Double gravitational lenses offer a new handle on hidden galaxy mass

Daniel P. Johnson and colleagues explore this opportunity in an arXiv preprint, Lessons from double-plane lenses for galaxy profiles, the Hubble tension, and the mass-sheet degeneracy. The supplied version does not establish that the work has completed peer review. Its central result is a method for constraining an important ambiguity, not a new measurement of the Hubble constant or a resolution of the Hubble tension.

Why convincing images can conceal uncertain mass

Gravitational-lens images do not uniquely reveal the mass distribution that produced them. Rescaling a lens’s projected mass profile and adding a uniform, sheet-like contribution can preserve image positions and relative magnifications. This is the mass-sheet degeneracy.

An infinite sheet is not a realistic galaxy component. However, an extended distribution that is nearly uniform over the region crossed by the observed light can approximately reproduce its effect. Here, the sheet parameter describes departures from an adopted reference mass profile; it is not a direct detection of a separate physical sheet.

The ambiguity matters for cosmic expansion. When a variable source produces multiple images, its brightness changes reach us at different times. These delays, combined with a lens model, can constrain the Hubble constant, H₀. But mass-sheet transformations rescale the predicted delays, changing the inferred H₀ without spoiling the image fit.

Two source distances supply another constraint

Double-plane systems contain additional geometric information, expressed through a distance ratio called η. Unlike the distances entering time-delay measurements, this ratio does not depend on H₀. It does depend on the universe’s relative expansion history and on matter along the light’s path.

The researchers compare the ratio inferred from lens images with a reference prediction. For their examples, that prediction uses a spatially flat cosmological model containing cold dark matter and a cosmological constant, with a matter-density constraint from Planck observations. Simulations estimate the additional uncertainty from intervening matter.

This comparison constrains a particular combination of the mass-sheet contributions in the two lens planes. It does not determine each contribution separately. Separating them requires more information or assumptions, such as stellar-motion measurements or a justified relationship between the galaxies’ mass profiles. The imaging-based combination itself needs neither time delays nor an assumed H₀.

Three examples, with an important warning

For J1721+8842, the “Einstein zig-zag” lens, the team measured the positions of six quasar images in Hubble Space Telescope observations. They fitted a foreground power-law mass model and a simpler isothermal model for the second deflector, keeping four nearby perturbing galaxies fixed. They obtained η = 1.0166 ± 0.0011 from the model.

But this precision has a major qualification. The fit allowed a positional uncertainty of 2 milliarcseconds for small-scale gravitational perturbations. A subsequent simulation estimated a substantially larger disturbance in the reconstructed source position, about 9.1 milliarcseconds. Using that allowance left η effectively unconstrained. The authors therefore explicitly present their tighter result as a proof of concept. Modelling the extended arcs, omitted from this exploratory analysis, is needed for stronger conclusions.

For the “Jackpot” lens J0946+1006 and AGEL0353, the researchers reused published distance-ratio measurements. Relative to the adopted power-law reference profiles, the inferred combined sheet parameter was approximately +0.052 and −0.191, respectively. Across the three examples, departures from both lenses being power laws were only mildly favoured, at roughly one to two standard deviations—not decisive evidence against those profiles.

The intervening-matter estimates also used random simulated sightlines rather than observations tailored to each system. They capture a spread of possibilities but not a systematic shift caused by a particular overdense or underdense environment.

Promise depends on the assumptions

Forecasts using 1,729 Euclid and 87 LSST double-plane systems suggest that large samples could tightly constrain the population of mass-profile departures. These are simulated samples, not reported discoveries. The forecasts assume either a shared Gaussian population for the two lens planes or a negligible sheet contribution in the second plane. The authors caution that neither assumption is currently robust.

For hypothetical systems with measurable time delays, the extra source could reduce H₀ uncertainty by as much as about 50% under the stated assumptions. That means smaller error bars, not a 50% change in H₀. Most forecast systems would not necessarily provide measurable delays.

The opportunity is therefore conditional but useful: double-plane lenses can expose combinations of mass-model uncertainties that single-plane images cannot, helping test the assumptions behind future measurements of cosmic expansion.