Pith. sign in

REVIEW 2 major objections 6 minor 70 references

A stochastic gravitational-wave background weakens pulsar-timing searches for dark-matter subhalos by one to three orders of magnitude.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · grok-4.5

2026-07-12 01:48 UTC pith:YG6ZQTV7

load-bearing objection Clean analytic + numerical quantification of how the GWB kills PTA DM-substructure reach by 1–3 orders of magnitude; the scalings and gauge-invariant observable are the real additions. the 2 major comments →

arxiv 2607.03533 v1 pith:YG6ZQTV7 submitted 2026-07-03 astro-ph.CO hep-ph

Pulsar Timing Sensitivity to Dark Matter Substructure in the Presence of a Stochastic Gravitational-Wave Background

Abhiram Cherukupalli , Vincent S. H. Lee , Kim Berghaus , Kathryn M. Zurek This is my paper
classification astro-ph.CO hep-ph
keywords pulsar timing arraysdark matter substructurestochastic gravitational-wave backgroundShapiro delayDoppler residualsignal-to-noise ratiored noise
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

Pulsar timing arrays can sense dark-matter subhalos by the tiny shifts they leave in pulse arrival times. A recently detected stochastic gravitational-wave background acts as red noise that competes with those shifts. This paper derives the full gauge-invariant proper-time delay a subhalo produces and a signal-to-noise framework that accounts for both that red noise and the quadratic timing model fitted to each pulsar. Analytic scalings then show how sensitivity falls in the static, dynamic, and stochastic regimes, and numerical forecasts for an SKA-like array confirm a one-to-three-order suppression relative to white-noise-only projections. The dynamic Shapiro delay is least affected and still offers the best reach near 0.01 solar masses. Even so, future arrays improve existing limits by up to two orders of magnitude, keeping pulsar timing competitive for small-scale dark-matter structure.

Core claim

The stochastic gravitational-wave background suppresses PTA sensitivity to dark-matter substructure by one to three orders of magnitude relative to white-noise-only forecasts; the precise factor depends only mildly (within a factor of three) on the background's amplitude and spectral index. Among all channels, the dynamic Shapiro signal suffers the smallest penalty and supplies the best sensitivity near 10^{-2} solar masses.

What carries the argument

A noise-weighted inner product that projects each timing residual orthogonal to the quadratic pulsar timing model, combined with the full gauge-invariant proper-time delay (Earth/pulsar Doppler + Shapiro + Einstein) of a transiting subhalo. The projection converts every signal into a low-frequency power-law spectrum whose SNR integral is then suppressed by the closed-form red-noise factor (f_star T)^{-min(gamma,n-1)} (or its squared counterpart for stochastic signals).

Load-bearing premise

Subhalos are treated as point masses all moving at the same speed, intrinsic pulsar red noise is ignored, and only the single-pulsar noise autocorrelation is used, so any extra degradation from diffuse profiles or residual red noise is left for later work.

What would settle it

If an SKA-like array, after 20 years and after full timing-model marginalization, recovers a substructure fraction near the white-noise-only forecasts rather than the one-to-three-order-worse curves of Fig. 3, the claimed GWB suppression is ruled out.

Watch this falsifier — get emailed when new claim-graph text bears on it.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 6 minor

Summary. The paper quantifies how a stochastic gravitational-wave background (GWB), treated as red noise, degrades pulsar-timing-array (PTA) sensitivity to dark-matter (DM) substructure. It derives the full gauge-invariant proper-time residual for a transiting subhalo (Doppler, Shapiro, and Einstein terms), builds an SNR framework that marginalizes the quadratic timing model under a red-noise-weighted inner product, and obtains closed-form scaling relations for the static, dynamic, and stochastic regimes (Table I). These are validated against a full Monte-Carlo reach for an SKA-like array at three points of the NANOGrav 15-year GWB posterior. The central result is that the GWB suppresses the substructure reach by one to three orders of magnitude relative to white-noise-only forecasts, with only O(1) variation across the posterior; the dynamic Shapiro channel is least suppressed and peaks near 10^{-2} M_⊙.

