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The HST-Gaia Near-Infrared Astrometric Reference Frame near the Milky Way Galactic Center

T0 review · 3 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read Fourteen epochs of HST imaging, anchored by 40 Gaia-DR3 stars, define the first near-infrared ICRS-tied reference frame at the Galactic center, with a systematic tie to Gaia-CRF3 of $0.025$ mas yr$^{-1}$ in proper motion and $0.044$ mas…

desk verdict A solid, carefully-built ICRS-tied reference frame for the Galactic center; the headline Gaia-consistency number is partly self-referential, but the independent maser check and the GP proper-motion method make this a serious referee-worthy paper. read the letter →

arxiv 2506.19933 v1 pith:VLB6LPQE submitted 2025-06-24 astro-ph.GA

Matthew W. Hosek Jr. , Tuan Do , Gregory D. Martinez , Rebecca Lewis-Merrill , Andrea M. Ghez , Jessica R. Lu , Shoko Sakai , Jay Anderson This is my paper · ORCID
classification astro-ph.GA
keywords GalacticcenterastrometricreferenceframepropermotionsICRSGaia-CRF3GaussianprocessSgrA*HubbleSpaceTelescope
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper sets out to establish the first high-precision near-infrared astrometric reference frame at the Milky Way's Galactic center that is tied to the International Celestial Reference System (ICRS). Because the central parsec is too dusty and crowded for Gaia to see, the authors bridge the gap by transforming 14 epochs of Hubble Space Telescope imaging into the Gaia-CRF3 frame using 40 stars in common with Gaia-DR3, and they publish a catalog of 2,876 stars around Sgr A*. They report that the frame agrees with Gaia-CRF3 to $0.025$ mas yr$^{-1}$ in proper motion and $0.044$ mas in position, making it, they argue, the first ICRS-based frame precise enough to probe the extended mass distribution inside the orbit of the star S0-2. The catalog is also the first near-infrared reference frame at the Galactic center that is independent of radio maser astrometry, which lets it test the maser-based frames used so far.

What carries the argument

Three components carry the argument. First, a second-order polynomial transformation fits HST pixel coordinates to Gaia-CRF3 sky coordinates using 40 carefully selected primary reference stars, with bootstrap estimates of the transformation error at each epoch. Second, each star's motion is modeled as a first-order polynomial plus one of several Gaussian-process correlation kernels (squared-exponential, step, confusion, or additive error), selected by leave-one-out cross-validation and an expected-log-probability criterion; this is what absorbs a magnitude- and position-angle-dependent systematic shift of up to $\sim2$ mas that would otherwise distort proper motions. Third, the frame is converted into SgrA*-at-Rest coordinates by subtracting the adopted ICRS position and proper motion of Sgr A* itself, so the catalog can be used directly for orbital dynamics. The paper identifies the position-angle systematic but leaves its physical origin open.

What would settle it

Recompute the HST-to-Gaia-CRF3 transformation after re-adding the ten rejected Gaia-DR3 stars with conservative weights and compare the resulting proper-motion bias; a shift larger than $0.025$ mas yr$^{-1}$ would show the outlier rejection biases the frame. Independently, fit the 40 primary stars from the two position-angle epochs separately: if the PA-dependent systematic is real, the two half-frame proper-motion ties should differ by more than their formal errors.

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Extended reading notes

Core claim

The central claim is that the HST-Gaia frame inherits the ICRS orientation through Gaia-CRF3 with no measurable bias: the error-weighted differences between HST-Gaia and Gaia-DR3 for the 40 primary stars are $-0.015\pm0.020$ mas yr$^{-1}$ in $\mu_{\alpha*}$ and $0.002\pm0.015$ mas yr$^{-1}$ in $\mu_\delta$, with a combined proper-motion precision of $0.025$ mas yr$^{-1}$, and position consistency of $0.044$ mas. The brightest catalog stars reach median errors of $0.03$ mas yr$^{-1}$ in proper motion and $0.11$ mas in position, roughly a factor of $20$ better than previous ICRS proper motions in this field. The paper further claims that a comparison of 13 stellar masers with the radio-based reference frame (D23) shows consistency within $0.041$ mas yr$^{-1}$ and $0.54$ mas at $99.7\%$ confidence, while flagging a possible $\sim2.5\sigma$ offset in the $\alpha_*$ direction that requires further observations to attribute.

