive Bi- nary Black Holes with Pulsar Timing Arrays, (2026), arXiv:2606.18241 [astro-ph.HE]

View on Pith Pith review arXiv 2026
[118]

K. Iemoto, B. Goncharov, G. Sato-Polito, and X. Bi, Bridging the Population Synthesis of Supermassive Bi- nary Black Holes and the Gravitational Wave Back- ground, (2026), arXiv:2609.07703 [astro-ph.HE]

View on Pith Pith review arXiv 2026
[119]

S. M. Tomson, R. van Haasteren, and B. Goncharov, Hierarchical Inference of the Supermassive Black Hole Binary Merger Rates from Joint Searches using Pul- sar Timing Arrays, (2026), arXiv:2609.09086 [astro- ph.HE]

View on Pith Pith review arXiv 2026
[120]

L. Blecha, An ”inside-out” approach to modeling supermassive black hole binary inspiral, (2026), arXiv:2608.06269 [astro-ph.HE]

View on Pith Pith review arXiv 2026
[121]

A. Kleinet al., Science with the space-based interfer- ometer eLISA: Supermassive black hole binaries, Phys. Rev. D93, 024003 (2016), arXiv:1511.05581

View on Pith Pith review arXiv 2016
[122]

E. Barausse, The evolution of massive black holes and their spins in their galactic hosts, Mon. Not. R. Astron. Soc.423, 2533 (2012), arXiv:1201.5888

View on Pith Pith review arXiv 2012
[123]

G. Ogiya, F. C. van den Bosch, O. Hahn, S. B. Green, T. B. Miller, and A. Burkert, DASH: a library of dy- namical subhalo evolution, Mon. Not. R. Astron. Soc. 485, 189 (2019), arXiv:1901.08601

View on Pith Pith review arXiv 2019
[124]

J. Pe˜ narrubia, A. J. Benson, M. G. Walker, G. Gilmore, A. W. McConnachie, and L. Mayer, The impact of dark matter cusps and cores on the satellite galaxy popula- tion around spiral galaxies, Mon. Not. R. Astron. Soc. 406, 1290 (2010), arXiv:1002.3376

View on Pith Pith review arXiv 2010
[125]

C. A. Correa, J. S. B. Wyithe, J. Schaye, and A. R. Duffy, The accretion history of dark matter haloes – III. A physical model for the concentration–mass re- lation, Mon. Not. R. Astron. Soc.452, 1217 (2015), arXiv:1502.00391 [astro-ph.CO]

View on Pith Pith review arXiv 2015

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [8]

N. Agarwalet al., The NANOGrav 15 yr Data Set: Impacts of Customized Chromatic Noise Models on Gravitational Wave Analyses, (2026), arXiv:2606.28554 [astro-ph.CO]

View on Pith Pith review arXiv 2026

[2] [1]

R. W. Hellings and G. S. Downs, Upper limits on the isotropic gravitational radiation background from pul- sar timing analysis, Astrophys. J. Lett.265, L39 (1983)

View on Pith 1983

[3] [2]

G. Agazieet al.(NANOGrav), The NANOGrav 15 yr data set: Evidence for a gravitational-wave background, Astrophys. J. Lett.951, L8 (2023), arXiv:2306.16213

View on Pith Pith review arXiv 2023

[4] [3]

J. Antoniadiset al.(EPTA, InPTA), The second data release from the European Pulsar Timing Array. III. Search for gravitational wave signals, Astron. Astro- phys.678, A50 (2023), arXiv:2306.16214

View on Pith Pith review arXiv 2023

[5] [4]

D. J. Reardonet al., Search for an isotropic gravitational-wave background with the Parkes Pul- sar Timing Array, Astrophys. J. Lett.951, L6 (2023), arXiv:2306.16215

View on Pith Pith review arXiv 2023

[6] [5]

H. Xuet al., Searching for the nano-hertz stochastic gravitational wave background with the Chinese Pulsar Timing Array Data Release I, Res. Astron. Astrophys. 23, 075024 (2023), arXiv:2306.16216

View on Pith Pith review arXiv 2023

[7] [6]

M. T. Mileset al., The MeerKAT Pulsar Timing Ar- ray: the 4.5-yr data release and the noise and stochastic signals of the millisecond pulsar population, Mon. Not. Roy. Astron. Soc.536, 1467 (2025), arXiv:2412.01148 [astro-ph.HE]

View on Pith Pith review arXiv 2025

[8] [7]

M. T. Mileset al., The MeerKAT Pulsar Timing Ar- ray: the first search for gravitational waves with the MeerKAT radio telescope, Mon. Not. Roy. Astron. Soc. 536, 1489 (2025), arXiv:2412.01153 [astro-ph.HE]

View on Pith Pith review arXiv 2025

[9] [9]

B. Larsenet al., The NANOGrav 15 yr Data Set: Cus- tomized Chromatic Noise Models, Astrophys. J.1005, 29 (2026), arXiv:2606.28571 [astro-ph.HE]

