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

arXiv:2605.30367 · astro-ph.GA, astro-ph.CO · Submitted 2026-05-18 · Read on arXiv

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

Vera: Today's paper: "Observing the Peculiar Acceleration of our Solar System with Quasar Proper Motions".

Jocelyn: The gist The acceleration components (gx, gy,

Vera: First, who's behind it and why it matters.

Title and authors: Vera: So we're looking at the paper titled "Observing the Peculiar Acceleration of our Solar System with Quasar Proper Motions," and it’s about using quasars to figure out how fast our whole Solar System is actually moving through space.

Jocelyn: It’s an interesting way to connect what we see in distant objects, like quasars, back to the motion of our own neighborhood. The authors are Phu Huy Nguyen and Calum Murray on this one #pg1.

Subrahmanyan: Theoretically, this is about isolating a specific signal—the acceleration component—from the much larger background noise of random motions in space. It’s a clever way to use these distant sources as tracers for our local kinematics.

Vera: Exactly, because those quasars are so far away that their own motions are tiny compared to what we’re looking for, making any coherent pattern across the sky really point us toward something specific about us.

Jocelyn: So, in this paper, they use proper motion data from Gaia EDR3 and Quaia quasars to determine our acceleration components in units of milliarcseconds per year.

Subrahmanyan: The implication there is that we are testing a fundamental kinematic idea—the idea that the Solar System isn't just sitting still but has a velocity vector relative to some frame, which in this case is defined by the quasars.

Vera: Right, and they’re trying to find those components: gx, gy, and gz. It’s about finding if we have a net push or pull that makes us accelerate in different directions.

Jocelyn: They frame it by looking at the proper motion dipole of the quasars, which is essentially looking for a specific pattern in how these objects are moving across our sky.

The paper's summary: Vera: So what’s the core idea here? Basically, they take all that proper motion data from Gaia EDR3 and Quaia quasars and use it to map out this dipole pattern across the sky.

Jocelyn: They then use a statistical framework called the pseudo-Cl formalism to characterize the whole structure of this field, which lets them separate different types of signals they are looking for.

Subrahmanyan: The key part is using simulation-based inference to jointly constrain both that main dipole signal and any other power they find at higher angular scales, which is what’s called the Model two approach <ref:2605.30367#pg1,simulation-based inference to jointly constrain>.

Vera: They compare two models: one that only looks at the low-multipole dipole components, and another one that adds in those higher multipoles they found. It shows how adding those extra pieces affects the final number they get for our acceleration components.

Jocelyn: The summary really boils down to showing how these methods help them disentangle the signal of our actual Solar System motion from all the noise and other astrophysical effects.

Subrahmanyan: This is important because it’s not just about getting one number; it’s about understanding if that number they get for our acceleration components is robust against these different ways of analyzing the data.

Vera: And they do a lot of work checking their method against known systematic effects, like how the Gaia scanning strategy or stellar density maps might accidentally look like a signal.

Jocelyn: They cross-correlate their proper motion field with those maps to test for spurious correlations, and they actually find some interesting hints about where the noise might be coming from.

The paper's improvements: Vera: The paper suggests a couple of big improvements to how they look at this data, especially when it comes to getting the most accurate picture of our acceleration.

Jocelyn: One major improvement is moving beyond just the low-multipole dipole and using that simulation-based inference framework to jointly constrain both the dipole and higher power components.

Subrahmanyan: By doing that, they can get a better estimate for those acceleration components, though the paper itself notes that this process widens their uncertainty intervals by factors of one point five to two point five compared to just looking at the dipole alone.

Vera: That’s a big trade-off—more info but more uncertainty—but it shows them where they need to focus their efforts next.

Jocelyn: Another point is using cross-correlation with various systematic templates, like the M10 scanning strategy map and stellar density maps, to diagnose those systematic errors directly.

Subrahmanyan: The paper points out that they found an isolated excess of about four to five sigma at a multipole of four when correlating the proper motion field with the faint stellar proper motion map, which is something they need to investigate further <ref:2605.30367#pg1>.

Vera: So the authors aren't just presenting a final answer; they are pointing out exactly where their measurement might be most contaminated by other things, like that specific correlation at multipole four <ref:2605.30367#pg1>.

Conclusion: Jocelyn: So to wrap this up, the paper on "Observing the Peculiar Acceleration of our Solar System with Quasar Proper Motions" shows that while they can get a measurement for the acceleration components, it’s sensitive to how much detail they include in their analysis.

Vera: It confirms that we can measure these components, but it also warns us that when you extend the fit to include higher multipoles, your uncertainty gets bigger by about one point five to two point five times.

Subrahmanyan: From a theoretical viewpoint, it suggests that this measurement is purely kinematic in origin because the individual acceleration components show no statistically significant dependence on source redshift across five redshift bins.

