Varstrometry for Off-nucleus and Dual sub-Kpc AGN (VODKA): Methodology and Initial Results with Gaia DR2

Hsiang-Chih Hwang; Nadia Zakamska; Xin Liu; Yue Shen

REVIEW 4 major objections 6 minor 82 references

Varstrometry for Off-nucleus and Dual sub-Kpc AGN (VODKA): Methodology and Initial Results with Gaia DR2

T0 review · 4 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

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

Pith's one-line read Varstrometry turns quasar flicker into a black-hole-pair finder

desk verdict Useful methods paper with a correct analytic core and a genuinely useful extended-host systematic measurement, but the PMS validation of the Gaia excess-noise proxy is fragile and the candidate numbers are upper limits, not detections. read the letter →

arxiv 1908.02292 v1 pith:FF3RP4XT submitted 2019-08-06 astro-ph.GA

Hsiang-Chih Hwang , Yue Shen , Nadia Zakamska , Xin Liu This is my paper · ORCID

classification astro-ph.GA

keywords varstrometrydualactivegalacticnucleioff-nucleusAGNsupermassiveblackholebinariesGaiaastrometryastrometricexcessnoisephotocentervariabilityquasar

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

Varstrometry is the idea that when two unresolved sources, such as two active galactic nuclei (AGN) or one AGN offset from its host galaxy, vary in brightness out of phase, the combined photocenter shifts by milliarcseconds. The paper argues that Gaia's astrometry is precise enough to detect or constrain this jitter, turning the stochastic flicker of quasars into a systematic search for supermassive black hole pairs and off-nucleus AGN at separations of roughly 10 pc to 1 kpc, a range that resolved imaging surveys cannot cover. It derives the expected jitter for dual and off-nucleus configurations, validates the scaling on 13 unresolved pre-main-sequence binaries whose Gaia jitter tracks the predicted values, and uses Gaia DR2 catalog quantities to flag candidate sub-kpc dual or off-nucleus AGN among roughly 37,000 SDSS quasars at $0.5

What carries the argument

The named machinery is varstrometry, the photocenter wobble: for two unresolved components separated by $D$ with instantaneous flux ratio $q'\equiv f_2/f_1$, the photocenter sits at $d_{\rm astro}=(D/2)(q'-1)/(q'+1)$ along the pair axis. Because AGN vary stochastically and independently, this displacement executes bound, aperiodic motion and is linearly correlated with the total flux; its RMS for a dual AGN and for an off-nucleus single AGN is given by Eqns. (3) and (5). In Gaia DR2 the paper substitutes cataloged astrometric excess noise as an upper limit on this RMS and the G-band flux scatter as a proxy for photometric variability; the two proxies, together with the expected correlation of Eq. (4), carry the selection of sub-kpc candidates.

What would settle it

A decisive test: obtain diffraction-limited imaging (HST or VLBI) of SDSSJ000252.60-034345.1 at roughly 81 mas resolution spanning the 2014-2016 Gaia epoch; if no double source of comparable flux appears at the predicted 700 pc separation, the excess-noise-to-separation conversion fails. Alternatively, once epoch astrometry is available, check whether the photocenter of high-excess-noise quasars moves along a fixed axis and correlates with the G-band light curve as Eq. (4) requires; absence of that correlation means the excess is not varstrometry.

Watch

Extended reading notes

Core claim

The paper's central claim is that variability-induced photocenter jitter can be detected or constrained with catalog-level Gaia DR2 data, and that it provides a previously missing route to sub-kpc dual and off-nucleus AGN. For an equal-flux pair with projected separation $D$, the expected astrometric RMS is approximately $(D/2)$ times the fractional photometric variability, so a 10% variability yields jitter at 5% of the separation; the paper tests this relation on 13 Gaia-unresolved pre-main-sequence binaries in Taurus-Auriga, where cataloged astrometric excess noise broadly tracks the jitter expected from Eq. (3). Applied to spectroscopically confirmed SDSS quasars brighter than $G=19.5$ and at $z>0.5$, the method combines photometric variability with astrometric excess noise above a roughly 1 mas reliability floor, and it identifies several hundred sub-kpc dual or off-nucleus AGN candidates, including SDSSJ000252.60-034345.1 at $z=1.39$ whose 3.7 mas excess noise would imply an 81 mas, about 700 pc, projected separation for an equal-flux pair. The paper also shows that extended host galaxies with $R_{50}>1''$ inflate Gaia's photometric and astrometric noise to roughly 15% and 10 mas, which is why the selection is restricted to redshifts where host light is subdominant.

Load-bearing premise

The load-bearing premise is that Gaia's reported astrometric excess noise is a faithful upper limit on variability-induced photocenter jitter in the selected quasars, rather than being dominated by extended-host morphology, scan-angle systematics, or faint unresolved companions.