View on Pith Pith review arXiv 2026

[10] [10]

M. Rajagopal and R. W. Romani, Ultralow frequency gravitational radiation from massive black hole binaries, Astrophys. J.446, 543 (1995), arXiv:astro-ph/9412038

View on Pith Pith review arXiv 1995

[11] [11]

A. H. Jaffe and D. C. Backer, Gravitational waves probe the coalescence rate of massive black hole binaries, As- trophys. J.583, 616 (2003), arXiv:astro-ph/0210148

View on Pith Pith review arXiv 2003

[12] [12]

J. S. B. Wyithe and A. Loeb, Low - frequency gravita- tional waves from massive black hole binaries: Predic- tions for LISA and pulsar timing arrays, Astrophys. J. 590, 691 (2003), arXiv:astro-ph/0211556

View on Pith Pith review arXiv 2003

[13] [13]

A. Sesana, A. Vecchio, and C. N. Colacino, The stochas- tic gravitational-wave background from massive black 17 hole binary systems: implications for observations with pulsar timing arrays, Mon. Not. R. Astron. Soc.390, 192 (2008), arXiv:0804.4476

View on Pith Pith review arXiv 2008

[14] [14]

G. Agazieet al.(NANOGrav), The NANOGrav 15 yr data set: Constraints on supermassive black hole bina- ries from the gravitational-wave background, Astrophys. J. Lett.952, L37 (2023), arXiv:2306.16220

View on Pith Pith review arXiv 2023

[15] [15]

A. Afzalet al.(NANOGrav), The NANOGrav 15 yr Data Set: Search for Signals from New Physics, As- trophys. J. Lett.951, L11 (2023), [Erratum: Astro- phys.J.Lett. 971, L27 (2024)], arXiv:2306.16219 [astro- ph.HE]

View on Pith Pith review arXiv 2023

[16] [16]

W. H. Press and P. Schechter, Formation of galaxies and clusters of galaxies by self-similar gravitational conden- sation, Astrophys. J.187, 425 (1974)

View on Pith 1974

[17] [17]

J. R. Bond, S. Cole, G. Efstathiou, and N. Kaiser, Ex- cursion set mass functions for hierarchical Gaussian fluc- tuations, Astrophys. J.379, 440 (1991)

View on Pith 1991

[18] [18]

C. Lacey and S. Cole, Merger rates in hierarchical mod- els of galaxy formation, Mon. Not. R. Astron. Soc.262, 627 (1993)

View on Pith 1993

[19] [19]

A. Sesana, Systematic investigation of the expected gravitational wave signal from supermassive black hole binaries in the pulsar timing band, Mon. Not. R. Astron. Soc.433, L1 (2013), arXiv:1211.5375

View on Pith Pith review arXiv 2013

[20] [20]

D. Izquierdo-Villalba, A. Sesana, S. Bonoli, and M. Colpi, Massive black hole evolution models con- fronting the nHz amplitude of the stochastic gravita- tional wave background, Mon. Not. R. Astron. Soc.509, 3488 (2022), arXiv:2108.11671

View on Pith Pith review arXiv 2022

[21] [21]

L. Z. Kelley, L. Blecha, L. Hernquist, A. Sesana, and S. R. Taylor, The gravitational wave background from massive black hole binaries in Illustris: spectral fea- tures and time to detection with pulsar timing ar- rays, Mon. Not. R. Astron. Soc.471, 4508 (2017), arXiv:1702.02180

View on Pith Pith review arXiv 2017

[22] [22]

J. Ellis, M. Fairbairn, G. H¨ utsi, M. Raidal, J. Urru- tia, V. Vaskonen, and H. Veerm¨ ae, Prospects for fu- ture binary black hole gravitational wave studies in light of PTA measurements, Astron. Astrophys.676, A38 (2023), arXiv:2301.13854

View on Pith Pith review arXiv 2023

[23] [23]

J. Ellis, M. Fairbairn, G. H¨ utsi, J. Raidal, J. Urru- tia, V. Vaskonen, and H. Veerm¨ ae, Gravitational waves from supermassive black hole binaries in light of the NANOGrav 15-year data, Phys. Rev. D109, L021302 (2024), arXiv:2306.17021

View on Pith Pith review arXiv 2024

[24] [24]

O. Fakhouri, C.-P. Ma, and M. Boylan-Kolchin, The merger rates and mass assembly histories of dark matter haloes in the two millennium simulations, Mon. Not. R. Astron. Soc.406, 2267 (2010), arXiv:1001.2304

View on Pith Pith review arXiv 2010

[25] [25]

X. Yang, H. J. Mo, Y. Zhang, and F. C. van den Bosch, An analytical model for the accretion of dark matter subhalos, Astrophys. J.741, 13 (2011), arXiv:1104.1757

View on Pith Pith review arXiv 2011

[26] [26]

N. Hiroshima, S. Ando, and T. Ishiyama, Model- ing evolution of dark matter substructure and an- nihilation boost, Phys. Rev. D97, 123002 (2018), arXiv:1803.07691

