Cosmic rays are particles that race across our Galaxy at enormous speeds. Their energies can be millions of times higher than those of particles in the most powerful accelerator on Earth. But the higher the energy, the fewer such particles there are: the plot of their numbers shows a noticeable kink, which is called the knee. For a long time, it was assumed that all cosmic-ray sources share the same energy limit — as if every factory only produced goods up to a certain price. But then the knee would be a sharp cliff, whereas in reality it is smooth.

A new study offers a different perspective. The sources are the remnants of exploded stars, and they are not identical: some are more powerful, others weaker. If each source has its own energy limit, together they produce a smooth bend. The authors showed that the shape of the knee depends on how these limits are distributed. For example, when the limits follow a lognormal distribution (many moderate ones, few very strong and very weak), the kink comes out smooth. But if there is a long tail of extremely powerful sources, the slope of the spectrum barely changes after the knee.

To test the idea, the scientists compared their calculations with the measured proton spectrum — protons being the most common particles in cosmic rays. It turned out that explaining the data requires a group of sources with fairly similar energy limits: a spread of only about 0.24 on a logarithmic scale. That is smaller than what would be expected from all supernova remnants in the Galaxy. So the knee is not shaped by the whole motley crowd of sources, but only by a relatively uniform subset — those capable of accelerating particles to energies of millions of billions of volts.

This approach removes the need for a rigid universal limit for all supernova remnants. Instead of one common boundary, there are many individual ones, and their combined effect creates a smooth bend. It is like a city where skyscrapers have different heights: the skyline is stepped, but from afar it looks like a smooth line. Understanding the shape of the knee helps clarify which stellar explosions contribute most to high-energy cosmic rays.