# Same rules for reflexes in the coffee cup and lenses in the cosmos

## Researchers discover mathematical principles that explain gravitational lens phenomena

Read outWhat does the play of light and shadow on the surface of their morning coffee have to do with distant galaxies and gravity? Maybe more than you think. Because American researchers present in the journal "Mathematical Physics" a newly discovered universal principle that combines both and could possibly contribute to be able to better identify dark matter in the cosmos in the future.

Light rays are reflected by curved surfaces, such as the interior of a coffee cup, in a curved, leaf-like pattern. In the center, it concentrates on one point and is the brightest on the edges, the so-called focal plane. "This happens frequently because the light rays gather in the curves, " explains Arlie Petters, professor of mathematics and physics at Duke University. In everyday life, we encounter the burn surfaces almost everywhere where water is involved, such as in the light reflections in the swimming pool or along a boat hull. Already Leonardo da Vinci knew and drew such Brennflächen in the early 16th century.

### Burning surfaces also in the cosmos

However, such surfaces also appear in cosmic phenomena, such as gravitational lenses. These arise when a very massive object passes in front of distant stars. The gravity of the object is then so strong that it even bends and distorts the light of these stars. Similar to the burning surfaces on the earth, some areas of the distorted image appear brighter; in some cases, several enlarged copies of the original background star are created.

### Does the brightness of the star images follow a rule?

Petters and his colleague Amir Aazami had previously determined from telescopic data analysis that in cases where the light source lies within a fuel arc, two unusually close-spaced copies of equal brightness are produced. Since these "clones" are equally bright, the subtraction of one of the other luminosity gives exactly zero. But what happens in other cases? Which rule do the projections follow? To find out, Aazami carried out further analyzes of astronomical data.

### The "zero" was the key

Aazami was using a computer program to test out a special case of the combustible theorem with the cryptic name "ellyptically umbilical" when he noticed a pattern: "It made zero again and again, " the researcher explains. No matter what scenario he tried. "So I thought, 'That must be a bug'. And started again and again and again, I received zero. And then came the moment where it suddenly made sense. That was the Aha! moment. Display

When the scientist told this to his professor, he realized that his doctoral student had encountered a universal mathematical principle that even describes the seemingly chaotic light diffraction of gravitational lenses. "It's amazing that what we see in a coffee cup is a mathematical theorem that also describes phenomena in the cosmos, " said Aazami.

### Universal principle ensures brightness compensation

For example, if such a lens produces a fourfold image of a star with different brightnesses, then the relative faintness of one of them corresponds to the relatively increased brightness of the others, so that they cancel each other out. "It's wonderful that they balance each other, " explains Petters. "This concerns very complex mathematics."

For the simple gravitational lens diffraction, the researchers have already prepared their new theorem, now they are waiting for the new "Low Synoptic Survey Telescope" (LSST), which is currently being built in Chile, to provide more accurate data as well from the more complex combustion phenomena of higher order. "We are very confident that these universal constants will also show up in the LSST data, " says Petters.

### Dark matter becomes visible as theorem break

The new theorem could also help with the exploration of dark matter. If there are two closely spaced images of different brightness at the higher-resolution focal points, then the theorem is broken, explains Petters. The reason would then be a substructure in the galaxy. For example, this could be dark matter that affects one of the images and changes its magnification or brightness.

(Duke University, 16.04.2009 - NPO)