View on Pith Pith review arXiv 2018

[27] [27]

S. Ando, T. Ishiyama, and N. Hiroshima, Halo substruc- ture boosts to the signatures of dark matter annihila- tion, Galaxies7, 68 (2019), arXiv:1903.11427

View on Pith Pith review arXiv 2019

[28] [28]

A. Dekker, S. Ando, C. A. Correa, and K. C. Y. Ng, Warm dark matter constraints using Milky Way satel- lite observations and subhalo evolution modeling, Phys. Rev. D106, 123026 (2022), arXiv:2111.13137

View on Pith Pith review arXiv 2022

[29] [29]

S. Ando, S. Horigome, E. O. Nadler, D. Yang, and H.-B. Yu, SASHIMI-SIDM: semi-analytical subhalo modelling for self-interacting dark matter at sub-galactic scales, JCAP02, 053, arXiv:2403.16633 [astro-ph.CO]

View on Pith Pith review arXiv

[30] [30]

R. K. Sheth and G. Tormen, Large scale bias and the peak background split, Mon. Not. R. Astron. Soc.308, 119 (1999), arXiv:astro-ph/9901122

View on Pith Pith review arXiv 1999

[31] [31]

M. G. Kitzbichler and S. D. M. White, A calibration of galaxy merger timescales from the millennium sim- ulation, Mon. Not. R. Astron. Soc.391, 1489 (2008), arXiv:0804.1965

View on Pith Pith review arXiv 2008

[32] [32]

M. Boylan-Kolchin, C.-P. Ma, and E. Quataert, Dynam- ical friction and galaxy merging timescales, Mon. Not. R. Astron. Soc.383, 93 (2008), arXiv:0707.2960

View on Pith Pith review arXiv 2008

[33] [33]

S. Chen, A. Sesana, and C. J. Conselice, Constrain- ing astrophysical observables of galaxy and supermas- sive black hole binary mergers using pulsar timing arrays, Mon. Not. R. Astron. Soc.488, 401 (2019), arXiv:1810.04184

View on Pith Pith review arXiv 2019

[34] [34]

J. Simon, Exploring proxies for the supermassive black hole mass function: Implications for pulsar timing arrays, Astrophys. J. Lett.949, L24 (2023), arXiv:2306.01832

View on Pith Pith review arXiv 2023

[35] [35]

F. Jiang, A. Dekel, J. Freundlich, F. C. van den Bosch, S. B. Green, P. F. Hopkins, A. Benson, and X. Du, Satgen: a semi-analytical satellite galaxy generator – i. the model and its application to local-group satellite statistics, Mon. Not. R. Astron. Soc.502, 621 (2021), arXiv:2005.05974

View on Pith Pith review arXiv 2021

[36] [36]

P. Boldrini, P. Di Matteo, D. Katz, L. Casamiquela, C. Laporte, M. Assuerus, M. Montuori, and G. van de Ven, CosmoDyn: a semi-analytic post-processing frame- work for the dynamical evolution of compact stellar systems and black holes in cosmological simulations, (2026), arXiv:2609.18821 [astro-ph.GA]

View on Pith Pith review arXiv 2026

[37] [37]

S. Chandrasekhar, Dynamical friction. I. General con- siderations: the coefficient of dynamical friction, Astro- phys. J.97, 255 (1943)

View on Pith 1943

[38] [38]

M. Tremmel, F. Governato, M. Volonteri, A. Pontzen, and T. R. Quinn, Wandering supermassive black holes in milky-way-mass halos, Astrophys. J. Lett.857, L22 (2018), [Erratum: Astrophys. J. Lett. 909, L31 (2021)], arXiv:1802.06783 [astro-ph.GA]

View on Pith Pith review arXiv 2018

[39] [39]

A. Ricarte, M. Tremmel, P. Natarajan, C. Zimmer, and T. Quinn, Origins and demographics of wandering black holes, Mon. Not. R. Astron. Soc.503, 6098 (2021), arXiv:2103.12124

View on Pith Pith review arXiv 2021

[40] [40]

D. Izquierdo-Villalba, S. Bonoli, M. Dotti, A. Sesana, Y. Rosas-Guevara, and D. Spinoso, From galactic nuclei to the halo outskirts: tracing supermassive black holes across cosmic history and environments, Mon. Not. R. Astron. Soc.495, 4681 (2020), arXiv:2001.10548

View on Pith Pith review arXiv 2020

[41] [41]

J. Untzaga, S. Bonoli, D. Izquierdo-Villalba, M. Mezcua, and D. Spinoso, A link to the past: characterizing wandering black holes in milky way-type galaxies, Mon. Not. R. Astron. Soc.535, 3293 (2024), arXiv:2404.12354

View on Pith Pith review arXiv 2024

[42] [42]

I. Dvorkin and E. Barausse, The nightmare scenario: measuring the stochastic gravitational-wave background from stalling massive black-hole binaries with pulsar- timing arrays, Mon. Not. Roy. Astron. Soc.470, 4547 (2017), arXiv:1702.06964 [astro-ph.GA]. 18