Significance. Given the NANOGrav evidence for a nHz GWB, prior white-noise PTA forecasts for DM substructure are no longer realistic. This work supplies the first transparent analytic account of the red-noise penalty, with scalings that match full gauge-invariant numerics deep in each regime (Fig. 4) and that can be reused for other PTA benchmarks. Strengths include the explicit gauge-invariance check (App. B), the red-noise integral asymptotics (App. C), the projected-norm calculations (App. D), and the Monte-Carlo sampling and Gaussian-validity diagnostics (App. E). The conclusion that f_DM ≲ 1 remains difficult even for SKA-scale arrays, while still improving substantially on existing NANOGrav limits, is a useful and falsifiable guide for survey design.

major comments (2)
  1. [Sec. II A, Eqs. (7)–(8)] Sec. II A and Eq. (7)–(8): pulsar-intrinsic red noise is set identically to zero, so the single-pulsar PSD is white noise plus the GWB diagonal only. For the absolute SKA reach curves in Fig. 3 this is an optimistic floor; many MSPs retain measurable spin noise at nHz frequencies. A short estimate (or a third curve) showing how an intrinsic red component comparable to current PTA levels would further shift f_DM would make the absolute forecasts more robust. The relative 1–3 order GWB suppression itself is not threatened, because it is controlled by the GWB term in S_n(f).
  2. [Sec. IV–V] Sec. IV–V and the companion-paper deferral: the Earth Doppler term and the full-array (Hellings–Downs-conditioned) statistic are omitted, with the claim that both change the single-pulsar reach only at O(1). That claim is plausible for well-separated pulsars, but the dynamic Shapiro knee near 10^{-2} M_⊙ is the only place where the projected reach approaches f_DM ∼ 1. A one-paragraph quantitative bound (even from a simplified two-pulsar estimate) on how much the Earth term or inter-pulsar conditioning could move that knee would strengthen the statement that f_DM < 1 remains a challenge.
minor comments (6)
  1. [Table I] Table I: the SNR scalings with T, f_DM, M, and N_P are very useful; adding a short footnote that the numerical prefactors are dropped (∼ rather than =) would prevent readers from treating the table as exact.
  2. [Fig. 2] Fig. 2 caption is dense; labeling the three panels explicitly as “static / dynamic / stochastic” in the figure itself (not only in the caption) would improve readability.
  3. [Eq. (38)] Eq. (38): the numerical prefactor “20 · 0.25^{1/γ} …” is hard to parse at a glance; writing f_⋆T ≃ 20 × (0.25)^{1/γ} × … would clarify the structure.
  4. [Sec. III] Sec. III: the Einstein terms are correctly identified as O(v)-suppressed relative to Doppler, but a one-line numerical check (e.g. ratio of norms for a typical flyby) would make the neglect fully transparent for non-specialists.
  5. [Fig. 4, App. E 3] App. E 3 / Fig. 7: the N_Q ≥ 10 validity cut is well motivated; stating in the main text (near Fig. 4) that the dotted stochastic segments are extrapolations, not quantitative forecasts, would reduce the chance of misreading.
  6. [Refs. / App. B] References: Ref. [26] (“in preparation”) carries the full proper-time derivation; if a public draft or arXiv version exists by revision time, citing it would help reproducibility of App. B.

Circularity Check

0 steps flagged

No significant circularity: GWB suppression of PTA DM reach follows from independent SNR integrals and external NANOGrav posterior, not from fitted or self-defined inputs.

full rationale

The paper’s load-bearing claim—that a stochastic GWB suppresses PTA sensitivity to DM substructure by one to three orders of magnitude relative to white-noise forecasts, with only O(1) variation across the NANOGrav 15-year posterior—is obtained by evaluating standard noise-weighted SNR integrals (Eqs. 17, 21, 40) on projected signal spectra derived from linearized gravity (Sec. III, App. B) and Poisson encounter statistics. The GWB amplitude and spectral index are taken as external inputs from the published NANOGrav 15-year posterior; they are not fitted to produce the suppression. The red-noise integrals I_{n,γ} and I^{(2)}_{n,γ} (App. C) are elementary scalings of power-law integrands once f⋆T ≫ 1; the static/dynamic/stochastic templates (Sec. IV, App. D) follow from Taylor or Fourier analysis of the proper-time observable and are checked against full Monte-Carlo numerics (Figs. 3–4). Self-citations to earlier PTA–DM works by overlapping authors supply prior signal forms and Bayesian context but are not used as uniqueness theorems or as the sole justification of the central scaling; the gauge-invariant observable and the red-noise projection framework are re-derived in place. No free parameter is adjusted so that a “prediction” is forced by construction. The result is therefore self-contained against its stated external benchmarks.

