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arxiv: 2605.30367 · v1 · pith:NPPXYEWOnew · submitted 2026-05-18 · 🌌 astro-ph.GA · astro-ph.CO

Observing the Peculiar Acceleration of our Solar System with Quasar Proper Motions

Phu Huy Nguyen , Calum Murray This is my paper

Pith reviewed 2026-06-30 18:34 UTC · model grok-4.3

classification 🌌 astro-ph.GA astro-ph.CO
keywords quasar proper motionssolar system accelerationGaia catalogueproper motion dipoleangular power spectrumsimulation-based inferenceastrometric systematics
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The pith

Quasar proper motions reveal Solar System acceleration at 5.72 μas per year, with uncertainties 1.5-2.5 times larger after accounting for higher multipoles.

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

The paper measures the dipole in quasar proper motions observed by Gaia to infer the acceleration of the Solar System relative to the distant quasar frame. It models the full angular power spectrum using the pseudo-C_ℓ approach and simulation-based inference to fit the dipole jointly with higher multipoles, then uses cross-correlations with scanning strategy and stellar maps to check for systematics. Applied to Gaia EDR3 and Quaia catalogues, the acceleration matches earlier values but with substantially wider credible intervals, and shows no redshift dependence.

Core claim

The acceleration of the Solar System is (0.40^{+0.70}_{-0.70}, -5.09^{+0.54}_{-0.54}, -2.40^{+0.55}_{-0.58}) μas yr^{-1} with amplitude 5.72 μas yr^{-1} from the Quaia catalogue. This value is consistent with prior determinations, yet the credible intervals widen by factors of 1.5 to 2.5 once higher-multipole degeneracies are marginalised, indicating earlier uncertainty estimates were optimistic. The signal exhibits no significant redshift dependence, supporting its kinematic origin.

What carries the argument

The pseudo-C_ℓ formalism paired with simulation-based inference that jointly constrains the dipole and higher multipole power in the proper motion field while using cross-correlations to diagnose systematics.

If this is right

  • Earlier published uncertainties on the Solar System acceleration were optimistic by factors of 1.5-2.5.
  • The absence of redshift dependence strengthens the case that the dipole is kinematic rather than systematic.
  • Joint modelling of dipole and higher multipoles is required for unbiased dipole inference in future astrometric catalogues.
  • The framework can be reapplied to larger or deeper quasar samples to tighten the acceleration constraints.

Where Pith is reading between the lines

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

  • Similar higher-multipole marginalisation may be needed in other large-scale astrometric dipole studies to avoid underestimating errors.
  • The widened intervals could shift how this acceleration measurement is combined with galactic dynamics or local group motion models.
  • If non-kinematic residuals remain after the cross-correlation tests, they would most likely appear as excess power at specific multipoles tied to the scanning law.

Load-bearing premise

Cross-correlations with Gaia scanning strategy, stellar density, and stellar proper motion maps suffice to identify and remove non-kinematic contributions to higher multipoles that could bias the dipole.

What would settle it

Detection of statistically significant redshift dependence in the measured acceleration amplitude or a result inconsistent with independent determinations of Solar System motion relative to the cosmic microwave background.

Figures

Figures reproduced from arXiv: 2605.30367 by Calum Murray, Phu Huy Nguyen.

Figure 1
Figure 1. Figure 1: Mollweide spatial distribution map of Gaia EDR3 quasars [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Mollweide spatial distribution map of Gaia EDR3 faint [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Auto-power spectra Cˆ ℓ of E mode and B mode in the proper motions of the quasar sources. The error bars represent the standard deviation across 500 Monte Carlo realisations. The blue dash line represents the power of E-mode of the field while the green dash line represents that of the B-mode. Galactic 19.2452 M10 value 21.5295 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The quantity M10, the median magnitude of sources with ≤ 10 Gaia transits two-component vector dp = (µα∗ ,p, µδ,p) T with the 2x2 inverse covariance matrix (Σp) −1 in Eq. 3. The forward model maps a set of VSH coefficients (x = a E ℓm , a B ℓm ) (for 1 ≤ ℓ ≤ ℓmax) to a predicted proper motion field on the sphere via a spin-1 spheri￾cal harmonic transform A: d model = A x (14) The spin-1 transform relates t… view at source ↗
Figure 5
Figure 5. Figure 5: Cross-power spectra Cˆ ℓ of E mode and B mode between the proper motion field and systematic templates. Each column shows a different template: the first column is the cross-correlation with the faint stellar density map, the second column is the cross-correlation with the faint stellar proper motion map, and the third column is the cross-correlation with the M10 map. Each row corresponds to a different ca… view at source ↗
Figure 6
Figure 6. Figure 6: Schematic of the simulation-based inference pipeline. It is organized in 3 sections: The first section [1] is to define models: [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: Marginal coverage test for all Model 2 parameters. The [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
Figure 7
Figure 7. Figure 7: Marginal coverage test for the three acceleration compo [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 9
Figure 9. Figure 9: Comparison of acceleration components inferred in this [PITH_FULL_IMAGE:figures/full_fig_p009_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Posterior distributions for the acceleration components ( [PITH_FULL_IMAGE:figures/full_fig_p010_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Posterior median values of acceleration (in [PITH_FULL_IMAGE:figures/full_fig_p011_11.png] view at source ↗
read the original abstract