View on Pith Pith review arXiv 2017

[43] [43]

W. G. Lamb, S. R. Taylor, and R. van Haasteren, Rapid refitting techniques for Bayesian spectral characteriza- tion of the gravitational wave background using pul- sar timing arrays, Phys. Rev. D108, 103019 (2023), arXiv:2303.15442

View on Pith Pith review arXiv 2023

[44] [44]

H. Middleton, W. Del Pozzo, W. M. Farr, A. Sesana, and A. Vecchio, Astrophysical constraints on massive black hole binary evolution from Pulsar Timing Ar- rays, Mon. Not. Roy. Astron. Soc.455, L72 (2016), arXiv:1507.00992 [astro-ph.CO]

View on Pith Pith review arXiv 2016

[45] [45]

H. Middleton, A. Sesana, S. Chen, A. Vecchio, W. Del Pozzo, and P. A. Rosado, Massive black hole binary systems and the NANOGrav 12.5 yr re- sults, Mon. Not. Roy. Astron. Soc.502, L99 (2021), arXiv:2011.01246 [astro-ph.HE]

View on Pith Pith review arXiv 2021

[46] [46]

J. Raidal, J. Urrutia, V. Vaskonen, and H. Veerm¨ ae, Ec- centricity effects on the supermassive black hole gravita- tional wave background, Astron. Astrophys.691, A212 (2024), arXiv:2406.05125

View on Pith Pith review arXiv 2024

[47] [47]

A. Toubiana, L. Sberna, M. Volonteri, E. Barausse, S. Babak, R. Enficiaud, D. I. Villalba, J. R. Gair, J. E. Greene, and H. Quelquejay Leclere, Reconciling PTA and JWST, and preparing for LISA with POM- POCO: a Parametrisation Of the Massive black hole POpulation for Comparison to Observations, Astron. Astrophys.700, A135 (2025), arXiv:2410.17916 [astro- ph.GA]

View on Pith Pith review arXiv 2025

[48] [48]

N. Aghanimet al.(Planck), Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys.641, A6 (2020), [Erratum: Astron.Astrophys. 652, C4 (2021)], arXiv:1807.06209 [astro-ph.CO]

View on Pith Pith review arXiv 2020

[49] [49]

C. A. Correa, J. S. B. Wyithe, J. Schaye, and A. R. Duffy, The accretion history of dark matter haloes – I. The physical origin of the universal function, Mon. Not. R. Astron. Soc.450, 1514 (2015), arXiv:1409.5228

View on Pith Pith review arXiv 2015

[50] [50]

A. D. Ludlow, S. Bose, R. E. Angulo, L. Wang, W. A. Hellwing, J. F. Navarro, S. Cole, and C. S. Frenk, The mass-concentration-redshift relation of cold and warm dark matter haloes, Mon. Not. R. Astron. Soc.460, 1214 (2016), arXiv:1601.02624

View on Pith Pith review arXiv 2016

[51] [51]

B. P. Moster, T. Naab, and S. D. M. White, Galactic star formation and accretion histories from matching galaxies to dark matter haloes, Mon. Not. R. Astron. Soc.428, 3121 (2013), arXiv:1205.5807

View on Pith Pith review arXiv 2013

[52] [52]

J. Kormendy and L. C. Ho, Coevolution (or not) of su- permassive black holes and host galaxies, Ann. Rev. As- tron. Astrophys.51, 511 (2013), arXiv:1304.7762

View on Pith Pith review arXiv 2013

[53] [53]

W. Jianget al., The Sinking Statistics of Dark Mat- ter Subhalos Across Hierarchical Levels, Sci. China Phys. Mech. Astron. 10.1007/s11433-026-3090-0 (2026), arXiv:2604.05580 [astro-ph.GA]

View on Pith Pith review arXiv 2026

[54] [54]

E. Leonova, M. Volonteri, C. Laigle, S. Nissanke, P. A. Oesch, and Y. Dubois, One Merge to Rule Them All: From Galaxy Interactions to Black Hole Mergers Using Horizon-AGN, (2026), arXiv:2605.12599 [astro-ph.GA]

View on Pith Pith review arXiv 2026

[55] [55]

P. R. Capelo, C. Moreno Martinez, N. Koren, T. Zana, E. Bortolas, M. Bonetti, J. Fluri, T. Hofmann, and L. Mayer, Emulating the complex galactic-scale orbital dynamics of LISA massive black hole pairs with normal- izing flows, (2026), arXiv:2607.26125 [astro-ph.GA]

View on Pith Pith review arXiv 2026

[56] [56]

J. Binney and S. Tremaine,Galactic Dynamics: Second Edition(Princeton University Press, 2008)

View on Pith 2008

[57] [57]

A. R. Zentner, A. A. Berlind, J. S. Bullock, A. V. Kravtsov, and R. H. Wechsler, The physics of galaxy clustering. 1. A model for subhalo populations, Astro- phys. J.624, 505 (2005), arXiv:astro-ph/0411586