Load-bearing premise

The frame tie rests on the assumption that the 40 Gaia-DR3 stars retained as primary references are an unbiased realization of the ICRS in a crowded, high-extinction field; if the ten rejected candidates carry real astrometric signal, or if the retained 40 have correlated errors, the quoted $0.025$ mas yr$^{-1}$ consistency with Gaia-CRF3 would not hold.

Editorial extensions

If this is right

  • Galactic-center stellar orbits can now be tied to an inertial ICRS frame rather than only to a radio-maser frame, so dynamical fits gain an independent constraint on the reference frame itself.
  • With the reported $0.025$ mas yr$^{-1}$ proper-motion consistency, the frame should detect an extended mass of roughly $3000\,M_\odot$ inside S0-2's orbit, dropping to roughly $1000\,M_\odot$ once Gaia-DR4 improves the tie.
  • The 2,823 secondary reference stars inside the ground-based AO field allow existing AO datasets to be re-registered to the ICRS without new observations.
  • The 13-maser cross-check gives the first independent near-infrared confirmation of the radio-maser frame at the $0.041$ mas yr$^{-1}$ level, with the paper leaving open whether the $\sim2.5\sigma$ $\alpha_*$ offset is real.

Reading between the lines

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

  • If the frame tie is as stable as reported, the same Gaussian-process modeling should create ICRS-tied reference frames in other crowded, reddened fields where Gaia stars are sparse but multi-epoch HST imaging exists.
  • A direct stress test of the central assumption is to repeat the transformation after re-adding the ten rejected Gaia candidates with conservative weights; a shift in the proper-motion bias above $0.025$ mas yr$^{-1}$ would implicate the outlier-rejection step.
  • The paper's own Table 6 suggests that the position part of the SgrA*-at-Rest comparison is limited by the adopted ICRS position of Sgr A* rather than by HST-Gaia; improving that VLBI anchor would tighten the maser comparison more than extra HST epochs would.
  • If the position-angle-dependent shift is really intra-exposure pointing drift, it should also appear in other long-exposure WFC3-IR programs with two roll angles, and confirming that would permit a physical correction instead of absorbing the effect into the GP kernel.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper presents a new near-infrared astrometric reference frame near the Galactic center, constructed by transforming 14 epochs of HST WFC3-IR astrometry into the Gaia-CRF3 frame using 40 Gaia-DR3 stars that overlap the HST field. The authors introduce a Gaussian-process framework for modeling stellar proper motions that simultaneously handles time-correlated systematics (e.g., a position-angle-dependent shift of up to ~2 mas for faint stars) and spatially correlated confusion. The resulting catalog contains 2,876 sources within ~25" of SgrA*, with the brightest stars achieving median proper-motion and position errors of ~0.03 mas/yr and ~0.11 mas, respectively. The central claim is that the HST-Gaia frame is consistent with Gaia-CRF3 to 0.025 mas/yr in proper motion and 0.044 mas in position, and that it is the first ICRS-based frame precise enough to probe the extended mass distribution near SgrA*. The authors also compare the frame to the radio maser-based frame of Darling et al. (2023), finding consistency within 0.041 mas/yr and 0.54 mas at 99.7% confidence, while noting a possible ~2.5-sigma offset in the alpha* direction.

Significance. If the frame-accuracy claim is correct, this is a valuable contribution: it is the first ICRS-tied NIR reference frame in the central parsec that is independent of radio masers, and the catalog (with ~2,900 sources, including 40 Gaia primary stars and 13 masers) will be a useful resource for GC dynamics. The Gaussian-process methodology for modeling systematic errors is a genuine methodological advance, and the paper provides a detailed pipeline description with machine-readable tables. The validation is reasonably thorough: the GP models are tested against leave-one-out cross-validation and the g-chi-squared_LOO distributions, and the radio maser comparison is an independent external check. However, the headline consistency with Gaia-CRF3 is not an independent validation, since it is measured on the same 40 stars that define the transformation; the only fully external test, the radio comparison, shows a possible ~2.5-sigma offset in alpha*. The significance of the extended-mass claim therefore rests on a precision estimate that is partly self-referential, and this needs to be addressed before the central claim can be accepted.