We measure the proper motion dipole of quasars observed by Gaia to determine the acceleration of the Solar System with respect to the quasar rest frame. We characterise the full angular power spectrum of the proper motion field using the pseudo-$C_\ell$ formalism and employ simulation-based inference to jointly constrain the dipole and higher multipole power. Cross-correlation with the Gaia scanning strategy, stellar density, and stellar proper motion maps is used to diagnose the origin of systematic power beyond the dipole. We apply this framework to both the Gaia EDR3 quasar catalogue and the Quaia catalogue. The inferred acceleration is consistent with the previous determination, but the credible intervals widen by factors of 1.5 to 2.5 when higher-multipole degeneracies are properly marginalised, indicating that previous uncertainty estimates were optimistic. Our best estimate, based on the Quaia catalogue is $(g_x,\, g_y, \,g_z) =( 0.40^{+0.70}_{-0.70},\,-5.09^{+0.54}_{-0.54},\,-2.40^{+0.55}_{-0.58}) \;\mu as \,yr^{-1}$, corresponding to an amplitude of $5.72_{-0.52}^{+0.53}\,\rm \mu as\,yr^{-1}$. The acceleration shows no significant dependence on source redshift, providing further evidence for its kinematic origin.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 2 minor

Summary. The paper measures the Solar System's acceleration vector via the dipole in quasar proper motions using Gaia EDR3 and Quaia catalogues. It characterizes the full angular power spectrum with the pseudo-C_ℓ estimator and uses simulation-based inference (SBI) to jointly constrain the dipole (g_x, g_y, g_z) and higher multipoles, applying cross-correlations with Gaia scanning strategy, stellar density, and stellar proper-motion maps to diagnose systematics. The inferred acceleration is consistent with prior results but with credible intervals widened by factors of 1.5–2.5; the best estimate from Quaia is (0.40^{+0.70}_{-0.70}, -5.09^{+0.54}_{-0.54}, -2.40^{+0.55}_{-0.58}) μas yr^{-1} (amplitude 5.72 μas yr^{-1}), with no significant redshift dependence, supporting a kinematic origin.

Significance. If the systematic control holds, the result provides a more conservative and robust determination of the acceleration by properly marginalizing higher-multipole degeneracies that previous analyses appear to have neglected, yielding wider but more reliable uncertainties. The absence of redshift dependence adds supporting evidence for the kinematic interpretation. The use of SBI for joint inference and explicit cross-correlation diagnostics are methodological strengths that could be adopted more broadly in astrometric dipole studies.

major comments (3)
  1. [Abstract, framework description] Abstract and framework description: the assertion that cross-correlations with the Gaia scanning law, stellar density, and stellar proper-motion maps are sufficient to diagnose and remove all non-kinematic contributions to higher multipoles is load-bearing for the central claim of a clean kinematic dipole. No quantitative completeness test (e.g., power-spectrum residuals after subtraction, null tests on injected systematics, or recovery fractions for simulated non-kinematic modes) is described, leaving open the possibility that residual power couples into the dipole even after SBI marginalization.
  2. [Results] Results section (Quaia best estimate): the reported credible intervals already incorporate higher-multipole marginalization, but without an explicit comparison table or figure showing the dipole posterior with versus without the higher-multipole model (or with versus without the cross-correlation cleaning step), it is difficult to quantify how much of the factor 1.5–2.5 widening is due to each component.
  3. [Methods] Methods (pseudo-C_ℓ + SBI): the pseudo-C_ℓ estimator and SBI prior must be shown to be insensitive to any unmodeled redshift-dependent selection or colour-dependent astrometric systematics that could survive the stellar-map cross-correlations; a dedicated injection-recovery test on the full pipeline would directly address this.
minor comments (2)
  1. [Abstract] Notation: the amplitude is quoted as 5.72_{-0.52}^{+0.53} while the vector components use asymmetric errors; a brief statement on how the amplitude posterior is derived from the vector components would improve clarity.
  2. [Figures] Figure clarity: the cross-correlation maps and power spectra should include explicit labels for which multipole ranges are used in the SBI fit versus those used only for diagnostics.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments. We address each major comment below and describe the revisions we will implement.