View on Pith Pith review arXiv 2005

[58] [58]

F. Dosopoulou and F. Antonini, Dynamical friction and the evolution of supermassive black hole binaries: the final hundred-parsec problem, Astrophys. J.840, 31 (2017), arXiv:1611.06573

View on Pith Pith review arXiv 2017

[59] [59]

M. C. Begelman, R. D. Blandford, and M. J. Rees, Mas- sive black hole binaries in active galactic nuclei, Nature 287, 307 (1980)

View on Pith 1980

[60] [60]

M. Milosavljevi´ c and D. Merritt, The final parsec prob- lem, AIP Conf. Proc.686, 201 (2003), arXiv:astro- ph/0212270

View on Pith 2003

[61] [61]

E. Barausse, I. Dvorkin, M. Tremmel, M. Volonteri, and M. Bonetti, Massive black hole merger rates: The effect of kiloparsec separation wandering and supernova feed- back, Astrophys. J.904, 16 (2020), arXiv:2006.03065

View on Pith Pith review arXiv 2020

[62] [62]

E. S. Phinney, A practical theorem on gravitational wave backgrounds, (2001), arXiv:astro-ph/0108028

View on Pith Pith review arXiv 2001

[63] [63]

G. D. Quinlan, The dynamical evolution of massive black hole binaries. 1. Hardening in a fixed stellar background, New Astron.1, 35 (1996), arXiv:astro- ph/9601092

View on Pith 1996

[64] [64]

A. Sesana and F. M. Khan, Scattering experiments meet N-body – I. A practical recipe for the evolution of mas- sive black hole binaries in stellar environments, Mon. Not. R. Astron. Soc.454, L66 (2015), arXiv:1505.02062

View on Pith Pith review arXiv 2015

[65] [65]

P. C. Peters, Gravitational radiation and the motion of two point masses, Phys. Rev.136, B1224 (1964)

View on Pith 1964

[66] [66]

L. Sampson, N. J. Cornish, and S. T. McWilliams, Constraining the Solution to the Last Parsec Problem with Pulsar Timing, Phys. Rev. D91, 084055 (2015), arXiv:1503.02662 [gr-qc]

View on Pith Pith review arXiv 2015

[67] [67]

S. R. Taylor, J. Simon, and L. Sampson, Constraints On The Dynamical Environments Of Supermassive Black-hole Binaries Using Pulsar-timing Arrays, Phys. Rev. Lett.118, 181102 (2017), arXiv:1612.02817 [astro- ph.GA]

View on Pith Pith review arXiv 2017

[68] [68]

B. Kocsis and A. Sesana, Gas driven massive black hole binaries: signatures in the nHz gravitational wave back- ground, Mon. Not. Roy. Astron. Soc.411, 1467 (2011), arXiv:1002.0584 [astro-ph.CO]

View on Pith Pith review arXiv 2011

[69] [69]

P. C. Peters and J. Mathews, Gravitational radiation from point masses in a keplerian orbit, Phys. Rev.131, 435 (1963)

View on Pith 1963

[70] [70]

M. Enoki and M. Nagashima, The effect of orbital eccen- tricity on gravitational wave background radiation from supermassive black hole binaries, Prog. Theor. Phys. 117, 241 (2007), arXiv:astro-ph/0609377

View on Pith Pith review arXiv 2007

[71] [71]

S. Chen, A. Sesana, and W. Del Pozzo, Efficient com- putation of the gravitational wave spectrum emitted by eccentric massive black hole binaries in stellar environ- ments, Mon. Not. R. Astron. Soc.470, 1738 (2017), arXiv:1612.00455

View on Pith Pith review arXiv 2017

[72] [72]

W. G. Lamb, S. R. Taylor, and R. van Haasteren, KDE representations of the gravitational wave background free spectra present in the NANOGrav 15-year dataset (v1.1.0), Zenodo (2023), doi:10.5281/zenodo.10344086

View on Pith doi:10.5281/zenodo.10344086 2023

[73] [73]

A. Mitridate, D. Wright, R. von Eckardstein, T. Schr¨ oder, J. Nay, K. Olum, K. Schmitz, and T. Trickle, PTArcade, (2023), arXiv:2306.16377

View on Pith Pith review arXiv 2023

[74] [74]

F. Elahi, D. Fortini, Y. Gouttenoire, N. Leister, and P. Schwaller, Big Bang Nucleosynthesis Con- fronts Domain Walls and First-Order Phase Transi- tions as the Pulsar Timing Array Explanations, (2026), 19 arXiv:2609.25950 [hep-ph]

View on Pith Pith review arXiv 2026

[75] [75]

J. Goodman and J. Weare, Ensemble samplers with affine invariance, Comm. App. Math. Comp. Sci.5, 65 (2010)

View on Pith 2010

[76] [76]