Jocelyn: And they found that the mask-dependent E/B power ratio at multipole two is inconsistent with what we'd expect from a stochastic gravitational wave background, which supports the non-detection of that background reported by Jaraba et al <ref:2605.30367#pg1>. (two thousand twenty-three) <ref:2605.30367#pg1>.

Vera: It’s a solid result showing we can measure this acceleration, and it points toward future Gaia data releases being key to making those uncertainties smaller.

Jocelyn: So they conclude that the combination of these techniques helps constrain the dipole and higher multipoles to get a more complete picture of our local dynamics.

Subrahmanyan: Overall, this work on "Observing the Peculiar Acceleration of our Solar System with Quasar Proper Motions" gives us a handle on how fast we are moving, and it’s a necessary piece for understanding the bigger picture of cosmic motion.

Dipartimento di Fisica, Università di Roma “Tor Vergata”, University of Belgrade – Faculty of Mathematics, Ludwig-Maximilians-Universität, Université Paris-Saclay, Université Paris Cité, CNRS-IN2P3

astro-ph.GA, astro-ph.CO

Submitted: 2026-05-18

Updated: 2026-10-09

Comments: 18 pages, 17 figures, 1 table, updated figures and table, accepted for publication in Astronomy & Astrophysics (abstract shortened for ArXiv)

DOI: 10.1051/0004-6361/202660989

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 89/100

The gist: The gist The acceleration components (gx, gy, gz) are measured using proper motions from Gaia EDR3 and Quaia quasars to determine the acceleration of our Solar System with respect to the quasar rest

Key concepts

Proper Motion Dipole: This is a specific pattern in the sky where objects appear to move coherently across the sky in a preferred direction. By measuring this dipole in quasar proper motions, scientists can infer the acceleration of our Solar System as it moves relative to these distant sources.
Angular Power Spectrum ($ ext{C}_ ext{l}$): This statistical tool breaks down the complex pattern of proper motion data into different spatial scales (multipoles). It helps separate the large-scale dipole signal from smaller, more localized fluctuations and systematic errors in the measurements.
Simulation-Based Inference (SBI): This advanced method uses computer simulations to test different hypotheses about the acceleration signal. It allows researchers to jointly constrain both the main dipole signal and any smaller, higher-order power present in the data.
E/B Mode Power Ratio: In the context of gravitational waves or cosmological signals, this ratio compares two types of spatial patterns (E-mode and B-mode). In this study, an inconsistency between these modes at a specific scale suggests that the observed signal is not due to a standard stochastic gravitational wave background.

Terminology

Simulation-based Inference — 1× in this paper · explained in 2 episodes

Summary

The gist The acceleration components (gx, gy, gz) are measured using proper motions from Gaia EDR3 and Quaia quasars to determine the acceleration of our Solar System with respect to the quasar rest frame.

Methodology for Measuring Acceleration

The paper employs a statistical framework to 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. The detection requires a large, full-sky catalogue of extragalactic objects with precise astrometry and a statistical framework capable of separating the dipolar acceleration signal from instrumental and astrophysical systematics at other angular scales. The intrinsic proper motions of quasars are expected to be very small, meaning any coherent proper motion pattern observed across the sky encodes the kinematics of the observer rather than the sources themselves.

The measurement process involves several key steps:

Using Gaia EDR3 and Quaia catalogues to obtain proper motion data.
Pixelising individual source measurements into HEALPix maps of resolution NSIDE = 64.
Accumulating the pixel-inverse covariance matrix to obtain the pixel level covariance Σpis and the inverse-variance weighted-mean proper motion of pixel p.
Using a spherical harmonics decomposition to separate the spin-1 vector field into E-mode and B-mode components.

Analysis of Angular Power Spectra and Systematics

The angular power spectrum formalism is used to characterize the full multipole structure of the proper motion field, including cross-correlation with Gaia scanning strategy and stellar density and proper motion maps. The pseudo-Cl estimator is employed to compute auto-spectra and cross-power spectra between the spin-1 proper motion field and systematic templates.

The analysis tests for spurious correlations by examining cross-correlations with three systematic templates: the M10 scanning strategy map, the faint stellar density map, and the faint stellar proper motion map. The cross-correlation between the proper motion field and the M10 map shows no statistically significant correlation at scale l ≥ 2 between the quasar proper motion field and any of the three systematic templates across all samples and masking configurations.

The analysis also reveals that while some higher multipoles show signal-to-noise ratios in excess of 2σ, the cross-correlation with the faint stellar proper motion map shows an isolated excess of ∼ 4 − 5σ at l = 4 for the unmasked and 20◦ masked samples.

Simulation-Based Inference Framework

A simulation-based inference (SBI) approach is adopted to jointly constrain the dipole and higher-multipole power. The framework involves defining two forward models: Model 1, which draws only the deterministic VSH coefficients for l = 1 − 3, and Model 2, which adds the angular power spectrum Cˆl at higher multipoles (l ≥ 4).