Axiom & Free-Parameter Ledger

4 free parameters · 5 axioms · 0 invented entities

The central claim rests on standard linearized gravity, a quadratic timing model, stationary Gaussian noise, Poisson subhalo statistics, and externally measured GWB parameters. No new particles or forces are postulated. The free parameters are either taken from NANOGrav or chosen as conventional SKA/DM benchmarks; their variation is shown to affect the reach only at the O(1) level.

free parameters (4)
  • A_GWB, γ_GWB = (13/3, 2.4e-15), (3.3, 6.1e-15), (2.3, 13.5e-15)
    Taken from three representative points of the NANOGrav 15-year posterior; the claimed 1–3 order suppression varies by less than a factor of three across them.
  • SKA benchmark (N_P, T, Δt, t_rms, L) = 200, 20 yr, 2 wk, 50 ns, 5 kpc
    Conventional Phase-II numbers taken from Rosado et al. 2015 for direct comparison with earlier white-noise forecasts; not fitted to data.
  • v = 340 km/s, ρ_DM = 0.46 GeV cm^{-3} = 340 km/s, 0.46 GeV/cm^3
    Standard local DM density and mean speed of the boosted Maxwell–Boltzmann distribution used in prior PTA-DM papers; order-unity changes leave the scalings intact.
  • SNR threshold = 4 = 4
    Chosen for 5 % false-alarm probability across ~200 pulsars; conservative at the O(1) level of the analytic estimates.
axioms (5)
  • domain assumption Linearized GR in Newtonian gauge yields a gauge-invariant proper-time residual that decomposes into Doppler + Shapiro + Einstein terms.
    Sec. III and App. B; standard for non-relativistic sources.
  • domain assumption Noise is a stationary Gaussian process whose PSD is white + power-law GWB; pulsar-intrinsic red noise is set to zero.
    Eqs. (4)–(8); stated explicitly as a simplification.
  • domain assumption Subhalos form a Poisson point process of identical point masses with isotropic velocities.
    Sec. IV; optimistic for diffuse profiles, as noted by the authors.
  • standard math The quadratic timing model (spin frequency + spin-down) is marginalized by noise-weighted projection onto Legendre modes ϕ1, ϕ2.
    Sec. II B and App. A; standard PTA practice.
  • domain assumption f_⋆ T ≫ 1 so that the red-noise integrals I_{n,γ} admit the closed min(γ, n-1) scaling.
    Eq. (38); satisfied for the SKA + NANOGrav benchmarks used.

pith-pipeline@v1.1.0-grok45 · 44320 in / 3072 out tokens · 27590 ms · 2026-07-12T01:48:30.141718+00:00 · methodology

0 comments
read the original abstract

Pulsar timing arrays (PTAs) can detect dark matter (DM) substructure through the small shifts a transiting DM subhalo imprints on pulse arrival times. Recently found evidence for a stochastic gravitational-wave background (GWB) acts as red noise and competes with the substructure signal. Here we provide an analytic understanding of how this background degrades PTA sensitivity to DM substructure. We derive the full gauge-invariant proper-time observable induced by a transiting DM subhalo and develop a framework for the expected signal-to-noise ratio in the presence of red noise, accounting for the degeneracy with the pulsar timing model. From this we obtain simple scaling relations for the reach across the static, dynamic, and stochastic regimes, and numerically compute the reach for a Square Kilometre Array benchmark at three representative points of the NANOGrav 15-year posterior. The GWB background suppresses the sensitivity to DM substructure by one to three orders of magnitude compared to forecasts in the presence of only white noise, and the suppression depends on the amplitude and spectral index of the background within a factor of three. The dynamic Shapiro signal suffers the smallest suppression and gives the best sensitivity to DM substructure near $10^{-2}\, M_\odot$. Probing the regime where subhalos make up all or part of the DM remains a challenge even for surveys with more pulsars and longer observing time. Despite this, PTA measurements remain a competitive probe of DM substructure, and future surveys will increase in sensitivity by up to two orders of magnitude from existing NANOGrav limits.

Figures

Figures reproduced from arXiv: 2607.03533 by Abhiram Cherukupalli, Kathryn M. Zurek, Kim Berghaus, Vincent S. H. Lee.

Figure 1
Figure 1. Figure 1: FIG. 1: Geometry of a DM subhalo transiting the Earth–pulsar system. The Earth (blue, left) and [PITH_FULL_IMAGE:figures/full_fig_p013_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Analytic spectra of the projected DM signal versus the noise PSD [PITH_FULL_IMAGE:figures/full_fig_p016_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Projected upper limits on the substructure fraction [PITH_FULL_IMAGE:figures/full_fig_p027_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Decomposition of the projected reach [PITH_FULL_IMAGE:figures/full_fig_p028_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: The Doppler-pulsar (left) and Shapiro line-of-sight (right) sampling capsules. A subhalo is [PITH_FULL_IMAGE:figures/full_fig_p046_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Detection distance [PITH_FULL_IMAGE:figures/full_fig_p047_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Stochastic projected reach [PITH_FULL_IMAGE:figures/full_fig_p050_7.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

