Why a denser dark matter core can become a weaker gravitational lens

Gravitational lensing bends light from a background object, sometimes producing enlarged images, arcs or rings. Because the bending depends on mass, astronomers use these distortions to investigate dark matter. Some inferred lenses appear unusually concentrated, prompting suggestions that they contain self-interacting dark matter whose central regions have collapsed.

A new preprint by Frank C. van den Bosch and Yarone M. Tokayer examines a hidden assumption in that explanation: does continued central compression necessarily make a stronger lens? Their calculations say no. The study, arXiv:2611.09546v1, was submitted on 6 November 2026 and is listed as submitted for publication in MNRAS; its findings remain preprint results.

Following a changing halo

Self-interacting dark matter, or SIDM, is a proposed form of dark matter whose particles scatter off one another. Those interactions redistribute heat. Initially, they can produce a broad, relatively uniform-density centre. Later, outward heat transport allows the centre to contract and grow denser, a process called gravothermal core collapse.

The researchers modelled this evolution by treating an isolated, spherical halo as a heat-conducting fluid. Their calculations began with a Navarro–Frenk–White, or NFW, density profile, a standard description of dark matter haloes. They ran one reference halo with 29 different interaction strengths, then built an emulator that rescales and interpolates those calculations for other halo properties.

Adaptive radial resolution let the fluid calculations follow very dense stages where particles travel only short distances between collisions. In two validation examples, the emulator reproduced the fluid model’s density profiles with time-weighted root-mean-square errors of about 0.15–0.22%, although maximum local discrepancies reached several percent. That agreement tests the emulator against its underlying model, not the model against nature.

The team then calculated how each evolving mass distribution would bend and magnify an extended background source. They also measured the areas of possible source positions that would yield high magnification or sufficiently bright multiple images. Some calculations included an external gravitational stretching effect, called shear.

Compression has diminishing returns

The typical sequence was a decline in magnification during core formation, a rise during early collapse, and another decline during advanced collapse—even as central density kept increasing.

One illustrative configuration magnified its source about sevenfold initially, dropped to roughly threefold during core formation, and peaked near 49-fold early in collapse. By four billion years of model evolution, its magnification was below the starting value despite an enormously denser centre. These are stages of a calculation, not changes observed in a real lens; the evolution is too slow to watch in an individual system.

The explanation is structural. Advanced collapse produces a small, dense inner core inside a broader, lower-density core. The inner core’s radius and mass both decrease. Its growing density therefore does not guarantee enough mass spread over the region that bends light into a large, bright image.

The most favourable stage usually occurred when the characteristic core surface density—core mass divided by its projected circular area—was around 60% of the critical surface density set by the lens–source geometry. That marker was not sufficient: the core also needed enough mass and size. Some more massive, concentrated models showed an additional favourable stage much later in collapse.

What counts as a stronger lens?

The answer depended on the measurement. For time-averaged magnification above a factor of 20, collapsing SIDM haloes could outperform or underperform their initial NFW counterparts, depending on concentration and interaction strength.

For producing multiple images with the second at least one-tenth as bright as the brightest, the tested time-averaged SIDM models performed better than their NFW counterparts. But mathematical image components are not necessarily separately visible through a telescope.

The researchers also compared SIDM haloes with generalized NFW profiles that maintain steep central density cusps. Those substitutes produced stronger time-averaged lensing and different combinations of arc size and thickness in the comparisons. A steep cusp was therefore a poor stand-in for the actual evolving SIDM structure.

Limits on the interpretation

The calculations omit stars and gas, which contribute gravity and can alter dark matter evolution. They also omit realistic halo shapes, growth histories and environmental processes such as tidal stripping. Interactions were elastic and independent of particle speed, unlike many proposed SIDM models.

Most calculations used one source profile and viewing geometry. Time averages weighted physical time uniformly over a finite collapse interval, rather than modelling a realistic population of halo ages. Telescope resolution, noise and image blending were not included in the lensing efficacy measures.

The study does not establish whether particular observed lenses contain SIDM. Its narrower lesson is that central density alone is inadequate: interpreting lensing requires the full mass distribution and the evolutionary stage that produced it.