Editorial extensions

If this is right

A systematic census of sub-kpc dual and off-nucleus AGN becomes possible, filling the gap between about 10 pc and 1 kpc that current imaging surveys cannot fill.
Non-detections of jitter become upper limits on offset distances for the whole quasar sample, so the technique can statistically constrain the wandering and recoiling supermassive black hole populations predicted by simulations.
Once Gaia releases epoch astrometry and light curves, the predicted linear correlation between photocenter position and flux, with slope $D/2$, turns a candidate into a measured separation without additional imaging.
The same proxy selection can be extended from SDSS quasars to the all-sky WISE quasar sample, turning a demonstration into a full-sky candidate catalog.
For known test systems like CID-42, agreement between expected and measured jitter shows the method also applies to systems that Gaia catalogues as a single unresolved source.

Reading between the lines

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

If the roughly 1 mas excess-noise floor is partly instrumental, the inferred candidate fraction at $z>0.5$ should be read as an upper bound; matching a random subset against HST or VLBI imaging would calibrate the false-positive rate.
The photocenter-flux correlation predicted by Eq. (4) can be tested with Gaia's future epoch data alone, and it would separate true varstrometry from host-morphology systematics without follow-up imaging.
For small-separation lensed quasars, the time delay between images should produce the same jitter, so known lens systems could provide an independent validation and a way to measure image separations below Gaia's resolution.
Because the jitter formula applies to any unresolved variable binary, the method could also serve as a Galactic surveyor for pre-main-sequence binaries and triple systems, not only for extragalactic AGN.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Colleague,

Read VODKA. Bottom line: this is a useful methods paper, but the feasibility validation is weaker than the abstract implies, and the candidate numbers should be read as upper limits, not detections. The work is still worth refereeing.

What is new: the equations are not new—Wielen/Makarov-Goldin for stars, Shen/Liu for AGN—but this is the first systematic attempt to use Gaia DR2 to select unresolved sub-kpc dual or off-nucleus AGN via astrometric excess noise plus photometric variability. The empirical quantification of extended-host systematics (Fig. 5, R50 > 1 arcsec gives ~10 mas astrometric excess noise and ~15% photometric RMS) is genuinely useful and will matter for future Gaia work. The candidate examples and the follow-up strategy are sensible.

The analytic framework (Eqs. 1–5) is correct and clearly presented. I have no circularity concern: the Eq. 3 prediction uses literature separations and flux ratios plus Gaia photometric RMS against Gaia AEN as an independent benchmark, and the paper itself flags the covariance in Fig. 9.

Where it gets soft: the PMS validation in Fig. 6/Table 1 is the load-bearing test, and it is fragile. The correlation is carried largely by GG Tau and RX J0438.2+2023—the widest or multi-component systems where duplicity systematics rather than varstrometry can produce AEN. Dropping them leaves a marginal correlation. Also, the predictor axis uses Gaia photometric RMS from the same unresolved windows and the same 22-month baseline as the AEN, so shared window contamination can inflate both axes coherently; the paper acknowledges this covariance for quasars but does not control it in the PMS test. There are no AEN uncertainties, so "broadly consistent" is a weak claim. The small-separation systems that do show jitter (DF Tau, V827 Tau) individually disagree with the predicted values in opposite directions. So the calibration of the AEN proxy is not established.

The quasar candidate analysis inherits this: the 6% of ~37,000 z = 0.5–1.5 SDSS quasars with AEN > 1 mas and the 81 mas / 700 pc inference for SDSSJ000252.60−034345.1 are interesting, but they are uncalibrated upper limits until the AEN proxy is validated on an independent sample or with time series. The authors actually say most of this in Section 5, which is to their credit.

Who is this for? Anyone working on dual/binary SMBH populations, AGN variability, or Gaia astrometric systematics. It deserves a serious referee, but I would send it back for major revision on the validation rather than accept as is. The method is worth pursuing; the current proof-of-concept is not yet a measurement.

Referee Report

4 major / 6 minor

Summary. This paper introduces 'varstrometry,' a method to identify unresolved sub-kpc dual or off-nucleus AGN by detecting variability-induced astrometric jitter of the photocenter. The authors derive analytic scaling relations (Eqs. 1-5) between pair separation, flux ratio, photometric variability, and expected astrometric RMS; illustrate the signal with simulations; then test the idea on 13 pre-main-sequence binaries in Taurus-Auriga using Gaia DR2 astrometric excess noise (AEN) as a proxy for the intrinsic jitter. They characterize the impact of extended host galaxies on Gaia DR2 astrometry and photometry, present candidate sub-kpc dual/off-nucleus AGN and lensed quasars from spectroscopically confirmed SDSS quasars and WISE-selected samples, and discuss follow-up strategies. The central claim is that Gaia DR2 AEN, combined with photometric variability, can systematically identify and constrain sub-kpc AGN pairs, with a specific example of SDSSJ000252.60-034345.1 given a projected separation of 81 mas (700 pc).