70 extracted references · 48 linked inside Pith

  1. [1]

    The cubic Taylor term of Eq

    Doppler We first consider timing signal from the Doppler term. The cubic Taylor term of Eq. (30),1 6 δt′′′ D(0)t 3 (evaluated explicitly in Ref. [14]), decomposes on the Legendre basis of Eq. (11) ast 3 = T 3 20 √ 7 ϕ3(t) + (timing-model modes), leaving the projected static Doppler signal δt⊥ D(t)≈ GM v T3 120 √ 7r 3 P ϕ⊥ 3 (t) ˆ v+3vtD,0 rP ˆ rP ·ˆ n. (4...

  2. [2]

    Shapiro Like the Doppler signal, the projected static Shapiro signal has low-frequency scaling|δ ˜t⊥|2 ∼f −6 (Table I), so the GWB suppression is identical. The sensitivity scaling differs, however, because the relevant impact parameter is the perpendicular distance to the line of sight rather than to the pulsar, the SNR therefore scales as (N P fDM)3/2 r...

  3. [3]

    (30) in frequency space is given by δ˜tD(f) = Z T 0 dt e−2πif tδtD(t), = GM τ v2 e−2πif tD,0 Z (T−t D,0)/τP −tD,0/τP dxP e−2πif τP xP q 1 +x 2 P ˆbP −arcsinh(x P )ˆ v ·ˆ n

    Doppler The Doppler signal from Eq. (30) in frequency space is given by δ˜tD(f) = Z T 0 dt e−2πif tδtD(t), = GM τ v2 e−2πif tD,0 Z (T−t D,0)/τP −tD,0/τP dxP e−2πif τP xP q 1 +x 2 P ˆbP −arcsinh(x P )ˆ v ·ˆ n. (53) For bulk events witht D,0 ≫τ P andT−t D,0 ≫τ P , the finite-window endpoints can be sent to±∞at leading order, and the resulting kernel Fourier...

  4. [4]

    Shapiro As in the Doppler case, in the limitτ ⊥ ≪T, we can Fourier transform the Shapiro signal in the close-encounter regime q r2 ∥ +r 2 ⊥ ≲L/2 from Eq. (36), by sending the finite-window endpoints to±∞ and dropping timing-model-degenerate pieces, to obtain δ˜tS(f) = Z T 0 dt e−2πif tδtS(t) ≈ −2GM τ⊥e−2πif tS,0 Z ∞ −∞ dx⊥ e−2πif τ⊥x⊥ ln(1 +x 2 ⊥) = 2GM f...

  5. [5]

    (54), eδt ⊥ D(f)≈ − GM bP v e−2πif tD,0 (2πf) 2 ˜s 2πf bP v ·ˆ n, (64) where we define ˜s(x)≡2x K1(x) ˆbP −iK 0(x)ˆ v

    Doppler We start from the expression forδt ⊥ D from Eq. (54), eδt ⊥ D(f)≈ − GM bP v e−2πif tD,0 (2πf) 2 ˜s 2πf bP v ·ˆ n, (64) where we define ˜s(x)≡2x K1(x) ˆbP −iK 0(x)ˆ v . As in Sec. IV B 1, we approximate eδt ⊥ D ≈ eδtD. As we assume each subhalo has a common speed, a flyby is parametrized by the direction of its velocity Ωv (drawn isotropically) and...

  6. [6]

    Starting fromδt ⊥ S in Eq

    Shapiro An ensemble of subhalos distributed along the Earth–pulsar line of sight produces a stochastic Shapiro signal. Starting fromδt ⊥ S in Eq. (59) and treating the flybys as a Poisson process, we average over epochst 0, impact parametersb ⊥, and the line-of-sight coordinatez; in this parametrization the spatial volume element isd 3r0 = 2v⊥db∥ db⊥ dt0,...

