Galaxy arcs sharpen models of double-image quasars

Why two images offer limited clues

A foreground galaxy can bend light from a distant quasar into multiple images. Because the light follows different paths through the galaxy’s gravitational field, changes in quasar brightness reach those images at different times. Combining these delays with a lens model can help estimate the Hubble constant, the Universe’s present-day expansion rate.

Previous TDCOSMO time-delay analyses have primarily relied on systems with four quasar images. Doubly imaged systems are more abundant but provide fewer geometric constraints. Ryan Brady and colleagues investigate the additional information supplied by the quasar’s host galaxy, whose extended light is stretched into arcs.

Their uniform analysis covers eight double-image systems. It provides groundwork for cosmology, not a new expansion-rate measurement or a resolution of the disagreement between existing Hubble-constant estimates.

A common modeling framework

The team used Hubble Space Telescope observations in three infrared and visible-light filters. The systems were selected because monitoring campaigns had already measured their time delays, although this paper does not combine those delays with the models to infer cosmological parameters.

Using the open-source Lenstronomy software, the researchers modeled the foreground galaxy’s mass and light, the compact quasar images, and extended host emission. Each main lens was represented by a singular isothermal ellipsoid: an elliptical mass distribution with a fixed radial density slope. An additional shear term described tidal distortions, while also potentially absorbing shortcomings in the assumed mass model.

The pipeline reconstructed and iteratively refined the telescope’s point-spread function—the pattern into which it spreads a point source’s light. Imperfect reconstruction can leave quasar residuals that interfere with nearby extended emission. The team jointly fitted the three bands and used Markov chain Monte Carlo sampling to estimate uncertainties. Some systems required additional components for a nearby galaxy or complex source structure.

Comparisons with models omitting the extended source favored including host emission in all eight systems, with Bayesian information criterion differences exceeding 300. This is evidence within the tested framework, not proof that reconstruction systematics have disappeared.

What the models recovered

Modeled Einstein radii, the characteristic angular scales of lensing deflection, differed from literature measurements by an average of 1.5 sigma. Excluding the largest outlier, J0407-5006, reduced that discrepancy to 0.92 sigma. The authors attribute differences to heterogeneous observations and modeling methods.

Modeled quasar-image separations differed from Gaia DR2 measurements by a root-mean-square 3.6 milliarcseconds. This calculation excludes J0407-5006, where one image lies only about 0.28 arcseconds from the lens galaxy, complicating deblending. J0602-4335 lacked Gaia comparison data. For that system, the paper reports its first lens-model measurements, including an Einstein radius of approximately 0.914 arcseconds and an image separation of 1.826 arcseconds.

The central result concerns the Fermat potential difference, which describes the combined geometric and gravitational contributions to the images’ different arrival times. Brighter arcs accompanied smaller fractional uncertainties in this modeled quantity. The reported correlation between arc magnitude and fractional uncertainty was 0.97, with a p-value of 0.0005. Larger magnitudes indicate fainter objects, so the positive correlation means fainter arcs accompanied poorer precision.

The brightest arc, in J1001+5027, yielded approximately 0.47% fractional statistical uncertainty; the faintest, in J1515+1511, yielded 2.99%. These are conditional lens-model uncertainties, not Hubble-constant uncertainties. Although the authors discuss surface-brightness information, the plotted brightness measure is integrated lensed-arc AB magnitude rather than brightness per unit angular area.

Testing what the arcs add

The researchers also constructed conjugate-point models, requiring the two quasar image positions to map back to a common source without reconstructing extended arcs. These fits used positions obtained from the full-image models, four-milliarcsecond positional uncertainties, and centroid constraints derived from the full-image results. They were not independent analyses of lower-resolution observations.

The position-based fits produced much broader allowed mass parameters, especially where ellipticity and shear could compensate for each other. Their Einstein radii nevertheless remained broadly consistent with full-image results.

Using covariance-matrix determinants as a proxy for posterior hypervolume, the authors report an average position-only to full-image ratio of approximately one billion. This is not a billion-fold improvement in any individual parameter or cosmological measurement. Greater compression accompanied brighter arcs, with a reported correlation of −0.87 and p-value of 0.005.

The comparison does not isolate arc light perfectly: full-image modeling also links mass and light through shared centroids and an orientation prior. The eight-system trend supports the value of resolved host emission, not a universal brightness-only rule.

Limits and publication status

The fixed radial mass slope is a major limitation. Freeing it would increase Fermat-potential uncertainty. Lensing images alone also cannot break the mass-sheet degeneracy, which allows different mass distributions to preserve image observables while changing inferred time-delay distances. This study does not sample that internal transformation freedom.

Some fits retain structured residuals. Photometric systematic floors were estimated from repeated fits to one representative system and applied across the sample; the authors describe them as approximate. A subsequent analysis is planned to incorporate time delays, stellar motions and greater mass-profile freedom before inferring the Hubble constant.

The study is published in the Open Journal of Astrophysics. The arXiv submission history confirms its original submission on April 27, 2026, at 18:40:35 UTC. The November 6 v4 revision corrects Fermat-potential signs for four systems in Table 3. Its results motivate deeper imaging of promising doubles for future cosmographic samples.