Significance. If the feasibility claim is established, varstrometry would open a new, all-sky observational window on the poorly constrained sub-kpc separation regime of supermassive-black-hole pairs, complementing direct imaging and VLBI. The analytic derivation in Eqs. (1)-(5) is simple, correct, and parameter-free within its stated assumptions, and the paper is commendably transparent about Gaia DR2's limitations, explicitly noting that AEN is an upper limit and that time series are not yet available. The extended-host systematics study (Section 3.2) and the follow-up strategy (Section 5.2) are useful contributions. However, the feasibility validation on pre-main-sequence binaries is not yet robust enough to support the quantitative candidate statistics and separation inferences presented in Section 4.3.

major comments (4)

[Section 3.3, Fig. 6, Table 1] The validation of the AEN proxy is fragile. The 13-point correlation between expected and cataloged AEN is carried primarily by the two systems with the largest measured AEN: GG Tau (AEN 6.97 mas vs. expected 1.49 mas) and RX J0438.2+2023 (AEN 12.08 mas vs. expected 8.21 mas). A simple re-analysis of Table 1 gives a Spearman rank correlation of about 0.74 (p approximately 0.003), but after excluding these two systems the correlation drops to about 0.64 with p approximately 0.07, no longer significant at the 5% level. GG Tau is a known multiple system with a circumbinary disk, and RX J0438.2+2023 has a projected separation of 0.464 arcsec, near the paper's own 0.5 arcsec cutoff for PSF-deviation effects. The authors should report the correlation statistic with significance for the full sample and for the sample excluding these two objects, and should justify why GG Tau is not simply an outlier against the model.
[Section 3.3] No uncertainties are provided for the measured AEN values in Fig. 6. The text explicitly states that astrometric_excess_noise_sig cannot be converted to an uncertainty estimate for astrometric_excess_noise, and the figure therefore has error bars on the predicted axis only. As a result, the claim that the cataloged AEN is 'broadly consistent' with the expected jitter is not quantitatively testable. The authors should provide an empirical uncertainty or noise floor for AEN, for example from a matched control sample of single non-variable stars, and use it to assess the significance of the observed scatter and of individual candidate AEN values in Section 4.3.
[Sections 3.1 and 4.3] The AEN proxy is not independently calibrated for quasars. The extended-host systematics are measured for z<0.6 inactive galaxies (Fig. 5), and the argument that they are negligible for z>0.5 quasars is based on the absence of a high-AEN tail in Fig. 9 rather than on a control sample of point-like sources with expected negligible varstrometric signal. The specific inferences in Section 4.3 — that 6% of about 37,000 z=0.5-1.5 quasars with AEN>1 mas are candidates, and that SDSSJ000252.60-034345.1 has a projected separation of 81 mas (700 pc) — assume that AEN is dominated by varstrometric jitter. The authors should either validate this assumption with a matched control sample (e.g., non-variable point sources or radio-loud quasars with expected low jitter) or explicitly present these numbers as order-of-magnitude illustrations with a systematic floor.
[Section 3.3 and Eq. (3)] The prediction for the expected astrometric noise in the PMS test uses the Gaia DR2 photometric fractional variability f_G, measured from the same unresolved windows and the same 22-month baseline that also produce the astrometric excess noise. Shared window contamination and scanning-law systematics could therefore inflate the apparent correlation in Fig. 6. The paper acknowledges covariance between photometric and astrometric RMS for the quasar distribution (Fig. 9 caption) but not for the PMS validation. To strengthen the test, the expected AEN should be recomputed using independent photometric variability measurements from the literature light curves, or the covariance contribution should be estimated and subtracted.

minor comments (6)

[Throughout] The symbol '&' appears in place of '≥' or '≳' in several places (e.g., '& 1 kpc', '& mas', '& 2 mas'); please correct these rendering errors.
[Title and Abstract] The word 'off-nucleus' appears with a typographic ligature as 'oﬀ-nucleus'; please use a standard spelling.
[Table 2] Several entries in Table 2 report 'nan' for parallax over error; please clarify whether these are missing values or undefined measurements, and how the reader should interpret them.
[Fig. 6] The right-hand panel shows AEN versus separation but does not include error bars on the predicted axis; adding error bars and a correlation statistic would make the panel more informative.
[Section 4.2] The statement that category (1) is 'a clean quasar sample' is stronger than the presented evidence supports, since 3 of the 9 objects have astrometric excess noise > 1 mas and may be of interest for varstrometry; please rephrase to allow for this.
[References] The citation to 'Shen et al. 2019' appears as 'in prep' with placeholder arXiv number (arXiv:xxxx.xxxx); please provide a complete reference or remove the placeholder.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the varstrometry formalism is derived from the flux-weighted photocenter definition, and the feasibility check compares an unfitted prediction with Gaia DR2 astrometric excess noise.