read point-by-point responses

  1. Referee: [Abstract, framework description] Abstract and framework description: the assertion that cross-correlations with the Gaia scanning law, stellar density, and stellar proper-motion maps are sufficient to diagnose and remove all non-kinematic contributions to higher multipoles is load-bearing for the central claim of a clean kinematic dipole. No quantitative completeness test (e.g., power-spectrum residuals after subtraction, null tests on injected systematics, or recovery fractions for simulated non-kinematic modes) is described, leaving open the possibility that residual power couples into the dipole even after SBI marginalization.

    Authors: We agree that quantitative validation strengthens the central claim. We will add a new subsection to the Methods describing power-spectrum residuals after modeled subtraction and injection-recovery tests using simulated non-kinematic modes. These tests will quantify residual coupling into the dipole after SBI marginalization and support the diagnostic power of the cross-correlations. revision: yes

  2. Referee: [Results] Results section (Quaia best estimate): the reported credible intervals already incorporate higher-multipole marginalization, but without an explicit comparison table or figure showing the dipole posterior with versus without the higher-multipole model (or with versus without the cross-correlation cleaning step), it is difficult to quantify how much of the factor 1.5–2.5 widening is due to each component.

    Authors: We will add a new figure to the Results section comparing the dipole posterior under four cases: full model, without higher-multipole marginalization, without cross-correlation cleaning, and without both. This will explicitly quantify the contribution of each element to the reported widening of the credible intervals. revision: yes

  3. Referee: [Methods] Methods (pseudo-C_ℓ + SBI): the pseudo-C_ℓ estimator and SBI prior must be shown to be insensitive to any unmodeled redshift-dependent selection or colour-dependent astrometric systematics that could survive the stellar-map cross-correlations; a dedicated injection-recovery test on the full pipeline would directly address this.

    Authors: We will add a dedicated injection-recovery test to the Methods section. Mock catalogues will be generated with injected redshift-dependent selection and colour-dependent astrometric systematics, processed through the full pseudo-C_ℓ + SBI pipeline, and the recovered dipole parameters examined for bias after cross-correlation cleaning. revision: yes

Circularity Check

0 steps flagged

No significant circularity; result is data-driven measurement from external catalogs

full rationale

The paper applies the pseudo-C_ℓ formalism and simulation-based inference to external Gaia EDR3 and Quaia quasar proper-motion catalogs to infer the solar acceleration dipole while marginalizing higher multipoles. Cross-correlations with scanning strategy and stellar maps are used only for diagnosis, not as a self-referential fit. The central claim (widened but consistent dipole with no redshift dependence) is a direct statistical output from the data and simulations; no equation reduces a prediction to a fitted input by construction, no load-bearing self-citation chain is invoked, and no ansatz or uniqueness theorem is smuggled in. The derivation remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on fitting acceleration parameters to the observed dipole while assuming the quasar frame is at rest and that higher multipoles can be marginalized without residual bias; the acceleration components are the primary fitted quantities.

free parameters (1)
  • acceleration vector components (g_x, g_y, g_z)
    Fitted parameters obtained via simulation-based inference on the proper motion dipole and higher multipoles.
axioms (1)
  • domain assumption Quasars define an inertial rest frame with negligible intrinsic proper motions on the relevant timescales
    Required for the dipole to be interpreted as purely kinematic Solar System acceleration.

pith-pipeline@v0.9.1-grok · 5783 in / 1417 out tokens · 32346 ms · 2026-06-30T18:34:10.953986+00:00 · methodology

discussion (0)

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Reference graph

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