The Subversive Role of Excessive External Shear in Concealing Lensing Anomalies

The Hidden Variable Masking Dark Matter Clues

When scientists model how gravity bends light from distant quasars, they often add a "correction factor" called external shear. This accounts for the gravitational influence of nearby galaxies or cosmic structures. However, a new study suggests that if this factor is too large, it can hide errors in the model. This can make it look like there is no dark matter clutter when there actually is.

This phenomenon is critical. Astronomers use these "clutter" signals—known as flux ratio anomalies (discrepancies in the brightness of lensed images)—to hunt for dark matter sub-structures. Because the narrow-line regions (NLRs; large emitting regions of a quasar) are too large to be distorted by individual stars, any brightness discrepancy is a prime target for finding dark matter clumps. If external shear is used to "fix" the model's math, it might erase the evidence researchers seek.

The flaw in smooth mass models

To map dark matter, researchers rely on strong gravitational lensing. A massive foreground galaxy acts like a cosmic magnifying glass. It creates multiple images of a distant background object. Historically, lens models have used simple, smoothly varying mass profiles. These assume mass is distributed in a clean, predictable shape like an ellipse.

The problem arises when these smooth models fail to match reality. They can often predict where images appear, but they frequently fail to predict how bright they should be. These discrepancies, or flux ratio anomalies, led Nierenberg et al. (2019) to conclude that small-scale dark matter sub-halos (clumps of dark matter) must be present. These clumps tug on the light and alter its magnification.

The authors of this paper argue that current practices rely on a dangerous assumption. They suggest external shear is often used to force predicted image positions to match observations. The authors describe this practice as "subversive." It can artificially smooth over the very anomalies that indicate dark matter presence.

Testing the shear tradeoff

The researchers investigated seven multiply-lensed quasar systems. They focused on four relatively isolated galaxies .

These galaxies do not reside in obvious galaxy groups or clusters. They wanted to see if "errors" in current models were caused by dark matter or by adjusting the external shear.

The study used a systematic approach to separate variables:

1. Mass Profile Selection: The authors tested three mathematical descriptions of mass. These included the Singular Isothermal Ellipsoid (SIE), a general power law (POW), and the Navarro-Frenk-White (NFW) profile (a standard model for dark matter halos).
2. Morphological Freedom: They ran two sets of tests. First, the model's shape followed the visible light of the galaxy. Second, they let the dark matter shape be independent of the light. This accounts for cases where the dark matter halo is misaligned with the stars.
3. Constraint Variation: They compared models constrained only by image positions against those constrained by both positions and flux ratios.

By treating the strength and angle of external shear as free parameters, the authors saw how much "mathematical help" the model needed to fit the data.

Artificial precision through excessive shear

The results show that external shear is a powerful tool for masking discrepancies. The paper finds that when models are constrained only by image positions, adding external shear can lead to near-perfect agreement with observed positions. This happens even when shear strengths far exceed typical cosmic shear (the background stretching of space).

As shown in, for a system like WGDJ0405, a model without shear leaves large gaps between predicted and observed positions (blue bars).

Once external shear is applied (curly arrows), those gaps vanish.

Crucially, this excessive shear also partially alleviates flux ratio anomalies. Even when models must account for both positions and brightness, adding unconstrained external shear can reduce discrepancies. In some cases, these errors drop to the $\gtrsim 2\sigma$ level (a statistical threshold indicating the error is becoming less significant). The authors note that the shear strengths required for these isolated galaxies are suspiciously high. They overlap with the much higher values expected in dense galaxy clusters.

Limits of the simulation

The study has specific boundaries. The analysis covers seven systems from Nierenberg et al. (2019). Other systems were excluded because they had poorly defined flux ratios due to overlapping images.

The paper does not explore every possible combination of mass profiles and shear. It focuses on the most common parametric approaches. While the authors suggest these findings might apply to larger datasets, such as JWST warm-dust surveys, the current evidence uses a small sample of Hubble Space Telescope images. The study also identifies a degeneracy. This is a situation where different model settings produce identical results. This makes it hard to tell if the signal comes from the lens or the shear.

A warning for dark matter hunters

Current lens modeling practices may be inadvertently hiding the truth. Using excessive external shear to "clean up" models can create a false sense of agreement. This masks the existence of dark matter sub-structures.

For practitioners, the takeaway is a call for stricter constraints. External shear should not be a free parameter used to tune a model until it looks "right." Instead, it must be physically motivated by the actual environment. Without this, the quest to understand dark matter particles may rely on mathematical convenience rather than physical reality. Code for the models is available at https://github.com/romms921/SubversiveExternalShear.