full rationale

The derivation chain is self-contained. Equations (1)-(5) follow algebraically from the definition of the photocenter as the center of flux of an unresolved pair, with no fitted parameters and no use of the target result as an input. The feasibility demonstration in Section 3.3 computes an expected astrometric jitter from Equation (3) using literature separations and flux ratios plus Gaia DR2 photometric RMS, and compares it with the cataloged astrometric excess noise, an externally measured quantity. No parameter is fitted to the astrometric excess noise to produce the prediction; the comparison is a genuine, if approximate, external benchmark. The paper's self-citations (Shen 2012, Liu 2015, and the companion Shen et al. 2019) motivate the idea and describe follow-up population constraints, but they are not load-bearing for the equations or the DR2 validation: the formalism is re-derived here and the PMS test uses independent literature data. The quasar candidate selections in Sections 4.2-4.4 are explicitly presented as provisional candidates or upper limits, with the paper acknowledging that astrometric excess noise may be contaminated by extended hosts, faint companions, or systematics; this is a caveat about interpretation, not a circular reduction of the prediction to its inputs. The fragility of the Fig. 6 validation noted by skeptics concerns statistical robustness and possible duplicity systematics, but does not amount to the predicted quantity being defined in terms of the measured quantity. No circular step meeting the required standard of exhibiting a specific reduction is present.

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

No free parameters are fitted to the central claim. The method depends on the stated astrophysical assumptions and on Gaia DR2 quality indicators as proxies; the proxy assumption is the most fragile, and the paper partly mitigates it by restricting to high redshift and bright magnitudes.

assumptions (5)

domain assumption AGN vary stochastically with typical RMS amplitudes of about 0.1-0.2 mag on days-to-years timescales.
Assumed throughout section 2; based on literature (Sesar et al. 2007) and used to derive expected photometric variability. If most AGN do not vary on Gaia timescales, varstrometry signals would be negligible.
domain assumption The two AGN components are spatially fixed over the Gaia DR2 observing baseline (2014-2016), so photocenter motion is due to flux variability, not orbital motion.
Stated in section 1: 'the positions of the two AGN are essentially fixed given the long (much greater than 100 yr) dynamical timescale of the pair.' Orbital motion would contaminate the signal but is negligible for sub-kpc separations.
domain assumption Astrometric excess noise from Gaia DR2 provides an upper limit on the intrinsic astrometric RMS of the photocenter.
Adopted in section 3.1: 'we use astrometric excess noise as a proxy (upper limit) for the intrinsic astrometric RMS in photocenter.' If excess noise is dominated by systematics unrelated to source variability, the candidate selection is invalid.
standard math Taylor expansion to leading order in fractional flux variation, with statistically independent variability between the two components.
Used to derive Eqs. (1)-(3) in section 2.1. Requires small fractional flux variations and independent, stochastic variability.
domain assumption Gaia DR2 photometric errors follow phot_g_mean_flux_error = sigma_G / sqrt(n_obs), so sigma_G reflects intrinsic variability after subtracting instrumental noise.
Used in section 3.1 to build the fG proxy; relies on the Gaia DR2 error model and the running-median instrumental calibration from nearby stars.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Varstrometry for Off-nucleus and Dual sub-Kpc AGN (VODKA): Methodology and Initial Results with Gaia DR2." pith.science (2026). https://pith.science/paper/FF3RP4XT

@misc{pith2026190802292,
  author       = {Pith},
  title        = {Pith review of: Varstrometry for Off-nucleus and Dual sub-Kpc AGN (VODKA): Methodology and Initial Results with Gaia DR2},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FF3RP4XT}},
  note         = {Machine review of arXiv:1908.02292}
}

abstract

Gaia's milli-arcsec (mas) astrometric precision allows systematic identification of optically-selected sub-kpc dual active galactic nuclei (AGN), off-nucleus AGN, and small-scale lensed quasars by `varstrometry' -- where variability-induced astrometric jitter, i.e., temporal displacements of photocenter in unresolved sources, can be reasonably well detected or constrained. This approach extends systematic searches for small-scale ($\gtrsim$ mas) dual and off-nucleus AGN to poorly explored regime between $\sim 10$ pc and $\sim 1$ kpc, with Gaia's full sky coverage and depth to $G\sim 21$. We outline the general principles of this method and calculate the expected astrometric signals from the full time series of photocenter measurements and light curves. We demonstrate the feasibility of varstrometry by using Gaia DR2 data on a sample of variable pre-main sequence stars with known close companions. We find that extended host galaxies have a significant impact on the accuracy of astrometric and photometric variability in Gaia DR2, a situation to be improved in future Gaia releases. Using spectroscopically confirmed SDSS quasars, we present several examples of candidate sub-kpc off-nucleus or dual AGN selected from Gaia DR2. We discuss the merits and limitations of this method and follow-up strategy for promising candidates. We highlight Gaia's potential of systematically discovering and characterizing the sub-kpc off-nucleus and dual AGN population in the entire optical sky.

Figures

Figures reproduced from arXiv: 1908.02292 by the authors.