    2000

  7. [7]

    C. J. Hogan and M. J. Rees, Axion miniclusters, Phys. Lett. B205, 228 (1988)

    1988

  8. [8]

    E. W. Kolb and I. I. Tkachev, Axion miniclusters and Bose stars, Phys. Rev. Lett.71, 3051 (1993), arXiv:hep-ph/9303313

    Pith/arXiv arXiv 1993

  9. [9]

    K. M. Zurek, C. J. Hogan, and T. R. Quinn, Astrophysical Effects of Scalar Dark Matter Miniclusters, Phys. Rev. D75, 043511 (2007), arXiv:astro-ph/0607341. 33

    Pith/arXiv arXiv 2007

  10. [10]

    Buschmann, J

    M. Buschmann, J. W. Foster, and B. R. Safdi, Early-Universe Simulations of the Cosmological Axion, Phys. Rev. Lett.124, 161103 (2020), arXiv:1906.00967 [astro-ph.CO]

    Pith/arXiv arXiv 2020

  11. [11]

    Eggemeier, J

    B. Eggemeier, J. Redondo, K. Dolag, J. C. Niemeyer, and A. Vaquero, First Simulations of Axion Mini- cluster Halos, Phys. Rev. Lett.125, 041301 (2020), arXiv:1911.09417 [astro-ph.CO]

    Pith/arXiv arXiv 2020

  12. [12]

    H. Xiao, I. Williams, and M. McQuinn, Simulations of axion minihalos, Phys. Rev. D104, 023515 (2021), arXiv:2101.04177 [astro-ph.CO]

    Pith/arXiv arXiv 2021

  13. [13]

    R. D. Peccei and H. R. Quinn, CP Conservation in the Presence of Instantons, Phys. Rev. Lett.38, 1440 (1977)

    1977

  14. [14]

    A. M. Green, S. Hofmann, and D. J. Schwarz, The First wimpy halos, JCAP08, 003, arXiv:astro- ph/0503387

    arXiv

  15. [15]

    E. R. Siegel, M. P. Hertzberg, and J. N. Fry, Probing Dark Matter Substructure with Pulsar Timing, Mon. Not. Roy. Astron. Soc.382, 879 (2007), arXiv:astro-ph/0702546

    Pith/arXiv arXiv 2007

  16. [16]

    Baghram, N

    S. Baghram, N. Afshordi, and K. M. Zurek, Prospects for Detecting Dark Matter Halo Substructure with Pulsar Timing, Phys. Rev. D84, 043511 (2011), arXiv:1101.5487 [astro-ph.CO]

    Pith/arXiv arXiv 2011

  17. [17]

    H. A. Clark, G. F. Lewis, and P. Scott, Investigating dark matter substructure with pulsar timing – I. Constraints on ultracompact minihaloes, Mon. Not. Roy. Astron. Soc.456, 1394 (2016), [Erratum: Mon.Not.Roy.Astron.Soc. 464, 2468 (2017)], arXiv:1509.02938 [astro-ph.CO]

    Pith/arXiv arXiv 2016

  18. [18]

    Schutz and A

    K. Schutz and A. Liu, Pulsar timing can constrain primordial black holes in the LIGO mass window, Phys. Rev. D95, 023002 (2017), arXiv:1610.04234 [astro-ph.CO]

    Pith/arXiv arXiv 2017

  19. [19]

    Kashiyama and M

    K. Kashiyama and M. Oguri, Detectability of Small-Scale Dark Matter Clumps with Pulsar Timing Arrays, (2018), arXiv:1801.07847 [astro-ph.CO]

    Pith/arXiv arXiv 2018

  20. [20]

    J. A. Dror, H. Ramani, T. Trickle, and K. M. Zurek, Pulsar Timing Probes of Primordial Black Holes and Subhalos, Phys. Rev. D100, 023003 (2019), arXiv:1901.04490 [astro-ph.CO]

    Pith/arXiv arXiv 2019

  21. [21]

    Ramani, T

    H. Ramani, T. Trickle, and K. M. Zurek, Observability of Dark Matter Substructure with Pulsar Timing Correlations, JCAP12, 033, arXiv:2005.03030 [astro-ph.CO]

    Pith/arXiv arXiv 2005

  22. [22]

    V. S. H. Lee, A. Mitridate, T. Trickle, and K. M. Zurek, Probing Small-Scale Power Spectra with Pulsar Timing Arrays, JHEP06, 028, arXiv:2012.09857 [astro-ph.CO]

    Pith/arXiv arXiv 2012

  23. [23]

    V. S. H. Lee, S. R. Taylor, T. Trickle, and K. M. Zurek, Bayesian Forecasts for Dark Matter Substructure Searches with Mock Pulsar Timing Data, JCAP08, 025, arXiv:2104.05717 [astro-ph.CO]

    Pith/arXiv arXiv

  24. [24]

    M. I. Gresham, V. S. H. Lee, and K. M. Zurek, Astrophysical observations of a dark matter-Baryon fifth force, JCAP02, 048, arXiv:2209.03963 [astro-ph.HE]

    Pith/arXiv arXiv

  25. [25]