major comments (3)
  1. [§3.3, Eq. (10)] The quoted 0.025 mas/yr proper-motion and 0.044 mas position consistency with Gaia-CRF3 is computed as the error-weighted mean residual of the 40 primary reference stars that are the same stars used to fit the second-order polynomial transformation. For a least-squares fit, the residuals on the fitting sample are minimized by construction, so these numbers quantify the internal scatter of the transformation residuals (i.e., its precision relative to the same data), not an independent measure of the accuracy of the frame tie to the ICRS. The authors should either add a leave-one-out or split-sample cross-validation (fit the transformation on a subset of primary stars and test on the remaining stars) or explicitly relabel the §3.3 result as an internal consistency check. This is load-bearing because the abstract and §5.3 use the 0.025 mas/yr value to argue that the frame is precise enough to probe the extended mass distribution near SgrA*.
  2. [§4.2.3] The only fully independent external validation, the 13-maser comparison, shows a possible tension in the alpha* direction: the average proper-motion offset is -0.076 ± 0.030 mas/yr and the position offset is -0.536 ± 0.230 mas (after adding systematics). The paper acknowledges a ~2.5-sigma tension, but the abstract and conclusions state consistency 'to within 0.041 mas/yr and 0.54 mas at 99.7% confidence,' which is misleading because the observed offset is larger than the quoted 1-sigma uncertainty and the 99.7% confidence interval includes non-zero values. The authors should report the offset and its significance explicitly in the abstract and conclusions, and discuss what a real offset of this magnitude would imply for the frame accuracy claim. If the offset is real, it would be comparable to the claimed 0.025 mas/yr precision and would weaken the extended-mass claim.
  3. [§3.1] The iterative 5-sigma outlier rejection removed 10 of the 50 Gaia reference stars (20%) from the sample that defines the transformation. The rejection is based on the differences between HST-Gaia proper motions and Gaia-DR3 proper motions, but the HST-Gaia proper motions are computed using the transformation that is fit to the same stars, introducing a circularity into the outlier selection. The paper notes that many removed stars had truncated PSFs or close neighbors, but the possibility that the retained 40-star sample is biased toward zero residual (and thus that the transformation errors are underestimated) should be addressed quantitatively. The authors should report the astrometric properties of the rejected stars and/or demonstrate that the outlier rejection does not alter the conclusions by repeating the analysis with a leave-one-out or a more robust fitting procedure.
minor comments (5)
  1. [Abstract / §4.2.3] The phrase 'consistent with zero to within 0.041 mas/yr at 99.7% confidence' is imprecise; the observed offset is -0.076 mas/yr with a 1-sigma uncertainty of 0.041 mas/yr. Please state the offset and its uncertainty, and phrase the consistency statement in terms of the confidence interval for the true offset.
  2. [§3.1] The abbreviation 'D23' is used in §4.1 and §4.2 without being defined at first use in the text; please spell out Darling et al. (2023) when the radio maser frame is first mentioned.
  3. [Table 3 note] The table note lists 'σ_α*, σ_δ, σ_μδ, σ_μδ'; the last two entries should be σ_{μα*} and σ_{μδ}. Also, several table captions contain the typo 'T able'.
  4. [§3.2] The ELPD model-selection threshold of ≥6 is stated as corresponding to ~3-sigma preference, but the mapping between the ELPD difference and a significance level is not derived; please provide a reference or a brief justification for this threshold.
  5. [§5.2] The predicted Gaia-DR4 improvement relies on the empirical constant α_obs ≈ 2.4 in Eq. (19), but the derivation of this constant is not described; please state how it is obtained from the current transformations and discuss its uncertainty.

Circularity Check

2 steps flagged · score 6.0 of 10

The 0.025 mas/yr Gaia-CRF3 consistency claim is computed as the weighted mean residual on the same 40 primary stars used to define the transformation, so it is a fit diagnostic rather than an independent external validation.