**Figure 1.** Physical and angular scales around a 108 M SMBH accreting at a typical Eddington ratio of 0.1 at z = 1. The four vertical line segments mark the location of 100 gravitational radii (rg), the typical distance of the broad-line region (BLR), the typical distance of the dust torus, and the sphere of influence (SOI) of the BH. There are more than a few tens confirmed dual AGN with separations greater than ∼ 1 kpc. The… view at source ↗

**Figure 2.** Examples of simulated photocenter and flux variations for an AGN offset from its host galaxy. In this mock observation, we generate light profiles for the AGN assuming a point source, and for the galaxy assuming a S´ersic profile (with a S´ersic index n = 4 and an effective radius of 10 pixels). The pixel scale of the mock imaging is 0.1”. We assume a doubleGaussian PSF with the core Gaussian σ = 2 pixels and the s… view at source ↗

**Figure 3.** Linear regression between the photocenter shift and the flux ratio measured from each epoch, using the Bayesian regression method in Kelly (2007). The two panels correspond to the two examples shown in [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Figures from the paper (13 more)

**Figure 4.** Figure 4: Distribution of SDSS quasars in the fractional photometric RMS and redshift plane, color-coded by the number of objects. The photometric RMS is estimated using the Gaia DR2 flux errors as described in §3.1. The trend of decreasing photometric variability with redshift…

**Figure 5.** Figure 5: The fractional photometric RMS variability (left) and the astrometric excess noise (right) with respect to the Petrosian radius R50 in r-band for star-forming galaxies. The black markers show the running median in each bin, and the x-axis bars indicate the range of the…

**Figure 6.** Figure 6: The comparison between the cataloged astrometric excess noise and the expected astrometric noise from Eqn 3 (left) and the separation from companions (right) for unresolved pre-main sequence binaries in the Taurus-Auriga star-forming region. The cataloged astrometric e…

**Figure 7.** Figure 7: Left: fractional photometric variability versus total proper motion for SDSS quasars that have two Gaia matches within 300. For sources where the photometric RMS is below the instrumental level, we place them below the dashed line with some small random vertical offset…

**Figure 8.** Figure 8: The HSC i-band image (left panel; north/east is up/left) and SDSS spectrum (right) of SDSSJ000710.01+005329.0, a quasar at z = 0.32. Gaia DR2 detects two sources separated by 0.7900 in the source, coincident with the two cores visible in the HSC image. There is also a …

**Figure 9.** Figure 9: Gaia astrometric excess noise versus photometric variability for spectroscopic SDSS quasars in three redshift ranges. There is a tail extending to high astrometric excess noise in the sample of z < 0.5. The tail is caused by extended host galaxies at lower redshifts an…

**Figure 10.** Figure 10: The Pan-STARRS i-band optical image (north/east is up/left) and SDSS spectrum of SDSSJ112101.30+080926.3, a quasar (centered in the image) that has an astrometric excess noise of 2.9 mas at z = 0.51. The i-band image shows some faint companions around the quasar, one …

**Figure 11.** Figure 11: The Pan-STARRS i-band optical image (north/east is up/left) and SDSS spectrum (right) of SDSSJ000252.60−034345.1, a quasar (centered in the image) that has an astrometric excess noise of 3.7 mas at z = 1.39. No source is strongly detected within 20 arcsec around the q…

**Figure 12.** Figure 12: The radio detection fraction for WISE-selected quasars that are classified as point source in Pan-STARRS and are within the FIRST footprint. Compared to [PITH_FULL_IMAGE:figures/full_fig_p017_12.png]

**Figure 13.** Figure 13: Pan-STARRS 1 color-composite images (left) and SDSS spectra (right) for genuine quasars with non-zero parallaxes from Gaia DR2. The red dots in the Pan-STARRS images are the Gaia detections at the J2015.5 epoch. Images have 1000 on each side, and north (east) is up (l…

**Figure 14.** Figure 14: Same as [PITH_FULL_IMAGE:figures/full_fig_p024_14.png]

**Figure 15.** Figure 15: Pan-STARRS 1 color-composite images (left) and SDSS spectra (right) for genuine quasars with non-zero proper motions from Gaia DR2. The red dots in the Pan-STARRS images are the Gaia detections at the J2015.5 epoch. Images have 1000 on each side, and north (east) is u…

**Figure 16.** Figure 16: Same as [PITH_FULL_IMAGE:figures/full_fig_p026_16.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

82 extracted references · 57 canonical work pages

[1]

2019, arXiv e-prints, arXiv:1905.12221

Aihara, H., AlSayyad, Y., Ando, M., et al. 2019, arXiv e-prints, arXiv:1905.12221

arXiv 2019
[2]

2018, A&A, 616, A17

Arenou, F., Luri, X., Babusiaux, C., et al. 2018, A&A, 616, A17

2018
[3]

1998, MNRAS, 301, 161

Bailey, J. 1998, MNRAS, 301, 161

1998
[4]

G., Centrella, J., Choi, D.-I., et al

Baker, J. G., Centrella, J., Choi, D.-I., et al. 2006, ApJL, 653, L93

work page 2006
[5]

A., Phillips, M

Baldwin, J. A., Phillips, M. M., & Terlevich, R. 1981, PASP, 93, 5

1981
[6]