D. Foreman-Mackey, D. W. Hogg, D. Lang, and J. Goodman, emcee: The MCMC hammer, Publ. As- tron. Soc. Pac.125, 306 (2013), arXiv:1202.3665

View on Pith Pith review arXiv 2013

[77] [77]

G. Sato-Polito, M. Zaldarriaga, and E. Quataert, Where are the supermassive black holes measured by PTAs?, Phys. Rev. D110, 063020 (2024), arXiv:2312.06756

View on Pith Pith review arXiv 2024

[78] [78]

S. T. McWilliams, J. P. Ostriker, and F. Pretorius, Gravitational waves and stalled satellites from massive galaxy mergers atz≤1, Astrophys. J.789, 156 (2014), arXiv:1211.5377 [astro-ph.CO]

View on Pith Pith review arXiv 2014

[79] [79]

S. Buttigieg, D. Sijacki, C. J. Moore, M. A. Bourne, and A. Sesana, Comparing gravitational wave back- ground predictions from cosmological simulations to pulsar timing observations, (2026), arXiv:2607.05208 [astro-ph.GA]

View on Pith Pith review arXiv 2026

[80] [80]

C. M. F. Mingarelliet al., Pulsar timing arrays: the emerging gravitational-wave landscape, (2026), arXiv:2603.13643 [astro-ph.HE]

View on Pith arXiv 2026

[81] [81]

C. Mattet al., Gravitational-wave Measurement of the MBH–Mbulge Intrinsic Scatter at High Redshift, As- trophys. J.1006, 63 (2026), arXiv:2603.11167 [astro- ph.HE]

View on Pith Pith review arXiv 2026

[82] [82]

F. Shankar, M. Bernardi, R. K. Sheth, L. Ferrarese, A. W. Graham, G. Savorgnan, V. Allevato, A. Mar- coni, R. L¨ asker, and A. Lapi, Selection bias in dynam- ically measured supermassive black hole samples: its consequences and the quest for the most fundamental relation, Mon. Not. Roy. Astron. Soc.460, 3119 (2016), arXiv:1603.01276 [astro-ph.GA]

View on Pith Pith review arXiv 2016

[83] [83]

C. J. Harris, K. Gultekin, and L. Blecha, Core Scour- ing Dynamics and Gravitational Wave Consequences: Constraints on Supermassive Black Hole Binary Hard- ening, Astrophys. J.1009, 131 (2026), arXiv:2601.07762 [astro-ph.GA]

View on Pith Pith review arXiv 2026

[84] [84]

E. C. Gardineret al., Constraints on Supermassive Black Hole Binaries from the Lack of Resolvable Sources in the NANOGrav 15-yr Dataset, (2026), arXiv:2609.32306 [astro-ph.HE]

View on Pith Pith review arXiv 2026

[85] [85]

T. L. Francoiset al., Scaling Relations for Binary Black Hole Merger Times from Cosmological Initial Condi- tions, (2026), arXiv:2607.07813 [astro-ph.GA]

View on Pith Pith review arXiv 2026

[86] [86]

E. J. Welleret al., Tracing black hole and galaxy growth across environments since cosmic noon, Astrophys. J. 1008, 70 (2026), arXiv:2607.07793 [astro-ph.GA]

View on Pith Pith review arXiv 2026

[87] [87]

S. Bonoli, D. Izquierdo-Villalba, D. Spinoso, M. Colpi, A. Sesana, M. Polkas, and V. Springel, Constraints on the early growth of massive black holes from PTA and JWST with L-GalaxiesBH, (2025), arXiv:2509.12325 [astro-ph.GA]

View on Pith arXiv 2025

[88] [88]

E. J. Welleret al., The black hole occupation frac- tion as a fossil record of seeding, dynamics, and galaxy assembly, Astrophys. J. Lett.1008, L54 (2026), arXiv:2607.09853 [astro-ph.GA]

View on Pith Pith review arXiv 2026

[89] [89]

A. K. Bhowmicket al., Supermassive Black Hole As- sembly from Heavy Seeds with Dynamical Friction in the BRAHMA Simulations: Implications for JWST, LISA, and the Local Universe, (2026), arXiv:2606.12851 [astro-ph.GA]

View on Pith Pith review arXiv 2026

[90] [90]

M. Guolo, Demographics of Wandering Black Holes Powering Off-Nuclear Tidal Disruption Events, (2026), arXiv:2602.12970 [astro-ph.GA]

View on Pith arXiv 2026

[91] [91]

I. Sfaradiet al., An Off-Nuclear Tidal Disruption Event Discovered At Late Times: The Case Of TDE 2023mfm, (2026), arXiv:2609.35998 [astro-ph.GA]

View on Pith Pith review arXiv 2026

[92] [92]

X. Liet al., A Wandering 35,000-Solar-Mass Black Hole Fed by a Gravitational Wake, (2026), arXiv:2608.10719 [astro-ph.GA]

View on Pith Pith review arXiv 2026

[93] [93]

U. Thakurdesaiet al., Hunting Wandering 3< z < 8 Black Holes: Spatial Offsets in Ionization Ratio and Continuum Emission, (2026), arXiv:2606.30715 [astro- ph.GA]