    Afzalet al.(NANOGrav), The NANOGrav 15 yr Data Set: Search for Signals from New Physics, Astrophys

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

    Pith/arXiv arXiv 2023

  26. [26]

    K. V. Berghaus, Y. Du, V. S. H. Lee, A. Prabhu, R. Reischke, L. Connor, and K. M. Zurek, Physics beyond the Standard Model with the DSA-2000, JCAP12, 035, arXiv:2505.23892 [hep-ph]

    arXiv 2000

  27. [27]

    Goldreich and W

    P. Goldreich and W. H. Julian, Pulsar electrodynamics, Astrophys. J.157, 869 (1969)

    1969

  28. [28]

    P. A. Sturrock, A Model of pulsars, Astrophys. J.164, 529 (1971)

    1971

  29. [29]

    S. R. Taylor, The Nanohertz Gravitational Wave Astronomer, (2021), arXiv:2105.13270 [astro-ph.HE]

    Pith/arXiv arXiv 2021

  30. [30]

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

    Pith/arXiv arXiv 2001

  31. [31]

    Agazieet al.(NANOGrav), The NANOGrav 15 yr Data Set: Evidence for a Gravitational-wave Back- ground, Astrophys

    G. Agazieet al.(NANOGrav), The NANOGrav 15 yr Data Set: Evidence for a Gravitational-wave Back- ground, Astrophys. J. Lett.951, L8 (2023), arXiv:2306.16213 [astro-ph.HE]. 34

    Pith/arXiv arXiv 2023

  32. [32]

    V. S. H. Lee, Proper time shifts in pulsar timing arrays (2026), in preparation

    2026

  33. [33]

    Mitridate, D

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

    Pith/arXiv arXiv 2023

  34. [34]

    Ellis and M

    J. Ellis and M. Lewicki, Cosmic String Interpretation of NANOGrav Pulsar Timing Data, Phys. Rev. Lett. 126, 041304 (2021), arXiv:2009.06555 [astro-ph.CO]

    Pith/arXiv arXiv 2021

  35. [35]

    Blasi, V

    S. Blasi, V. Brdar, and K. Schmitz, Has NANOGrav found first evidence for cosmic strings?, Phys. Rev. Lett.126, 041305 (2021), arXiv:2009.06607 [astro-ph.CO]

    Pith/arXiv arXiv 2021

  36. [36]

    Ellis, M

    J. Ellis, M. Lewicki, C. Lin, and V. Vaskonen, Cosmic superstrings revisited in light of NANOGrav 15-year data, Phys. Rev. D108, 103511 (2023), arXiv:2306.17147 [astro-ph.CO]

    Pith/arXiv arXiv 2023

  37. [37]

    P. W. Graham, D. E. Kaplan, J. Mardon, S. Rajendran, and W. A. Terrano, Dark Matter Direct Detection with Accelerometers, Phys. Rev. D93, 075029 (2016), arXiv:1512.06165 [hep-ph]

    Pith/arXiv arXiv 2016

  38. [38]

    N. K. Poraykoet al., Parkes Pulsar Timing Array constraints on ultralight scalar-field dark matter, Phys. Rev. D98, 102002 (2018), arXiv:1810.03227 [astro-ph.CO]

    Pith/arXiv arXiv 2018

  39. [39]

    D. E. Kaplan, A. Mitridate, and T. Trickle, Constraining fundamental constant variations from ultralight dark matter with pulsar timing arrays, Phys. Rev. D106, 035032 (2022), arXiv:2205.06817 [hep-ph]

    Pith/arXiv arXiv 2022

  40. [40]

    Kim and A

    H. Kim and A. Mitridate, Stochastic ultralight dark matter fluctuations in pulsar timing arrays, Phys. Rev. D109, 055017 (2024), arXiv:2312.12225 [hep-ph]

    Pith/arXiv arXiv 2024

  41. [41]

    Antoniadiset al.(EPTA, InPTA), The second data release from the European Pulsar Timing Array - IV

    J. Antoniadiset al.(EPTA, InPTA), The second data release from the European Pulsar Timing Array - IV. Implications for massive black holes, dark matter, and the early Universe, Astron. Astrophys.685, A94 (2024), arXiv:2306.16227 [astro-ph.CO]

    Pith/arXiv arXiv 2024

  42. [42]

    Smarraet al.(European Pulsar Timing Array), Second Data Release from the European Pulsar Tim- ing Array: Challenging the Ultralight Dark Matter Paradigm, Phys