Romani, R. W. 2017, ApJ, 843, 14

work page 2017
[7]

S., Comerford, J

Barrows, R. S., Comerford, J. M., Greene, J. E., & Pooley, D. 2017, ApJ, 838, 129

work page 2017
[8]

J., Bentz, M

Barth, A. J., Bentz, M. C., Greene, J. E., & Ho, L. C. 2008, ApJL, 683, L119

work page 2008

Show all 82 references

[9]

H., White, R

Becker, R. H., White, R. L., & Helfand, D. J. 1995, ApJ, 450, 559

1995
[10]

C., Blandford, R

Begelman, M. C., Blandford, R. D., & Rees, M. J. 1980, Nature, 287, 307

1980
[11]

J., et al

Belokurov, V., Erkal, D., Deason, A. J., et al. 2017, MNRAS, 466, 4711

2017
[12]

A., & Evans, N

Belokurov, V. A., & Evans, N. W. 2002, MNRAS, 331, 649

2002
[13]

H., & Socrates, A

Blaes, O., Lee, M. H., & Socrates, A. 2002, ApJ, 578, 775

2002
[14]

D., & Narayan, R

Blandford, R. D., & Narayan, R. 1992, ARA&A, 30, 311

1992
[15]

Z., et al

Blecha, L., Sijacki, D., Kelley, L. Z., et al. 2016, MNRAS, 456, 961 Bogdanovi´ c, T. 2015, Astrophysics and Space Science Proceedings, 40, 103 Bogdanovi´ c, T., Reynolds, C. S., & Miller, M. C. 2007, ApJL, 661, L147

2016
[16]

2011, MNRAS, 410, 2113

Burke-Spolaor, S. 2011, MNRAS, 410, 2113

2011
[17]

G., Kelly, B

Centrella, J., Baker, J. G., Kelly, B. J., & van Meter, J. R. 2010, Reviews of Modern Physics, 82, 3069

2010
[18]

C., Magnier, E

Chambers, K. C., Magnier, E. A., Metcalfe, N., et al. 2016, arXiv e-prints, arXiv:1612.05560

2016 arXiv
[19]

2010, ApJ, 717, 209 —

Civano, F., Elvis, M., Lanzuisi, G., et al. 2010, ApJ, 717, 209 —. 2012, ApJ, 752, 49

2010
[20]

J., Strauss, M

Collinge, M. J., Strauss, M. A., Hall, P. B., et al. 2005, AJ, 129, 2542

2005
[21]

2011, Advanced Science Letters, 4, 181

Colpi, M., & Dotti, M. 2011, Advanced Science Letters, 4, 181

2011
[22]

M., & Greene, J

Comerford, J. M., & Greene, J. E. 2014, ApJ, 789, 112

2014
[23]

M., Pooley, D., Barrows, R

Comerford, J. M., Pooley, D., Barrows, R. S., et al. 2015, ApJ, 806, 219

2015
[24]

T., Neilsen, E., Gruendl, R., et al

Diehl, H. T., Neilsen, E., Gruendl, R., et al. 2016, in Proc. SPIE, Vol. 9910, Observatory Operations:

2016
[25]

2017, ApJ, 840, 31

Dosopoulou, F., & Antonini, F. 2017, ApJ, 840, 31

2017
[26]

2012, Advances in Astronomy, 2012, arXiv:1111.0664

Dotti, M., Sesana, A., & Decarli, R. 2012, Advances in Astronomy, 2012, arXiv:1111.0664

2012 arXiv
[27]

2018, ArXiv e-prints 1805.07359, arXiv:1805.07359

Ducourant, C., Wertz, O., Krone-Martins, A., et al. 2018, ArXiv e-prints 1805.07359, arXiv:1805.07359

2018 arXiv
[28]

Eracleous, M., & Halpern, J. P. 1994, ApJS, 90, 1

1994
[29]

W., Riello, M., De Angeli, F., et al

Evans, D. W., Riello, M., De Angeli, F., et al. 2018, A&A, 616, A4 Event Horizon Telescope Collaboration, Akiyama, K.,

2018
[30]

2019, ApJ, 875, L2

Alberdi, A., et al. 2019, ApJ, 875, L2

2019
[31]

D., et al

Fu, H., Yan, L., Myers, A. D., et al. 2012, ApJ, 745, 67 Gaia Collaboration, Prusti, T., de Bruijne, J. H. J., et al. 2016, A&A, 595, doi:10.1051/0004-6361/201629272 Gaia Collaboration, Brown, A. G. A., Vallenari, A., et al. 2018a, A&A, 616, A1 Gaia Collaboration, Mignard, F.,...