  1. self definitional [Section 3.3, Equations 10-11, Figure 5; abstract]
    "We define the bias between the HST-Gaia and Gaia-CRF3 reference frames as the error-weighted mean difference between the positions and proper motion values for the primary reference stars: ... For the proper motions, we derive the bias to be ∆µα∗ = -0.015 ±0.020 mas yr−1 and ∆µδ = 0.002±0.015 mas yr−1. This indicates that there is no evidence for a bias between the HST-Gaia and Gaia-CRF3 proper motions to a total precision of σ∆pm = 0.025 mas yr−1."

    The primary reference stars in Equation 10 are the same 40 stars onto which the per-epoch second-order polynomial (Equations 1-2) is fit by linear least squares in Section 3.1. Because that fit includes a free constant term at every epoch, and linear and quadratic spatial terms, any coherent HST-versus-Gaia offset in position or proper motion is absorbable by the transformation; the error-weighted mean residual of the fit stars is therefore minimized by construction. Reporting this residual as consistency with Gaia-CRF3 to 0.025 mas/yr states the fitting residual as an external validation.

  2. fitted input called prediction [Section 3.1, primary reference star selection; Section 3.3]
    "Reference stars with either position or proper motion differences larger than 5σ (where σ is the quadratic sum of the HST-Gaia and Gaia-DR3 errors) are considered outliers. ... These iterations continue until no outliers are found to exist, which was achieved after 10 Gaia stars are eliminated from the primary reference star sample."

    The 40 stars that survive this iterative 5σ trim are then used both to transform HST astrometry into Gaia-CRF3 and to define the no-bias statistic in Equation 10. Outlier rejection is applied to exactly the quantity being tested, removing the stars with the largest HST-versus-Gaia differences, so the subsequent claim of 0.025 mas/yr consistency is computed on a sample selected for HST-Gaia agreement. The paper plausibly explains the rejected stars as edge or confusion cases, but that does not make the surviving-sample consistency test independent of the fit; the test is blind to the stars that disagreed most strongly.

full rationale

The main derivation pipeline is not circular: HST astrometry is transformed into Gaia-CRF3 using 40 primary stars, proper motions are modeled with Gaussian Processes whose kernel choice is validated by leave-one-out cross-validation, and the catalog is internally self-consistent. No load-bearing self-citation chain or imported uniqueness theorem was found. The circularity is confined to the headline claim of consistency with Gaia-CRF3. Equation 10 defines the bias as the error-weighted mean difference on the primary reference stars, which are exactly the stars used in the least-squares polynomial fit of Section 3.1 and which have been iteratively trimmed to remove disagreements larger than 5σ with Gaia. A per-epoch polynomial with free constant and spatial terms can absorb global position and proper-motion offsets, so a near-zero residual mean is expected by construction; the quoted 0.025 mas/yr therefore measures the fit residual, not an independent check against an external ICRS realization. The radio-maser comparison in Section 4.2.3 is genuinely independent, using 13 masers not used in the transformation, and provides some external support; however, it is made in the SgrA*-at-rest frame, depends on the adopted SgrA* ICRS position, and shows a possible ~2.5σ tension in α* for both position and proper motion. Overall, the central frame-consistency claim partially reduces by construction to its own fitting residuals, warranting a score of 6.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The central claims rest on the Gaia-DR3 tie, the GP kernel hyperparameters, the PA-systematic assumption, and the empirical alpha_obs; no new physical entities are introduced.

