The galaxy NGC 1560 is a modest island of stars and gas ten million light-years away. Its rotation curve, first measured in 1991, became an icon for those seeking an alternative to dark matter. The plot of rotation speed versus radius shows bends that seem to exactly mirror the bends in the distribution of ordinary matter. That is Renzo's rule: every detail in the visible matter should leave a fingerprint in the rotation curve, and vice versa. A beautiful idea, but until now no one had tested it systematically.

The authors of the new study decided to compare fingerprints for real. They smoothed the rotation curves using Gaussian processes (a method that separates the large-scale shape from small fluctuations) and extracted features: regions where the signal exceeds the noise by more than a factor of two. Then, for each galaxy, they built predictions from two models: the standard cosmological ΛCDM (with dark matter) and modified Newtonian dynamics MOND (without dark matter). The similarity of the residuals was assessed using the Pearson correlation coefficient and the dynamic time warping cost (an algorithm that compares two data sequences).

But when the authors moved to the SPARC database of 60 galaxies, the picture changed. Features in the observed rotation curves were found in 25 galaxies, but none in the baryonic curves. On average, the correlation between observed and baryonic velocities was 3σ below the expectations of both models. In the MaGICC and CLUES simulations, the correlations did not exceed the level expected from a smooth dark matter halo. The fingerprints do not match.

To understand how bad things are, the authors ran mock tests. It turned out that distinguishing MOND from ΛCDM at the 5σ level would require reducing the observational noise by about 80%. This means that current data are too coarse to definitively bury or resurrect Renzo's rule. But it is already clear that intuitively compelling examples like NGC 1560 could be statistical fluctuations. The work moves Renzo's rule from the realm of visual impressions into quantitative testing and narrows the space for alternative gravity theories.

Ahead lie more precise observations, for instance with the future SKA radio telescope. They will reveal whether dark matter truly leaves its own, still invisible fingerprints. For now, NGC 1560 remains a beautiful puzzle: a lone galaxy whose rotation curve bends so closely mirror the bends in its visible matter that one cannot help but believe in a simple explanation without dark matter. But statistics is a strict science, and it says: do not be fooled.