Semi-Analytic Predictions for Strong-Lensing Perturbers in Cold and Self-Interacting Dark Matter

The universe is filled with invisible matter that holds galaxies together, a substance scientists call dark matter. For decades, the leading theory has been that this matter is "cold," meaning its particles move slowly and do not bump into one another, behaving like a ghostly gas that only interacts through gravity. This idea explains the large-scale structure of the cosmos well, but it struggles to explain what happens inside the smallest, faintest clumps of dark matter. An alternative theory suggests these particles might be "self-interacting," meaning they can scatter off each other like billiard balls, transferring heat and reshaping the very centers of dark matter clouds. This difference in behavior could leave a distinct fingerprint on the universe's smallest structures, but because these clumps are too dim to see directly, astronomers must look for their gravitational shadows.

To find these shadows, researchers use a phenomenon called strong gravitational lensing. When a massive galaxy sits between Earth and a distant background object, its gravity bends the light from that background object, creating distorted, magnified, or multiple images. If a smaller, invisible clump of dark matter sits within that foreground galaxy, it acts like a tiny lens within a lens, creating a subtle, localized ripple in the distorted image. By studying these ripples, astronomers can weigh the invisible clumps and measure how dense their centers are. This paper takes that concept a step further by asking a specific question: if we look at these ripples, do they match the predictions of the standard cold dark matter theory, or do they point toward the self-interacting version?

The researchers built a sophisticated computer framework to simulate the life stories of billions of dark matter clumps. Instead of running expensive, slow simulations that track every single particle, they used a semi-analytic approach. They started with the known history of how dark matter clumps form and merge in the standard cold model, then applied a set of rules to see how those same clumps would change if the particles could bump into each other. In the cold model, these clumps remain relatively smooth and diffuse. In the self-interacting model, the particles transfer heat from the center to the edges, causing the center to expand into a "core" and, in some cases, to eventually collapse inward, becoming incredibly dense and compact. The team generated thousands of these simulated clumps, calculating exactly how much mass they would project onto the sky and how steep their density slopes would be, creating a vast library of what these invisible objects should look like if they existed.

They then compared this library against three real, observed dark matter clumps that astronomers have already detected through gravitational lensing in systems named PJ011646, SDSS J0946+1006, and JVAS B1938+666. These three objects are unique because their internal structures have been measured with high precision. The researchers asked a simple but difficult question: how often does a standard cold dark matter clump look like one of these three real objects, and how often does a self-interacting clump look like them? The answer revealed a clear preference for the self-interacting model. For the object in PJ011646, the standard model produced a matching clump only about twice in every thousand simulations, while the self-interacting model produced a match roughly six hundred times in the same number of trials. For the object in SDSS J0946+1006, the standard model failed to produce a single match in nine hundred simulations, whereas the self-interacting model found several matches, specifically those that had undergone a gravitational collapse to become extremely dense.

The study also looked at the third object, JVAS B1938+666, which is a very small, compact clump. Here, the standard model was again rare, finding a match only about once in five hundred attempts, and those matches required the clump to have fallen into its host galaxy at an exceptionally early time in the universe's history. In contrast, the self-interacting model found hundreds of matches, many of which had collapsed into dense cores. The researchers found that to explain all three of these different objects simultaneously with a single set of rules, the self-interacting particles must have a specific property: they must be able to interact strongly even when moving at high speeds. If the interaction strength drops off too quickly as speed increases, the massive clumps needed to explain the second object would never collapse. The data suggests the interaction remains strong up to speeds of about one hundred kilometers per second.

While the results strongly favor the self-interacting model for these specific cases, the authors are careful to note the limitations of their work. Their simulations did not include the effects of normal matter, such as stars and gas, which can also change the shape of a dark matter clump. If normal matter is present, it could potentially make the standard cold model look more like the observations, though the researchers suspect this would not be enough to fully close the gap. Furthermore, the exact behavior of dark matter in the final stages of collapse is still a subject of active research, and different assumptions about this process could shift the numbers slightly. However, the core finding remains robust: the specific, compact structures observed in these three lensing systems are far more common in a universe where dark matter particles bump into each other than in one where they pass through each other like ghosts. This suggests that the invisible scaffolding of our universe may be more dynamic and interactive than previously thought, with its smallest building blocks capable of dramatic internal transformations.