free parameters (5)
  • GP kernel hyperparameters (sigma_0, tau) per star = fitted per star
    The squared-exponential and step kernels introduce an amplitude and timescale fitted to each star's residuals; these free parameters absorb correlated noise and directly affect the reported proper motion errors (Appendix B.3).
  • Confusion kernel length scale (ell) = fitted per star
    Spatial correlation kernel length used in poly+confusion models, selected for 2.6% of stars (Appendix B.4).
  • Additive error inflation = fitted per star
    The poly+add model inflates measurement uncertainties by a constant value; selected for 1.4% of stars (Appendix B).
  • Empirical scaling constant alpha_obs = approximately 2.4
    Used in Eq. 19 to predict Gaia-DR4 improvement in transformation uncertainty, derived by fitting current transformation errors (Section 5.2).
  • Second-order polynomial transformation coefficients (6 per epoch) = fitted per epoch
    They map HST pixel coordinates into Gaia-CRF3 for each of the 14 epochs; systematic errors in these coefficients propagate directly into the proper motions (Section 3.1, Eqs. 1-2).
assumptions (6)
  • domain assumption Gaia-DR3 astrometry is a valid realization of the ICRS toward the Galactic center, with no unmodeled large-scale systematics beyond those quoted in Gaia-CRF3 papers.
    The entire HST-Gaia frame inherits its ICRS alignment from the 40 Gaia-DR3 primary stars (Section 3.1); any local warp or bulk motion in Gaia-DR3 toward the GC is absorbed into the frame.
  • ad hoc to paper The position-angle-dependent systematic offset is constant in time and amplitude across the dataset, so a single GP kernel can absorb it without biasing proper motions.
    Appendix A, Figure 11, supports this via consistency of PA-separated proper motions, but the physical origin is unclear; if the systematic drifts, the PM model would be biased.
  • domain assumption Iterative 5-sigma outlier rejection on the primary reference stars and on 5.5% of astrometric measurements removes only corrupted measurements and does not bias the sample.
    Section 3.1 removes 10 of 50 candidate Gaia stars; Section 3.2 removes outlier epochs via LOO-CV. The retained sample is assumed unbiased after these cuts.
  • ad hoc to paper The second-order polynomial transformation fully captures the geometric distortion and reference-frame rotation across the 2'x2' HST field.
    Section 3.1 states first-order was insufficient and third-order gave no improvement; this is an empirical modeling choice that could leave residual spatial patterns in the PM.
  • standard math Standard Gaussian Process machinery (Rasmussen and Williams 2006) with the stated kernels and LOO-CV is applicable to sparsely sampled astrometric time series.
    The derivation in Appendix B assumes the marginal likelihood and LOO predictive equations hold for the HST epoch sampling (10-14 epochs per star).
  • domain assumption The ICRS position and proper motion of SgrA* from Xu et al. (2022) are accurate; alternative measurements differ mainly in position.
    Used to convert HST-Gaia to SgrA*-at-rest in Section 3.4; Appendix C shows the maser comparison is robust to this choice, but the absolute position offsets depend on it.

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Pith. "Pith review of The HST-Gaia Near-Infrared Astrometric Reference Frame near the Milky Way Galactic Center." pith.science (2026). https://pith.science/paper/VLB6LPQE

@misc{pith2026250619933,
  author       = {Pith},
  title        = {Pith review of: The HST-Gaia Near-Infrared Astrometric Reference Frame near the Milky Way Galactic Center},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VLB6LPQE}},
  note         = {Machine review of arXiv:2506.19933}
}
abstract

We present the first high-precision proper motion catalog, tied to the International Celestial Reference System (ICRS), of infrared astrometric reference stars within R $\leq$ 25" (1 pc) of the central supermassive black hole at the Galactic center (GC). This catalog contains $\sim$2,900 sources in a highly extinguished region that is inaccessible via Gaia. New astrometric measurements are extracted from HST observations (14 epochs, 2010 - 2023) and transformed into the ICRS using 40 stars in common with Gaia-DR3. We implement a new method for modeling proper motions via Gaussian Processes that accounts for systematic errors, greatly improving measurement accuracy. Proper motion and position measurements reach precisions of $\sim$0.03 mas/yr and $\sim$0.11 mas, respectively, representing a factor of $\sim$20x improvement over previous ICRS proper motion catalogs in the region. These measurements define a novel HST-Gaia reference frame that is consistent with Gaia-CRF3 to within 0.025 mas/yr in proper motion and 0.044 mas in position, making it the first ICRS-based reference frame precise enough to probe the distribution of extended mass within the orbits of stars near SgrA*. In addition, HST-Gaia provides an independent test of the radio measurements of stellar masers that form the basis of current GC reference frames. We find that the HST-Gaia and radio measurements are consistent to within 0.041 mas/yr in proper motion and 0.54 mas in position at 99.7% confidence. Gaia-DR4 is expected to reduce the HST-Gaia reference frame uncertainties by another factor of $\sim$2x, further improving the reference frame for dynamical studies.