    C. Smarraet al.(European Pulsar Timing Array), Second Data Release from the European Pulsar Tim- ing Array: Challenging the Ultralight Dark Matter Paradigm, Phys. Rev. Lett.131, 171001 (2023), arXiv:2306.16228 [astro-ph.HE]

    Pith/arXiv arXiv 2023

  43. [43]

    Smarraet al., Constraints on conformal ultralight dark matter couplings from the European Pulsar Timing Array, Phys

    C. Smarraet al., Constraints on conformal ultralight dark matter couplings from the European Pulsar Timing Array, Phys. Rev. D110, 043033 (2024), arXiv:2405.01633 [astro-ph.HE]

    Pith/arXiv arXiv 2024

  44. [44]

    X. Gan, H. Kim, and A. Mitridate, Probing quadratically coupled ultralight dark matter with pulsar timing arrays, Phys. Rev. D113, 063034 (2026), arXiv:2510.13945 [hep-ph]

    Pith/arXiv arXiv 2026

  45. [45]

    K. K. Boddy, J. A. Dror, and A. Lam, Ultralight Dark Matter Statistics for Pulsar Timing Detection, Phys. Rev. Lett.135, 101001 (2025), arXiv:2502.15874 [hep-ph]

    arXiv 2025

  46. [46]

    J. A. Dror and Q. Wei, Pulsar timing detection of ultralight vector dark matter, Phys. Rev. D112, 075024 (2025), arXiv:2505.22719 [hep-ph]

    arXiv 2025

  47. [47]

    Huet al., Constraints on ultralight scalar and dark photon dark matter from PPTA DR3 and EPTA DR2, Phys

    X.-S. Huet al., Constraints on ultralight scalar and dark photon dark matter from PPTA DR3 and EPTA DR2, Phys. Rev. D113, 123019 (2026), arXiv:2605.02172 [astro-ph.CO]

    Pith/arXiv arXiv 2026

  48. [48]

    Cherukupalli, V

    A. Cherukupalli, V. S. H. Lee, K. V. Berghaus, and K. Zurek (2026), in preparation

    2026

  49. [49]

    Lentatiet al., From Spin Noise to Systematics: Stochastic Processes in the First International Pulsar Timing Array Data Release, Mon

    L. Lentatiet al., From Spin Noise to Systematics: Stochastic Processes in the First International Pulsar Timing Array Data Release, Mon. Not. Roy. Astron. Soc.458, 2161 (2016), arXiv:1602.05570 [astro-ph.IM]

    Pith/arXiv arXiv 2016

  50. [50]

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

    1983

  51. [51]

    van Haasteren and Y

    R. van Haasteren and Y. Levin, Understanding and analysing time-correlated stochastic signals in pulsar timing, Mon. Not. Roy. Astron. Soc.428, 1147 (2013), arXiv:1202.5932 [astro-ph.IM]

    Pith/arXiv arXiv 2013

  52. [52]

    Y. Du, V. S. H. Lee, Y. Wang, and K. M. Zurek, Macroscopic dark matter detection with gravitational wave experiments, Phys. Rev. D108, 122003 (2023), arXiv:2306.13122 [astro-ph.CO]. 35

    Pith/arXiv arXiv 2023

  53. [53]

    V. S. H. Lee and K. M. Zurek, Proper time observables of general gravitational perturbations in laser interferometry-based gravitational wave detectors, Phys. Rev. D111, 124037 (2025), arXiv:2408.03363 [hep-ph]

    Pith/arXiv arXiv 2025

  54. [54]

    Badurina, Y

    L. Badurina, Y. Du, V. S. H. Lee, Y. Wang, and K. M. Zurek, Signatures of linearized gravity in atom in- terferometers: A simplified computational framework, Phys. Rev. D111, 042002 (2025), arXiv:2409.03828 [gr-qc]

    Pith/arXiv arXiv 2025

  55. [55]

    Badurina, Y

    L. Badurina, Y. Du, V. S. H. Lee, Y. Wang, and K. M. Zurek, Detecting gravitational signatures of dark matter with atom gradiometers, Phys. Rev. D112, 063014 (2025), arXiv:2505.00781 [hep-ph]

    Pith/arXiv arXiv 2025

  56. [56]

    P. A. Rosado, A. Sesana, and J. Gair, Expected properties of the first gravitational wave signal detected with pulsar timing arrays, Mon. Not. Roy. Astron. Soc.451, 2417 (2015), arXiv:1503.04803 [astro-ph.HE]

    Pith/arXiv arXiv 2015

  57. [57]

    Janssenet al., Gravitational wave astronomy with the SKA, PoSAASKA14, 037 (2015), arXiv:1501.00127 [astro-ph.IM]

