How to measure cosmic shear without drawing galaxy shapes

Weak gravitational lensing is the slight distortion of distant galaxies by the gravity of matter between them and us. Measuring this stretching across many galaxies can help astronomers map matter in the universe. The challenge is that the signal is subtle, while each galaxy’s own shape and the instrument’s response complicate the measurement.

Radio interferometers add a particular difficulty: they sample spatial-frequency information, called visibilities, rather than directly recording a conventional image. Reconstructing an image from those samples can introduce artefacts that affect shape measurements. In a preprint, Ezequiel Centofanti and colleagues propose working with the visibilities themselves instead.

Their method builds a forward model: it generates a candidate galaxy, applies a possible gravitational shear, and simulates how the radio interferometer would sample the result. The predicted visibilities are compared with the observations. By analysing multiple galaxies together, under the assumption that they share a common shear, the researchers use Monte Carlo sampling to estimate a probability distribution for the shear and its uncertainty.

The team tested the approach on simulated observations using an SKA-Mid antenna configuration. In one test, it simulated 10,000 galaxies with parametric profiles—mathematical shapes that the model could represent—and processed them in batches of 100. Under these matched conditions, the researchers report unbiased shear estimates with sub-percent accuracy. Compared with the DeepShape estimator in their study, their method produced uncertainties up to three times smaller and showed no apparent multiplicative bias, a systematic tendency to over- or understate the shear. The comparison used results supplied by the DeepShape team; the authors considered the different simulated profiles sufficiently similar for comparison, so it was not a fully matched reanalysis.

The researchers also tested whether the method’s reported uncertainties were reliable. In a coverage test, the empirical coverage was broadly consistent with the expected coverage, but lay somewhat below the ideal level. The authors note that more simulations are needed to investigate this difference.

A second test exposed a central challenge: the galaxy model must be realistic enough. The team adapted optical images of COSMOS galaxies into simulated radio-like observations. When it fitted these complex morphologies using the simpler parametric model, the shear estimate was biased by more than 10 standard deviations in that test. Modelling the instrument alone was not enough; the assumed galaxy shapes also mattered.

To address this mismatch, the researchers used a generative model based on an autoencoder trained on real COSMOS images. An autoencoder learns a compact representation of images and can reconstruct a range of galaxy forms. With this more flexible model, the bias in the same test fell below the 2-sigma level. This is evidence from a particular simulated setup, not a demonstration on actual radio weak-lensing observations: the galaxies began as optical images and were adapted to produce simulated radio data.

That distinction matters. The authors say suitable real radio observations—with enough resolution and galaxy density for this kind of analysis—are not yet available. Their simulations also simplify the observing situation: galaxies are treated individually rather than together across a full field, and the same instrumental response is used for each. The study does not account for effects including galaxy-detection selection, calibration errors, radio-frequency interference, frequency-dependent galaxy properties, or intrinsic alignments—correlations between galaxy orientations that can occur even without lensing. The authors identify these as issues for future work.

The flexible model is also computationally demanding. The team explored a faster maximum-a-posteriori point estimate, but this does not provide the same direct uncertainty information as sampling a full probability distribution. The authors say further tests are needed to establish whether the shortcut can introduce bias.

The preprint therefore presents a method and a set of simulated tests, not proof that radio weak lensing is ready for routine use. Its results highlight both the promise of modelling interferometer measurements directly and a key uncertainty: reliable shear estimates depend on how well the model represents real galaxy diversity. The findings should be treated as provisional pending further validation and review.