Figures

Figures reproduced from arXiv: 2506.19933 by the authors.

Figure 1
Figure 1. The HST WFC3-IR field (red = F153M, green = F139M, blue = F127M), which is approximately centered on SgrA* (blue cross). The HST astrometry is transformed into Gaia-CRF3 using 40 primary reference stars found in the Gaia-DR3 catalog (green circles). We report HST-Gaia positions and proper motions for these sources as well as for 2823 secondary reference stars located in a 22”x22” region that overlaps ground-based AO… view at source ↗
Figure 2
Figure 2. The transformation errors (σtrans) for the HST-Gaia astrometry, which varies as a function of time and position. Left: Average σtrans as a function of time, which generally increases as the time from the Gaia-DR3 reference epoch (2016) increases. Right: σtrans as a function of position on the HST detector for the 2012 epoch (pixel scale = 1.21” pix−1 ) , with the positions of the Gaia reference stars shown by black … view at source ↗
Figure 3
Figure 3. An example application of the new kinematic models introduced in this paper to the proper motion of the star S3-374. The left panel shows the poly-only model fit while the right panel show the poly+sqexp model fit. For each panel, the top plot shows the model (red, with the shaded region showing the uncertainty) compared to the observed data (black points), with the corresponding ELPD of the model printed to the low… view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: The observed and expected distributions of χg2 loo for the astrometric reference stars presented in this paper, with α∗ on the left and δ on the right. In both cases, the observed distribution of the best-fit kinematic models (solid red histograms) peak at similar valu…
Figure 5
Figure 5. Figure 5: The differences between the the HST-Gaia and Gaia-DR3 proper motions (left) and positions (right) for the primary reference stars, which constrain the consistency between the HST-Gaia and Gaia-CRF3 coordinate systems. We find no evidence for systematic biases between t…
Figure 6
Figure 6. Figure 6: Average HST-Gaia proper motion errors (left) and reference epoch position errors (right) as a function of F153M magnitude for the sample of stars presented in this paper. Primary reference stars (from Gaia-DR3) are shown as blue diamonds, newly-created secondary refere…
Figure 7
Figure 7. Figure 7: Proper motion (left) and position (right) differences for the masers between the HST-Gaia and radio measurements in SgrA*-at-Rest coordinates (red points). We calculate an average offset of (-0.076 ± 0.030, -0.042 ± 0.028) mas yr−1 in the (µ s α∗, µ s δ ) proper motion…
Figure 8
Figure 8. Figure 8: The average proper motions errors (left) and reference epoch position errors (right) as a function of F153M magnitude for the 542 stars in common between the HST-Gaia and Sakai et al. (2019) reference star catalogs. The HST-Gaia measurements are shown by the red points…
Figure 9
Figure 9. Figure 9: The improvement in the proper motion precision of the HST-Gaia reference frame as a function of time, com￾pared to the requirements for various science cases at the GC. The black points correspond to the reference frame pre￾cision during the era of Gaia-DR2, the red po…
Figure 10
Figure 10. Figure 10: Systematic difference in HST astrometry measured at PA = -45◦ and PA = 134◦ epochs as a function of magnitude, in detector X and Y coordinates (left and right panels, respectively). The red line and shaded region shows the average and standard deviation of the positio…
Figure 11
Figure 11. Figure 11: The difference between proper motions measured from PA = -45◦ and PA = 134◦ epochs independently as a function of mag. The red and blue lines and corresponding shaded regions correspond to the average and standard deviation of the differences in the detector X and Y d…
Figure 12
Figure 12. Figure 12: The impact of choosing different ICRS positions and proper motions for SgrA* on the comparison between the HST-Gaia and radio measurements of the stellar masers near SgrA* (e.g. §4.2.3). The error-weighted mean difference in the maser proper motions (left) and positio…

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Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.