    G. Janssenet al., Gravitational wave astronomy with the SKA, PoSAASKA14, 037 (2015), arXiv:1501.00127 [astro-ph.IM]

    Pith/arXiv arXiv 2015

  58. [58]

    Science with the Next-Generation VLA and Pulsar Timing Arrays, (2018), arXiv:1810.06594 [astro-ph.IM]

    Pith/arXiv arXiv 2018

  59. [59]

    Hobbset al., The international pulsar timing array project: using pulsars as a gravitational wave detector, Class

    G. Hobbset al., The international pulsar timing array project: using pulsars as a gravitational wave detector, Class. Quant. Grav.27, 084013 (2010), arXiv:0911.5206 [astro-ph.SR]

    Pith/arXiv arXiv 2010

  60. [60]

    J. I. Read, The Local Dark Matter Density, J. Phys. G41, 063101 (2014), arXiv:1404.1938 [astro-ph.GA]

    Pith/arXiv arXiv 2014

  61. [61]

    P. F. de Salas and A. Widmark, Dark matter local density determination: recent observations and future prospects, Rept. Prog. Phys.84, 104901 (2021), arXiv:2012.11477 [astro-ph.GA]

    Pith/arXiv arXiv 2021

  62. [62]

    N. P. Pitjev and E. V. Pitjeva, Constraints on dark matter in the solar system, Astronomy Letters39, 141 (2013), arXiv:1306.5534 [astro-ph.EP]

    Pith/arXiv arXiv 2013

  63. [63]

    Agazieet al.(NANOGrav), The NANOGrav 15 yr Data Set: Bayesian Limits on Gravitational Waves from Individual Supermassive Black Hole Binaries, Astrophys

    G. Agazieet al.(NANOGrav), The NANOGrav 15 yr Data Set: Bayesian Limits on Gravitational Waves from Individual Supermassive Black Hole Binaries, Astrophys. J. Lett.951, L50 (2023), arXiv:2306.16222 [astro-ph.HE]

    Pith/arXiv arXiv 2023

  64. [64]

    J. W. Foster, T. Trickle, and F. Vassallo, Projecting the ultimate pulsar timing sensitivity to dark matter substructure in a stochastic gravitational wave background, (2026), arXiv:2606.18329 [astro-ph.CO]

    Pith/arXiv arXiv 2026

  65. [65]

    Allen and J

    B. Allen and J. D. Romano, Detecting a stochastic background of gravitational radiation: Signal processing strategies and sensitivities, Phys. Rev. D59, 102001 (1999), arXiv:gr-qc/9710117. Appendix A: Statistical Framework of PTA Signals This appendix derives the results quoted in Sec. II: that marginalizing over the timing model is equivalent to projecti...

    Pith/arXiv arXiv 1999

  66. [66]

    Static Limit Because the timing model fits away the constant, linear, and quadratic components of the residuals, a slowly varying DM flyby contributes only through the part of the signal orthogonal to that subspace. In the static limit the leading non-degenerate piece is cubic in time, so the detection statistic depends on the projected cubic templateϕ ⊥ ...

  67. [67]

    Dynamic Limit In the dynamic limit, flybys have an encounter timescale short compared to the observing baseline, τ≪T; however, even after the distributional pieces are removed, their residuals are not compactly supported in time and leave low-frequency power that overlaps with the timing model. Working with bulk events — those whose closest approach lies ...

  68. [68]

    Sampling Geometries We first describe how the subhalo worldlines are sampled. Sampling uniformly over all of space would waste nearly every draw on undetectable worldlines, where the integrand is too small, so we restrict the draws to the region that contributes. The size of the sampled region is set by a quantity we call thedetection distance,R det,(c)(M...

  69. [69]

    (77), which is the noise-weighted norm of the signal after marginalizing the timing model

    Integrand Evaluation in the Time Domain After each subhalo worldline is drawn randomly, we have to evaluate the single-event SNR defined above Eq. (77), which is the noise-weighted norm of the signal after marginalizing the timing model. In App. A, and in the analytic estimates of Sec. IV, we imposed this by projecting the signal, (δt ⊥ |δt ⊥). That is no...

  70. [70]

    For the Doppler signal the ensemble covariance diverges, though only logarithmically (Sec

    Cutoff Insensitivity of the Stochastic Limit Reach The stochastic covariance is dominated by the closest encounters: a handful of loud events can outweigh the entire population of weak ones. For the Doppler signal the ensemble covariance diverges, though only logarithmically (Sec. IV C). We therefore regulate it with a percentile cut, retaining only event...