View on Pith Pith review arXiv 2026

[94] [94]

N. J. McConnell and C.-P. Ma, Revisiting the Scaling Relations of Black Hole Masses and Host Galaxy Prop- erties, Astrophys. J.764, 184 (2013), arXiv:1211.2816 [astro-ph.CO]

View on Pith Pith review arXiv 2013

[95] [95]

A. Marconi and L. K. Hunt, The relation between black hole mass, bulge mass, and near-infrared lumi- nosity, Astrophys. J. Lett.589, L21 (2003), arXiv:astro- ph/0304274

View on Pith 2003

[96] [96]

M. M. Kozhikkal, S. Chen, G. Theureau, M. Habouzit, and A. Sesana, Mass-redshift dependency of supermas- sive black hole binaries for the gravitational wave back- ground, Mon. Not. R. Astron. Soc.531, 1931 (2024), arXiv:2305.18293

View on Pith Pith review arXiv 2024

[97] [97]

C. Mattet al., Inferring M BH–Mbulge Evolution from the Gravitational-wave Background, Astrophys. J.997, 188 (2026), arXiv:2508.18126 [astro-ph.HE]

View on Pith arXiv 2026

[98] [98]

J. L. Tinker, A. V. Kravtsov, A. Klypin, K. Abazajian, M. S. Warren, G. Yepes, S. Gottl¨ ober, and D. E. Holz, Toward a halo mass function for precision cosmology: The limits of universality, Astrophys. J.688, 709 (2008), arXiv:0803.2706 [astro-ph]

View on Pith Pith review arXiv 2008

[99] [99]

M. Shirasaki, T. Ishiyama, and S. Ando, Virial halo mass function in the Planck cosmology, Astrophys. J. 922, 89 (2021), arXiv:2108.11038 [astro-ph.CO]

View on Pith Pith review arXiv 2021

[100] [100]

A. W. Graham, Galaxy morphology dependent (black hole mass)-(velocity dispersion) relations: implications for gravitational wave forecasts and cosmological simu- lations, (2026), arXiv:2606.05808 [astro-ph.GA]

View on Pith Pith review arXiv 2026

[101] [101]

G. Sato-Polito and M. Zaldarriaga, Uncertainties in the supermassive black hole abundance and implications for the GW background, Phys. Rev. D114, 063052 (2026), arXiv:2509.08041 [astro-ph.GA]

View on Pith Pith review arXiv 2026

[102] [102]

M. T. Tillman, B. Burkhart, C. M. F. Mingarelli, J. A. Casey-Clyde, L. Hernquist, S. Bose, E. Reg˝ os, and C. Hern´ andez-Aguayo, Implications of the Nanohertz Gravitational-wave Background for Galactic Feedback and Massive Black Hole Growth, Astrophys. J. Lett. 1003, L50 (2026), arXiv:2602.15938 [astro-ph.GA]

View on Pith Pith review arXiv 2026

[103] [103]

S. Dattathriet al., Not all cores are equal: Phase- space origins of dynamical friction, stalling and buoy- ancy, Open J. Astrophys. 10.33232/001c.169864 (2025), arXiv:2511.11804 [astro-ph.GA]

View on Pith Pith review arXiv 2025

[104] [104]

B. T. Chiang, F. C. van den Bosch, and M. A. Keim, Scatter, bias, and chaos of satellite orbits in triaxial dark matter haloes, (2026), arXiv:2608.26249 [astro-ph.GA]

View on Pith Pith review arXiv 2026

[105] [105]

M. Bonetti, A. Sesana, E. Barausse, and F. Haardt, Post-Newtonian evolution of massive black hole triplets in galactic nuclei – III. A robust lower limit to the nhz stochastic background of gravitational waves, Mon. Not. R. Astron. Soc.477, 2599 (2018), arXiv:1709.06095

View on Pith Pith review arXiv 2018

[106] [106]

K. Liet al., Set them free: extending RAMCOAL to model massive black hole triplets in hydrodynam- ical simulations of galaxies, (2026), arXiv:2607.04121 20 [astro-ph.GA]

View on Pith Pith review arXiv 2026

[107] [107]

G. Sato-Polito and M. Zaldarriaga, Distribution of the gravitational-wave background from supermas- sive black holes, Phys. Rev. D111, 023043 (2025), arXiv:2406.17010 [astro-ph.CO]

View on Pith Pith review arXiv 2025

[108] [108]

H. Hisamatsu and K. Kyutoku, Higher-order statistics of the stochastic gravitational wave background from supermassive black hole binaries, Phys. Rev. D114, 063041 (2026), arXiv:2605.17983 [astro-ph.HE]

View on Pith Pith review arXiv 2026

[109] [109]

M. Zaldarriaga and G. Sato-Polito, Anisotropies in the PTA gravitational wave background: what can they teach us about supermassive black hole binaries?, (2026), arXiv:2608.22164 [astro-ph.CO]