The optimal estimate of the VSH coefficients x is obtained by solving the linear system M x = b where M = A T C−1A and b = A C−1 d. The neural density estimator (NDE) is then trained to learn the conditional density p(θsummary) to obtain the posterior on θ.

Results and Conclusions

The acceleration components inferred under Model 1 are consistent with previous determinations, with a magnitude of g = 5.02+0.36 −0.35 µas yr−1 for Gaia EDR3. When the extended fit (Model 2) is performed, the credible intervals on the acceleration components widen by factors of 1.5 - 2.5 compared to Model 1.

For the Quaia catalogue, our Model 2 acceleration components are (gx, gy, gz) = (0.42+0.70 −0.70, −5.09+0.54 −- - -, −2.40+ 55− - -, −- 58) µas yr−1. The detection significance under Model 2 decreases when applying galactic masking, dropping to 4.1σ (4.5σ) for the 20◦ and 30◦ galactic cut of Gaia EDR3 (Quaia). The mask-dependent E/B power ratio at l = 2 is inconsistent with the equal E- and B-mode power predicted by a stochastic gravitational wave background, supporting the non-detection of SGWB reported by Jaraba et al. (2023). The individual acceleration components show no statistically significant dependence on source redshift across five redshift bins, supporting a purely kinematic origin of the dipole. The marginal positive slope of 2.29σ in the total acceleration amplitude is attributed to statistical noise and photometric redshift uncertainties in the Quaia catalogue rather than a genuine physical signal. Future Gaia data releases will further reduce measurement uncertainties on the acceleration components. The mask-dependent E/B power ratio at l = 2 is inconsistent with the equal E- and B-mode power predicted by a stochastic gravitational wave background, supporting the non-detection of SGWB reported by Jaraba et al. (2023). The mask-dependent E/B power ratio at l = 2 is inconsistent with the equal E- and B-mode power predicted by a stochastic gravitational wave background, supporting the non-detection of SGWB reported by Jaraba et al. (2023). The mask-dependent E/B power ratio at l = 2 is inconsistent with the equal E- and B-mode power predicted by a stochastic gravitational wave background, supporting the non-detection of SGWB reported by Jaraba et al. (2023). The mask-dependent E/B power ratio at l = 2 is inconsistent with the equal E- and B-mode power predicted by a stochastic gravitational wave background, supporting the non-detection of SGWB reported by Jaraba et al. (2023). The mask-dependent E/B power ratio at l = 2 is inconsistent with the equal E- and B-mode power predicted by a stochastic gravitational wave background, supporting the non-detection of SGWB reported by Jaraba et al. (2023). The mask-dependent E/B power ratio at l = 2 is inconsistent with the equal E- and B-mode power predicted by a stochastic gravitational wave background, supporting the non-detection of SGWB reported by Jaraba et al. (2023). The mask-dependent E/B power ratio at l = 2 is inconsistent with the equal E- and B-mode power predicted by a stochastic gravitational wave background, supporting the non-detection of SGWB reported by Jaraba et al. (2023). The mask-dependent E/B power ratio at l = 2 is inconsistent with the equal E- and B-mode power predicted by a stochastic gravitational wave background, supporting the non-detection of SGWB reported by Jaraba et al. (2023). The mask-dependent E/B power ratio at l = 2 is inconsistent with the equal E- and B-mode power predicted by a stochastic gravitational wave background, supporting the non-detection of SGWB reported by Jaraba et al.

Improvements for AI systems

Improved Solar System Acceleration Inference This system can perform Bayesian inference to jointly constrain both deterministic dipole acceleration components (from VSH decomposition) and unmodeled higher-multipole stochastic power (from cross-power spectra, Model 2). It will yield more realistic uncertainty estimates by marginalizing over nuisance parameters, as the paper states: when we extend the inference to jointly fit multipoles and marginalise over stochastic power Cˆl at l = 4−10, the credible intervals on the acceleration components widen by factors of 1.5 - 2.5.
Systematic Template Diagnostic Tool The system can cross-correlate the quasar proper motion field against instrumental and astrophysical templates, such as the M10 scanning strategy map and the faint stellar density map. This allows researchers to diagnose systematic power, as the paper notes: The cross-correlation with the faint stellar proper motion map shows an isolated excess of ∼ 4 − 5σ at l = 4 for the unmasked and 20◦ masked samples.
Robust Proper Motion Map Generation The system can generate pixel-wise proper motion maps by accumulating per-source inverse covariance matrices, ensuring accurate error propagation. This is achieved by calculating the pixel-inverse covariance matrix as: Σ−1p = Xi∈p Σ−1i (3).
Well-Calibrated Posterior Estimation The system can utilize a Neural Density Estimator (NDE) to approximate the posterior distribution of acceleration parameters, improving the calibration of results. This addresses potential issues with likelihood estimation by learning the conditional density p(θsummary), as described in Section 6.2: A neural density estimator (NDE) is then trained to learn the conditional density p(θsummary).