2012 doi
[32]

M., Neugebauer, G., & Matthews, K

Ghez, A. M., Neugebauer, G., & Matthews, K. 1993, AJ, 106, 2005

1993
[33]

M., White, R

Ghez, A. M., White, R. J., & Simon, M. 1997, ApJ, 490, 353

1997
[34]

2000, ApJL, 532, L29

Gould, A., & Rix, H.-W. 2000, ApJL, 532, L29

2000
[35]

D., Pardo, K., Greene, J

Goulding, A. D., Pardo, K., Greene, J. E., et al. 2019, arXiv e-prints, arXiv:1907.03757 Gravity Collaboration, Sturm, E., Dexter, J., et al. 2018, Nature, 563, 657

2019 arXiv
[36]

Haehnelt, M. G. 1994, MNRAS, 269, 199

1994
[37]

2000, Physical Review Letters, 85, 1158

Hu, W., Barkana, R., & Gruzinov, A. 2000, Physical Review Letters, 85, 1158

2000
[38]

Hughes, S. A. 2009, ARA&A, 47, 107

2009
[39]

P., Tremaine, S., & Witten, E

Hui, L., Ostriker, J. P., Tremaine, S., & Witten, E. 2017, PhRvD, 95, 043541 Jaﬀe, A. H., & Backer, D. C. 2003, ApJ, 583, 616 Kauﬀmann, G., Heckman, T. M., Tremonti, C., et al. 2003, MNRAS, 346, 1055

2017
[40]

Z., Blecha, L., & Hernquist, L

Kelley, L. Z., Blecha, L., & Hernquist, L. 2017, MNRAS, 464, 3131

2017
[41]

Kelly, B. C. 2007, ApJ, 665, 1489 20 Hwang et al

2007
[42]

J., Dopita, M

Kewley, L. J., Dopita, M. A., Sutherland, R. S., Heisler, C. A., & Trevena, J. 2001, ApJ, 556, 121

2001
[43]

M., Holley-Bockelmann, K., Berczik, P., & Just, A

Khan, F. M., Holley-Bockelmann, K., Berczik, P., & Just, A. 2013, ApJ, 773, 100

2013
[44]

1998, A&A, 331, 977

Kohler, R., & Leinert, C. 1998, A&A, 331, 977

1998
[45]

2003, ApJL, 582, L15

Komossa, S., Burwitz, V., Hasinger, G., et al. 2003, ApJL, 582, L15

2003
[46]

J., Shaya, E

Kristian, J., Groth, E. J., Shaya, E. J., et al. 1993, AJ, 106, 1330

1993
[47]

1993, A&A, 278, 129

Leinert, C., Zinnecker, H., Weitzel, N., et al. 1993, A&A, 278, 129

1993
[48]

Koposov, S. E. 2017, MNRAS, 472, 5023

2017
[49]

1978, in IAU Colloq

Lindegren, L. 1978, in IAU Colloq. 48: Modern Astrometry, ed. F. V. Prochazka & R. H. Tucker, 197–217

1978
[50]

2012, A&A, 538, A78

Lindegren, L., Lammers, U., Hobbs, D., et al. 2012, A&A, 538, A78

2012
[51]

2018, A&A, 616, A2

Lindegren, L., Hern´ andez, J., Bombrun, A., et al. 2018, A&A, 616, A2

2018
[52]

E., Shen, Y., & Strauss, M

Liu, X., Greene, J. E., Shen, Y., & Strauss, M. A. 2010, ApJL, 715, L30

2010
[53]

E., & Strauss, M

Liu, X., Guo, H., Shen, Y., Greene, J. E., & Strauss, M. A. 2018, ApJ, 862, 29

2018
[54]

2015, A&A, 580, A133 —

Liu, Y. 2015, A&A, 580, A133 —. 2016, A&A, 592, L4

2015
[55]

L., Ivezi´ c,ˇZ., Sesar, B., et al

MacLeod, C. L., Ivezi´ c,ˇZ., Sesar, B., et al. 2012, ApJ, 753, 106

2012
[56]

1988, Nature, 334, 325

Kayser, R. 1988, Nature, 334, 325

1988
[57]

V., & Goldin, A

Makarov, V. V., & Goldin, A. 2016, ApJS, 224, 19

2016
[58]

J., et al

Mateos, S., Alonso-Herrero, A., Carrera, F. J., et al. 2012, MNRAS, 426, 3271

2012
[59]

2013, Dynamics and Evolution of Galactic

Merritt, D. 2013, Dynamics and Evolution of Galactic

2013
[60]

2001, ApJ, 563, 34 M¨ uller-S´ anchez, F., Comerford, J., Stern, D., & Harrison, F

Nuclei, Princeton Series in Astrophysics (Princeton University Press) Milosavljevi´ c, M., & Merritt, D. 2001, ApJ, 563, 34 M¨ uller-S´ anchez, F., Comerford, J., Stern, D., & Harrison, F. A. 2016, ApJ, 830, 50

2001
[61]

2012, ApJ, 745, 119 Pˆ aris, I., Petitjean, P., Aubourg,´E., et al

Jayawardhana, R. 2012, ApJ, 745, 119 Pˆ aris, I., Petitjean, P., Aubourg,´E., et al. 2018, A&A, 613, A51

2012
[62]