View on Pith Pith review arXiv 2026

[110] [110]

J. Raidal, J. Urrutia, V. Vaskonen, and H. Veerm¨ ae, Heavy tailed non-Gaussianity of the supermassive black hole gravitational wave background, Phys. Rev. D114, 043550 (2026), arXiv:2604.08506 [astro-ph.CO]

View on Pith Pith review arXiv 2026

[111] [111]

M. Falxa, Approximating the statistics of a gravitational wave background, (2026), arXiv:2609.07686 [astro- ph.IM]

View on Pith Pith review arXiv 2026

[112] [112]

W. G. Lamb, J. M. Wachter, A. Mitridate, S. C. Sarde- sai, B. B´ ecsy, E. L. Hagen, S. R. Taylor, and L. Z. Kelley, Finite populations and finite time: The non-Gaussianity of a gravitational wave background, Phys. Rev. D113, 123065 (2026), arXiv:2511.09659 [gr-qc]

View on Pith Pith review arXiv 2026

[113] [113]

J. Yu, Z. Pan, X. Xue, and L. Dai, Population statis- tics of nanohertz gravitational wave sources, (2026), arXiv:2607.07477 [astro-ph.HE]

View on Pith Pith review arXiv 2026

[114] [114]

M.-X. Lin, A. Lidz, and C.-P. Ma, Realization Vari- ance of Gravitational Wave Background Anisotropies from Shot Noise for Pulsar Timing Arrays, (2026), arXiv:2608.09929 [astro-ph.CO]

View on Pith Pith review arXiv 2026

[115] [115]

J. Ellis, M. Fairbairn, J. Urrutia, and V. Vaskonen, Constraints on Dark Matter Models from Supermas- sive Black Hole Evolution, Phys. Rev. Lett.136, 131001 (2026), arXiv:2509.06955 [astro-ph.CO]

View on Pith arXiv 2026

[116] [116]

J. Raidal, V. Vaskonen, J. Urrutia, and H. Veerm¨ ae, The Loud Tail of the Supermassive Black Hole Binary Population: Multimessenger Candidates and Prospects for SKAO, (2026), arXiv:2609.13363 [astro-ph.CO]

View on Pith Pith review arXiv 2026

[117] [117]

B. Goncharov, G. Sato-Polito, X. Bi, and M. Zal- darriaga, A Joint Optimal Search for Gravitational Waves from Resolved and Unresolved Supermassive Bi- nary Black Holes with Pulsar Timing Arrays, (2026), arXiv:2606.18241 [astro-ph.HE]

View on Pith Pith review arXiv 2026

[118] [118]

K. Iemoto, B. Goncharov, G. Sato-Polito, and X. Bi, Bridging the Population Synthesis of Supermassive Bi- nary Black Holes and the Gravitational Wave Back- ground, (2026), arXiv:2609.07703 [astro-ph.HE]

View on Pith Pith review arXiv 2026

[119] [119]

S. M. Tomson, R. van Haasteren, and B. Goncharov, Hierarchical Inference of the Supermassive Black Hole Binary Merger Rates from Joint Searches using Pul- sar Timing Arrays, (2026), arXiv:2609.09086 [astro- ph.HE]

View on Pith Pith review arXiv 2026

[120] [120]

L. Blecha, An ”inside-out” approach to modeling supermassive black hole binary inspiral, (2026), arXiv:2608.06269 [astro-ph.HE]

View on Pith Pith review arXiv 2026

[121] [121]

A. Kleinet al., Science with the space-based interfer- ometer eLISA: Supermassive black hole binaries, Phys. Rev. D93, 024003 (2016), arXiv:1511.05581

View on Pith Pith review arXiv 2016

[122] [122]

E. Barausse, The evolution of massive black holes and their spins in their galactic hosts, Mon. Not. R. Astron. Soc.423, 2533 (2012), arXiv:1201.5888

View on Pith Pith review arXiv 2012

[123] [123]

G. Ogiya, F. C. van den Bosch, O. Hahn, S. B. Green, T. B. Miller, and A. Burkert, DASH: a library of dy- namical subhalo evolution, Mon. Not. R. Astron. Soc. 485, 189 (2019), arXiv:1901.08601

View on Pith Pith review arXiv 2019

[124] [124]

J. Pe˜ narrubia, A. J. Benson, M. G. Walker, G. Gilmore, A. W. McConnachie, and L. Mayer, The impact of dark matter cusps and cores on the satellite galaxy popula- tion around spiral galaxies, Mon. Not. R. Astron. Soc. 406, 1290 (2010), arXiv:1002.3376

View on Pith Pith review arXiv 2010

[125] [125]

C. A. Correa, J. S. B. Wyithe, J. Schaye, and A. R. Duffy, The accretion history of dark matter haloes – III. A physical model for the concentration–mass re- lation, Mon. Not. R. Astron. Soc.452, 1217 (2015), arXiv:1502.00391 [astro-ph.CO]

View on Pith Pith review arXiv 2015