B., Zavala, R

Rodriguez, C., Taylor, G. B., Zavala, R. T., et al. 2006, ApJ, 646, 49

2006
[63]

J., Dudik, R

Secrest, N. J., Dudik, R. P., Dorland, B. N., et al. 2015, ApJS, 221, 12

2015
[64]

H., et al

Sesar, B., Ivezi´ c,ˇZ., Lupton, R. H., et al. 2007, AJ, 134, 2236

2007
[65]

C., Zakamska, N., & Liu, X

Shen, Y., Hwang, H. C., Zakamska, N., & Liu, X. 2019, ApJ, submitted, arXiv:xxxx.xxxx

2019
[66]

M., Leinert, C., et al

Simon, M., Ghez, A. M., Leinert, C., et al. 1995, ApJ, 443, 625

1995
[67]

K., Dolag, K., Comerford, J

Steinborn, L. K., Dolag, K., Comerford, J. M., et al. 2016, MNRAS, 458, 1013

2016
[68]

F., & Pott, J.-U

Stern, J., Hennawi, J. F., & Pott, J.-U. 2015, ApJ, 804, 57

2015
[69]

V., Strauss, M

Strateva, I. V., Strauss, M. A., Hao, L., et al. 2003, AJ, 126, 1720

2003
[70]

2013, MNRAS, 431, 1383

Thomas, D., Steele, O., Maraston, C., et al. 2013, MNRAS, 431, 1383

2013
[71]

R., & Pontzen, A

Tremmel, M., Governato, F., Volonteri, M., Quinn, T. R., & Pontzen, A. 2018, MNRAS, 475, 4967

2018
[72]

2018, Frontiers in Astronomy and Space Sciences, 5, 11 Vanden Berk, D

Vallenari, A. 2018, Frontiers in Astronomy and Space Sciences, 5, 11 Vanden Berk, D. E., Wilhite, B. C., Kron, R. G., et al. 2004, ApJ, 601, 692

2018
[73]

2016, IAU Focus Meeting, 29, 285

Volonteri, M., Bogdanovi´ c, T., Dotti, M., & Colpi, M. 2016, IAU Focus Meeting, 29, 285

2016
[74]

2003, ApJ, 582, 559

Volonteri, M., Haardt, F., & Madau, P. 2003, ApJ, 582, 559

2003
[75]

J., Latham, D., Angel, J

Weymann, R. J., Latham, D., Angel, J. R. P., et al. 1980, Nature, 285, 641

1980
[76]

L., Becker, R

White, R. L., Becker, R. H., Helfand, D. J., & Gregg, M. D. 1997, ApJ, 475, 479

1997
[77]

1996, A&A, 314, 679

Wielen, R. 1996, A&A, 314, 679

1996
[78]

L., Eisenhardt, P

Wright, E. L., Eisenhardt, P. R. M., Mainzer, A. K., et al. 2010, AJ, 140, 1868

2010
[79]

1981, ApJ, 244, 723

Kristian, J. 1981, ApJ, 244, 723

1981
[80]

2011, ApJ, 738, 92

Yu, Q., Lu, Y., Mohayaee, R., & Colin, J. 2011, ApJ, 738, 92

2011
[81]

A., & Zakamska, N

Yuan, S., Strauss, M. A., & Zakamska, N. L. 2016, MNRAS, 462, 1603

2016
[82]

L., & Greene, J

Zakamska, N. L., & Greene, J. E. 2014, MNRAS, 442, 784 VODKA: Methodology 21 T able 2. List of genuine quasars that have signiﬁcant non-zero parallaxes from Gaia DR2. Positions are also from Gaia DR2 and have precisions of∼ 0.04 mas. Some SDSS quasars have two Gaia matches wit...

2014

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

2019, arXiv e-prints, arXiv:1905.12221

Aihara, H., AlSayyad, Y., Ando, M., et al. 2019, arXiv e-prints, arXiv:1905.12221

arXiv 2019

[2] [2]

2018, A&A, 616, A17

Arenou, F., Luri, X., Babusiaux, C., et al. 2018, A&A, 616, A17

2018

[3] [3]

1998, MNRAS, 301, 161

Bailey, J. 1998, MNRAS, 301, 161

1998

[4] [4]

G., Centrella, J., Choi, D.-I., et al

Baker, J. G., Centrella, J., Choi, D.-I., et al. 2006, ApJL, 653, L93

work page 2006

[5] [5]

A., Phillips, M

Baldwin, J. A., Phillips, M. M., & Terlevich, R. 1981, PASP, 93, 5

1981

[6] [6]

Romani, R. W. 2017, ApJ, 843, 14

work page 2017

[7] [7]

S., Comerford, J

Barrows, R. S., Comerford, J. M., Greene, J. E., & Pooley, D. 2017, ApJ, 838, 129

work page 2017

[8] [8]

J., Bentz, M

Barth, A. J., Bentz, M. C., Greene, J. E., & Ho, L. C. 2008, ApJL, 683, L119

work page 2008